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@@ -1513,8 +1513,8 @@ 37.3.1.2. 2nd example
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-Wall time: 4.72 s
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@@ -1528,8 +1528,8 @@ 37.3.1.2. 2nd example
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diff --git a/BCG_incomplete_mkts.html b/BCG_incomplete_mkts.html
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@@ -288,7 +288,9 @@ 38. Equilibrium Capital Structures with
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diff --git a/_notebooks/BCG_complete_mkts.ipynb b/_notebooks/BCG_complete_mkts.ipynb
index 874127c3..f428fa9a 100644
--- a/_notebooks/BCG_complete_mkts.ipynb
+++ b/_notebooks/BCG_complete_mkts.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "12c27dce",
+ "id": "08fda670",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "065833c3",
+ "id": "c55fce53",
"metadata": {},
"source": [
"# Irrelevance of Capital Structures with Complete Markets\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c6d77452",
+ "id": "cd15232d",
"metadata": {
"hide-output": false
},
@@ -34,7 +34,7 @@
},
{
"cell_type": "markdown",
- "id": "eef0c8d6",
+ "id": "b9de6bea",
"metadata": {},
"source": [
"## Introduction\n",
@@ -67,7 +67,7 @@
},
{
"cell_type": "markdown",
- "id": "08584d46",
+ "id": "341e481a",
"metadata": {},
"source": [
"### Setup\n",
@@ -100,7 +100,7 @@
},
{
"cell_type": "markdown",
- "id": "353584b1",
+ "id": "8367fc37",
"metadata": {},
"source": [
"### Endowments\n",
@@ -125,7 +125,7 @@
},
{
"cell_type": "markdown",
- "id": "ffe7fa0f",
+ "id": "8230290d",
"metadata": {},
"source": [
"### Technology:\n",
@@ -142,7 +142,7 @@
},
{
"cell_type": "markdown",
- "id": "9b10edd4",
+ "id": "7b81eb20",
"metadata": {},
"source": [
"### Preferences:\n",
@@ -167,7 +167,7 @@
},
{
"cell_type": "markdown",
- "id": "3ecf63d6",
+ "id": "df891a2a",
"metadata": {},
"source": [
"### Parameterizations\n",
@@ -190,7 +190,7 @@
},
{
"cell_type": "markdown",
- "id": "9423e6d6",
+ "id": "a327a240",
"metadata": {},
"source": [
"### Pareto criterion and planning problem\n",
@@ -248,7 +248,7 @@
},
{
"cell_type": "markdown",
- "id": "971bc9bb",
+ "id": "1df04ebb",
"metadata": {},
"source": [
"### Helpful observations and bookkeeping\n",
@@ -329,7 +329,7 @@
},
{
"cell_type": "markdown",
- "id": "8dc2684c",
+ "id": "c89dbd10",
"metadata": {},
"source": [
"#### Remarks\n",
@@ -348,7 +348,7 @@
},
{
"cell_type": "markdown",
- "id": "94326d03",
+ "id": "2c05d7b3",
"metadata": {},
"source": [
"## Competitive equilibrium\n",
@@ -367,7 +367,7 @@
},
{
"cell_type": "markdown",
- "id": "d00278e8",
+ "id": "12de0121",
"metadata": {},
"source": [
"### Measures of agents and firms\n",
@@ -419,7 +419,7 @@
},
{
"cell_type": "markdown",
- "id": "6920292f",
+ "id": "88c2f496",
"metadata": {},
"source": [
"#### Ownership\n",
@@ -459,7 +459,7 @@
},
{
"cell_type": "markdown",
- "id": "0fa2848c",
+ "id": "fff22a9a",
"metadata": {},
"source": [
"#### Asset markets\n",
@@ -478,7 +478,7 @@
},
{
"cell_type": "markdown",
- "id": "72ddf4ba",
+ "id": "086550f0",
"metadata": {},
"source": [
"### Objects appearing in a competitive equilibrium\n",
@@ -507,7 +507,7 @@
},
{
"cell_type": "markdown",
- "id": "ad793d26",
+ "id": "99e443d4",
"metadata": {},
"source": [
"### A representative firm’s problem\n",
@@ -554,7 +554,7 @@
},
{
"cell_type": "markdown",
- "id": "a7c27ccc",
+ "id": "f6fb4885",
"metadata": {},
"source": [
"### A consumer’s problem\n",
@@ -727,7 +727,7 @@
},
{
"cell_type": "markdown",
- "id": "8d81f8a8",
+ "id": "ce10fe14",
"metadata": {},
"source": [
"### Computing competitive equilibrium prices and quantities\n",
@@ -822,7 +822,7 @@
},
{
"cell_type": "markdown",
- "id": "0912bd67",
+ "id": "d391569a",
"metadata": {},
"source": [
"### Modigliani-Miller theorem\n",
@@ -904,7 +904,7 @@
},
{
"cell_type": "markdown",
- "id": "36f29683",
+ "id": "eed6cba7",
"metadata": {},
"source": [
"## Code\n",
@@ -978,7 +978,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0331fe28",
+ "id": "4065aa47",
"metadata": {
"hide-output": false
},
@@ -994,7 +994,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "69f6906f",
+ "id": "153b4c9d",
"metadata": {
"hide-output": false
},
@@ -1189,7 +1189,7 @@
},
{
"cell_type": "markdown",
- "id": "e503a774",
+ "id": "171080f5",
"metadata": {},
"source": [
"### Examples\n",
@@ -1199,7 +1199,7 @@
},
{
"cell_type": "markdown",
- "id": "99bb06f6",
+ "id": "3da0ee68",
"metadata": {},
"source": [
"#### 1st example\n",
@@ -1218,7 +1218,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d7548180",
+ "id": "a6fa7186",
"metadata": {
"hide-output": false
},
@@ -1231,7 +1231,7 @@
},
{
"cell_type": "markdown",
- "id": "87439a98",
+ "id": "55cc9488",
"metadata": {},
"source": [
"Let’s plot the agents’ time-1 endowments with respect to shocks to see\n",
@@ -1241,7 +1241,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b1c3cfcc",
+ "id": "65f0422a",
"metadata": {
"hide-output": false
},
@@ -1278,7 +1278,7 @@
},
{
"cell_type": "markdown",
- "id": "50424823",
+ "id": "4a886d2b",
"metadata": {},
"source": [
"Let’s also compare the optimal capital stock, $ k $, and optimal\n",
@@ -1288,7 +1288,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "95a8df8d",
+ "id": "f210b4f6",
"metadata": {
"hide-output": false
},
@@ -1311,7 +1311,7 @@
},
{
"cell_type": "markdown",
- "id": "ab0f3605",
+ "id": "a35368e8",
"metadata": {},
"source": [
"#### 2nd example\n",
@@ -1326,7 +1326,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4a1b600d",
+ "id": "e8805e2c",
"metadata": {
"hide-output": false
},
@@ -1358,7 +1358,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "aa7cab49",
+ "id": "156f1425",
"metadata": {
"hide-output": false
},
@@ -1371,7 +1371,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bbcadb48",
+ "id": "f6fe4b27",
"metadata": {
"hide-output": false
},
@@ -1385,7 +1385,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a6c2c160",
+ "id": "e74c9af9",
"metadata": {
"hide-output": false
},
@@ -1416,7 +1416,7 @@
}
],
"metadata": {
- "date": 1723011579.9793224,
+ "date": 1723517845.990379,
"filename": "BCG_complete_mkts.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/BCG_incomplete_mkts.ipynb b/_notebooks/BCG_incomplete_mkts.ipynb
index 460650f3..deee55a7 100644
--- a/_notebooks/BCG_incomplete_mkts.ipynb
+++ b/_notebooks/BCG_incomplete_mkts.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "70ec1ace",
+ "id": "ead9112e",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "383a72ae",
+ "id": "0dceb097",
"metadata": {},
"source": [
"# Equilibrium Capital Structures with Incomplete Markets\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "706e79ca",
+ "id": "c7bb996a",
"metadata": {
"hide-output": false
},
@@ -34,7 +34,7 @@
},
{
"cell_type": "markdown",
- "id": "ecbfcdba",
+ "id": "e8a6dcc3",
"metadata": {},
"source": [
"## Introduction\n",
@@ -84,7 +84,7 @@
},
{
"cell_type": "markdown",
- "id": "a0b4d06f",
+ "id": "a63e0c5c",
"metadata": {},
"source": [
"### Setup\n",
@@ -108,7 +108,7 @@
},
{
"cell_type": "markdown",
- "id": "e30aefa8",
+ "id": "d0e0e17a",
"metadata": {},
"source": [
"### Ownership\n",
@@ -123,7 +123,7 @@
},
{
"cell_type": "markdown",
- "id": "aae2c4a1",
+ "id": "327696f3",
"metadata": {},
"source": [
"### Measures of agents and firms\n",
@@ -200,7 +200,7 @@
},
{
"cell_type": "markdown",
- "id": "b55333ce",
+ "id": "3f18ea54",
"metadata": {},
"source": [
"### Endowments\n",
@@ -217,7 +217,7 @@
},
{
"cell_type": "markdown",
- "id": "5b78a26e",
+ "id": "f9cb4865",
"metadata": {},
"source": [
"### Feasibility:\n",
@@ -236,7 +236,7 @@
},
{
"cell_type": "markdown",
- "id": "e8ee9755",
+ "id": "8cfab663",
"metadata": {},
"source": [
"### Parameterizations\n",
@@ -259,7 +259,7 @@
},
{
"cell_type": "markdown",
- "id": "43f1c6c3",
+ "id": "bac00a4c",
"metadata": {},
"source": [
"### Preferences:\n",
@@ -284,7 +284,7 @@
},
{
"cell_type": "markdown",
- "id": "85ab0db6",
+ "id": "6f60070e",
"metadata": {},
"source": [
"### Risk-sharing motives\n",
@@ -304,7 +304,7 @@
},
{
"cell_type": "markdown",
- "id": "1d3a1e94",
+ "id": "0c632b84",
"metadata": {},
"source": [
"## Asset Markets\n",
@@ -360,7 +360,7 @@
},
{
"cell_type": "markdown",
- "id": "2b538c80",
+ "id": "7f21256f",
"metadata": {},
"source": [
"### Consumers\n",
@@ -451,7 +451,7 @@
},
{
"cell_type": "markdown",
- "id": "097f014c",
+ "id": "0441e6f3",
"metadata": {},
"source": [
"### Pricing functions\n",
@@ -490,7 +490,7 @@
},
{
"cell_type": "markdown",
- "id": "2b534a16",
+ "id": "e02073ae",
"metadata": {},
"source": [
"### Firms\n",
@@ -547,7 +547,7 @@
},
{
"cell_type": "markdown",
- "id": "3ae2c9fd",
+ "id": "cf125657",
"metadata": {},
"source": [
"#### Firm’s optimization problem\n",
@@ -620,7 +620,7 @@
},
{
"cell_type": "markdown",
- "id": "2662899d",
+ "id": "9711f3a1",
"metadata": {},
"source": [
"## Equilibrium verification\n",
@@ -647,7 +647,7 @@
},
{
"cell_type": "markdown",
- "id": "7b6c3c69",
+ "id": "3d618d63",
"metadata": {},
"source": [
"## Pseudo Code\n",
@@ -745,7 +745,7 @@
},
{
"cell_type": "markdown",
- "id": "8b220f74",
+ "id": "4bf4902c",
"metadata": {},
"source": [
"## Code\n",
@@ -792,7 +792,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0eb1e5ec",
+ "id": "1649b6e0",
"metadata": {
"hide-output": false
},
@@ -807,7 +807,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9ccb2e70",
+ "id": "e8ec8180",
"metadata": {
"hide-output": false
},
@@ -1300,7 +1300,7 @@
},
{
"cell_type": "markdown",
- "id": "2879a11d",
+ "id": "9f54ee78",
"metadata": {},
"source": [
"## Examples\n",
@@ -1310,7 +1310,7 @@
},
{
"cell_type": "markdown",
- "id": "c9848561",
+ "id": "2a9746a5",
"metadata": {},
"source": [
"### First example\n",
@@ -1322,7 +1322,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5aed3206",
+ "id": "64b5fe24",
"metadata": {
"hide-output": false
},
@@ -1335,7 +1335,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6fb3372e",
+ "id": "a108f88a",
"metadata": {
"hide-output": false
},
@@ -1348,7 +1348,7 @@
},
{
"cell_type": "markdown",
- "id": "51b21e8b",
+ "id": "b1875613",
"metadata": {},
"source": [
"Python reports to us that the equilibrium firm value is $ V=0.101 $,\n",
@@ -1365,7 +1365,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "08eeb777",
+ "id": "2bab059c",
"metadata": {
"hide-output": false
},
@@ -1379,7 +1379,7 @@
},
{
"cell_type": "markdown",
- "id": "125fec0b",
+ "id": "98f7d144",
"metadata": {},
"source": [
"Up to the approximation involved in using a discrete grid, these numbers\n",
@@ -1396,7 +1396,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fc54da1c",
+ "id": "12262315",
"metadata": {
"hide-output": false
},
@@ -1437,7 +1437,7 @@
},
{
"cell_type": "markdown",
- "id": "890b33d8",
+ "id": "3d184b49",
"metadata": {},
"source": [
"#### A Modigliani-Miller theorem?\n",
@@ -1532,7 +1532,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "45a8a625",
+ "id": "767aa0f9",
"metadata": {
"hide-output": false
},
@@ -1756,7 +1756,7 @@
},
{
"cell_type": "markdown",
- "id": "90679603",
+ "id": "3d036f9b",
"metadata": {},
"source": [
"Here is our strategy for checking *stability* of an equilibrium.\n",
@@ -1782,7 +1782,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "61bf0ce9",
+ "id": "e8ed9541",
"metadata": {
"hide-output": false
},
@@ -1830,7 +1830,7 @@
},
{
"cell_type": "markdown",
- "id": "bbb4f71b",
+ "id": "4af53059",
"metadata": {},
"source": [
"In the above 3D surface of prospective firm valuations, the perturbed\n",
@@ -1848,7 +1848,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dd22830b",
+ "id": "718ce584",
"metadata": {
"hide-output": false
},
@@ -1895,7 +1895,7 @@
},
{
"cell_type": "markdown",
- "id": "3340bc11",
+ "id": "29d6bb92",
"metadata": {},
"source": [
"In contrast to $ (k^*,b^* - e) $, the 3D surface for\n",
@@ -1915,7 +1915,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1fea4c12",
+ "id": "fe4642a6",
"metadata": {
"hide-output": false
},
@@ -1926,7 +1926,7 @@
},
{
"cell_type": "markdown",
- "id": "5257ff42",
+ "id": "f1ad6d16",
"metadata": {},
"source": [
"Our two *stability experiments* suggest that the equilibrium capital\n",
@@ -1940,7 +1940,7 @@
},
{
"cell_type": "markdown",
- "id": "ceba18e2",
+ "id": "29499998",
"metadata": {},
"source": [
"#### Equilibrium equity and bond price functions\n",
@@ -1953,7 +1953,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fb96fdb8",
+ "id": "5de27290",
"metadata": {
"hide-output": false
},
@@ -1991,7 +1991,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a696234f",
+ "id": "0ca161de",
"metadata": {
"hide-output": false
},
@@ -2028,7 +2028,7 @@
},
{
"cell_type": "markdown",
- "id": "e589d87a",
+ "id": "9dd9738f",
"metadata": {},
"source": [
"### Comments on equilibrium pricing functions\n",
@@ -2044,7 +2044,7 @@
},
{
"cell_type": "markdown",
- "id": "856c49db",
+ "id": "6b015d00",
"metadata": {},
"source": [
"### Another example economy\n",
@@ -2070,7 +2070,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0389c8b9",
+ "id": "52bf3d97",
"metadata": {
"hide-output": false
},
@@ -2125,7 +2125,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6ef6284c",
+ "id": "a9e7b44e",
"metadata": {
"hide-output": false
},
@@ -2164,7 +2164,7 @@
},
{
"cell_type": "markdown",
- "id": "1032ecc2",
+ "id": "077f6d02",
"metadata": {},
"source": [
"## A picture worth a thousand words\n",
@@ -2184,7 +2184,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "41d45c53",
+ "id": "e97f5f3e",
"metadata": {
"hide-output": false
},
@@ -2216,7 +2216,7 @@
},
{
"cell_type": "markdown",
- "id": "08e84a9e",
+ "id": "64fbad16",
"metadata": {},
"source": [
"It is rewarding to stare at the above plots too.\n",
@@ -2232,7 +2232,7 @@
}
],
"metadata": {
- "date": 1723011580.0441456,
+ "date": 1723517846.2269802,
"filename": "BCG_incomplete_mkts.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/additive_functionals.ipynb b/_notebooks/additive_functionals.ipynb
index d50a379e..dd1c2c4e 100644
--- a/_notebooks/additive_functionals.ipynb
+++ b/_notebooks/additive_functionals.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "0c8e9ca2",
+ "id": "9248274d",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "a55a5981",
+ "id": "b3a6c723",
"metadata": {},
"source": [
"# Additive and Multiplicative Functionals\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2c252f9f",
+ "id": "cebba9e1",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "7d90a1be",
+ "id": "605c5304",
"metadata": {},
"source": [
"## Overview\n",
@@ -80,7 +80,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "baed4bd0",
+ "id": "13617fd8",
"metadata": {
"hide-output": false
},
@@ -95,7 +95,7 @@
},
{
"cell_type": "markdown",
- "id": "24bebf62",
+ "id": "621df52f",
"metadata": {},
"source": [
"## A Particular Additive Functional\n",
@@ -149,7 +149,7 @@
},
{
"cell_type": "markdown",
- "id": "2518356b",
+ "id": "cd46f903",
"metadata": {},
"source": [
"### Linear State-Space Representation\n",
@@ -220,7 +220,7 @@
},
{
"cell_type": "markdown",
- "id": "6e2a9818",
+ "id": "6dfd635b",
"metadata": {},
"source": [
"## Dynamics\n",
@@ -269,7 +269,7 @@
},
{
"cell_type": "markdown",
- "id": "df2f7ebf",
+ "id": "4465a81c",
"metadata": {},
"source": [
"### Simulation\n",
@@ -287,7 +287,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "598dafef",
+ "id": "b0140e14",
"metadata": {
"hide-output": false
},
@@ -447,7 +447,7 @@
},
{
"cell_type": "markdown",
- "id": "4a9eaf86",
+ "id": "6a78367b",
"metadata": {},
"source": [
"#### Plotting\n",
@@ -458,7 +458,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fe404851",
+ "id": "16000f76",
"metadata": {
"hide-output": false
},
@@ -741,7 +741,7 @@
},
{
"cell_type": "markdown",
- "id": "3c7ee7ce",
+ "id": "09d469e0",
"metadata": {},
"source": [
"For now, we just plot $ y_t $ and $ x_t $, postponing until later a description of exactly how we compute them.\n",
@@ -753,7 +753,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1fcb4414",
+ "id": "1daeb0bc",
"metadata": {
"hide-output": false
},
@@ -792,7 +792,7 @@
},
{
"cell_type": "markdown",
- "id": "2acd0b86",
+ "id": "9a4a52d6",
"metadata": {},
"source": [
"Notice the irregular but persistent growth in $ y_t $."
@@ -800,7 +800,7 @@
},
{
"cell_type": "markdown",
- "id": "4e2632f9",
+ "id": "edf80773",
"metadata": {},
"source": [
"### Decomposition\n",
@@ -936,7 +936,7 @@
},
{
"cell_type": "markdown",
- "id": "19f3f128",
+ "id": "61b1f06d",
"metadata": {},
"source": [
"## Code\n",
@@ -959,7 +959,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "713bb727",
+ "id": "fce17c3f",
"metadata": {
"hide-output": false
},
@@ -971,7 +971,7 @@
},
{
"cell_type": "markdown",
- "id": "0790f626",
+ "id": "05e9a1f8",
"metadata": {},
"source": [
"When we plot multiple realizations of a component in the 2nd, 3rd, and 4th panels, we also plot the population 95% probability coverage sets computed using the LinearStateSpace class.\n",
@@ -988,7 +988,7 @@
},
{
"cell_type": "markdown",
- "id": "036b9fe7",
+ "id": "291e2932",
"metadata": {},
"source": [
"### Associated Multiplicative Functional\n",
@@ -1035,7 +1035,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b7ee1d27",
+ "id": "14ed71cc",
"metadata": {
"hide-output": false
},
@@ -1047,7 +1047,7 @@
},
{
"cell_type": "markdown",
- "id": "34f63c72",
+ "id": "9b00c189",
"metadata": {},
"source": [
"As before, when we plotted multiple realizations of a component in the 2nd, 3rd, and 4th panels, we also plotted population 95% confidence bands computed using the LinearStateSpace class.\n",
@@ -1065,7 +1065,7 @@
},
{
"cell_type": "markdown",
- "id": "bc002cde",
+ "id": "dd9687f3",
"metadata": {},
"source": [
"### Peculiar Large Sample Property\n",
@@ -1090,7 +1090,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "84f18143",
+ "id": "63838c6b",
"metadata": {
"hide-output": false
},
@@ -1103,7 +1103,7 @@
},
{
"cell_type": "markdown",
- "id": "a99f392d",
+ "id": "36bf84d6",
"metadata": {},
"source": [
"The dotted line in the above graph is the mean $ E \\tilde M_t = 1 $ of the martingale.\n",
@@ -1115,7 +1115,7 @@
},
{
"cell_type": "markdown",
- "id": "3f3c18d6",
+ "id": "2b3ce438",
"metadata": {},
"source": [
"## More About the Multiplicative Martingale\n",
@@ -1136,7 +1136,7 @@
},
{
"cell_type": "markdown",
- "id": "a461d17a",
+ "id": "eb1763a7",
"metadata": {},
"source": [
"### Simulating a Multiplicative Martingale Again\n",
@@ -1153,7 +1153,7 @@
},
{
"cell_type": "markdown",
- "id": "2c032eea",
+ "id": "99c66f1b",
"metadata": {},
"source": [
"### Sample Paths\n",
@@ -1166,7 +1166,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cbeca4df",
+ "id": "cef3dd80",
"metadata": {
"hide-output": false
},
@@ -1278,7 +1278,7 @@
},
{
"cell_type": "markdown",
- "id": "e7a352f3",
+ "id": "b6d0fa52",
"metadata": {},
"source": [
"The heavy lifting is done inside the `AMF_LSS_VAR` class.\n",
@@ -1289,7 +1289,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "82f6da99",
+ "id": "2508d6be",
"metadata": {
"hide-output": false
},
@@ -1339,7 +1339,7 @@
},
{
"cell_type": "markdown",
- "id": "2a014979",
+ "id": "934f680c",
"metadata": {},
"source": [
"Now that we have these functions in our toolkit, let’s apply them to run some\n",
@@ -1349,7 +1349,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ee345995",
+ "id": "92ba90cf",
"metadata": {
"hide-output": false
},
@@ -1392,7 +1392,7 @@
},
{
"cell_type": "markdown",
- "id": "647234a3",
+ "id": "0eb6b18c",
"metadata": {},
"source": [
"Let’s plot the probability density functions for $ \\log {\\widetilde M}_t $ for\n",
@@ -1419,7 +1419,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bf619e96",
+ "id": "61ee7a6c",
"metadata": {
"hide-output": false
},
@@ -1474,7 +1474,7 @@
},
{
"cell_type": "markdown",
- "id": "62b451a4",
+ "id": "c51b8378",
"metadata": {},
"source": [
"These probability density functions help us understand mechanics underlying the **peculiar property** of our multiplicative martingale\n",
@@ -1489,7 +1489,7 @@
},
{
"cell_type": "markdown",
- "id": "a0d3d41c",
+ "id": "1baed8b9",
"metadata": {},
"source": [
"### Multiplicative Martingale as Likelihood Ratio Process\n",
@@ -1505,7 +1505,7 @@
}
],
"metadata": {
- "date": 1723011580.0832446,
+ "date": 1723517846.2645457,
"filename": "additive_functionals.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/amss.ipynb b/_notebooks/amss.ipynb
index 99713858..c82807c5 100644
--- a/_notebooks/amss.ipynb
+++ b/_notebooks/amss.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "96d7f855",
+ "id": "f98a29db",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "fbc50ee9",
+ "id": "d7620f5a",
"metadata": {},
"source": [
"# Optimal Taxation without State-Contingent Debt\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d6fed394",
+ "id": "490ed387",
"metadata": {
"hide-output": false
},
@@ -34,7 +34,7 @@
},
{
"cell_type": "markdown",
- "id": "e065decb",
+ "id": "d6a78e1e",
"metadata": {},
"source": [
"## Overview\n",
@@ -45,7 +45,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "28acb6a3",
+ "id": "d400baa8",
"metadata": {
"hide-output": false
},
@@ -62,7 +62,7 @@
},
{
"cell_type": "markdown",
- "id": "195cc166",
+ "id": "882ac7ad",
"metadata": {},
"source": [
"In [an earlier lecture](https://python-advanced.quantecon.org/opt_tax_recur.html), we described a model of\n",
@@ -86,7 +86,7 @@
},
{
"cell_type": "markdown",
- "id": "3f19853c",
+ "id": "8822cad4",
"metadata": {},
"source": [
"## Competitive Equilibrium with Distorting Taxes\n",
@@ -150,7 +150,7 @@
},
{
"cell_type": "markdown",
- "id": "567c513c",
+ "id": "e9c9da91",
"metadata": {},
"source": [
"### Risk-free One-Period Debt Only\n",
@@ -284,7 +284,7 @@
},
{
"cell_type": "markdown",
- "id": "dcef2303",
+ "id": "4dd1aae5",
"metadata": {},
"source": [
"### Comparison with Lucas-Stokey Economy\n",
@@ -300,7 +300,7 @@
},
{
"cell_type": "markdown",
- "id": "a9712415",
+ "id": "bede00e2",
"metadata": {},
"source": [
"### Ramsey Problem Without State-contingent Debt\n",
@@ -338,7 +338,7 @@
},
{
"cell_type": "markdown",
- "id": "18792c16",
+ "id": "6491a607",
"metadata": {},
"source": [
"#### Lagrangian Formulation\n",
@@ -374,7 +374,7 @@
},
{
"cell_type": "markdown",
- "id": "00f86dc6",
+ "id": "8d9a4b46",
"metadata": {},
"source": [
"### Some Calculations\n",
@@ -464,7 +464,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "69ccc31d",
+ "id": "52ae530b",
"metadata": {
"hide-output": false
},
@@ -672,7 +672,7 @@
},
{
"cell_type": "markdown",
- "id": "902aa3d9",
+ "id": "048a8279",
"metadata": {},
"source": [
"To analyze the AMSS model, we find it useful to adopt a recursive formulation\n",
@@ -681,7 +681,7 @@
},
{
"cell_type": "markdown",
- "id": "099266f0",
+ "id": "392a064b",
"metadata": {},
"source": [
"## Recursive Version of AMSS Model\n",
@@ -704,7 +704,7 @@
},
{
"cell_type": "markdown",
- "id": "c7e40833",
+ "id": "63cce8e7",
"metadata": {},
"source": [
"### Recasting State Variables\n",
@@ -773,7 +773,7 @@
},
{
"cell_type": "markdown",
- "id": "58bab347",
+ "id": "d49c794f",
"metadata": {},
"source": [
"### Measurability Constraints\n",
@@ -802,7 +802,7 @@
},
{
"cell_type": "markdown",
- "id": "578dfd5b",
+ "id": "953e3e97",
"metadata": {},
"source": [
"### Two Bellman Equations\n",
@@ -866,7 +866,7 @@
},
{
"cell_type": "markdown",
- "id": "f830263e",
+ "id": "e408ea53",
"metadata": {},
"source": [
"### Martingale Supercedes State-Variable Degeneracy\n",
@@ -915,7 +915,7 @@
},
{
"cell_type": "markdown",
- "id": "e9c69ce1",
+ "id": "79171102",
"metadata": {},
"source": [
"### Exercise 44.1\n",
@@ -927,7 +927,7 @@
},
{
"cell_type": "markdown",
- "id": "416b31ca",
+ "id": "8569df92",
"metadata": {},
"source": [
"### Absence of State Variable Degeneracy\n",
@@ -956,7 +956,7 @@
},
{
"cell_type": "markdown",
- "id": "8f049145",
+ "id": "2343a238",
"metadata": {},
"source": [
"### Digression on Non-negative Transfers\n",
@@ -993,7 +993,7 @@
},
{
"cell_type": "markdown",
- "id": "554ff520",
+ "id": "e19cf625",
"metadata": {},
"source": [
"### Code\n",
@@ -1004,7 +1004,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "62bf5ba3",
+ "id": "73ac285b",
"metadata": {
"hide-output": false
},
@@ -1226,7 +1226,7 @@
},
{
"cell_type": "markdown",
- "id": "e7454b53",
+ "id": "6f2dc41f",
"metadata": {},
"source": [
"## Examples\n",
@@ -1236,7 +1236,7 @@
},
{
"cell_type": "markdown",
- "id": "45ed5861",
+ "id": "95a2d3ea",
"metadata": {},
"source": [
"### Anticipated One-Period War\n",
@@ -1302,7 +1302,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d96f8760",
+ "id": "68fe3e7a",
"metadata": {
"hide-output": false
},
@@ -1358,7 +1358,7 @@
},
{
"cell_type": "markdown",
- "id": "6bf8f04c",
+ "id": "af2e23a9",
"metadata": {},
"source": [
"The following figure plots Ramsey plans under complete and incomplete\n",
@@ -1374,7 +1374,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a7dcaffb",
+ "id": "12c99261",
"metadata": {
"hide-output": false
},
@@ -1410,7 +1410,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a8900afe",
+ "id": "a51fe6c5",
"metadata": {
"hide-output": false
},
@@ -1432,7 +1432,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "43e6d663",
+ "id": "41872455",
"metadata": {
"hide-output": false
},
@@ -1446,7 +1446,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1b750f93",
+ "id": "2103cbda",
"metadata": {
"hide-output": false
},
@@ -1459,7 +1459,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e76ff7c4",
+ "id": "4fe8f0dc",
"metadata": {
"hide-output": false
},
@@ -1493,7 +1493,7 @@
},
{
"cell_type": "markdown",
- "id": "378791f1",
+ "id": "f49a8c31",
"metadata": {},
"source": [
"How a Ramsey planner responds to war depends on the structure of the asset market.\n",
@@ -1537,7 +1537,7 @@
},
{
"cell_type": "markdown",
- "id": "f5aaad18",
+ "id": "3495202c",
"metadata": {},
"source": [
"#### Perpetual War Alert\n",
@@ -1562,7 +1562,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5ac77b78",
+ "id": "f9554997",
"metadata": {
"hide-output": false
},
@@ -1608,7 +1608,7 @@
},
{
"cell_type": "markdown",
- "id": "bb68ae2b",
+ "id": "f87cc7ae",
"metadata": {},
"source": [
"With these preferences, Ramsey tax rates will vary even in the Lucas-Stokey\n",
@@ -1622,7 +1622,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ebda5804",
+ "id": "87e9bc02",
"metadata": {
"hide-output": false
},
@@ -1659,7 +1659,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "123411cd",
+ "id": "436e958a",
"metadata": {
"hide-output": false
},
@@ -1674,7 +1674,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d018393d",
+ "id": "40bd815b",
"metadata": {
"hide-output": false
},
@@ -1686,7 +1686,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "357d59d0",
+ "id": "7259e187",
"metadata": {
"hide-output": false
},
@@ -1718,7 +1718,7 @@
},
{
"cell_type": "markdown",
- "id": "a1dbe7e5",
+ "id": "2201827f",
"metadata": {},
"source": [
"When the government experiences a prolonged period of peace, it is able to reduce\n",
@@ -1740,7 +1740,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bb1ac68a",
+ "id": "9cbda0ec",
"metadata": {
"hide-output": false
},
@@ -1756,7 +1756,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f5444001",
+ "id": "2d3e7f8f",
"metadata": {
"hide-output": false
},
@@ -1784,7 +1784,7 @@
},
{
"cell_type": "markdown",
- "id": "46c2e375",
+ "id": "0db1d5ec",
"metadata": {},
"source": [
"[1] In an allocation that solves the Ramsey problem and that levies distorting\n",
@@ -1804,7 +1804,7 @@
}
],
"metadata": {
- "date": 1723011580.1362457,
+ "date": 1723517846.3180559,
"filename": "amss.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/amss2.ipynb b/_notebooks/amss2.ipynb
index 2d1c0baf..7b3fb409 100644
--- a/_notebooks/amss2.ipynb
+++ b/_notebooks/amss2.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "8fab0fb5",
+ "id": "ba703834",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "8bf75853",
+ "id": "b96d3c4a",
"metadata": {},
"source": [
"# Fluctuating Interest Rates Deliver Fiscal Insurance\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ea60f8de",
+ "id": "9427d750",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "44a57b8c",
+ "id": "e72bc2a2",
"metadata": {},
"source": [
"## Overview\n",
@@ -95,7 +95,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "91ffb1cc",
+ "id": "62d4f1a6",
"metadata": {
"hide-output": false
},
@@ -107,7 +107,7 @@
},
{
"cell_type": "markdown",
- "id": "d8014d8b",
+ "id": "17cd484f",
"metadata": {},
"source": [
"## Forces at Work\n",
@@ -137,7 +137,7 @@
},
{
"cell_type": "markdown",
- "id": "e6d44f37",
+ "id": "b2f28976",
"metadata": {},
"source": [
"## Logical Flow of Lecture\n",
@@ -157,7 +157,7 @@
},
{
"cell_type": "markdown",
- "id": "e3e39942",
+ "id": "5debe7f9",
"metadata": {},
"source": [
"### Equations from Lucas-Stokey (1983) Model\n",
@@ -226,7 +226,7 @@
},
{
"cell_type": "markdown",
- "id": "3bcf47e2",
+ "id": "345133b9",
"metadata": {},
"source": [
"### Specification with CRRA Utility\n",
@@ -284,7 +284,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "763a6d8b",
+ "id": "2528a8c4",
"metadata": {
"hide-output": false
},
@@ -332,7 +332,7 @@
},
{
"cell_type": "markdown",
- "id": "b4895916",
+ "id": "fc9f91f7",
"metadata": {},
"source": [
"## Example Economy\n",
@@ -366,7 +366,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "41b078e8",
+ "id": "4ef7e7d2",
"metadata": {
"hide-output": false
},
@@ -535,7 +535,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3f03cc9a",
+ "id": "c8994fe1",
"metadata": {
"hide-output": false
},
@@ -844,7 +844,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3c338b16",
+ "id": "fcc2a800",
"metadata": {
"hide-output": false
},
@@ -923,7 +923,7 @@
},
{
"cell_type": "markdown",
- "id": "ed4e4281",
+ "id": "0e76e238",
"metadata": {},
"source": [
"## Reverse Engineering Strategy\n",
@@ -974,7 +974,7 @@
},
{
"cell_type": "markdown",
- "id": "88bcb20b",
+ "id": "1eec83af",
"metadata": {},
"source": [
"## Code for Reverse Engineering\n",
@@ -985,7 +985,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5b1d4a61",
+ "id": "e399ce3f",
"metadata": {
"hide-output": false
},
@@ -1031,7 +1031,7 @@
},
{
"cell_type": "markdown",
- "id": "47c3037d",
+ "id": "9122c33d",
"metadata": {},
"source": [
"To recover and print out $ \\bar b $"
@@ -1040,7 +1040,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0234c91a",
+ "id": "7823039d",
"metadata": {
"hide-output": false
},
@@ -1052,7 +1052,7 @@
},
{
"cell_type": "markdown",
- "id": "42a51326",
+ "id": "e18a05d5",
"metadata": {},
"source": [
"To complete the reverse engineering exercise by jointly determining $ c_0, b_0 $, we\n",
@@ -1062,7 +1062,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7f0495a8",
+ "id": "609ba70b",
"metadata": {
"hide-output": false
},
@@ -1089,7 +1089,7 @@
},
{
"cell_type": "markdown",
- "id": "d31ce4d8",
+ "id": "e7ed62d6",
"metadata": {},
"source": [
"To solve the equations for $ c_0, b_0 $, we use SciPy’s fsolve function"
@@ -1098,7 +1098,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ad2efec1",
+ "id": "7f8eb2ce",
"metadata": {
"hide-output": false
},
@@ -1111,7 +1111,7 @@
},
{
"cell_type": "markdown",
- "id": "bb03c688",
+ "id": "e5b9cd5d",
"metadata": {},
"source": [
"Thus, we have reverse engineered an initial $ b0 = -1.038698407551764 $ that ought to render the AMSS measurability constraints slack."
@@ -1119,7 +1119,7 @@
},
{
"cell_type": "markdown",
- "id": "2faaf875",
+ "id": "ec5c05db",
"metadata": {},
"source": [
"## Short Simulation for Reverse-engineered: Initial Debt\n",
@@ -1133,7 +1133,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a360fe27",
+ "id": "429a527c",
"metadata": {
"hide-output": false
},
@@ -1181,7 +1181,7 @@
},
{
"cell_type": "markdown",
- "id": "9db4247f",
+ "id": "4155edc3",
"metadata": {},
"source": [
"The Ramsey allocations and Ramsey outcomes are **identical** for the Lucas-Stokey and AMSS economies.\n",
@@ -1195,7 +1195,7 @@
},
{
"cell_type": "markdown",
- "id": "7d5f24df",
+ "id": "210bac99",
"metadata": {},
"source": [
"## Long Simulation\n",
@@ -1230,7 +1230,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "51740acc",
+ "id": "60beb0bc",
"metadata": {
"hide-output": false
},
@@ -1258,7 +1258,7 @@
},
{
"cell_type": "markdown",
- "id": "b64e4b8c",
+ "id": "a64e0d70",
"metadata": {},
"source": [
"### Remarks about Long Simulation\n",
@@ -1279,7 +1279,7 @@
},
{
"cell_type": "markdown",
- "id": "e912acc8",
+ "id": "07323170",
"metadata": {},
"source": [
"## BEGS Approximations of Limiting Debt and Convergence Rate\n",
@@ -1322,7 +1322,7 @@
},
{
"cell_type": "markdown",
- "id": "cc4d985b",
+ "id": "2d57ed88",
"metadata": {},
"source": [
"### Asymptotic Mean\n",
@@ -1362,7 +1362,7 @@
},
{
"cell_type": "markdown",
- "id": "14bafa5a",
+ "id": "91c21f61",
"metadata": {},
"source": [
"### Rate of Convergence\n",
@@ -1380,7 +1380,7 @@
},
{
"cell_type": "markdown",
- "id": "5e66f26a",
+ "id": "7bf80577",
"metadata": {},
"source": [
"### Formulas and Code Details\n",
@@ -1428,7 +1428,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2f5879e5",
+ "id": "36ea54e4",
"metadata": {
"hide-output": false
},
@@ -1450,7 +1450,7 @@
},
{
"cell_type": "markdown",
- "id": "dbc96e45",
+ "id": "aca93668",
"metadata": {},
"source": [
"Now let’s form the two random variables $ {\\mathcal R}, {\\mathcal X} $ appearing in the BEGS approximating formulas"
@@ -1459,7 +1459,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "245798b0",
+ "id": "5cdab54d",
"metadata": {
"hide-output": false
},
@@ -1485,7 +1485,7 @@
},
{
"cell_type": "markdown",
- "id": "c6e90fb0",
+ "id": "122b68df",
"metadata": {},
"source": [
"Now let’s compute the ingredient of the approximating limit and the approximating rate of convergence"
@@ -1494,7 +1494,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "68311d3d",
+ "id": "fad1ea89",
"metadata": {
"hide-output": false
},
@@ -1508,7 +1508,7 @@
},
{
"cell_type": "markdown",
- "id": "f7ac00ea",
+ "id": "7e459618",
"metadata": {},
"source": [
"Print out $ \\hat b $ and $ \\bar b $"
@@ -1517,7 +1517,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ac4afbbb",
+ "id": "c16068ce",
"metadata": {
"hide-output": false
},
@@ -1528,7 +1528,7 @@
},
{
"cell_type": "markdown",
- "id": "7408a373",
+ "id": "c74b8724",
"metadata": {},
"source": [
"So we have"
@@ -1537,7 +1537,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9d0ebd91",
+ "id": "71f7f437",
"metadata": {
"hide-output": false
},
@@ -1548,7 +1548,7 @@
},
{
"cell_type": "markdown",
- "id": "6abcedb7",
+ "id": "a0a3b1ba",
"metadata": {},
"source": [
"These outcomes show that $ \\hat b $ does a remarkably good job of approximating $ \\bar b $.\n",
@@ -1559,7 +1559,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "57f39066",
+ "id": "3a6defe0",
"metadata": {
"hide-output": false
},
@@ -1571,7 +1571,7 @@
},
{
"cell_type": "markdown",
- "id": "9793ac9a",
+ "id": "7944544a",
"metadata": {},
"source": [
"This is *machine zero*, a verification that $ \\hat b $ succeeds in minimizing the nonnegative fiscal cost criterion $ J ( {\\mathcal B}^*) $ defined in\n",
@@ -1583,7 +1583,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f539c14d",
+ "id": "959f19a0",
"metadata": {
"hide-output": false
},
@@ -1596,7 +1596,7 @@
},
{
"cell_type": "markdown",
- "id": "63d85e43",
+ "id": "ffb32e26",
"metadata": {},
"source": [
"Now let’s compute the implied meantime to get to within 0.01 of the limit"
@@ -1605,7 +1605,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6230e8be",
+ "id": "ef9d4259",
"metadata": {
"hide-output": false
},
@@ -1617,7 +1617,7 @@
},
{
"cell_type": "markdown",
- "id": "a1dbde65",
+ "id": "5e607794",
"metadata": {},
"source": [
"The slow rate of convergence and the implied time of getting within one percent of the limiting value do a good job of approximating\n",
@@ -1628,7 +1628,7 @@
}
],
"metadata": {
- "date": 1723011580.3850067,
+ "date": 1723517846.371155,
"filename": "amss2.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/amss3.ipynb b/_notebooks/amss3.ipynb
index 874151ed..d0c0b587 100644
--- a/_notebooks/amss3.ipynb
+++ b/_notebooks/amss3.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "e34aa31a",
+ "id": "2b47daf2",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "6d2bdcad",
+ "id": "b36f7343",
"metadata": {},
"source": [
"# Fiscal Risk and Government Debt\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0c4d9233",
+ "id": "ce5c9e2b",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "d1eba14d",
+ "id": "03aab58c",
"metadata": {},
"source": [
"## Overview\n",
@@ -81,7 +81,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "510b49b3",
+ "id": "0129d5b8",
"metadata": {
"hide-output": false
},
@@ -93,7 +93,7 @@
},
{
"cell_type": "markdown",
- "id": "1597a948",
+ "id": "53b90799",
"metadata": {},
"source": [
"## The Economy\n",
@@ -138,7 +138,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "12881f01",
+ "id": "545712f5",
"metadata": {
"hide-output": false
},
@@ -186,7 +186,7 @@
},
{
"cell_type": "markdown",
- "id": "0fae4997",
+ "id": "b5b344e4",
"metadata": {},
"source": [
"### First and Second Moments\n",
@@ -199,7 +199,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8e60597f",
+ "id": "4542b89d",
"metadata": {
"hide-output": false
},
@@ -221,7 +221,7 @@
},
{
"cell_type": "markdown",
- "id": "3edd3a6f",
+ "id": "bb1ac780",
"metadata": {},
"source": [
"## Long Simulation\n",
@@ -236,7 +236,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8a440ed2",
+ "id": "7d722f78",
"metadata": {
"hide-output": false
},
@@ -405,7 +405,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f21569de",
+ "id": "b1771f20",
"metadata": {
"hide-output": false
},
@@ -714,7 +714,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "93583ac9",
+ "id": "e6860426",
"metadata": {
"hide-output": false
},
@@ -793,7 +793,7 @@
},
{
"cell_type": "markdown",
- "id": "886115aa",
+ "id": "6f5fd7c2",
"metadata": {},
"source": [
"Next, we show the code that we use to generate a very long simulation starting from initial\n",
@@ -805,7 +805,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "da63bb48",
+ "id": "0c51baa3",
"metadata": {
"hide-output": false
},
@@ -846,7 +846,7 @@
},
{
"cell_type": "markdown",
- "id": "8e1a7def",
+ "id": "688a4ea7",
"metadata": {},
"source": [
"\n",
@@ -878,7 +878,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5ece19af",
+ "id": "22422e85",
"metadata": {
"hide-output": false
},
@@ -906,7 +906,7 @@
},
{
"cell_type": "markdown",
- "id": "12a8041b",
+ "id": "b194b2a1",
"metadata": {},
"source": [
"\n",
@@ -922,7 +922,7 @@
},
{
"cell_type": "markdown",
- "id": "9dcbf728",
+ "id": "bd54dc74",
"metadata": {},
"source": [
"## Asymptotic Mean and Rate of Convergence\n",
@@ -976,7 +976,7 @@
},
{
"cell_type": "markdown",
- "id": "eb00b0c3",
+ "id": "fa77dbc7",
"metadata": {},
"source": [
"### Asymptotic Mean\n",
@@ -1019,7 +1019,7 @@
},
{
"cell_type": "markdown",
- "id": "922445fd",
+ "id": "4b47b17b",
"metadata": {},
"source": [
"### Rate of Convergence\n",
@@ -1038,7 +1038,7 @@
},
{
"cell_type": "markdown",
- "id": "a21f02b9",
+ "id": "ca05a8ac",
"metadata": {},
"source": [
"### More Advanced Topic\n",
@@ -1050,7 +1050,7 @@
},
{
"cell_type": "markdown",
- "id": "531f6a38",
+ "id": "7e8dc519",
"metadata": {},
"source": [
"### Chicken and Egg\n",
@@ -1075,7 +1075,7 @@
},
{
"cell_type": "markdown",
- "id": "1b1a1ced",
+ "id": "420227eb",
"metadata": {},
"source": [
"### Approximating the Ergodic Mean\n",
@@ -1097,7 +1097,7 @@
},
{
"cell_type": "markdown",
- "id": "b9c51900",
+ "id": "0cc1c600",
"metadata": {},
"source": [
"### Step by Step\n",
@@ -1240,7 +1240,7 @@
},
{
"cell_type": "markdown",
- "id": "2d2db9d0",
+ "id": "b2fca0ca",
"metadata": {},
"source": [
"### Execution\n",
@@ -1250,7 +1250,7 @@
},
{
"cell_type": "markdown",
- "id": "aeb8f871",
+ "id": "f4d31a54",
"metadata": {},
"source": [
"#### Step 1"
@@ -1259,7 +1259,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7387fd66",
+ "id": "095f9756",
"metadata": {
"hide-output": false
},
@@ -1283,7 +1283,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "207d427a",
+ "id": "27a1d8bb",
"metadata": {
"hide-output": false
},
@@ -1294,7 +1294,7 @@
},
{
"cell_type": "markdown",
- "id": "e1a7a0be",
+ "id": "c7f62594",
"metadata": {},
"source": [
"#### Step 2"
@@ -1303,7 +1303,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a497c6ea",
+ "id": "73fa98ec",
"metadata": {
"hide-output": false
},
@@ -1314,7 +1314,7 @@
},
{
"cell_type": "markdown",
- "id": "83a98e71",
+ "id": "53d6e8ff",
"metadata": {},
"source": [
"### Note about Code\n",
@@ -1331,7 +1331,7 @@
},
{
"cell_type": "markdown",
- "id": "227daae5",
+ "id": "1969b80b",
"metadata": {},
"source": [
"### Running the code\n",
@@ -1345,7 +1345,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "95062aea",
+ "id": "71f763a3",
"metadata": {
"hide-output": false
},
@@ -1364,7 +1364,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e949ede9",
+ "id": "2259201b",
"metadata": {
"hide-output": false
},
@@ -1376,7 +1376,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3a25e41d",
+ "id": "ec198668",
"metadata": {
"hide-output": false
},
@@ -1387,7 +1387,7 @@
},
{
"cell_type": "markdown",
- "id": "4b88dabe",
+ "id": "9d72a75c",
"metadata": {},
"source": [
"We only want unconditional expectations because we are in an IID case.\n",
@@ -1399,7 +1399,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d98b2fa8",
+ "id": "41cfccf9",
"metadata": {
"hide-output": false
},
@@ -1412,7 +1412,7 @@
},
{
"cell_type": "markdown",
- "id": "313c1694",
+ "id": "8d80665e",
"metadata": {},
"source": [
"Let’s look at the random variables $ {\\mathcal R}, {\\mathcal X} $"
@@ -1421,7 +1421,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ead46287",
+ "id": "15c035fc",
"metadata": {
"hide-output": false
},
@@ -1433,7 +1433,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "acf77f38",
+ "id": "d0b1fa77",
"metadata": {
"hide-output": false
},
@@ -1445,7 +1445,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "451e1395",
+ "id": "1df254cb",
"metadata": {
"hide-output": false
},
@@ -1457,7 +1457,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "33346284",
+ "id": "dcb9ab24",
"metadata": {
"hide-output": false
},
@@ -1469,7 +1469,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "307606c1",
+ "id": "50c02a97",
"metadata": {
"hide-output": false
},
@@ -1480,7 +1480,7 @@
},
{
"cell_type": "markdown",
- "id": "77b56e08",
+ "id": "30c45ef6",
"metadata": {},
"source": [
"#### Step 3"
@@ -1489,7 +1489,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3da8e1cf",
+ "id": "687bce72",
"metadata": {
"hide-output": false
},
@@ -1502,7 +1502,7 @@
},
{
"cell_type": "markdown",
- "id": "22e135e8",
+ "id": "7c469777",
"metadata": {},
"source": [
"Note that $ B $ is a scalar.\n",
@@ -1513,7 +1513,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5b4c9db8",
+ "id": "7cb02358",
"metadata": {
"hide-output": false
},
@@ -1528,7 +1528,7 @@
},
{
"cell_type": "markdown",
- "id": "bce4f9c8",
+ "id": "d78bae05",
"metadata": {},
"source": [
"In the above cell, B is fixed at 1 and $ \\tau $ is to be computed as\n",
@@ -1540,7 +1540,7 @@
},
{
"cell_type": "markdown",
- "id": "aed786b4",
+ "id": "1b849af8",
"metadata": {},
"source": [
"#### Step 4"
@@ -1549,7 +1549,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "63b28d90",
+ "id": "d03d9b54",
"metadata": {
"hide-output": false
},
@@ -1565,7 +1565,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "92aa6fb3",
+ "id": "45de150d",
"metadata": {
"hide-output": false
},
@@ -1576,7 +1576,7 @@
},
{
"cell_type": "markdown",
- "id": "81de6eae",
+ "id": "f3ff5170",
"metadata": {},
"source": [
"#### Step 6"
@@ -1585,7 +1585,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0f42f741",
+ "id": "1233d712",
"metadata": {
"hide-output": false
},
@@ -1598,7 +1598,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d5b8660b",
+ "id": "7612924c",
"metadata": {
"hide-output": false
},
@@ -1610,7 +1610,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d398c99f",
+ "id": "0f9298e7",
"metadata": {
"hide-output": false
},
@@ -1624,7 +1624,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d693b7f6",
+ "id": "9711ce91",
"metadata": {
"hide-output": false
},
@@ -1637,7 +1637,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cfbfeb19",
+ "id": "b0708210",
"metadata": {
"hide-output": false
},
@@ -1650,7 +1650,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "baa3f01f",
+ "id": "12b62d79",
"metadata": {
"hide-output": false
},
@@ -1663,7 +1663,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "49c69d99",
+ "id": "3da67f29",
"metadata": {
"hide-output": false
},
@@ -1676,7 +1676,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4c45e5fc",
+ "id": "b88bab95",
"metadata": {
"hide-output": false
},
@@ -1687,7 +1687,7 @@
}
],
"metadata": {
- "date": 1723011580.4482102,
+ "date": 1723517846.433113,
"filename": "amss3.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/arellano.ipynb b/_notebooks/arellano.ipynb
index 78272bbb..ca867b8d 100644
--- a/_notebooks/arellano.ipynb
+++ b/_notebooks/arellano.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "875b2496",
+ "id": "e412c068",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "ec29593b",
+ "id": "df661840",
"metadata": {},
"source": [
"# Default Risk and Income Fluctuations\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1564ca64",
+ "id": "9a2c16ac",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "5d11d174",
+ "id": "c9f0b6f1",
"metadata": {},
"source": [
"## Overview\n",
@@ -85,7 +85,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ea8962a7",
+ "id": "faeb7418",
"metadata": {
"hide-output": false
},
@@ -99,7 +99,7 @@
},
{
"cell_type": "markdown",
- "id": "4b016fcc",
+ "id": "353335f4",
"metadata": {},
"source": [
"## Structure\n",
@@ -109,7 +109,7 @@
},
{
"cell_type": "markdown",
- "id": "4d123a6f",
+ "id": "ba5e5796",
"metadata": {},
"source": [
"### Output, Consumption and Debt\n",
@@ -151,7 +151,7 @@
},
{
"cell_type": "markdown",
- "id": "7e10a1a3",
+ "id": "6f9ef9c4",
"metadata": {},
"source": [
"### Asset Markets\n",
@@ -193,7 +193,7 @@
},
{
"cell_type": "markdown",
- "id": "32d8e5ae",
+ "id": "8118fa44",
"metadata": {},
"source": [
"### Financial Markets\n",
@@ -225,7 +225,7 @@
},
{
"cell_type": "markdown",
- "id": "0c40e44d",
+ "id": "ba19cb47",
"metadata": {},
"source": [
"### Government’s Decisions\n",
@@ -251,7 +251,7 @@
},
{
"cell_type": "markdown",
- "id": "8dbf0685",
+ "id": "bc05b7fe",
"metadata": {},
"source": [
"### Reentering International Credit Market\n",
@@ -262,7 +262,7 @@
},
{
"cell_type": "markdown",
- "id": "8a893f0c",
+ "id": "4bb417b4",
"metadata": {},
"source": [
"## Equilibrium\n",
@@ -354,7 +354,7 @@
},
{
"cell_type": "markdown",
- "id": "b3647054",
+ "id": "5cd1d5dd",
"metadata": {},
"source": [
"### Definition of Equilibrium\n",
@@ -379,7 +379,7 @@
},
{
"cell_type": "markdown",
- "id": "222a7d3b",
+ "id": "2e4f747d",
"metadata": {},
"source": [
"## Computation\n",
@@ -425,7 +425,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "72e3acb8",
+ "id": "e050291a",
"metadata": {
"hide-output": false
},
@@ -472,7 +472,7 @@
},
{
"cell_type": "markdown",
- "id": "75959e6e",
+ "id": "a2eb47bd",
"metadata": {},
"source": [
"Notice how the class returns the data it stores as simple numerical values and\n",
@@ -488,7 +488,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8d48a8a9",
+ "id": "1edf89fe",
"metadata": {
"hide-output": false
},
@@ -501,7 +501,7 @@
},
{
"cell_type": "markdown",
- "id": "7e459d6f",
+ "id": "fea37c51",
"metadata": {},
"source": [
"Here is a function to compute the bond price at each state, given $ v_c $ and\n",
@@ -511,7 +511,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3f5e6cb4",
+ "id": "9734dc4a",
"metadata": {
"hide-output": false
},
@@ -538,7 +538,7 @@
},
{
"cell_type": "markdown",
- "id": "547da4c6",
+ "id": "52a9681d",
"metadata": {},
"source": [
"Next we introduce Bellman operators that updated $ v_d $ and $ v_c $."
@@ -547,7 +547,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "03d788d2",
+ "id": "fd6d80b7",
"metadata": {
"hide-output": false
},
@@ -599,7 +599,7 @@
},
{
"cell_type": "markdown",
- "id": "3cdc47b0",
+ "id": "989abb9c",
"metadata": {},
"source": [
"Here is a fast function that calls these operators in the right sequence."
@@ -608,7 +608,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4c215652",
+ "id": "c7fcf3fd",
"metadata": {
"hide-output": false
},
@@ -645,7 +645,7 @@
},
{
"cell_type": "markdown",
- "id": "6027cefe",
+ "id": "4fbaf77b",
"metadata": {},
"source": [
"We can now write a function that will use the `Arellano_Economy` class and the\n",
@@ -662,7 +662,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7cf9010a",
+ "id": "cec25dc6",
"metadata": {
"hide-output": false
},
@@ -706,7 +706,7 @@
},
{
"cell_type": "markdown",
- "id": "c8e2929c",
+ "id": "0dac12bd",
"metadata": {},
"source": [
"Finally, we write a function that will allow us to simulate the economy once\n",
@@ -716,7 +716,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d952c7f2",
+ "id": "38c78fd6",
"metadata": {
"hide-output": false
},
@@ -786,7 +786,7 @@
},
{
"cell_type": "markdown",
- "id": "4dd36104",
+ "id": "9b9fd63c",
"metadata": {},
"source": [
"## Results\n",
@@ -857,7 +857,7 @@
},
{
"cell_type": "markdown",
- "id": "607568ac",
+ "id": "1e9052d1",
"metadata": {},
"source": [
"## Exercises\n",
@@ -868,7 +868,7 @@
},
{
"cell_type": "markdown",
- "id": "8feaede8",
+ "id": "67737206",
"metadata": {},
"source": [
"## Exercise 13.1\n",
@@ -881,7 +881,7 @@
},
{
"cell_type": "markdown",
- "id": "1008a2ee",
+ "id": "69406fca",
"metadata": {},
"source": [
"## Solution to[ Exercise 13.1](https://python-advanced.quantecon.org/#arella_ex1)\n",
@@ -892,7 +892,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7db28495",
+ "id": "be2eba72",
"metadata": {
"hide-output": false
},
@@ -904,7 +904,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "527990c1",
+ "id": "553bf25e",
"metadata": {
"hide-output": false
},
@@ -915,7 +915,7 @@
},
{
"cell_type": "markdown",
- "id": "ad717174",
+ "id": "f4516fca",
"metadata": {},
"source": [
"Compute the bond price schedule as seen in figure 3 of Arellano (2008)"
@@ -924,7 +924,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d632791e",
+ "id": "8f59b769",
"metadata": {
"hide-output": false
},
@@ -960,7 +960,7 @@
},
{
"cell_type": "markdown",
- "id": "78c10d8d",
+ "id": "b6342978",
"metadata": {},
"source": [
"Draw a plot of the value functions"
@@ -969,7 +969,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3968ebf8",
+ "id": "910f7aad",
"metadata": {
"hide-output": false
},
@@ -989,7 +989,7 @@
},
{
"cell_type": "markdown",
- "id": "7b7598a6",
+ "id": "057ad1b1",
"metadata": {},
"source": [
"Draw a heat map for default probability"
@@ -998,7 +998,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a8bd2626",
+ "id": "43d98475",
"metadata": {
"hide-output": false
},
@@ -1023,7 +1023,7 @@
},
{
"cell_type": "markdown",
- "id": "7e3dd42c",
+ "id": "0b0094e0",
"metadata": {},
"source": [
"Plot a time series of major variables simulated from the model"
@@ -1032,7 +1032,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "543e0793",
+ "id": "55615cd3",
"metadata": {
"hide-output": false
},
@@ -1081,7 +1081,7 @@
}
],
"metadata": {
- "date": 1723011580.4827392,
+ "date": 1723517846.621057,
"filename": "arellano.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/arma.ipynb b/_notebooks/arma.ipynb
index d9582f96..1ade7ca4 100644
--- a/_notebooks/arma.ipynb
+++ b/_notebooks/arma.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "ccdd898a",
+ "id": "0600f058",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "8d93f3e6",
+ "id": "81271d10",
"metadata": {},
"source": [
"# Covariance Stationary Processes\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "57f9adf9",
+ "id": "49085ce3",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "19c96e3d",
+ "id": "ca9ab2b7",
"metadata": {},
"source": [
"## Overview\n",
@@ -52,7 +52,7 @@
},
{
"cell_type": "markdown",
- "id": "4c980fe2",
+ "id": "ad2d7c19",
"metadata": {},
"source": [
"### ARMA Processes\n",
@@ -68,7 +68,7 @@
},
{
"cell_type": "markdown",
- "id": "3fd27556",
+ "id": "17b701a8",
"metadata": {},
"source": [
"### Spectral Analysis\n",
@@ -89,7 +89,7 @@
},
{
"cell_type": "markdown",
- "id": "103e66de",
+ "id": "0dbaaa6d",
"metadata": {},
"source": [
"### Other Reading\n",
@@ -102,7 +102,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8395ee2f",
+ "id": "c04466a3",
"metadata": {
"hide-output": false
},
@@ -115,7 +115,7 @@
},
{
"cell_type": "markdown",
- "id": "5fc060a1",
+ "id": "ade706ae",
"metadata": {},
"source": [
"## Introduction\n",
@@ -137,7 +137,7 @@
},
{
"cell_type": "markdown",
- "id": "cddf6b50",
+ "id": "e2cb1d35",
"metadata": {},
"source": [
"### Definitions\n",
@@ -159,7 +159,7 @@
},
{
"cell_type": "markdown",
- "id": "5908c683",
+ "id": "78e37f1d",
"metadata": {},
"source": [
"### Example 1: White Noise\n",
@@ -182,7 +182,7 @@
},
{
"cell_type": "markdown",
- "id": "86eac39b",
+ "id": "591ed565",
"metadata": {},
"source": [
"### Example 2: General Linear Processes\n",
@@ -221,7 +221,7 @@
},
{
"cell_type": "markdown",
- "id": "a105edd6",
+ "id": "46e89469",
"metadata": {},
"source": [
"### Wold Representation\n",
@@ -249,7 +249,7 @@
},
{
"cell_type": "markdown",
- "id": "7033a7e0",
+ "id": "1816c30a",
"metadata": {},
"source": [
"### AR and MA\n",
@@ -292,7 +292,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f625e0db",
+ "id": "654cd062",
"metadata": {
"hide-output": false
},
@@ -316,7 +316,7 @@
},
{
"cell_type": "markdown",
- "id": "4f5f7a39",
+ "id": "21d7a7a7",
"metadata": {},
"source": [
"Another very simple process is the MA(1) process (here MA means “moving average”)\n",
@@ -342,7 +342,7 @@
},
{
"cell_type": "markdown",
- "id": "61b34643",
+ "id": "c5cc7db6",
"metadata": {},
"source": [
"### ARMA Processes\n",
@@ -411,7 +411,7 @@
},
{
"cell_type": "markdown",
- "id": "baf98dbe",
+ "id": "9f80a27d",
"metadata": {},
"source": [
"## Spectral Analysis\n",
@@ -429,7 +429,7 @@
},
{
"cell_type": "markdown",
- "id": "b2c0ef87",
+ "id": "af382997",
"metadata": {},
"source": [
"### Complex Numbers\n",
@@ -470,7 +470,7 @@
},
{
"cell_type": "markdown",
- "id": "c570e15f",
+ "id": "54e1c701",
"metadata": {},
"source": [
"### Spectral Densities\n",
@@ -512,7 +512,7 @@
},
{
"cell_type": "markdown",
- "id": "d3870ae4",
+ "id": "8a4e8a9c",
"metadata": {},
"source": [
"### Example 1: White Noise\n",
@@ -528,7 +528,7 @@
},
{
"cell_type": "markdown",
- "id": "e218fa25",
+ "id": "664bdffb",
"metadata": {},
"source": [
"### Example 2: AR and MA and ARMA\n",
@@ -576,7 +576,7 @@
},
{
"cell_type": "markdown",
- "id": "ca2f2de5",
+ "id": "289f6919",
"metadata": {},
"source": [
"### Interpreting the Spectral Density\n",
@@ -589,7 +589,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "285e3de7",
+ "id": "609a57c5",
"metadata": {
"hide-output": false
},
@@ -616,7 +616,7 @@
},
{
"cell_type": "markdown",
- "id": "b0f2c470",
+ "id": "51a1d17b",
"metadata": {},
"source": [
"These spectral densities correspond to the autocovariance functions for the\n",
@@ -650,7 +650,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "19e5996a",
+ "id": "1d6f3ace",
"metadata": {
"hide-output": false
},
@@ -693,7 +693,7 @@
},
{
"cell_type": "markdown",
- "id": "1fed271b",
+ "id": "2d05d5da",
"metadata": {},
"source": [
"On the other hand, if we evaluate $ f(\\omega) $ at $ \\omega = \\pi / 3 $, then the cycles are\n",
@@ -704,7 +704,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d7d65568",
+ "id": "e530b303",
"metadata": {
"hide-output": false
},
@@ -747,7 +747,7 @@
},
{
"cell_type": "markdown",
- "id": "c2fabcec",
+ "id": "2fda85bd",
"metadata": {},
"source": [
"In summary, the spectral density is large at frequencies $ \\omega $ where the autocovariance function exhibits damped cycles."
@@ -755,7 +755,7 @@
},
{
"cell_type": "markdown",
- "id": "8f6986e8",
+ "id": "3cb5dacf",
"metadata": {},
"source": [
"### Inverting the Transformation\n",
@@ -781,7 +781,7 @@
},
{
"cell_type": "markdown",
- "id": "d2966ae1",
+ "id": "77ae2ff7",
"metadata": {},
"source": [
"### Mathematical Theory\n",
@@ -870,7 +870,7 @@
},
{
"cell_type": "markdown",
- "id": "44c0de57",
+ "id": "ddc65982",
"metadata": {},
"source": [
"## Implementation\n",
@@ -891,7 +891,7 @@
},
{
"cell_type": "markdown",
- "id": "a3a17e13",
+ "id": "c4d6369b",
"metadata": {},
"source": [
"### Application\n",
@@ -904,7 +904,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "546bd625",
+ "id": "532fac0f",
"metadata": {
"hide-output": false
},
@@ -965,7 +965,7 @@
},
{
"cell_type": "markdown",
- "id": "b33a2208",
+ "id": "f5d8373c",
"metadata": {},
"source": [
"Now let’s call these functions to generate plots.\n",
@@ -976,7 +976,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9b7da1ef",
+ "id": "ae74f9d2",
"metadata": {
"hide-output": false
},
@@ -990,7 +990,7 @@
},
{
"cell_type": "markdown",
- "id": "acab4560",
+ "id": "3bd51a07",
"metadata": {},
"source": [
"If we look carefully, things look good: the spectrum is the flat line at $ 10^0 $ at the very top of the spectrum graphs,\n",
@@ -1012,7 +1012,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a353cb64",
+ "id": "3ab7d3c4",
"metadata": {
"hide-output": false
},
@@ -1026,7 +1026,7 @@
},
{
"cell_type": "markdown",
- "id": "24d20078",
+ "id": "9a1845bb",
"metadata": {},
"source": [
"Ljungqvist and Sargent’s second model is $ X_t = .9 X_{t-1} + \\epsilon_t $"
@@ -1035,7 +1035,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e8c00dec",
+ "id": "67f2fe6a",
"metadata": {
"hide-output": false
},
@@ -1049,7 +1049,7 @@
},
{
"cell_type": "markdown",
- "id": "e25fb835",
+ "id": "668842dc",
"metadata": {},
"source": [
"Ljungqvist and Sargent’s third model is $ X_t = .8 X_{t-4} + \\epsilon_t $"
@@ -1058,7 +1058,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dce9a61e",
+ "id": "6e945f96",
"metadata": {
"hide-output": false
},
@@ -1072,7 +1072,7 @@
},
{
"cell_type": "markdown",
- "id": "738d393f",
+ "id": "65e61fca",
"metadata": {},
"source": [
"Ljungqvist and Sargent’s fourth model is $ X_t = .98 X_{t-1} + \\epsilon_t -.7 \\epsilon_{t-1} $"
@@ -1081,7 +1081,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3c81d605",
+ "id": "cd93b3f4",
"metadata": {
"hide-output": false
},
@@ -1095,7 +1095,7 @@
},
{
"cell_type": "markdown",
- "id": "32a8e5cb",
+ "id": "fa037a10",
"metadata": {},
"source": [
"### Explanation\n",
@@ -1153,7 +1153,7 @@
},
{
"cell_type": "markdown",
- "id": "a1921515",
+ "id": "5f1e32f3",
"metadata": {},
"source": [
"### Computing the Autocovariance Function\n",
@@ -1198,7 +1198,7 @@
}
],
"metadata": {
- "date": 1723011580.5371983,
+ "date": 1723517846.6731813,
"filename": "arma.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/asset_pricing_lph.ipynb b/_notebooks/asset_pricing_lph.ipynb
index 7654a5e0..244ef04f 100644
--- a/_notebooks/asset_pricing_lph.ipynb
+++ b/_notebooks/asset_pricing_lph.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "c5aee880",
+ "id": "acdaeb4e",
"metadata": {},
"source": [
"# Elementary Asset Pricing Theory\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "400be509",
+ "id": "68c21a53",
"metadata": {},
"source": [
"## Overview\n",
@@ -58,7 +58,7 @@
},
{
"cell_type": "markdown",
- "id": "a5c6e33b",
+ "id": "d07108d5",
"metadata": {},
"source": [
"## Key Equation\n",
@@ -102,7 +102,7 @@
},
{
"cell_type": "markdown",
- "id": "bbc877c8",
+ "id": "6dfbe06c",
"metadata": {},
"source": [
"## Implications of Key Equation\n",
@@ -178,7 +178,7 @@
},
{
"cell_type": "markdown",
- "id": "45df42de",
+ "id": "03ee3734",
"metadata": {},
"source": [
"## Expected Return - Beta Representation\n",
@@ -297,7 +297,7 @@
},
{
"cell_type": "markdown",
- "id": "44b51503",
+ "id": "11cb78dd",
"metadata": {},
"source": [
"## Mean-Variance Frontier\n",
@@ -371,7 +371,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9874967e",
+ "id": "a181ff79",
"metadata": {
"hide-output": false
},
@@ -419,7 +419,7 @@
},
{
"cell_type": "markdown",
- "id": "35f2e413",
+ "id": "dd69129a",
"metadata": {},
"source": [
"The figure shows two straight lines, the blue upper one being the locus of $ ( \\sigma(R^i), E(R^i) $ pairs that are on\n",
@@ -454,7 +454,7 @@
},
{
"cell_type": "markdown",
- "id": "703d6c18",
+ "id": "cd300cfb",
"metadata": {},
"source": [
"## Sharpe Ratios and the Price of Risk\n",
@@ -479,7 +479,7 @@
},
{
"cell_type": "markdown",
- "id": "6bd85740",
+ "id": "71af0201",
"metadata": {},
"source": [
"## Mathematical Structure of Frontier\n",
@@ -511,7 +511,7 @@
},
{
"cell_type": "markdown",
- "id": "1c1704d6",
+ "id": "ed60e053",
"metadata": {},
"source": [
"## Multi-factor Models\n",
@@ -549,7 +549,7 @@
},
{
"cell_type": "markdown",
- "id": "d2985e5a",
+ "id": "561cb48b",
"metadata": {},
"source": [
"## Empirical Implementations\n",
@@ -613,7 +613,7 @@
},
{
"cell_type": "markdown",
- "id": "fb81d1ab",
+ "id": "5d7838a2",
"metadata": {},
"source": [
"## Exercises\n",
@@ -624,7 +624,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "94056a8c",
+ "id": "016482a9",
"metadata": {
"hide-output": false
},
@@ -637,7 +637,7 @@
},
{
"cell_type": "markdown",
- "id": "976d6450",
+ "id": "4dce6bcd",
"metadata": {},
"source": [
"Lots of our calculations will involve computing population and sample OLS regressions.\n",
@@ -648,7 +648,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "07d92416",
+ "id": "269bfc00",
"metadata": {
"hide-output": false
},
@@ -670,7 +670,7 @@
},
{
"cell_type": "markdown",
- "id": "1035c322",
+ "id": "386a774a",
"metadata": {},
"source": [
"## Exercise 35.1\n",
@@ -686,7 +686,7 @@
},
{
"cell_type": "markdown",
- "id": "5317e0f4",
+ "id": "48503f31",
"metadata": {},
"source": [
"## Solution to[ Exercise 35.1](https://python-advanced.quantecon.org/#apl_ex1)\n",
@@ -712,7 +712,7 @@
},
{
"cell_type": "markdown",
- "id": "de345d8f",
+ "id": "d7637594",
"metadata": {},
"source": [
"## Exercise 35.2\n",
@@ -722,7 +722,7 @@
},
{
"cell_type": "markdown",
- "id": "0ab3ef5a",
+ "id": "b06e4cdd",
"metadata": {},
"source": [
"## Solution to[ Exercise 35.2](https://python-advanced.quantecon.org/#apl_ex2)\n",
@@ -736,7 +736,7 @@
},
{
"cell_type": "markdown",
- "id": "764127a0",
+ "id": "577b89ff",
"metadata": {},
"source": [
"## Exercise 35.3\n",
@@ -791,7 +791,7 @@
},
{
"cell_type": "markdown",
- "id": "ee6170bc",
+ "id": "d6a46f05",
"metadata": {},
"source": [
"## Solution to[ Exercise 35.3](https://python-advanced.quantecon.org/#apl_ex3)\n",
@@ -802,7 +802,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "abda1687",
+ "id": "e5401fbc",
"metadata": {
"hide-output": false
},
@@ -822,7 +822,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "422b364d",
+ "id": "aba2ca49",
"metadata": {
"hide-output": false
},
@@ -837,7 +837,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "36a3e5c8",
+ "id": "19aec5a5",
"metadata": {
"hide-output": false
},
@@ -852,7 +852,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d660994e",
+ "id": "2c59fbfc",
"metadata": {
"hide-output": false
},
@@ -873,7 +873,7 @@
},
{
"cell_type": "markdown",
- "id": "0ba41d9a",
+ "id": "6510151b",
"metadata": {},
"source": [
"Now that we have a panel of data, we’d like to solve the inverse problem by assuming the theory specified above and estimating the coefficients given above."
@@ -882,7 +882,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f036608d",
+ "id": "4762030b",
"metadata": {
"hide-output": false
},
@@ -893,7 +893,7 @@
},
{
"cell_type": "markdown",
- "id": "425564b5",
+ "id": "5c4f70a5",
"metadata": {},
"source": [
"**Inverse Problem:**\n",
@@ -906,7 +906,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b5a1adaf",
+ "id": "a54ad8a7",
"metadata": {
"hide-output": false
},
@@ -918,7 +918,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "090aa73d",
+ "id": "05118bb1",
"metadata": {
"hide-output": false
},
@@ -929,7 +929,7 @@
},
{
"cell_type": "markdown",
- "id": "0ae43f9b",
+ "id": "ea97c5fd",
"metadata": {},
"source": [
"Let’s compare these with the *true* population parameter values."
@@ -938,7 +938,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e82ef83f",
+ "id": "2fbd1e37",
"metadata": {
"hide-output": false
},
@@ -949,7 +949,7 @@
},
{
"cell_type": "markdown",
- "id": "3d59958e",
+ "id": "cf18dfff",
"metadata": {},
"source": [
"1. $ \\xi $ and $ \\lambda $ "
@@ -958,7 +958,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b0c1c706",
+ "id": "c9fde020",
"metadata": {
"hide-output": false
},
@@ -970,7 +970,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6828427e",
+ "id": "f1a9b7b2",
"metadata": {
"hide-output": false
},
@@ -982,7 +982,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bc7d7276",
+ "id": "52073b89",
"metadata": {
"hide-output": false
},
@@ -993,7 +993,7 @@
},
{
"cell_type": "markdown",
- "id": "a0c3f903",
+ "id": "99899a4a",
"metadata": {},
"source": [
"1. $ \\beta_{i, R^m} $ and $ \\sigma_i $ "
@@ -1002,7 +1002,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "31c8d462",
+ "id": "efb21c33",
"metadata": {
"hide-output": false
},
@@ -1018,7 +1018,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dc955452",
+ "id": "0c18a672",
"metadata": {
"hide-output": false
},
@@ -1030,7 +1030,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e9203191",
+ "id": "4081ec9b",
"metadata": {
"hide-output": false
},
@@ -1041,7 +1041,7 @@
},
{
"cell_type": "markdown",
- "id": "0b303ebc",
+ "id": "0ab72ac6",
"metadata": {},
"source": [
"Q: How close did your estimates come to the parameters we specified?"
@@ -1049,7 +1049,7 @@
},
{
"cell_type": "markdown",
- "id": "c659f2ec",
+ "id": "3bb68227",
"metadata": {},
"source": [
"## Exercise 35.4\n",
@@ -1063,7 +1063,7 @@
},
{
"cell_type": "markdown",
- "id": "4de96e52",
+ "id": "2a0872bd",
"metadata": {},
"source": [
"## Solution to[ Exercise 35.4](https://python-advanced.quantecon.org/#apl_ex4)\n",
@@ -1081,7 +1081,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8f52e5b6",
+ "id": "b07cb37f",
"metadata": {
"hide-output": false
},
@@ -1104,7 +1104,7 @@
},
{
"cell_type": "markdown",
- "id": "707a847c",
+ "id": "49f2635b",
"metadata": {},
"source": [
"Let’s try to solve $ a $ and $ b $ using the actual model parameters."
@@ -1113,7 +1113,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cedae945",
+ "id": "7f29a1ad",
"metadata": {
"hide-output": false
},
@@ -1125,7 +1125,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "30cd7662",
+ "id": "a8f77953",
"metadata": {
"hide-output": false
},
@@ -1136,7 +1136,7 @@
},
{
"cell_type": "markdown",
- "id": "00e98cc0",
+ "id": "0d5a73b8",
"metadata": {},
"source": [
"## Exercise 35.5\n",
@@ -1146,7 +1146,7 @@
},
{
"cell_type": "markdown",
- "id": "8f86de66",
+ "id": "8adc7a2f",
"metadata": {},
"source": [
"## Solution to[ Exercise 35.5](https://python-advanced.quantecon.org/#apl_ex5)\n",
@@ -1157,7 +1157,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cf827783",
+ "id": "c6926636",
"metadata": {
"hide-output": false
},
@@ -1169,7 +1169,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2c70cf6e",
+ "id": "60717e15",
"metadata": {
"hide-output": false
},
@@ -1180,7 +1180,7 @@
}
],
"metadata": {
- "date": 1723011580.588927,
+ "date": 1723517846.7239914,
"filename": "asset_pricing_lph.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/black_litterman.ipynb b/_notebooks/black_litterman.ipynb
index 6745de85..e7c12746 100644
--- a/_notebooks/black_litterman.ipynb
+++ b/_notebooks/black_litterman.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "99dd596f",
+ "id": "ccdc69ba",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "9baa5b6b",
+ "id": "8b94cbfa",
"metadata": {},
"source": [
"# Two Modifications of Mean-Variance Portfolio Theory"
@@ -21,7 +21,7 @@
},
{
"cell_type": "markdown",
- "id": "ce645840",
+ "id": "99ad80fb",
"metadata": {},
"source": [
"## Overview\n",
@@ -81,7 +81,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a4f76c7e",
+ "id": "ac3e5a7d",
"metadata": {
"hide-output": false
},
@@ -95,7 +95,7 @@
},
{
"cell_type": "markdown",
- "id": "3d9f4735",
+ "id": "bf004770",
"metadata": {},
"source": [
"## Mean-Variance Portfolio Choice\n",
@@ -158,7 +158,7 @@
},
{
"cell_type": "markdown",
- "id": "52320644",
+ "id": "111f3931",
"metadata": {},
"source": [
"## Estimating Mean and Variance\n",
@@ -178,7 +178,7 @@
},
{
"cell_type": "markdown",
- "id": "ae319013",
+ "id": "2949133a",
"metadata": {},
"source": [
"## Black-Litterman Starting Point\n",
@@ -196,7 +196,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ec89989d",
+ "id": "3fa24812",
"metadata": {
"hide-output": false
},
@@ -249,7 +249,7 @@
},
{
"cell_type": "markdown",
- "id": "0702a1cb",
+ "id": "28136323",
"metadata": {},
"source": [
"Black and Litterman’s responded to this situation in the following way:\n",
@@ -277,7 +277,7 @@
},
{
"cell_type": "markdown",
- "id": "569420f9",
+ "id": "ea66f0ed",
"metadata": {},
"source": [
"## Details\n",
@@ -349,7 +349,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "34663524",
+ "id": "fa2cced7",
"metadata": {
"hide-output": false
},
@@ -384,7 +384,7 @@
},
{
"cell_type": "markdown",
- "id": "180651aa",
+ "id": "cdb53125",
"metadata": {},
"source": [
"## Adding Views\n",
@@ -447,7 +447,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "db0e511f",
+ "id": "3b2c384e",
"metadata": {
"hide-output": false
},
@@ -511,7 +511,7 @@
},
{
"cell_type": "markdown",
- "id": "fd74ded1",
+ "id": "e4403470",
"metadata": {},
"source": [
"## Bayesian Interpretation\n",
@@ -561,7 +561,7 @@
},
{
"cell_type": "markdown",
- "id": "75c54ad8",
+ "id": "be49b80c",
"metadata": {},
"source": [
"## Curve Decolletage\n",
@@ -691,7 +691,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7e36dad1",
+ "id": "ec5cd8f2",
"metadata": {
"hide-output": false
},
@@ -769,7 +769,7 @@
},
{
"cell_type": "markdown",
- "id": "da159b35",
+ "id": "9c5ecab3",
"metadata": {},
"source": [
"Note that the line that connects the two points\n",
@@ -790,7 +790,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "edb4aeef",
+ "id": "449b2dcc",
"metadata": {
"hide-output": false
},
@@ -840,7 +840,7 @@
},
{
"cell_type": "markdown",
- "id": "76ba06c3",
+ "id": "5d01a5d0",
"metadata": {},
"source": [
"## Black-Litterman Recommendation as Regularization\n",
@@ -996,7 +996,7 @@
},
{
"cell_type": "markdown",
- "id": "aa583d79",
+ "id": "6992f900",
"metadata": {},
"source": [
"## A Robust Control Operator\n",
@@ -1136,7 +1136,7 @@
},
{
"cell_type": "markdown",
- "id": "cec23cf9",
+ "id": "64aa6a39",
"metadata": {},
"source": [
"## A Robust Mean-Variance Portfolio Model\n",
@@ -1207,7 +1207,7 @@
},
{
"cell_type": "markdown",
- "id": "e29bbf3c",
+ "id": "e5872d14",
"metadata": {},
"source": [
"## Appendix\n",
@@ -1283,7 +1283,7 @@
},
{
"cell_type": "markdown",
- "id": "92f35c3f",
+ "id": "4b6bd85d",
"metadata": {},
"source": [
"## Special Case – IID Sample\n",
@@ -1326,7 +1326,7 @@
},
{
"cell_type": "markdown",
- "id": "0dc06a02",
+ "id": "79841980",
"metadata": {},
"source": [
"## Dependence and Sampling Frequency\n",
@@ -1391,7 +1391,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7def298a",
+ "id": "7170206c",
"metadata": {
"hide-output": false
},
@@ -1422,7 +1422,7 @@
},
{
"cell_type": "markdown",
- "id": "afb89897",
+ "id": "30c55d02",
"metadata": {},
"source": [
"## Frequency and the Mean Estimator\n",
@@ -1504,7 +1504,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b373035c",
+ "id": "885443c6",
"metadata": {
"hide-output": false
},
@@ -1532,7 +1532,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b6c92c59",
+ "id": "1248d9b9",
"metadata": {
"hide-output": false
},
@@ -1578,7 +1578,7 @@
},
{
"cell_type": "markdown",
- "id": "ad0bc8d4",
+ "id": "b5c6bfbc",
"metadata": {},
"source": [
"The above figure illustrates the relationship between the asymptotic\n",
@@ -1596,7 +1596,7 @@
}
],
"metadata": {
- "date": 1723011580.63527,
+ "date": 1723517846.772456,
"filename": "black_litterman.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/calvo.ipynb b/_notebooks/calvo.ipynb
index 276035e0..f6bd11ef 100644
--- a/_notebooks/calvo.ipynb
+++ b/_notebooks/calvo.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "6ab7a84c",
+ "id": "b339f0a0",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "c7e09ed3",
+ "id": "7efc6315",
"metadata": {},
"source": [
"# Ramsey Plans, Time Inconsistency, Sustainable Plans\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "83f92433",
+ "id": "b4e69859",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "c9cfdb89",
+ "id": "22fd4abc",
"metadata": {},
"source": [
"## Overview\n",
@@ -81,7 +81,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e69872d5",
+ "id": "0362a6fc",
"metadata": {
"hide-output": false
},
@@ -92,7 +92,7 @@
},
{
"cell_type": "markdown",
- "id": "101e27a5",
+ "id": "0a113cb8",
"metadata": {},
"source": [
"We’ll start with some imports:"
@@ -101,7 +101,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c909a78f",
+ "id": "b34bb2f9",
"metadata": {
"hide-output": false
},
@@ -117,7 +117,7 @@
},
{
"cell_type": "markdown",
- "id": "219f696b",
+ "id": "4da54310",
"metadata": {},
"source": [
"## Model components\n",
@@ -260,7 +260,7 @@
},
{
"cell_type": "markdown",
- "id": "2c4fe552",
+ "id": "0b7eb4f0",
"metadata": {},
"source": [
"## Friedman’s optimal rate of deflation\n",
@@ -293,7 +293,7 @@
},
{
"cell_type": "markdown",
- "id": "4f8ae96f",
+ "id": "92210aed",
"metadata": {},
"source": [
"## Calvo’s perturbation of optimal deflation rate\n",
@@ -374,7 +374,7 @@
},
{
"cell_type": "markdown",
- "id": "7e5ff10a",
+ "id": "67f74277",
"metadata": {},
"source": [
"## Structure\n",
@@ -411,7 +411,7 @@
},
{
"cell_type": "markdown",
- "id": "f04235f4",
+ "id": "a8edbda3",
"metadata": {},
"source": [
"## Intertemporal structure\n",
@@ -439,7 +439,7 @@
},
{
"cell_type": "markdown",
- "id": "661f18a8",
+ "id": "fe329912",
"metadata": {},
"source": [
"## Four timing protocols\n",
@@ -504,7 +504,7 @@
},
{
"cell_type": "markdown",
- "id": "3421c926",
+ "id": "834e3035",
"metadata": {},
"source": [
"## A Ramsey planner\n",
@@ -531,7 +531,7 @@
},
{
"cell_type": "markdown",
- "id": "5a1eaeed",
+ "id": "2fd3672a",
"metadata": {},
"source": [
"### Subproblem 1\n",
@@ -657,7 +657,7 @@
},
{
"cell_type": "markdown",
- "id": "36f364ab",
+ "id": "2e5e1ed9",
"metadata": {},
"source": [
"### Subproblem 2\n",
@@ -696,7 +696,7 @@
},
{
"cell_type": "markdown",
- "id": "81dcefea",
+ "id": "344d9d5c",
"metadata": {},
"source": [
"### Representation of Ramsey plan\n",
@@ -773,7 +773,7 @@
},
{
"cell_type": "markdown",
- "id": "e9f14bca",
+ "id": "6a91f5dd",
"metadata": {},
"source": [
"### Digression on timeless perspective\n",
@@ -789,7 +789,7 @@
},
{
"cell_type": "markdown",
- "id": "b3c251cb",
+ "id": "9923294c",
"metadata": {},
"source": [
"### Multiple roles of $ \\theta_t $\n",
@@ -811,7 +811,7 @@
},
{
"cell_type": "markdown",
- "id": "6279b2f4",
+ "id": "4adbaf04",
"metadata": {},
"source": [
"### Time inconsistency\n",
@@ -829,7 +829,7 @@
},
{
"cell_type": "markdown",
- "id": "d1415a58",
+ "id": "1936a01e",
"metadata": {},
"source": [
"## Constrained-to-constant-growth-rate Ramsey plan\n",
@@ -885,7 +885,7 @@
},
{
"cell_type": "markdown",
- "id": "434cacc4",
+ "id": "6aff1e45",
"metadata": {},
"source": [
"## Markov perfect governments\n",
@@ -1003,7 +1003,7 @@
},
{
"cell_type": "markdown",
- "id": "894f8c3a",
+ "id": "72eae8d8",
"metadata": {},
"source": [
"## Outcomes under three timing protocols\n",
@@ -1059,7 +1059,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6c1fe7c4",
+ "id": "c40190bc",
"metadata": {
"hide-output": false
},
@@ -1180,7 +1180,7 @@
},
{
"cell_type": "markdown",
- "id": "353095ee",
+ "id": "6a863821",
"metadata": {},
"source": [
"Let’s create an instance of ChangLQ with the following parameters:"
@@ -1189,7 +1189,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6b2d2374",
+ "id": "e5500a94",
"metadata": {
"hide-output": false
},
@@ -1200,7 +1200,7 @@
},
{
"cell_type": "markdown",
- "id": "77e39aa9",
+ "id": "cc77b73f",
"metadata": {},
"source": [
"The following code plots value functions for a continuation Ramsey\n",
@@ -1210,7 +1210,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ab94de9b",
+ "id": "3854c47b",
"metadata": {
"hide-output": false
},
@@ -1280,7 +1280,7 @@
},
{
"cell_type": "markdown",
- "id": "f6630fb5",
+ "id": "eee92c31",
"metadata": {},
"source": [
"The dotted line in the above graph is the 45-degree line.\n",
@@ -1314,7 +1314,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "75034242",
+ "id": "0317e0c1",
"metadata": {
"hide-output": false
},
@@ -1355,7 +1355,7 @@
},
{
"cell_type": "markdown",
- "id": "dc438e80",
+ "id": "8f0a364e",
"metadata": {},
"source": [
"In the above graph, notice that $ \\theta^* < \\theta_\\infty^R < \\theta^{CR} < \\theta_0^R < \\theta^{MPE} . $\n",
@@ -1366,7 +1366,7 @@
},
{
"cell_type": "markdown",
- "id": "11ee2060",
+ "id": "c30d9c5c",
"metadata": {},
"source": [
"### Ramsey planner’s value function\n",
@@ -1400,7 +1400,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "37d48571",
+ "id": "bbebbbb8",
"metadata": {
"hide-output": false
},
@@ -1413,7 +1413,7 @@
},
{
"cell_type": "markdown",
- "id": "864110d1",
+ "id": "2bca79f5",
"metadata": {},
"source": [
"So our claim that $ J(\\theta_\\infty^R) = V^{CR}(\\theta_\\infty^R) $is verified numerically.\n",
@@ -1440,7 +1440,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e1390605",
+ "id": "4a192403",
"metadata": {
"hide-output": false
},
@@ -1554,7 +1554,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "361ce57c",
+ "id": "c0a46a4e",
"metadata": {
"hide-output": false
},
@@ -1571,7 +1571,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7fff2e0c",
+ "id": "d344302d",
"metadata": {
"hide-output": false
},
@@ -1582,7 +1582,7 @@
},
{
"cell_type": "markdown",
- "id": "32667fc1",
+ "id": "7e3c7a1d",
"metadata": {},
"source": [
"The above graphs and table convey many useful things.\n",
@@ -1613,7 +1613,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5af9303b",
+ "id": "b07e24a1",
"metadata": {
"hide-output": false
},
@@ -1630,7 +1630,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "074ca4c8",
+ "id": "40586d73",
"metadata": {
"hide-output": false
},
@@ -1641,7 +1641,7 @@
},
{
"cell_type": "markdown",
- "id": "22e18b70",
+ "id": "80016e0e",
"metadata": {},
"source": [
"The above table and figures show how\n",
@@ -1659,7 +1659,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5f7d4620",
+ "id": "f15eb83d",
"metadata": {
"hide-output": false
},
@@ -1675,7 +1675,7 @@
},
{
"cell_type": "markdown",
- "id": "7ffed06d",
+ "id": "7b58098e",
"metadata": {},
"source": [
"The above graphs indicate that as $ c $ approaches zero, $ \\theta_\\infty^R, \\theta_0^R, \\theta^{CR} $,\n",
@@ -1699,7 +1699,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "39971fcf",
+ "id": "7cc6625e",
"metadata": {
"hide-output": false
},
@@ -1766,7 +1766,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f7f99231",
+ "id": "b819efbd",
"metadata": {
"hide-output": false
},
@@ -1780,7 +1780,7 @@
},
{
"cell_type": "markdown",
- "id": "46e2ca0d",
+ "id": "55491dd5",
"metadata": {},
"source": [
"Notice how $ d_1 $ changes as we raise the discount factor parameter $ \\beta $.\n",
@@ -1791,7 +1791,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "907f9a68",
+ "id": "37e3df52",
"metadata": {
"hide-output": false
},
@@ -1806,7 +1806,7 @@
},
{
"cell_type": "markdown",
- "id": "d2190ded",
+ "id": "29991206",
"metadata": {},
"source": [
"Evidently, increasing $ c $ causes the decay factor $ d_1 $ to increase.\n",
@@ -1818,7 +1818,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "69e09eb4",
+ "id": "c91e6782",
"metadata": {
"hide-output": false
},
@@ -1833,7 +1833,7 @@
},
{
"cell_type": "markdown",
- "id": "d7eccf49",
+ "id": "58a869d6",
"metadata": {},
"source": [
"The above panels for an $ \\alpha = 4 $ setting indicate that $ \\alpha $ and $ c $ affect outcomes\n",
@@ -1844,7 +1844,7 @@
},
{
"cell_type": "markdown",
- "id": "97bd8880",
+ "id": "a6a0e998",
"metadata": {},
"source": [
"### Time inconsistency of Ramsey plan\n",
@@ -1869,7 +1869,7 @@
},
{
"cell_type": "markdown",
- "id": "338807e9",
+ "id": "fdaaa71a",
"metadata": {},
"source": [
"### Implausibility of Ramsey plan\n",
@@ -1891,7 +1891,7 @@
},
{
"cell_type": "markdown",
- "id": "10b93ff3",
+ "id": "b622a196",
"metadata": {},
"source": [
"### Ramsey plan strikes back\n",
@@ -1908,7 +1908,7 @@
},
{
"cell_type": "markdown",
- "id": "412d44f5",
+ "id": "c93829a7",
"metadata": {},
"source": [
"## A fourth model of government decision making\n",
@@ -1931,7 +1931,7 @@
},
{
"cell_type": "markdown",
- "id": "7d7682d1",
+ "id": "7831f871",
"metadata": {},
"source": [
"### Government decisions\n",
@@ -1967,7 +1967,7 @@
},
{
"cell_type": "markdown",
- "id": "ffe5b3bb",
+ "id": "cdef8228",
"metadata": {},
"source": [
"### Temptation to deviate from plan\n",
@@ -1999,7 +1999,7 @@
},
{
"cell_type": "markdown",
- "id": "8c33b173",
+ "id": "94160a61",
"metadata": {},
"source": [
"## Sustainable or credible plan\n",
@@ -2042,7 +2042,7 @@
},
{
"cell_type": "markdown",
- "id": "9ac069e9",
+ "id": "93f99f7f",
"metadata": {},
"source": [
"### Abreu’s self-enforcing plan\n",
@@ -2114,7 +2114,7 @@
},
{
"cell_type": "markdown",
- "id": "54df1e2e",
+ "id": "de9477b5",
"metadata": {},
"source": [
"### Abreu’s carrot-stick plan\n",
@@ -2156,7 +2156,7 @@
},
{
"cell_type": "markdown",
- "id": "014ddaec",
+ "id": "be51ea60",
"metadata": {},
"source": [
"### Example of self-enforcing plan\n",
@@ -2185,7 +2185,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f9f6dfbc",
+ "id": "1ba6f1cc",
"metadata": {
"hide-output": false
},
@@ -2243,7 +2243,7 @@
},
{
"cell_type": "markdown",
- "id": "acc89db2",
+ "id": "5cadb2ff",
"metadata": {},
"source": [
"To confirm that the plan $ \\vec \\mu^A $ is **self-enforcing**, we\n",
@@ -2266,7 +2266,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "86af6b86",
+ "id": "1c8f7dc8",
"metadata": {
"hide-output": false
},
@@ -2277,7 +2277,7 @@
},
{
"cell_type": "markdown",
- "id": "3d860f49",
+ "id": "8da0804b",
"metadata": {},
"source": [
"Given that plan $ \\vec \\mu^A $ is self-enforcing, we can check that\n",
@@ -2291,7 +2291,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "646eb06a",
+ "id": "676d957f",
"metadata": {
"hide-output": false
},
@@ -2312,7 +2312,7 @@
},
{
"cell_type": "markdown",
- "id": "f6cf3918",
+ "id": "43f91976",
"metadata": {},
"source": [
"### Recursive representation of a sustainable plan\n",
@@ -2349,7 +2349,7 @@
},
{
"cell_type": "markdown",
- "id": "da9dbbf3",
+ "id": "2b6723b9",
"metadata": {},
"source": [
"## Whose plan is it?\n",
@@ -2372,7 +2372,7 @@
},
{
"cell_type": "markdown",
- "id": "5a340976",
+ "id": "25efbc22",
"metadata": {},
"source": [
"## Comparison of equilibrium values\n",
@@ -2397,7 +2397,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "80ee3b23",
+ "id": "9a693dd6",
"metadata": {
"hide-output": false
},
@@ -2409,7 +2409,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8ecfbfe0",
+ "id": "aeee003c",
"metadata": {
"hide-output": false
},
@@ -2421,7 +2421,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "022ccc0f",
+ "id": "cc8a4292",
"metadata": {
"hide-output": false
},
@@ -2432,7 +2432,7 @@
},
{
"cell_type": "markdown",
- "id": "12885cad",
+ "id": "61f2d8f6",
"metadata": {},
"source": [
"We have also computed **credible plans** for a government or sequence\n",
@@ -2447,7 +2447,7 @@
},
{
"cell_type": "markdown",
- "id": "2c1e382e",
+ "id": "4c6a00ab",
"metadata": {},
"source": [
"## Note on dynamic programming squared\n",
@@ -2469,7 +2469,7 @@
}
],
"metadata": {
- "date": 1723011580.9427352,
+ "date": 1723517847.0328875,
"filename": "calvo.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/calvo_machine_learn.ipynb b/_notebooks/calvo_machine_learn.ipynb
index 0af26675..d1a37c07 100644
--- a/_notebooks/calvo_machine_learn.ipynb
+++ b/_notebooks/calvo_machine_learn.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "7aaf85f3",
+ "id": "05376b6e",
"metadata": {},
"source": [
"# Machine Learning a Ramsey Plan"
@@ -10,7 +10,7 @@
},
{
"cell_type": "markdown",
- "id": "2b7d6e65",
+ "id": "a4b9ed60",
"metadata": {},
"source": [
"## Introduction\n",
@@ -71,7 +71,7 @@
},
{
"cell_type": "markdown",
- "id": "9b78c801",
+ "id": "dbefb338",
"metadata": {},
"source": [
"## The Model\n",
@@ -95,7 +95,7 @@
},
{
"cell_type": "markdown",
- "id": "abe59aac",
+ "id": "52b8e85b",
"metadata": {},
"source": [
"## Model components\n",
@@ -147,7 +147,7 @@
},
{
"cell_type": "markdown",
- "id": "29ea1009",
+ "id": "47158cdd",
"metadata": {},
"source": [
"## \n",
@@ -224,7 +224,7 @@
},
{
"cell_type": "markdown",
- "id": "2ddf4470",
+ "id": "5e070fa3",
"metadata": {},
"source": [
"## Parameters and variables\n",
@@ -246,7 +246,7 @@
},
{
"cell_type": "markdown",
- "id": "cb5e8419",
+ "id": "44e6ab8d",
"metadata": {},
"source": [
"### Basic objects\n",
@@ -315,7 +315,7 @@
},
{
"cell_type": "markdown",
- "id": "bac4fc0a",
+ "id": "972c15df",
"metadata": {},
"source": [
"## Approximations\n",
@@ -394,7 +394,7 @@
},
{
"cell_type": "markdown",
- "id": "b1b1c8b8",
+ "id": "0ba05584",
"metadata": {},
"source": [
"## A gradient algorithm\n",
@@ -408,7 +408,7 @@
},
{
"cell_type": "markdown",
- "id": "90fab0dd",
+ "id": "93d403c9",
"metadata": {},
"source": [
"### Implementation\n",
@@ -421,7 +421,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b956d8bb",
+ "id": "69942f96",
"metadata": {
"hide-output": false
},
@@ -435,7 +435,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d59b6cf6",
+ "id": "05735e8f",
"metadata": {
"hide-output": false
},
@@ -452,7 +452,7 @@
},
{
"cell_type": "markdown",
- "id": "13f84708",
+ "id": "cf7d7ba3",
"metadata": {},
"source": [
"First, because we’ll want to compare the results we obtain here with those obtained with another, more structured, approach, we copy the class `ChangLQ` to solve the LQ Chang model in this quantecon lecture [Ramsey Plans, Time Inconsistency, Sustainable Plans](https://python-advanced.quantecon.org/calvo.html).\n",
@@ -463,7 +463,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b5614500",
+ "id": "3de4839b",
"metadata": {
"hide-output": false
},
@@ -584,7 +584,7 @@
},
{
"cell_type": "markdown",
- "id": "c27e4ec6",
+ "id": "7fa46b78",
"metadata": {},
"source": [
"Now we compute the value of $ V $ under this setup, and compare it against those obtained in [Outcomes under three timing protocols](https://python-advanced.quantecon.org/calvo.html#compute-lq)."
@@ -593,7 +593,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bde203c6",
+ "id": "0fe5a893",
"metadata": {
"hide-output": false
},
@@ -607,7 +607,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4beac21c",
+ "id": "0d3a935d",
"metadata": {
"hide-output": false
},
@@ -665,7 +665,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0505e5c0",
+ "id": "d8f8dc99",
"metadata": {
"hide-output": false
},
@@ -679,7 +679,7 @@
},
{
"cell_type": "markdown",
- "id": "9f33e284",
+ "id": "04dbeeab",
"metadata": {},
"source": [
"Now we want to maximize the function $ V $ by choice of $ \\mu $.\n",
@@ -690,7 +690,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "01d7effa",
+ "id": "d240594b",
"metadata": {
"hide-output": false
},
@@ -730,7 +730,7 @@
},
{
"cell_type": "markdown",
- "id": "0a423ef7",
+ "id": "ebb0ecb3",
"metadata": {},
"source": [
"Here we use automatic differentiation functionality in JAX with `grad`."
@@ -739,7 +739,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "20c50df9",
+ "id": "4b440383",
"metadata": {
"hide-output": false
},
@@ -756,7 +756,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f185c5c0",
+ "id": "05b19a8f",
"metadata": {
"hide-output": false
},
@@ -773,7 +773,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0dd21522",
+ "id": "8a5273dd",
"metadata": {
"hide-output": false
},
@@ -785,7 +785,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e4fe137b",
+ "id": "c980b299",
"metadata": {
"hide-output": false
},
@@ -797,7 +797,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "79ca687a",
+ "id": "70adfa43",
"metadata": {
"hide-output": false
},
@@ -809,7 +809,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "389973be",
+ "id": "320a652f",
"metadata": {
"hide-output": false
},
@@ -820,7 +820,7 @@
},
{
"cell_type": "markdown",
- "id": "508df1c3",
+ "id": "9b98491b",
"metadata": {},
"source": [
"### Restricting $ \\mu_t = \\bar \\mu $ for all $ t $\n",
@@ -838,7 +838,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6faa0cf3",
+ "id": "ec0e69b4",
"metadata": {
"hide-output": false
},
@@ -859,7 +859,7 @@
},
{
"cell_type": "markdown",
- "id": "2d00a89d",
+ "id": "b6eaed13",
"metadata": {},
"source": [
"Compare it to $ \\mu^{CR} $ in [Ramsey Plans, Time Inconsistency, Sustainable Plans](https://python-advanced.quantecon.org/calvo.html), we again obtained a close estimate."
@@ -868,7 +868,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b09415ab",
+ "id": "d24c0b74",
"metadata": {
"hide-output": false
},
@@ -880,7 +880,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f3190f22",
+ "id": "90ca302d",
"metadata": {
"hide-output": false
},
@@ -893,7 +893,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "71c54fe0",
+ "id": "efd53478",
"metadata": {
"hide-output": false
},
@@ -904,7 +904,7 @@
},
{
"cell_type": "markdown",
- "id": "bcd895f6",
+ "id": "31477280",
"metadata": {},
"source": [
"## A more structured ML algorithm\n",
@@ -989,7 +989,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bbdbd017",
+ "id": "01d53d28",
"metadata": {
"hide-output": false
},
@@ -1008,7 +1008,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b9480dfe",
+ "id": "cd46857c",
"metadata": {
"hide-output": false
},
@@ -1022,7 +1022,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "50f2bb93",
+ "id": "df2f5691",
"metadata": {
"hide-output": false
},
@@ -1036,7 +1036,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a1b0c705",
+ "id": "43af1d79",
"metadata": {
"hide-output": false
},
@@ -1047,7 +1047,7 @@
},
{
"cell_type": "markdown",
- "id": "d950de02",
+ "id": "06db7de8",
"metadata": {},
"source": [
"As before, the Ramsey planner’s criterion is\n",
@@ -1133,7 +1133,7 @@
},
{
"cell_type": "markdown",
- "id": "0646bcce",
+ "id": "2576c6b9",
"metadata": {},
"source": [
"### Two implementations\n",
@@ -1144,7 +1144,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1dc7e638",
+ "id": "331a89ca",
"metadata": {
"hide-output": false
},
@@ -1172,7 +1172,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e7d46de7",
+ "id": "cf10f341",
"metadata": {
"hide-output": false
},
@@ -1189,7 +1189,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ef718668",
+ "id": "7cbfbbe2",
"metadata": {
"hide-output": false
},
@@ -1206,7 +1206,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ad551cd1",
+ "id": "c1818326",
"metadata": {
"hide-output": false
},
@@ -1218,7 +1218,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "176f3892",
+ "id": "2f1b7e38",
"metadata": {
"hide-output": false
},
@@ -1230,7 +1230,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "78a38ef2",
+ "id": "5ac99984",
"metadata": {
"hide-output": false
},
@@ -1242,7 +1242,7 @@
},
{
"cell_type": "markdown",
- "id": "1c9aec6f",
+ "id": "72bbaeae",
"metadata": {},
"source": [
"We find that by exploiting more knowledge about the structure of the problem, we can significantly speed up our computation.\n",
@@ -1253,7 +1253,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f608a9f9",
+ "id": "0cc2269f",
"metadata": {
"hide-output": false
},
@@ -1280,7 +1280,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d5416b13",
+ "id": "78ce4584",
"metadata": {
"hide-output": false
},
@@ -1292,7 +1292,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1ca91420",
+ "id": "16d0687f",
"metadata": {
"hide-output": false
},
@@ -1304,7 +1304,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "29871b90",
+ "id": "cff2b4aa",
"metadata": {
"hide-output": false
},
@@ -1315,7 +1315,7 @@
},
{
"cell_type": "markdown",
- "id": "29bf0237",
+ "id": "858d58fc",
"metadata": {},
"source": [
"We can check the gradient of the analytical solution against the `JAX` computed version"
@@ -1324,7 +1324,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eb38c373",
+ "id": "f7da1383",
"metadata": {
"hide-output": false
},
@@ -1352,7 +1352,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "10ee7b8e",
+ "id": "66cd379a",
"metadata": {
"hide-output": false
},
@@ -1364,7 +1364,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c7e3bd9c",
+ "id": "ba06009d",
"metadata": {
"hide-output": false
},
@@ -1376,7 +1376,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8bfb6cb5",
+ "id": "82af02ad",
"metadata": {
"hide-output": false
},
@@ -1387,7 +1387,7 @@
},
{
"cell_type": "markdown",
- "id": "8885dc7e",
+ "id": "3c1ac701",
"metadata": {},
"source": [
"## Some Exploratory Regressions\n",
@@ -1419,7 +1419,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e4e91d16",
+ "id": "ba9683b7",
"metadata": {
"hide-output": false
},
@@ -1441,7 +1441,7 @@
},
{
"cell_type": "markdown",
- "id": "3154672b",
+ "id": "4f3fb7f6",
"metadata": {},
"source": [
"We notice that $ \\theta_t $ is less than $ \\mu_t $for low $ t $’s but that it eventually converges to\n",
@@ -1459,7 +1459,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e8634cad",
+ "id": "442773ba",
"metadata": {
"hide-output": false
},
@@ -1477,7 +1477,7 @@
},
{
"cell_type": "markdown",
- "id": "67914e64",
+ "id": "df811859",
"metadata": {},
"source": [
"Our regression tells us that along the Ramsey outcome $ \\vec \\mu, \\vec \\theta $ the linear function\n",
@@ -1498,7 +1498,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "606fa75e",
+ "id": "9f58502a",
"metadata": {
"hide-output": false
},
@@ -1514,7 +1514,7 @@
},
{
"cell_type": "markdown",
- "id": "91975ff5",
+ "id": "9b5bf1fe",
"metadata": {},
"source": [
"The time $ 0 $ pair $ (\\theta_0, \\mu_0) $ appears as the point on the upper right.\n",
@@ -1529,7 +1529,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "43e73224",
+ "id": "594920a0",
"metadata": {
"hide-output": false
},
@@ -1549,7 +1549,7 @@
},
{
"cell_type": "markdown",
- "id": "a7b38d60",
+ "id": "0658fa71",
"metadata": {},
"source": [
"We find that the regression line fits perfectly and thus discover the affine relationship\n",
@@ -1566,7 +1566,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a8defbba",
+ "id": "311a912d",
"metadata": {
"hide-output": false
},
@@ -1584,7 +1584,7 @@
},
{
"cell_type": "markdown",
- "id": "b36de2a6",
+ "id": "c730902a",
"metadata": {},
"source": [
"Points for succeeding times appear further and further to the lower left and eventually converge to\n",
@@ -1593,7 +1593,7 @@
},
{
"cell_type": "markdown",
- "id": "cd6426d5",
+ "id": "cf0dbc68",
"metadata": {},
"source": [
"### Continuation Values\n",
@@ -1618,7 +1618,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d80a9127",
+ "id": "d8390406",
"metadata": {
"hide-output": false
},
@@ -1655,7 +1655,7 @@
},
{
"cell_type": "markdown",
- "id": "4fa6fbcd",
+ "id": "501dbd01",
"metadata": {},
"source": [
"The initial continuation value $ v_0 $ should equals the optimized value of the Ramsey planner’s criterion $ V $ defined\n",
@@ -1667,7 +1667,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eb40dd88",
+ "id": "886319f0",
"metadata": {
"hide-output": false
},
@@ -1678,7 +1678,7 @@
},
{
"cell_type": "markdown",
- "id": "fb35a5a3",
+ "id": "47b41d33",
"metadata": {},
"source": [
"We can also verify approximate equality by inspecting a graph of $ v_t $ against $ t $ for $ t=0, \\ldots, T $ along with the value attained by a restricted Ramsey planner $ V^{CR} $ and the optimized value of the ordinary Ramsey planner $ V^R $"
@@ -1687,7 +1687,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "18e24e10",
+ "id": "46a5ba06",
"metadata": {
"hide-output": false
},
@@ -1714,7 +1714,7 @@
},
{
"cell_type": "markdown",
- "id": "09a165d9",
+ "id": "9284a01d",
"metadata": {},
"source": [
"Figure Fig. 41.1 shows several striking patterns:\n",
@@ -1740,7 +1740,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f119c307",
+ "id": "076e236d",
"metadata": {
"hide-output": false
},
@@ -1759,7 +1759,7 @@
},
{
"cell_type": "markdown",
- "id": "9bd6873e",
+ "id": "727bbbd5",
"metadata": {},
"source": [
"The regression has an $ R^2 $ equal to $ 1 $ and so fits perfectly.\n",
@@ -1773,7 +1773,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "21330c9b",
+ "id": "ac8e786c",
"metadata": {
"hide-output": false
},
@@ -1784,7 +1784,7 @@
},
{
"cell_type": "markdown",
- "id": "1fb9d7a1",
+ "id": "c3399911",
"metadata": {},
"source": [
"Let’s plot $ v_t $ against $ \\theta_t $ along with the nonlinear regression line."
@@ -1793,7 +1793,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2e12fe9d",
+ "id": "d22bb74a",
"metadata": {
"hide-output": false
},
@@ -1820,7 +1820,7 @@
},
{
"cell_type": "markdown",
- "id": "3f0f3f45",
+ "id": "ebe59ed7",
"metadata": {},
"source": [
"The highest continuation value $ v_0 $ at $ t=0 $ appears at the peak of the function quadratic function\n",
@@ -1835,7 +1835,7 @@
},
{
"cell_type": "markdown",
- "id": "777a7df5",
+ "id": "a7735742",
"metadata": {},
"source": [
"## What has Machine Learning Taught Us?\n",
@@ -1915,7 +1915,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "23632be2",
+ "id": "f6d352c7",
"metadata": {
"hide-output": false
},
@@ -1926,7 +1926,7 @@
},
{
"cell_type": "markdown",
- "id": "dc341cb7",
+ "id": "2e1b2be9",
"metadata": {},
"source": [
"Now let’s print out the decision rule for $ \\mu_t $ uncovered by applying dynamic programming squared."
@@ -1935,7 +1935,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "726fe33b",
+ "id": "e47f0e6e",
"metadata": {
"hide-output": false
},
@@ -1947,7 +1947,7 @@
},
{
"cell_type": "markdown",
- "id": "428a63f7",
+ "id": "87fa6d88",
"metadata": {},
"source": [
"Now let’s print out the decision rule for $ \\theta_{t+1} $ uncovered by applying dynamic programming squared."
@@ -1956,7 +1956,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "66ec67be",
+ "id": "45c4b9da",
"metadata": {
"hide-output": false
},
@@ -1968,7 +1968,7 @@
},
{
"cell_type": "markdown",
- "id": "5ccc791d",
+ "id": "ad592b18",
"metadata": {},
"source": [
"Evidently, these agree with the relationships that we discovered by running regressions on the Ramsey outcomes $ \\vec \\mu^R, \\vec \\theta^R $ that we constructed with either of our machine learning algorithms.\n",
@@ -1989,7 +1989,7 @@
}
],
"metadata": {
- "date": 1723011581.0167055,
+ "date": 1723517847.1052845,
"filename": "calvo_machine_learn.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/cattle_cycles.ipynb b/_notebooks/cattle_cycles.ipynb
index 5e08c559..2b453f89 100644
--- a/_notebooks/cattle_cycles.ipynb
+++ b/_notebooks/cattle_cycles.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "b6a39835",
+ "id": "139f4746",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "43f859aa",
+ "id": "42d1b1eb",
"metadata": {},
"source": [
"# Cattle Cycles\n",
@@ -27,7 +27,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "003245fd",
+ "id": "2b021dae",
"metadata": {
"hide-output": false
},
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "5beabf55",
+ "id": "37465581",
"metadata": {},
"source": [
"This lecture uses the DLE class to construct instances of the “Cattle Cycles” model\n",
@@ -53,7 +53,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3fb6de84",
+ "id": "58dd6dbc",
"metadata": {
"hide-output": false
},
@@ -68,7 +68,7 @@
},
{
"cell_type": "markdown",
- "id": "359e6825",
+ "id": "db3bd433",
"metadata": {},
"source": [
"## The Model\n",
@@ -130,7 +130,7 @@
},
{
"cell_type": "markdown",
- "id": "9eedfd10",
+ "id": "70294416",
"metadata": {},
"source": [
"## Mapping into HS2013 Framework"
@@ -138,7 +138,7 @@
},
{
"cell_type": "markdown",
- "id": "3228495a",
+ "id": "1239f17a",
"metadata": {},
"source": [
"### Preferences\n",
@@ -153,7 +153,7 @@
},
{
"cell_type": "markdown",
- "id": "c868cddf",
+ "id": "6475843c",
"metadata": {},
"source": [
"### Technology\n",
@@ -203,7 +203,7 @@
},
{
"cell_type": "markdown",
- "id": "60f1fd47",
+ "id": "545fb9ef",
"metadata": {},
"source": [
"### Information\n",
@@ -242,7 +242,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3ed26a64",
+ "id": "cb7e398a",
"metadata": {
"hide-output": false
},
@@ -258,7 +258,7 @@
},
{
"cell_type": "markdown",
- "id": "59d8738b",
+ "id": "4be28461",
"metadata": {},
"source": [
"We set parameters to those used by [[Rosen *et al.*, 1994](https://python-advanced.quantecon.org/zreferences.html#id70)]"
@@ -267,7 +267,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ea5dc34f",
+ "id": "8c7e896e",
"metadata": {
"hide-output": false
},
@@ -341,7 +341,7 @@
},
{
"cell_type": "markdown",
- "id": "e7d41231",
+ "id": "7657888a",
"metadata": {},
"source": [
"Notice that we have set $ \\rho_1 = \\rho_2 = 0 $, so $ h_t $ and\n",
@@ -358,7 +358,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6d34ef90",
+ "id": "8e4194c3",
"metadata": {
"hide-output": false
},
@@ -391,7 +391,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6a3bfefa",
+ "id": "b4b5cc79",
"metadata": {
"hide-output": false
},
@@ -410,7 +410,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e6aea79c",
+ "id": "d25d141a",
"metadata": {
"hide-output": false
},
@@ -421,7 +421,7 @@
},
{
"cell_type": "markdown",
- "id": "050d983e",
+ "id": "440b8492",
"metadata": {},
"source": [
"[[Rosen *et al.*, 1994](https://python-advanced.quantecon.org/zreferences.html#id70)] use the model to understand the\n",
@@ -434,7 +434,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "642c2e54",
+ "id": "540e3bcb",
"metadata": {
"hide-output": false
},
@@ -451,7 +451,7 @@
},
{
"cell_type": "markdown",
- "id": "73fdc4b2",
+ "id": "375e410b",
"metadata": {},
"source": [
"In their Figure 3, [[Rosen *et al.*, 1994](https://python-advanced.quantecon.org/zreferences.html#id70)] plot the impulse response functions\n",
@@ -464,7 +464,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e4d719c8",
+ "id": "dd458947",
"metadata": {
"hide-output": false
},
@@ -493,7 +493,7 @@
},
{
"cell_type": "markdown",
- "id": "57462eef",
+ "id": "b494cf24",
"metadata": {},
"source": [
"The above figures show how consumption patterns differ markedly,\n",
@@ -516,7 +516,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "29813e61",
+ "id": "d9cb9745",
"metadata": {
"hide-output": false
},
@@ -538,7 +538,7 @@
},
{
"cell_type": "markdown",
- "id": "b4787d41",
+ "id": "170eae3a",
"metadata": {},
"source": [
"The fact that $ y_t $ is a weighted moving average of $ x_t $\n",
@@ -549,7 +549,7 @@
}
],
"metadata": {
- "date": 1723011581.0387359,
+ "date": 1723517847.1267962,
"filename": "cattle_cycles.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/chang_credible.ipynb b/_notebooks/chang_credible.ipynb
index 0a7d0027..07eee0a9 100644
--- a/_notebooks/chang_credible.ipynb
+++ b/_notebooks/chang_credible.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "bec6d9ee",
+ "id": "862e7fd3",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "e4b66f9a",
+ "id": "94f8dd42",
"metadata": {},
"source": [
"# Credible Government Policies in a Model of Chang\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a53e309a",
+ "id": "72ace7b7",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "4f3b60f2",
+ "id": "f1e3a6f1",
"metadata": {},
"source": [
"## Overview\n",
@@ -92,7 +92,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e745c9e3",
+ "id": "5f9fd976",
"metadata": {
"hide-output": false
},
@@ -105,7 +105,7 @@
},
{
"cell_type": "markdown",
- "id": "b400f0d9",
+ "id": "b616dfbb",
"metadata": {},
"source": [
"## The Setting\n",
@@ -160,7 +160,7 @@
},
{
"cell_type": "markdown",
- "id": "5b6443d7",
+ "id": "54096150",
"metadata": {},
"source": [
"### The Household’s Problem\n",
@@ -221,7 +221,7 @@
},
{
"cell_type": "markdown",
- "id": "3261dba0",
+ "id": "1c09b731",
"metadata": {},
"source": [
"### Government\n",
@@ -263,10 +263,9 @@
"y_t = f(x_t) \\tag{48.5}\n",
"$$\n",
"\n",
- "where $ f: \\mathbb{R}\\rightarrow \\mathbb{R} $ satisfies $ f(x) > 0 $,\n",
- "is twice continuously differentiable, $ f''(x) < 0 $, and\n",
- "$ f(x) = f(-x) $ for all $ x \\in\n",
- "\\mathbb{R} $, so that subsidies and taxes are equally distorting.\n",
+ "where $ f: \\mathbb{R}\\rightarrow \\mathbb{R} $ satisfies $ f(x) > 0 $, $ f(x) $\n",
+ "is twice continuously differentiable, $ f''(x) < 0 $, $ f'(0) = 0 $, and\n",
+ "$ f(x) = f(-x) $ for all $ x \\in \\mathbb{R} $, so that subsidies and taxes are equally distorting.\n",
"\n",
"The purpose is not to model the causes of tax distortions in any detail but simply to summarize\n",
"the *outcome* of those distortions via the function $ f(x) $.\n",
@@ -280,7 +279,7 @@
},
{
"cell_type": "markdown",
- "id": "ee260de5",
+ "id": "27c7c477",
"metadata": {},
"source": [
"### Within-period Timing Protocol\n",
@@ -310,7 +309,7 @@
},
{
"cell_type": "markdown",
- "id": "62a7f98b",
+ "id": "b7c2e1fd",
"metadata": {},
"source": [
"### Household’s Problem\n",
@@ -377,7 +376,7 @@
},
{
"cell_type": "markdown",
- "id": "3c0b33e4",
+ "id": "25f71524",
"metadata": {},
"source": [
"### Competitive Equilibrium\n",
@@ -403,7 +402,7 @@
},
{
"cell_type": "markdown",
- "id": "a29a0a1b",
+ "id": "a76a795c",
"metadata": {},
"source": [
"### A Credible Government Policy\n",
@@ -486,7 +485,7 @@
},
{
"cell_type": "markdown",
- "id": "12ed64dd",
+ "id": "521a18cf",
"metadata": {},
"source": [
"### Sustainable Plans\n",
@@ -663,7 +662,7 @@
},
{
"cell_type": "markdown",
- "id": "4673e27e",
+ "id": "8df1d363",
"metadata": {},
"source": [
"## Calculating the Set of Sustainable Promise-Value Pairs\n",
@@ -851,7 +850,7 @@
"following functional forms:\n",
"\n",
"$$\n",
- "u(c) = log(c)\n",
+ "u(c) = \\log(c)\n",
"$$\n",
"\n",
"$$\n",
@@ -879,7 +878,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b68157e2",
+ "id": "ba856c97",
"metadata": {
"hide-output": false
},
@@ -1387,7 +1386,7 @@
},
{
"cell_type": "markdown",
- "id": "70db6595",
+ "id": "e6b216a2",
"metadata": {},
"source": [
"### Comparison of Sets\n",
@@ -1402,7 +1401,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bc13b21d",
+ "id": "15685ea7",
"metadata": {
"hide-output": false
},
@@ -1414,7 +1413,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6ee911a4",
+ "id": "53d92867",
"metadata": {
"hide-output": false
},
@@ -1425,7 +1424,7 @@
},
{
"cell_type": "markdown",
- "id": "952443ab",
+ "id": "7de228af",
"metadata": {},
"source": [
"The following plot shows both the set of $ w,\\theta $ pairs associated with competitive equilibria (in red)\n",
@@ -1435,7 +1434,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e1eda8fd",
+ "id": "2f1dc2fd",
"metadata": {
"hide-output": false
},
@@ -1477,7 +1476,7 @@
},
{
"cell_type": "markdown",
- "id": "6685afd7",
+ "id": "15afd969",
"metadata": {},
"source": [
"Evidently, the Ramsey plan, denoted by the $ R $, is not sustainable.\n",
@@ -1488,7 +1487,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1f0c85ce",
+ "id": "e0cb7c58",
"metadata": {
"hide-output": false
},
@@ -1501,7 +1500,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e939866c",
+ "id": "210d63da",
"metadata": {
"hide-output": false
},
@@ -1512,7 +1511,7 @@
},
{
"cell_type": "markdown",
- "id": "449c2f6c",
+ "id": "662fb0ac",
"metadata": {},
"source": [
"Let’s plot both sets"
@@ -1521,7 +1520,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4cdbf33f",
+ "id": "8f86b3a5",
"metadata": {
"hide-output": false
},
@@ -1532,7 +1531,7 @@
},
{
"cell_type": "markdown",
- "id": "efad2ee2",
+ "id": "cd6d8f76",
"metadata": {},
"source": [
"Evidently, the Ramsey plan is now sustainable."
@@ -1540,7 +1539,7 @@
}
],
"metadata": {
- "date": 1723011581.0839624,
+ "date": 1723517847.1704562,
"filename": "chang_credible.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/chang_ramsey.ipynb b/_notebooks/chang_ramsey.ipynb
index 2ca902d2..26c7bd8d 100644
--- a/_notebooks/chang_ramsey.ipynb
+++ b/_notebooks/chang_ramsey.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "ff3207a1",
+ "id": "765b48ac",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "c66dfcf6",
+ "id": "310caf20",
"metadata": {},
"source": [
"# Competitive Equilibria of a Model of Chang\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "197563bc",
+ "id": "d357ff1b",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "f21d9663",
+ "id": "d8254cfd",
"metadata": {},
"source": [
"## Overview\n",
@@ -81,7 +81,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cfd20bba",
+ "id": "a9f403b3",
"metadata": {
"hide-output": false
},
@@ -94,7 +94,7 @@
},
{
"cell_type": "markdown",
- "id": "8bf5f255",
+ "id": "5dd152f9",
"metadata": {},
"source": [
"### The Setting\n",
@@ -152,15 +152,15 @@
},
{
"cell_type": "markdown",
- "id": "ce8a0eea",
+ "id": "32b57f3b",
"metadata": {},
"source": [
- "## Setting"
+ "## Decisions"
]
},
{
"cell_type": "markdown",
- "id": "be4de7d8",
+ "id": "92403422",
"metadata": {},
"source": [
"### The Household’s Problem\n",
@@ -169,7 +169,7 @@
"$ \\vec q $ and sequences $ \\vec y, \\vec x $ of income and total\n",
"tax collections, respectively.\n",
"\n",
- "The household chooses nonnegative\n",
+ "Facing vector $ \\vec q $ as a price taker, the representative household chooses nonnegative\n",
"sequences $ \\vec c, \\vec M $ of consumption and nominal balances,\n",
"respectively, to maximize\n",
"\n",
@@ -211,8 +211,8 @@
"Inequality [(47.2)](#equation-eqn-chang-ramsey2) is the household’s time $ t $ budget constraint.\n",
"\n",
"It tells how real balances $ q_t M_t $ carried out of period $ t $ depend\n",
- "on income, consumption, taxes, and real balances $ q_t M_{t-1} $\n",
- "carried into the period.\n",
+ "on real balances $ q_t M_{t-1} $\n",
+ "carried into period $ t $, income, consumption, taxes.\n",
"\n",
"Equation [(47.3)](#equation-eqn-chang-ramsey3) imposes an exogenous upper bound\n",
"$ \\bar m $ on the household’s choice of real balances, where\n",
@@ -221,7 +221,7 @@
},
{
"cell_type": "markdown",
- "id": "ce2aa067",
+ "id": "124fa2a2",
"metadata": {},
"source": [
"### Government\n",
@@ -232,8 +232,28 @@
"[ \\underline \\pi, \\overline \\pi] $, where\n",
"$ 0 < \\underline \\pi < 1 < { 1 \\over \\beta } \\leq \\overline \\pi $.\n",
"\n",
- "The government faces a sequence of budget constraints with time\n",
- "$ t $ component\n",
+ "The government purchases no goods.\n",
+ "\n",
+ "It taxes only to acquire paper currency that it will withdraw from circulation (e.g., by burning it).\n",
+ "\n",
+ "Let $ p_t $ be the price level at time $ t $, measured as time $ t $ dollars per unit of the consumption good.\n",
+ "\n",
+ "Evidently, the value of paper currency meassured in units of the consumption good at time $ t $ is\n",
+ "\n",
+ "$$\n",
+ "q_t = \\frac{1}{p_t} .\n",
+ "$$\n",
+ "\n",
+ "The government faces a sequence of budget constraints with time $ t $ component\n",
+ "\n",
+ "$$\n",
+ "x_t + \\frac{M_{t} - M_{t-1}}{p_t} = 0,\n",
+ "$$\n",
+ "\n",
+ "where $ x_t $ is the real value of revenue that the government raises from taxes and $ \\frac{M_{t} - M_{t-1}}{p_t} $ is\n",
+ "the real value of revenue that the government raises by printing new paper currency.\n",
+ "\n",
+ "Evidently, this budget constraint can be rewritten as\n",
"\n",
"$$\n",
"-x_t = q_t (M_t - M_{t-1})\n",
@@ -248,7 +268,7 @@
"-x_t = m_t (1-h_t) \\tag{47.4}\n",
"$$\n",
"\n",
- "The restrictions $ m_t \\in [0, \\bar m] $ and $ h_t \\in \\Pi $ evidently\n",
+ "The restrictions $ m_t \\in [0, \\bar m] $ and $ h_t \\in \\Pi = [\\underline \\pi, \\overline \\pi] $ evidently\n",
"imply that $ x_t \\in X \\equiv [(\\underline \\pi -1)\\bar m,\n",
"(\\overline \\pi -1) \\bar m] $.\n",
"\n",
@@ -264,10 +284,27 @@
"y_t = f(x_t), \\tag{47.5}\n",
"$$\n",
"\n",
- "where $ f: \\mathbb{R}\\rightarrow \\mathbb{R} $ satisfies $ f(x) > 0 $,\n",
- "is twice continuously differentiable, $ f''(x) < 0 $, and\n",
- "$ f(x) = f(-x) $ for all $ x \\in\n",
- "\\mathbb{R} $, so that subsidies and taxes are equally distorting.\n",
+ "where $ f: \\mathbb{R}\\rightarrow \\mathbb{R} $ satisfies $ f(x) > 0 $, $ f(x) $\n",
+ "is twice continuously differentiable, $ f''(x) < 0 $, $ f'(0) = 0 $, and\n",
+ "$ f(x) = f(-x) $ for all $ x \\in \\mathbb{R} $, so that subsidies and taxes are equally distorting.\n",
+ "\n",
+ "**Example parameterizations**\n",
+ "\n",
+ "In some of our Python code deployed later in this lecture, we’ll assume the following functional forms:\n",
+ "\n",
+ "$$\n",
+ "u(c) = \\log(c)\n",
+ "$$\n",
+ "\n",
+ "$$\n",
+ "v(m) = \\frac{1}{500}(m \\bar m - 0.5m^2)^{0.5}\n",
+ "$$\n",
+ "\n",
+ "$$\n",
+ "f(x) = 180 - (0.4x)^2\n",
+ "$$\n",
+ "\n",
+ "**The tax distortion function**\n",
"\n",
"Calvo’s and Chang’s purpose is not to model the causes of tax distortions in\n",
"any detail but simply to summarize\n",
@@ -313,7 +350,7 @@
},
{
"cell_type": "markdown",
- "id": "80ab372a",
+ "id": "71954310",
"metadata": {},
"source": [
"### Household’s Problem\n",
@@ -385,7 +422,7 @@
},
{
"cell_type": "markdown",
- "id": "d3c8507b",
+ "id": "40ebddeb",
"metadata": {},
"source": [
"## Competitive Equilibrium\n",
@@ -411,7 +448,7 @@
},
{
"cell_type": "markdown",
- "id": "4a5fe353",
+ "id": "eb7a92f9",
"metadata": {},
"source": [
"## Inventory of Objects in Play\n",
@@ -470,7 +507,7 @@
},
{
"cell_type": "markdown",
- "id": "5401c5ba",
+ "id": "51a308cd",
"metadata": {},
"source": [
"## Analysis\n",
@@ -644,7 +681,7 @@
},
{
"cell_type": "markdown",
- "id": "fcd18d7f",
+ "id": "a0568025",
"metadata": {},
"source": [
"### Some Useful Notation\n",
@@ -711,7 +748,7 @@
},
{
"cell_type": "markdown",
- "id": "347efee8",
+ "id": "b543499b",
"metadata": {},
"source": [
"### Another Operator\n",
@@ -813,7 +850,7 @@
},
{
"cell_type": "markdown",
- "id": "eb024127",
+ "id": "8a20a29b",
"metadata": {},
"source": [
"## Calculating all Promise-Value Pairs in CE\n",
@@ -941,7 +978,7 @@
"following functional forms:\n",
"\n",
"$$\n",
- "u(c) = log(c)\n",
+ "u(c) = \\log(c)\n",
"$$\n",
"\n",
"$$\n",
@@ -966,7 +1003,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d367a3fb",
+ "id": "dbed865f",
"metadata": {
"hide-output": false
},
@@ -1475,7 +1512,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "84f4f7d2",
+ "id": "534cec99",
"metadata": {
"hide-output": false
},
@@ -1488,7 +1525,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fe9cc42f",
+ "id": "5a379129",
"metadata": {
"hide-output": false
},
@@ -1529,7 +1566,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "789ca9fc",
+ "id": "4dc9afcb",
"metadata": {
"hide-output": false
},
@@ -1543,7 +1580,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "014fe4c5",
+ "id": "db474d52",
"metadata": {
"hide-output": false
},
@@ -1554,7 +1591,7 @@
},
{
"cell_type": "markdown",
- "id": "841d89d1",
+ "id": "3351a51d",
"metadata": {},
"source": [
"## Solving a Continuation Ramsey Planner’s Bellman Equation\n",
@@ -1615,7 +1652,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bb7b2bdf",
+ "id": "193a3183",
"metadata": {
"hide-output": false
},
@@ -1630,7 +1667,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ec6f8007",
+ "id": "79993065",
"metadata": {
"hide-output": false
},
@@ -1642,7 +1679,7 @@
},
{
"cell_type": "markdown",
- "id": "0343a5fa",
+ "id": "ae7213c2",
"metadata": {},
"source": [
"First, a quick check that our approximations of the value functions are\n",
@@ -1654,7 +1691,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3a712a1d",
+ "id": "92c161f8",
"metadata": {
"hide-output": false
},
@@ -1665,7 +1702,7 @@
},
{
"cell_type": "markdown",
- "id": "78e9c0f6",
+ "id": "70493818",
"metadata": {},
"source": [
"The value functions plotted below trace out the right edges of the sets\n",
@@ -1675,7 +1712,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "21a5ad14",
+ "id": "daf48244",
"metadata": {
"hide-output": false
},
@@ -1694,7 +1731,7 @@
},
{
"cell_type": "markdown",
- "id": "599a4ed2",
+ "id": "3c24ec93",
"metadata": {},
"source": [
"The next figure plots the optimal policy functions; values of\n",
@@ -1704,7 +1741,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e7e15018",
+ "id": "87966cf1",
"metadata": {
"hide-output": false
},
@@ -1729,7 +1766,7 @@
},
{
"cell_type": "markdown",
- "id": "e56d11e3",
+ "id": "62bcfe88",
"metadata": {},
"source": [
"With the first set of parameter values, the value of $ \\theta' $ chosen by the Ramsey\n",
@@ -1750,7 +1787,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c044d31e",
+ "id": "3db1052f",
"metadata": {
"hide-output": false
},
@@ -1769,7 +1806,7 @@
},
{
"cell_type": "markdown",
- "id": "32298a6e",
+ "id": "3c016374",
"metadata": {},
"source": [
"Subproblem 2 is equivalent to the planner choosing the initial value of\n",
@@ -1785,7 +1822,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5d2d12da",
+ "id": "6e03df5f",
"metadata": {
"hide-output": false
},
@@ -1808,7 +1845,7 @@
},
{
"cell_type": "markdown",
- "id": "d451c64d",
+ "id": "a8e6a226",
"metadata": {},
"source": [
"### Next Steps\n",
@@ -1824,7 +1861,7 @@
}
],
"metadata": {
- "date": 1723011581.3473868,
+ "date": 1723517847.2300484,
"filename": "chang_ramsey.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/classical_filtering.ipynb b/_notebooks/classical_filtering.ipynb
index bae6805a..656d6f6d 100644
--- a/_notebooks/classical_filtering.ipynb
+++ b/_notebooks/classical_filtering.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "46d54900",
+ "id": "40273a9d",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "82954f52",
+ "id": "5f701783",
"metadata": {},
"source": [
"# Classical Prediction and Filtering With Linear Algebra"
@@ -19,7 +19,7 @@
},
{
"cell_type": "markdown",
- "id": "64a8ee55",
+ "id": "0879792f",
"metadata": {},
"source": [
"## Overview\n",
@@ -72,7 +72,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9789f9ed",
+ "id": "b5c471c2",
"metadata": {
"hide-output": false
},
@@ -83,7 +83,7 @@
},
{
"cell_type": "markdown",
- "id": "da50445b",
+ "id": "4d691b51",
"metadata": {},
"source": [
"### References\n",
@@ -93,7 +93,7 @@
},
{
"cell_type": "markdown",
- "id": "09a512c4",
+ "id": "30e859cb",
"metadata": {},
"source": [
"## Finite Dimensional Prediction\n",
@@ -245,7 +245,7 @@
},
{
"cell_type": "markdown",
- "id": "446ae0e2",
+ "id": "976c8d0e",
"metadata": {},
"source": [
"### Implementation\n",
@@ -256,7 +256,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f147549a",
+ "id": "dcf9ecbe",
"metadata": {
"hide-output": false
},
@@ -572,7 +572,7 @@
},
{
"cell_type": "markdown",
- "id": "76f1f4cf",
+ "id": "f15665f5",
"metadata": {},
"source": [
"Let’s use this code to tackle two interesting examples."
@@ -580,7 +580,7 @@
},
{
"cell_type": "markdown",
- "id": "f101e363",
+ "id": "1d8fabeb",
"metadata": {},
"source": [
"### Example 1\n",
@@ -603,7 +603,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1756fe30",
+ "id": "b5d13215",
"metadata": {
"hide-output": false
},
@@ -619,7 +619,7 @@
},
{
"cell_type": "markdown",
- "id": "bb61491b",
+ "id": "31f348be",
"metadata": {},
"source": [
"The Wold representation is computed by `example.coeffs_of_c()`.\n",
@@ -630,7 +630,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0fb3075e",
+ "id": "14b23ec3",
"metadata": {
"hide-output": false
},
@@ -642,7 +642,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1a38de6a",
+ "id": "8473df47",
"metadata": {
"hide-output": false
},
@@ -653,7 +653,7 @@
},
{
"cell_type": "markdown",
- "id": "5eac7cd2",
+ "id": "779f1843",
"metadata": {},
"source": [
"Now let’s form the covariance matrix of a time series vector of length $ N $\n",
@@ -666,7 +666,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7897cfac",
+ "id": "d5ef0e71",
"metadata": {
"hide-output": false
},
@@ -678,7 +678,7 @@
},
{
"cell_type": "markdown",
- "id": "3a1ea752",
+ "id": "893bf2c5",
"metadata": {},
"source": [
"Notice how the lower rows of the “moving average representations” are converging to the appropriate infinite history Wold representation\n",
@@ -688,7 +688,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0724ff9f",
+ "id": "7b8b0886",
"metadata": {
"hide-output": false
},
@@ -700,7 +700,7 @@
},
{
"cell_type": "markdown",
- "id": "52ac66f6",
+ "id": "6e520bfb",
"metadata": {},
"source": [
"Notice how the lower rows of the “autoregressive representations” are converging to the appropriate infinite-history\n",
@@ -710,7 +710,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b2c992aa",
+ "id": "56bea0af",
"metadata": {
"hide-output": false
},
@@ -722,7 +722,7 @@
},
{
"cell_type": "markdown",
- "id": "496c6160",
+ "id": "d05b16d7",
"metadata": {},
"source": [
"### Example 2\n",
@@ -749,7 +749,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "57cdb558",
+ "id": "5d7d37fc",
"metadata": {
"hide-output": false
},
@@ -767,7 +767,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "20f38ac1",
+ "id": "f360c92c",
"metadata": {
"hide-output": false
},
@@ -779,7 +779,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "43705dc1",
+ "id": "87fe6528",
"metadata": {
"hide-output": false
},
@@ -792,7 +792,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7335e125",
+ "id": "52872552",
"metadata": {
"hide-output": false
},
@@ -805,7 +805,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "08d8d083",
+ "id": "2f90d866",
"metadata": {
"hide-output": false
},
@@ -817,7 +817,7 @@
},
{
"cell_type": "markdown",
- "id": "6e30bf4e",
+ "id": "3839f4be",
"metadata": {},
"source": [
"### Prediction\n",
@@ -899,7 +899,7 @@
},
{
"cell_type": "markdown",
- "id": "6aed92dc",
+ "id": "f3c2ced6",
"metadata": {},
"source": [
"## Combined Finite Dimensional Control and Prediction\n",
@@ -987,7 +987,7 @@
},
{
"cell_type": "markdown",
- "id": "da01cb99",
+ "id": "5a3a4634",
"metadata": {},
"source": [
"## Infinite Horizon Prediction and Filtering Problems\n",
@@ -1053,7 +1053,7 @@
},
{
"cell_type": "markdown",
- "id": "67e86202",
+ "id": "04226fec",
"metadata": {},
"source": [
"### Problem Formulation\n",
@@ -1433,7 +1433,7 @@
},
{
"cell_type": "markdown",
- "id": "3eeeb933",
+ "id": "3643437f",
"metadata": {},
"source": [
"## Exercises"
@@ -1441,7 +1441,7 @@
},
{
"cell_type": "markdown",
- "id": "f38766fc",
+ "id": "3cdfd9d8",
"metadata": {},
"source": [
"## Exercise 32.1\n",
@@ -1476,7 +1476,7 @@
},
{
"cell_type": "markdown",
- "id": "ec915f9b",
+ "id": "bce95764",
"metadata": {},
"source": [
"## Exercise 32.2\n",
@@ -1556,7 +1556,7 @@
}
],
"metadata": {
- "date": 1723011581.401782,
+ "date": 1723517847.2810225,
"filename": "classical_filtering.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/coase.ipynb b/_notebooks/coase.ipynb
index cc52c36b..c43c9ea7 100644
--- a/_notebooks/coase.ipynb
+++ b/_notebooks/coase.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "5a85cd6c",
+ "id": "828f6e19",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "ee5d9f1c",
+ "id": "978d171d",
"metadata": {},
"source": [
"# Coase’s Theory of the Firm"
@@ -19,7 +19,7 @@
},
{
"cell_type": "markdown",
- "id": "eae938be",
+ "id": "f57735d8",
"metadata": {},
"source": [
"## Overview\n",
@@ -50,7 +50,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "512dd6fe",
+ "id": "f1f9b473",
"metadata": {
"hide-output": false
},
@@ -63,7 +63,7 @@
},
{
"cell_type": "markdown",
- "id": "a53b9f85",
+ "id": "7a32ee68",
"metadata": {},
"source": [
"### Why Firms Exist\n",
@@ -96,7 +96,7 @@
},
{
"cell_type": "markdown",
- "id": "2cdf7450",
+ "id": "e5e89c8f",
"metadata": {},
"source": [
"### A Trade-Off\n",
@@ -133,7 +133,7 @@
},
{
"cell_type": "markdown",
- "id": "0744861c",
+ "id": "4543bbd5",
"metadata": {},
"source": [
"### Summary\n",
@@ -147,7 +147,7 @@
},
{
"cell_type": "markdown",
- "id": "61d310b8",
+ "id": "2f200bee",
"metadata": {},
"source": [
"### A Quantitative Interpretation\n",
@@ -165,7 +165,7 @@
},
{
"cell_type": "markdown",
- "id": "5de9a5c8",
+ "id": "69f56de5",
"metadata": {},
"source": [
"## The Model\n",
@@ -181,7 +181,7 @@
},
{
"cell_type": "markdown",
- "id": "1f4afc52",
+ "id": "867a1d1d",
"metadata": {},
"source": [
"### Subcontracting\n",
@@ -224,7 +224,7 @@
},
{
"cell_type": "markdown",
- "id": "9814fc6a",
+ "id": "f942e373",
"metadata": {},
"source": [
"### Costs\n",
@@ -254,7 +254,7 @@
},
{
"cell_type": "markdown",
- "id": "9f667847",
+ "id": "6f7d178c",
"metadata": {},
"source": [
"## Equilibrium\n",
@@ -277,7 +277,7 @@
},
{
"cell_type": "markdown",
- "id": "18632bd9",
+ "id": "16be544a",
"metadata": {},
"source": [
"### Informal Definition of Equilibrium\n",
@@ -291,7 +291,7 @@
},
{
"cell_type": "markdown",
- "id": "dbb2189a",
+ "id": "8d40b143",
"metadata": {},
"source": [
"### Formal Definition of Equilibrium\n",
@@ -349,7 +349,7 @@
},
{
"cell_type": "markdown",
- "id": "27862621",
+ "id": "1f26c37a",
"metadata": {},
"source": [
"## Existence, Uniqueness and Computation of Equilibria\n",
@@ -359,7 +359,7 @@
},
{
"cell_type": "markdown",
- "id": "4e3b1ab6",
+ "id": "b0737123",
"metadata": {},
"source": [
"### A Fixed Point Method\n",
@@ -460,7 +460,7 @@
},
{
"cell_type": "markdown",
- "id": "a3d6b5c1",
+ "id": "f71802b0",
"metadata": {},
"source": [
"### Marginal Conditions\n",
@@ -514,7 +514,7 @@
},
{
"cell_type": "markdown",
- "id": "6b19eaca",
+ "id": "d22cd991",
"metadata": {},
"source": [
"## Implementation\n",
@@ -539,7 +539,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bda0326d",
+ "id": "99c1479e",
"metadata": {
"hide-output": false
},
@@ -558,7 +558,7 @@
},
{
"cell_type": "markdown",
- "id": "7fd6024e",
+ "id": "13bf09da",
"metadata": {},
"source": [
"Now let’s implement and iterate with $ T $ until convergence.\n",
@@ -570,7 +570,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a7bab599",
+ "id": "abd73645",
"metadata": {
"hide-output": false
},
@@ -609,7 +609,7 @@
},
{
"cell_type": "markdown",
- "id": "07402a0a",
+ "id": "bbde6a6a",
"metadata": {},
"source": [
"The next function computes optimal choice of upstream boundary and range of\n",
@@ -619,7 +619,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "05082969",
+ "id": "ef2537ea",
"metadata": {
"hide-output": false
},
@@ -646,7 +646,7 @@
},
{
"cell_type": "markdown",
- "id": "59848cc9",
+ "id": "0b24e23b",
"metadata": {},
"source": [
"The allocation of firms can be computed by recursively stepping through firms’ choices of\n",
@@ -658,7 +658,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f45b47dd",
+ "id": "58d80a36",
"metadata": {
"hide-output": false
},
@@ -675,7 +675,7 @@
},
{
"cell_type": "markdown",
- "id": "e2079116",
+ "id": "688e488f",
"metadata": {},
"source": [
"Let’s try this at the default parameters.\n",
@@ -687,7 +687,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "56fffa9e",
+ "id": "289b5654",
"metadata": {
"hide-output": false
},
@@ -710,7 +710,7 @@
},
{
"cell_type": "markdown",
- "id": "1f894225",
+ "id": "3940897c",
"metadata": {},
"source": [
"Here’s the function $ \\ell^* $, which shows how large a firm with\n",
@@ -720,7 +720,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "13b05de8",
+ "id": "3a16683f",
"metadata": {
"hide-output": false
},
@@ -739,7 +739,7 @@
},
{
"cell_type": "markdown",
- "id": "829160a3",
+ "id": "26a20951",
"metadata": {},
"source": [
"Note that downstream firms choose to be larger, a point we return to below."
@@ -747,7 +747,7 @@
},
{
"cell_type": "markdown",
- "id": "c8715016",
+ "id": "15d6cf4b",
"metadata": {},
"source": [
"## Exercises\n",
@@ -758,7 +758,7 @@
},
{
"cell_type": "markdown",
- "id": "07d187ba",
+ "id": "ac7d53e6",
"metadata": {},
"source": [
"## Exercise 15.1\n",
@@ -772,7 +772,7 @@
},
{
"cell_type": "markdown",
- "id": "53f612d6",
+ "id": "170b9fb3",
"metadata": {},
"source": [
"## Solution to[ Exercise 15.1](https://python-advanced.quantecon.org/#coa_ex1)\n",
@@ -783,7 +783,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "54cd18aa",
+ "id": "c9c6dfd3",
"metadata": {
"hide-output": false
},
@@ -800,7 +800,7 @@
},
{
"cell_type": "markdown",
- "id": "bb479883",
+ "id": "c77f8c2f",
"metadata": {},
"source": [
"## Exercise 15.2\n",
@@ -816,7 +816,7 @@
},
{
"cell_type": "markdown",
- "id": "4639a8c9",
+ "id": "0c5f54ec",
"metadata": {},
"source": [
"## Solution to[ Exercise 15.2](https://python-advanced.quantecon.org/#coa_ex2)\n",
@@ -839,7 +839,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a46979e8",
+ "id": "0a995f9e",
"metadata": {
"hide-output": false
},
@@ -863,7 +863,7 @@
}
],
"metadata": {
- "date": 1723011581.4371223,
+ "date": 1723517847.4981983,
"filename": "coase.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/cons_news.ipynb b/_notebooks/cons_news.ipynb
index edd92376..5075806d 100644
--- a/_notebooks/cons_news.ipynb
+++ b/_notebooks/cons_news.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "a7bd072d",
+ "id": "16e7bd0f",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "d849fe21",
+ "id": "c22f384f",
"metadata": {},
"source": [
"# Information and Consumption Smoothing\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ea3304d8",
+ "id": "91754cde",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "0bd68fbc",
+ "id": "0c0023dd",
"metadata": {},
"source": [
"## Overview\n",
@@ -59,7 +59,7 @@
},
{
"cell_type": "markdown",
- "id": "e0d051a7",
+ "id": "5a41d45b",
"metadata": {},
"source": [
"### Same non-financial incomes, different information\n",
@@ -120,7 +120,7 @@
},
{
"cell_type": "markdown",
- "id": "4360f0ec",
+ "id": "5880e7a2",
"metadata": {},
"source": [
"## Two Representations of One Nonfinancial Income Process\n",
@@ -251,7 +251,7 @@
},
{
"cell_type": "markdown",
- "id": "ebce9928",
+ "id": "b0ad8c59",
"metadata": {},
"source": [
"## Application of Kalman filter\n",
@@ -299,7 +299,7 @@
},
{
"cell_type": "markdown",
- "id": "f87d5816",
+ "id": "0e91be97",
"metadata": {},
"source": [
"## News Shocks and Less Informative Shocks\n",
@@ -398,7 +398,7 @@
},
{
"cell_type": "markdown",
- "id": "0784276f",
+ "id": "71ce514f",
"metadata": {},
"source": [
"## Representation of $ \\epsilon_t $ Shock in Terms of Future $ y_t $\n",
@@ -430,7 +430,7 @@
},
{
"cell_type": "markdown",
- "id": "eb7afcb8",
+ "id": "76c966b8",
"metadata": {},
"source": [
"## Representation in Terms of $ a_t $ Shocks\n",
@@ -459,7 +459,7 @@
},
{
"cell_type": "markdown",
- "id": "6f82c2f8",
+ "id": "10b5a7bc",
"metadata": {},
"source": [
"## Permanent Income Consumption-Smoothing Model\n",
@@ -515,7 +515,7 @@
},
{
"cell_type": "markdown",
- "id": "cb4d8ae5",
+ "id": "5e75d7ff",
"metadata": {},
"source": [
"## State Space Representations\n",
@@ -557,7 +557,7 @@
},
{
"cell_type": "markdown",
- "id": "64fc4eb1",
+ "id": "a448bacd",
"metadata": {},
"source": [
"## Computations\n",
@@ -678,7 +678,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "71cc01de",
+ "id": "804e7bfe",
"metadata": {
"hide-output": false
},
@@ -692,7 +692,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "886ddf0b",
+ "id": "5c984e46",
"metadata": {
"hide-output": false
},
@@ -714,7 +714,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7d2cea95",
+ "id": "9cad8e5c",
"metadata": {
"hide-output": false
},
@@ -735,7 +735,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "455a6f11",
+ "id": "b7260237",
"metadata": {
"hide-output": false
},
@@ -747,7 +747,7 @@
},
{
"cell_type": "markdown",
- "id": "ad184965",
+ "id": "496ade58",
"metadata": {},
"source": [
"Evidently, optimal consumption and debt decision rules for the consumer\n",
@@ -766,7 +766,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a0e066b7",
+ "id": "5d15b904",
"metadata": {
"hide-output": false
},
@@ -786,7 +786,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e9d12fc4",
+ "id": "665574da",
"metadata": {
"hide-output": false
},
@@ -797,7 +797,7 @@
},
{
"cell_type": "markdown",
- "id": "7f04d8e3",
+ "id": "2d198787",
"metadata": {},
"source": [
"For a consumer having access only to the information associated with the\n",
@@ -850,7 +850,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "50c3ab7c",
+ "id": "0ddaa739",
"metadata": {
"hide-output": false
},
@@ -870,7 +870,7 @@
},
{
"cell_type": "markdown",
- "id": "530b795e",
+ "id": "d4b979fe",
"metadata": {},
"source": [
"The following code computes impulse response functions of\n",
@@ -880,7 +880,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e8b6dd25",
+ "id": "0e17711d",
"metadata": {
"hide-output": false
},
@@ -900,7 +900,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "063f0862",
+ "id": "f2533938",
"metadata": {
"hide-output": false
},
@@ -912,7 +912,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "935626d5",
+ "id": "b2d2efbf",
"metadata": {
"hide-output": false
},
@@ -926,7 +926,7 @@
},
{
"cell_type": "markdown",
- "id": "4e0fa0d7",
+ "id": "001c0bf1",
"metadata": {},
"source": [
"The above two impulse response functions show that when the consumer has\n",
@@ -942,7 +942,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4c09cc69",
+ "id": "b8f1d220",
"metadata": {
"hide-output": false
},
@@ -954,7 +954,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8f38610d",
+ "id": "a2758cf9",
"metadata": {
"hide-output": false
},
@@ -969,7 +969,7 @@
},
{
"cell_type": "markdown",
- "id": "5fa75aa6",
+ "id": "ebab96e3",
"metadata": {},
"source": [
"The above impulse responses show that when the consumer has only the\n",
@@ -993,7 +993,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7815ddcf",
+ "id": "fb7553e6",
"metadata": {
"hide-output": false
},
@@ -1006,7 +1006,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bf02ea99",
+ "id": "dc242e98",
"metadata": {
"hide-output": false
},
@@ -1023,7 +1023,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1c927f61",
+ "id": "5939c874",
"metadata": {
"hide-output": false
},
@@ -1039,7 +1039,7 @@
},
{
"cell_type": "markdown",
- "id": "6d56a4c8",
+ "id": "6e38a5c6",
"metadata": {},
"source": [
"## Simulating Income Process and Two Associated Shock Processes\n",
@@ -1078,7 +1078,7 @@
},
{
"cell_type": "markdown",
- "id": "9d55e69e",
+ "id": "209bca58",
"metadata": {},
"source": [
"## Calculating Innovations in Another Way\n",
@@ -1106,7 +1106,7 @@
},
{
"cell_type": "markdown",
- "id": "dde6a19a",
+ "id": "0802a9e8",
"metadata": {},
"source": [
"## Another Invertibility Issue\n",
@@ -1120,7 +1120,7 @@
}
],
"metadata": {
- "date": 1723011581.481741,
+ "date": 1723517847.5406587,
"filename": "cons_news.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/discrete_dp.ipynb b/_notebooks/discrete_dp.ipynb
index b543bbf3..1322e277 100644
--- a/_notebooks/discrete_dp.ipynb
+++ b/_notebooks/discrete_dp.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "3163622f",
+ "id": "814a45e1",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "b9cdba19",
+ "id": "b9a3468d",
"metadata": {},
"source": [
"# Discrete State Dynamic Programming\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "792d7c86",
+ "id": "4fed62d1",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "48702d44",
+ "id": "ecd26115",
"metadata": {},
"source": [
"## Overview\n",
@@ -73,7 +73,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8e22e0d6",
+ "id": "1cef73c8",
"metadata": {
"hide-output": false
},
@@ -89,7 +89,7 @@
},
{
"cell_type": "markdown",
- "id": "b37251bb",
+ "id": "a2f3c3e3",
"metadata": {},
"source": [
"### How to Read this Lecture\n",
@@ -105,7 +105,7 @@
},
{
"cell_type": "markdown",
- "id": "65fb0d1a",
+ "id": "74cf7a84",
"metadata": {},
"source": [
"### Code\n",
@@ -124,7 +124,7 @@
},
{
"cell_type": "markdown",
- "id": "f795c681",
+ "id": "dd60efab",
"metadata": {},
"source": [
"### References\n",
@@ -146,7 +146,7 @@
},
{
"cell_type": "markdown",
- "id": "6b89f34b",
+ "id": "3c18e533",
"metadata": {},
"source": [
"## Discrete DPs\n",
@@ -185,7 +185,7 @@
},
{
"cell_type": "markdown",
- "id": "6ae7708e",
+ "id": "0d9604e4",
"metadata": {},
"source": [
"### Policies\n",
@@ -216,7 +216,7 @@
},
{
"cell_type": "markdown",
- "id": "28c5efc7",
+ "id": "26983462",
"metadata": {},
"source": [
"### Formal Definition\n",
@@ -279,7 +279,7 @@
},
{
"cell_type": "markdown",
- "id": "019eac66",
+ "id": "e33c2a65",
"metadata": {},
"source": [
"### Value and Optimality\n",
@@ -324,7 +324,7 @@
},
{
"cell_type": "markdown",
- "id": "b868b3bd",
+ "id": "1baa6122",
"metadata": {},
"source": [
"### Two Operators\n",
@@ -376,7 +376,7 @@
},
{
"cell_type": "markdown",
- "id": "7cb81aa4",
+ "id": "6beec2a2",
"metadata": {},
"source": [
"### The Bellman Equation and the Principle of Optimality\n",
@@ -412,7 +412,7 @@
},
{
"cell_type": "markdown",
- "id": "b860a7ed",
+ "id": "d8acb8b6",
"metadata": {},
"source": [
"## Solving Discrete DPs\n",
@@ -433,7 +433,7 @@
},
{
"cell_type": "markdown",
- "id": "c74ae943",
+ "id": "87010128",
"metadata": {},
"source": [
"### Value Function Iteration\n",
@@ -449,7 +449,7 @@
},
{
"cell_type": "markdown",
- "id": "9c411672",
+ "id": "76cfe408",
"metadata": {},
"source": [
"### Policy Function Iteration\n",
@@ -472,7 +472,7 @@
},
{
"cell_type": "markdown",
- "id": "828b0878",
+ "id": "9660009e",
"metadata": {},
"source": [
"### Modified Policy Function Iteration\n",
@@ -491,7 +491,7 @@
},
{
"cell_type": "markdown",
- "id": "4fb8c333",
+ "id": "56f16fb3",
"metadata": {},
"source": [
"## Example: A Growth Model\n",
@@ -523,7 +523,7 @@
},
{
"cell_type": "markdown",
- "id": "be47b33f",
+ "id": "e0318514",
"metadata": {},
"source": [
"### Discrete DP Representation\n",
@@ -556,7 +556,7 @@
},
{
"cell_type": "markdown",
- "id": "d5890626",
+ "id": "fafae3e2",
"metadata": {},
"source": [
"### Defining a DiscreteDP Instance\n",
@@ -585,7 +585,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "09b9b315",
+ "id": "82737045",
"metadata": {
"hide-output": false
},
@@ -636,7 +636,7 @@
},
{
"cell_type": "markdown",
- "id": "ee7b2ef5",
+ "id": "00d79c24",
"metadata": {},
"source": [
"Let’s run this code and create an instance of `SimpleOG`."
@@ -645,7 +645,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "87056807",
+ "id": "9d2bb178",
"metadata": {
"hide-output": false
},
@@ -656,7 +656,7 @@
},
{
"cell_type": "markdown",
- "id": "a4dd50a8",
+ "id": "4738c194",
"metadata": {},
"source": [
"Instances of `DiscreteDP` are created using the signature `DiscreteDP(R, Q, β)`.\n",
@@ -667,7 +667,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9e6072ca",
+ "id": "5e254b67",
"metadata": {
"hide-output": false
},
@@ -678,7 +678,7 @@
},
{
"cell_type": "markdown",
- "id": "419a9094",
+ "id": "74769835",
"metadata": {},
"source": [
"Now that we have an instance `ddp` of `DiscreteDP` we can solve it as follows"
@@ -687,7 +687,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5c020750",
+ "id": "7aecfd50",
"metadata": {
"hide-output": false
},
@@ -698,7 +698,7 @@
},
{
"cell_type": "markdown",
- "id": "2785d0cd",
+ "id": "e4fd7798",
"metadata": {},
"source": [
"Let’s see what we’ve got here"
@@ -707,7 +707,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "902df23a",
+ "id": "0be13bb9",
"metadata": {
"hide-output": false
},
@@ -718,7 +718,7 @@
},
{
"cell_type": "markdown",
- "id": "998b2c22",
+ "id": "c7cbb1b8",
"metadata": {},
"source": [
"(In IPython version 4.0 and above you can also type `results.` and hit the tab key)\n",
@@ -729,7 +729,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8d14cb09",
+ "id": "00f44cdf",
"metadata": {
"hide-output": false
},
@@ -741,7 +741,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ed6b58cc",
+ "id": "7e26e33a",
"metadata": {
"hide-output": false
},
@@ -752,7 +752,7 @@
},
{
"cell_type": "markdown",
- "id": "d03a64a8",
+ "id": "bfcbe700",
"metadata": {},
"source": [
"Since we’ve used policy iteration, these results will be exact unless we hit the iteration bound `max_iter`.\n",
@@ -763,7 +763,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e8d997b9",
+ "id": "6900a8ff",
"metadata": {
"hide-output": false
},
@@ -775,7 +775,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dc071e6d",
+ "id": "119e35b4",
"metadata": {
"hide-output": false
},
@@ -786,7 +786,7 @@
},
{
"cell_type": "markdown",
- "id": "9aa4866e",
+ "id": "db776cb7",
"metadata": {},
"source": [
"Another interesting object is `results.mc`, which is the controlled chain defined by $ Q_{\\sigma^*} $, where $ \\sigma^* $ is the optimal policy.\n",
@@ -800,7 +800,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8c854db3",
+ "id": "9f6ca5bb",
"metadata": {
"hide-output": false
},
@@ -811,7 +811,7 @@
},
{
"cell_type": "markdown",
- "id": "b7d7a60b",
+ "id": "262afa79",
"metadata": {},
"source": [
"Here’s the same information in a bar graph\n",
@@ -825,7 +825,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0b0a5469",
+ "id": "3e9b6b0a",
"metadata": {
"hide-output": false
},
@@ -838,7 +838,7 @@
},
{
"cell_type": "markdown",
- "id": "4eb25d9d",
+ "id": "9df2538b",
"metadata": {},
"source": [
"If we look at the bar graph we can see the rightward shift in probability mass\n",
@@ -848,7 +848,7 @@
},
{
"cell_type": "markdown",
- "id": "d5217280",
+ "id": "03739a26",
"metadata": {},
"source": [
"### State-Action Pair Formulation\n",
@@ -872,7 +872,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "651501d2",
+ "id": "ac31663a",
"metadata": {
"hide-output": false
},
@@ -905,7 +905,7 @@
},
{
"cell_type": "markdown",
- "id": "d51238e4",
+ "id": "edadfa95",
"metadata": {},
"source": [
"For larger problems, you might need to write this code more efficiently by vectorizing or using Numba."
@@ -913,7 +913,7 @@
},
{
"cell_type": "markdown",
- "id": "a29941aa",
+ "id": "cd33cd7f",
"metadata": {},
"source": [
"## Exercises\n",
@@ -925,7 +925,7 @@
},
{
"cell_type": "markdown",
- "id": "4009218a",
+ "id": "372a5ede",
"metadata": {},
"source": [
"## Solutions"
@@ -933,7 +933,7 @@
},
{
"cell_type": "markdown",
- "id": "b60fa836",
+ "id": "5039bd27",
"metadata": {},
"source": [
"### Setup\n",
@@ -947,7 +947,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "120a446c",
+ "id": "b6141989",
"metadata": {
"hide-output": false
},
@@ -961,7 +961,7 @@
},
{
"cell_type": "markdown",
- "id": "36b90435",
+ "id": "5490cb81",
"metadata": {},
"source": [
"Here we want to solve a finite state version of the continuous state model above.\n",
@@ -972,7 +972,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "535edf27",
+ "id": "dcd6621e",
"metadata": {
"hide-output": false
},
@@ -985,7 +985,7 @@
},
{
"cell_type": "markdown",
- "id": "66678b32",
+ "id": "174ad2f4",
"metadata": {},
"source": [
"We choose the action to be the amount of capital to save for the next\n",
@@ -1014,7 +1014,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "af75c8a8",
+ "id": "df187a25",
"metadata": {
"hide-output": false
},
@@ -1036,7 +1036,7 @@
},
{
"cell_type": "markdown",
- "id": "6101a6ec",
+ "id": "6f5327f0",
"metadata": {},
"source": [
"Reward vector `R` (of length `L`):"
@@ -1045,7 +1045,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0371bf1f",
+ "id": "2c1a01c0",
"metadata": {
"hide-output": false
},
@@ -1056,7 +1056,7 @@
},
{
"cell_type": "markdown",
- "id": "902ab6c6",
+ "id": "2b37903c",
"metadata": {},
"source": [
"(Degenerate) transition probability matrix `Q` (of shape `(L, grid_size)`), where we choose the [scipy.sparse.lil_matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.lil_matrix.html) format, while any format will do (internally it will be converted to the csr format):"
@@ -1065,7 +1065,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "851b170b",
+ "id": "e0b5047d",
"metadata": {
"hide-output": false
},
@@ -1077,7 +1077,7 @@
},
{
"cell_type": "markdown",
- "id": "6554c758",
+ "id": "0aef0a75",
"metadata": {},
"source": [
"(If you are familiar with the data structure of [scipy.sparse.csr_matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csr_matrix.html), the following is the most efficient way to create the `Q` matrix in\n",
@@ -1087,7 +1087,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "baba20fe",
+ "id": "3ae07ad2",
"metadata": {
"hide-output": false
},
@@ -1100,7 +1100,7 @@
},
{
"cell_type": "markdown",
- "id": "3d2098e6",
+ "id": "a1ef6f02",
"metadata": {},
"source": [
"Discrete growth model:"
@@ -1109,7 +1109,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4871e5f6",
+ "id": "5073d8eb",
"metadata": {
"hide-output": false
},
@@ -1120,7 +1120,7 @@
},
{
"cell_type": "markdown",
- "id": "0a1baf5e",
+ "id": "2a8ed37d",
"metadata": {},
"source": [
"**Notes**\n",
@@ -1132,7 +1132,7 @@
},
{
"cell_type": "markdown",
- "id": "e606460f",
+ "id": "8a9ea84c",
"metadata": {},
"source": [
"### Solving the Model\n",
@@ -1143,7 +1143,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eaf464c0",
+ "id": "f3c1c228",
"metadata": {
"hide-output": false
},
@@ -1156,7 +1156,7 @@
},
{
"cell_type": "markdown",
- "id": "f75c96d7",
+ "id": "b35fd058",
"metadata": {},
"source": [
"Note that `sigma` contains the *indices* of the optimal *capital\n",
@@ -1167,7 +1167,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eab32ba6",
+ "id": "342a6b42",
"metadata": {
"hide-output": false
},
@@ -1190,7 +1190,7 @@
},
{
"cell_type": "markdown",
- "id": "0ed3f7e2",
+ "id": "533a36f9",
"metadata": {},
"source": [
"Let us compare the solution of the discrete model with that of the\n",
@@ -1200,7 +1200,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d779b572",
+ "id": "60cf2443",
"metadata": {
"hide-output": false
},
@@ -1229,7 +1229,7 @@
},
{
"cell_type": "markdown",
- "id": "891d97b4",
+ "id": "f1b983a4",
"metadata": {},
"source": [
"The outcomes appear very close to those of the continuous version.\n",
@@ -1240,7 +1240,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "658dd0b4",
+ "id": "1860fcbd",
"metadata": {
"hide-output": false
},
@@ -1252,7 +1252,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3bd85168",
+ "id": "ebf58105",
"metadata": {
"hide-output": false
},
@@ -1263,7 +1263,7 @@
},
{
"cell_type": "markdown",
- "id": "5e1e1323",
+ "id": "ebc0e144",
"metadata": {},
"source": [
"The optimal consumption functions are close as well:"
@@ -1272,7 +1272,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a4f0e23f",
+ "id": "3f818dd8",
"metadata": {
"hide-output": false
},
@@ -1283,7 +1283,7 @@
},
{
"cell_type": "markdown",
- "id": "8fbdcba8",
+ "id": "3250c48f",
"metadata": {},
"source": [
"In fact, the optimal consumption obtained in the discrete version is not\n",
@@ -1293,7 +1293,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3326a562",
+ "id": "d5c4ca5d",
"metadata": {
"hide-output": false
},
@@ -1306,7 +1306,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "419a66fb",
+ "id": "6ce1c408",
"metadata": {
"hide-output": false
},
@@ -1319,7 +1319,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c30e8dc6",
+ "id": "c320ab71",
"metadata": {
"hide-output": false
},
@@ -1330,7 +1330,7 @@
},
{
"cell_type": "markdown",
- "id": "8a4c7f99",
+ "id": "2205ab7e",
"metadata": {},
"source": [
"The value function is monotone:"
@@ -1339,7 +1339,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fe10cddb",
+ "id": "d12f9e1f",
"metadata": {
"hide-output": false
},
@@ -1350,7 +1350,7 @@
},
{
"cell_type": "markdown",
- "id": "6ea4056a",
+ "id": "407ade89",
"metadata": {},
"source": [
"### Comparison of the Solution Methods\n",
@@ -1360,7 +1360,7 @@
},
{
"cell_type": "markdown",
- "id": "1c4f440b",
+ "id": "4640c134",
"metadata": {},
"source": [
"#### Value Iteration"
@@ -1369,7 +1369,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d55e649e",
+ "id": "54f4c1de",
"metadata": {
"hide-output": false
},
@@ -1384,7 +1384,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "92c4708e",
+ "id": "e0c28766",
"metadata": {
"hide-output": false
},
@@ -1395,7 +1395,7 @@
},
{
"cell_type": "markdown",
- "id": "4924f750",
+ "id": "0f2816e8",
"metadata": {},
"source": [
"#### Modified Policy Iteration"
@@ -1404,7 +1404,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8db9386d",
+ "id": "598ce072",
"metadata": {
"hide-output": false
},
@@ -1417,7 +1417,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "478ab436",
+ "id": "c429ef3d",
"metadata": {
"hide-output": false
},
@@ -1428,7 +1428,7 @@
},
{
"cell_type": "markdown",
- "id": "b9e9246f",
+ "id": "0b80f2d9",
"metadata": {},
"source": [
"#### Speed Comparison"
@@ -1437,7 +1437,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d11d1e8e",
+ "id": "6b2e553d",
"metadata": {
"hide-output": false
},
@@ -1450,7 +1450,7 @@
},
{
"cell_type": "markdown",
- "id": "1e98897f",
+ "id": "99947822",
"metadata": {},
"source": [
"As is often the case, policy iteration and modified policy iteration are\n",
@@ -1459,7 +1459,7 @@
},
{
"cell_type": "markdown",
- "id": "33269773",
+ "id": "30ea8be6",
"metadata": {},
"source": [
"### Replication of the Figures\n",
@@ -1469,7 +1469,7 @@
},
{
"cell_type": "markdown",
- "id": "5d95c18a",
+ "id": "a12173ad",
"metadata": {},
"source": [
"#### Convergence of Value Iteration\n",
@@ -1482,7 +1482,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c96969f2",
+ "id": "7cfda779",
"metadata": {
"hide-output": false
},
@@ -1507,7 +1507,7 @@
},
{
"cell_type": "markdown",
- "id": "dda984fd",
+ "id": "6410059e",
"metadata": {},
"source": [
"We next plot the consumption policies along with the value iteration"
@@ -1516,7 +1516,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "66b82d89",
+ "id": "e727ba77",
"metadata": {
"hide-output": false
},
@@ -1549,7 +1549,7 @@
},
{
"cell_type": "markdown",
- "id": "46212d10",
+ "id": "6330cb04",
"metadata": {},
"source": [
"#### Dynamics of the Capital Stock\n",
@@ -1564,7 +1564,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2f43bb3d",
+ "id": "3d20099c",
"metadata": {
"hide-output": false
},
@@ -1599,7 +1599,7 @@
},
{
"cell_type": "markdown",
- "id": "9d161801",
+ "id": "a30d1f79",
"metadata": {},
"source": [
"\n",
@@ -1608,7 +1608,7 @@
},
{
"cell_type": "markdown",
- "id": "34f8b041",
+ "id": "fcb38391",
"metadata": {},
"source": [
"## Appendix: Algorithms\n",
@@ -1623,7 +1623,7 @@
},
{
"cell_type": "markdown",
- "id": "304f897e",
+ "id": "68b45cfc",
"metadata": {},
"source": [
"### Value Iteration\n",
@@ -1650,7 +1650,7 @@
},
{
"cell_type": "markdown",
- "id": "2941b29e",
+ "id": "a778feaa",
"metadata": {},
"source": [
"### Policy Iteration\n",
@@ -1676,7 +1676,7 @@
},
{
"cell_type": "markdown",
- "id": "6cea89cc",
+ "id": "aea43640",
"metadata": {},
"source": [
"### Modified Policy Iteration\n",
@@ -1702,7 +1702,7 @@
}
],
"metadata": {
- "date": 1723011581.5445042,
+ "date": 1723517847.6030302,
"filename": "discrete_dp.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/dyn_stack.ipynb b/_notebooks/dyn_stack.ipynb
index ec83e66b..b1daff18 100644
--- a/_notebooks/dyn_stack.ipynb
+++ b/_notebooks/dyn_stack.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "bc835756",
+ "id": "1abf8f46",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "8c519522",
+ "id": "304c13c2",
"metadata": {},
"source": [
"# Stackelberg Plans\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "711ce765",
+ "id": "e88ccdfc",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "0c0fb2a3",
+ "id": "11529295",
"metadata": {},
"source": [
"## Overview\n",
@@ -58,7 +58,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "249bc92c",
+ "id": "db4b0a60",
"metadata": {
"hide-output": false
},
@@ -73,7 +73,7 @@
},
{
"cell_type": "markdown",
- "id": "bdec8117",
+ "id": "91d311f5",
"metadata": {},
"source": [
"## Duopoly\n",
@@ -123,7 +123,7 @@
},
{
"cell_type": "markdown",
- "id": "fd6daaed",
+ "id": "df468b13",
"metadata": {},
"source": [
"### Stackelberg Leader and Follower\n",
@@ -149,7 +149,7 @@
},
{
"cell_type": "markdown",
- "id": "c96f5e68",
+ "id": "52e1d0f8",
"metadata": {},
"source": [
"### Statement of Leader’s and Follower’s Problems\n",
@@ -201,7 +201,7 @@
},
{
"cell_type": "markdown",
- "id": "bef70a48",
+ "id": "23b6d8f4",
"metadata": {},
"source": [
"### Firms’ Problems\n",
@@ -358,7 +358,7 @@
},
{
"cell_type": "markdown",
- "id": "70fd1310",
+ "id": "14204ef2",
"metadata": {},
"source": [
"## Stackelberg Problem\n",
@@ -445,7 +445,7 @@
},
{
"cell_type": "markdown",
- "id": "bc7255df",
+ "id": "9c87d96b",
"metadata": {},
"source": [
"### Interpretation of Second Block of Equations\n",
@@ -480,7 +480,7 @@
},
{
"cell_type": "markdown",
- "id": "fafeca47",
+ "id": "9d4ed6ec",
"metadata": {},
"source": [
"### More Mechanical Details\n",
@@ -507,7 +507,7 @@
},
{
"cell_type": "markdown",
- "id": "8b93a8fd",
+ "id": "f770a15b",
"metadata": {},
"source": [
"### Two Subproblems\n",
@@ -556,7 +556,7 @@
},
{
"cell_type": "markdown",
- "id": "5fb8811b",
+ "id": "95e8a6ad",
"metadata": {},
"source": [
"## Two Bellman Equations\n",
@@ -627,7 +627,7 @@
},
{
"cell_type": "markdown",
- "id": "14c712e5",
+ "id": "c013fc96",
"metadata": {},
"source": [
"## Stackelberg Plan for Duopoly\n",
@@ -672,7 +672,7 @@
},
{
"cell_type": "markdown",
- "id": "42860218",
+ "id": "78a769a2",
"metadata": {},
"source": [
"### Calculations to Prepare Duopoly Model\n",
@@ -690,7 +690,7 @@
},
{
"cell_type": "markdown",
- "id": "a9ab1965",
+ "id": "534072c1",
"metadata": {},
"source": [
"### Firm 1’s Problem\n",
@@ -788,7 +788,7 @@
},
{
"cell_type": "markdown",
- "id": "34f602ff",
+ "id": "407f0d20",
"metadata": {},
"source": [
"## Recursive Representation of Stackelberg Plan\n",
@@ -879,7 +879,7 @@
},
{
"cell_type": "markdown",
- "id": "5240d320",
+ "id": "aff7862d",
"metadata": {},
"source": [
"### Comments and Interpretations\n",
@@ -899,7 +899,7 @@
},
{
"cell_type": "markdown",
- "id": "61110777",
+ "id": "febd4b8f",
"metadata": {},
"source": [
"## Dynamic Programming and Time Consistency of Follower’s Problem\n",
@@ -918,7 +918,7 @@
},
{
"cell_type": "markdown",
- "id": "f2bcf9ac",
+ "id": "06281104",
"metadata": {},
"source": [
"### Recursive Formulation of a Follower’s Problem\n",
@@ -1041,7 +1041,7 @@
},
{
"cell_type": "markdown",
- "id": "2bc8b498",
+ "id": "6c343326",
"metadata": {},
"source": [
"### Time Consistency of Follower’s Plan\n",
@@ -1059,7 +1059,7 @@
},
{
"cell_type": "markdown",
- "id": "f43d5cb0",
+ "id": "b8873608",
"metadata": {},
"source": [
"## Computing Stackelberg Plan\n",
@@ -1073,7 +1073,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "169d3478",
+ "id": "17cc67f0",
"metadata": {
"hide-output": false
},
@@ -1097,7 +1097,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "798399c2",
+ "id": "032eef44",
"metadata": {
"hide-output": false
},
@@ -1157,7 +1157,7 @@
},
{
"cell_type": "markdown",
- "id": "e99ef4de",
+ "id": "67b8cbe2",
"metadata": {},
"source": [
"## Time Series for Price and Quantities\n",
@@ -1170,7 +1170,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "44af924a",
+ "id": "883949c0",
"metadata": {
"hide-output": false
},
@@ -1193,7 +1193,7 @@
},
{
"cell_type": "markdown",
- "id": "323bd398",
+ "id": "43a6a35d",
"metadata": {},
"source": [
"### Value of Stackelberg Leader\n",
@@ -1208,7 +1208,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "44b29998",
+ "id": "e896ddaf",
"metadata": {
"hide-output": false
},
@@ -1226,7 +1226,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "33f0d290",
+ "id": "51a5b9c8",
"metadata": {
"hide-output": false
},
@@ -1240,7 +1240,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "980169f5",
+ "id": "f4cf7e8d",
"metadata": {
"hide-output": false
},
@@ -1255,7 +1255,7 @@
},
{
"cell_type": "markdown",
- "id": "9391475e",
+ "id": "7739a640",
"metadata": {},
"source": [
"## Time Inconsistency of Stackelberg Plan\n",
@@ -1275,7 +1275,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7c2dc2c5",
+ "id": "bf7f1b98",
"metadata": {
"hide-output": false
},
@@ -1296,7 +1296,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b055e3b3",
+ "id": "89c7f684",
"metadata": {
"hide-output": false
},
@@ -1325,7 +1325,7 @@
},
{
"cell_type": "markdown",
- "id": "560ebd65",
+ "id": "f1a42598",
"metadata": {},
"source": [
"The figure above shows\n",
@@ -1340,7 +1340,7 @@
},
{
"cell_type": "markdown",
- "id": "30db4c1e",
+ "id": "5babdb02",
"metadata": {},
"source": [
"## Recursive Formulation of Follower’s Problem\n",
@@ -1355,7 +1355,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4a2dad5b",
+ "id": "424ef551",
"metadata": {
"hide-output": false
},
@@ -1383,7 +1383,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cb8db8a2",
+ "id": "75680fce",
"metadata": {
"hide-output": false
},
@@ -1400,7 +1400,7 @@
},
{
"cell_type": "markdown",
- "id": "88a2ad84",
+ "id": "6cdff140",
"metadata": {},
"source": [
"Note: Variables with `_tilde` are obtained from solving the follower’s\n",
@@ -1410,7 +1410,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ebdc6b4a",
+ "id": "7e8f4c11",
"metadata": {
"hide-output": false
},
@@ -1424,7 +1424,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8b870024",
+ "id": "edc15b69",
"metadata": {
"hide-output": false
},
@@ -1436,7 +1436,7 @@
},
{
"cell_type": "markdown",
- "id": "91ed321b",
+ "id": "54abba9a",
"metadata": {},
"source": [
"### Explanation of Alignment\n",
@@ -1454,7 +1454,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1a6dcf1c",
+ "id": "7ea63533",
"metadata": {
"hide-output": false
},
@@ -1467,7 +1467,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fb3a4a09",
+ "id": "9a53d84b",
"metadata": {
"hide-output": false
},
@@ -1480,7 +1480,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c8079529",
+ "id": "c49e6488",
"metadata": {
"hide-output": false
},
@@ -1493,7 +1493,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9744e6cb",
+ "id": "6df31d3f",
"metadata": {
"hide-output": false
},
@@ -1506,7 +1506,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5ccaabf5",
+ "id": "28ee2245",
"metadata": {
"hide-output": false
},
@@ -1525,7 +1525,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c71a33cf",
+ "id": "158df6e9",
"metadata": {
"hide-output": false
},
@@ -1538,7 +1538,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d2b85dd6",
+ "id": "525a3e35",
"metadata": {
"hide-output": false
},
@@ -1551,7 +1551,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "70a30409",
+ "id": "180d6482",
"metadata": {
"hide-output": false
},
@@ -1594,7 +1594,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "25987d57",
+ "id": "cdccd760",
"metadata": {
"hide-output": false
},
@@ -1620,7 +1620,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "449d56eb",
+ "id": "81ec5975",
"metadata": {
"hide-output": false
},
@@ -1632,7 +1632,7 @@
},
{
"cell_type": "markdown",
- "id": "c85eac3a",
+ "id": "c0c35315",
"metadata": {},
"source": [
"## Markov Perfect Equilibrium\n",
@@ -1672,7 +1672,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "05908bb0",
+ "id": "76b14d4a",
"metadata": {
"hide-output": false
},
@@ -1715,7 +1715,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b27f7c12",
+ "id": "a85bdc8b",
"metadata": {
"hide-output": false
},
@@ -1738,7 +1738,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "011d7d87",
+ "id": "a6d4a794",
"metadata": {
"hide-output": false
},
@@ -1751,7 +1751,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "46169266",
+ "id": "e29000d9",
"metadata": {
"hide-output": false
},
@@ -1779,7 +1779,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a763b9db",
+ "id": "fb92f1cf",
"metadata": {
"hide-output": false
},
@@ -1797,7 +1797,7 @@
},
{
"cell_type": "markdown",
- "id": "0e54f798",
+ "id": "0e2b4b85",
"metadata": {},
"source": [
"## Comparing Markov Perfect Equilibrium and Stackelberg Outcome\n",
@@ -1815,7 +1815,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d04a1a22",
+ "id": "67724ad0",
"metadata": {
"hide-output": false
},
@@ -1841,7 +1841,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "752bec46",
+ "id": "8d4fbe1b",
"metadata": {
"hide-output": false
},
@@ -1857,7 +1857,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f21335ee",
+ "id": "a9fa2ad7",
"metadata": {
"hide-output": false
},
@@ -1869,7 +1869,7 @@
}
],
"metadata": {
- "date": 1723011581.5996025,
+ "date": 1723517847.6596775,
"filename": "dyn_stack.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/entropy.ipynb b/_notebooks/entropy.ipynb
index 233d3370..ee6c1f52 100644
--- a/_notebooks/entropy.ipynb
+++ b/_notebooks/entropy.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "185cae70",
+ "id": "e8d7dadd",
"metadata": {},
"source": [
"# Etymology of Entropy\n",
@@ -26,7 +26,7 @@
},
{
"cell_type": "markdown",
- "id": "7feed8d5",
+ "id": "0ea2beda",
"metadata": {},
"source": [
"## Information Theory\n",
@@ -65,7 +65,7 @@
},
{
"cell_type": "markdown",
- "id": "74f037ee",
+ "id": "0bed889f",
"metadata": {},
"source": [
"## A Measure of Unpredictability\n",
@@ -85,7 +85,7 @@
},
{
"cell_type": "markdown",
- "id": "13bfb9d1",
+ "id": "fe02d4b7",
"metadata": {},
"source": [
"### Example\n",
@@ -119,7 +119,7 @@
},
{
"cell_type": "markdown",
- "id": "5f5a7d04",
+ "id": "7706bf15",
"metadata": {},
"source": [
"### Example\n",
@@ -142,7 +142,7 @@
},
{
"cell_type": "markdown",
- "id": "65df6b41",
+ "id": "786ba4e4",
"metadata": {},
"source": [
"## Mathematical Properties of Entropy\n",
@@ -160,7 +160,7 @@
},
{
"cell_type": "markdown",
- "id": "ee567e7f",
+ "id": "b047a610",
"metadata": {},
"source": [
"## Conditional Entropy\n",
@@ -182,7 +182,7 @@
},
{
"cell_type": "markdown",
- "id": "f24502d3",
+ "id": "acb1860a",
"metadata": {},
"source": [
"## Independence as Maximum Conditional Entropy\n",
@@ -212,7 +212,7 @@
},
{
"cell_type": "markdown",
- "id": "c8bc77a7",
+ "id": "7bbb819d",
"metadata": {},
"source": [
"## Thermodynamics\n",
@@ -235,7 +235,7 @@
},
{
"cell_type": "markdown",
- "id": "a0491103",
+ "id": "22b5e602",
"metadata": {},
"source": [
"## Statistical Divergence\n",
@@ -270,7 +270,7 @@
},
{
"cell_type": "markdown",
- "id": "8d1926a9",
+ "id": "241feb4c",
"metadata": {},
"source": [
"## Continuous distributions\n",
@@ -284,7 +284,7 @@
},
{
"cell_type": "markdown",
- "id": "ef8f9a9c",
+ "id": "264cf3b6",
"metadata": {},
"source": [
"## Relative entropy and Gaussian distributions\n",
@@ -375,7 +375,7 @@
},
{
"cell_type": "markdown",
- "id": "a6c6cbf5",
+ "id": "2a94426a",
"metadata": {},
"source": [
"## Von Neumann Entropy\n",
@@ -401,7 +401,7 @@
},
{
"cell_type": "markdown",
- "id": "0d6d4afa",
+ "id": "1fa8d01d",
"metadata": {},
"source": [
"## Backus-Chernov-Zin Entropy\n",
@@ -453,7 +453,7 @@
},
{
"cell_type": "markdown",
- "id": "67619b56",
+ "id": "80d117f1",
"metadata": {},
"source": [
"## Wiener-Kolmogorov Prediction Error Formula as Entropy\n",
@@ -500,7 +500,7 @@
},
{
"cell_type": "markdown",
- "id": "554bead7",
+ "id": "14b132a9",
"metadata": {},
"source": [
"## Multivariate Processes\n",
@@ -537,7 +537,7 @@
},
{
"cell_type": "markdown",
- "id": "0afd3a2f",
+ "id": "4c63c25a",
"metadata": {},
"source": [
"## Frequency Domain Robust Control\n",
@@ -570,7 +570,7 @@
},
{
"cell_type": "markdown",
- "id": "cf0738b5",
+ "id": "04291ff5",
"metadata": {},
"source": [
"## Relative Entropy for a Continuous Random Variable\n",
@@ -610,7 +610,7 @@
}
],
"metadata": {
- "date": 1723011581.8683457,
+ "date": 1723517847.8641298,
"filename": "entropy.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/estspec.ipynb b/_notebooks/estspec.ipynb
index 6e5b52bc..3bb5dde4 100644
--- a/_notebooks/estspec.ipynb
+++ b/_notebooks/estspec.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "c24075b5",
+ "id": "96959117",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "62e6c09a",
+ "id": "59fd7579",
"metadata": {},
"source": [
"# Estimation of Spectra\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "52d15bf4",
+ "id": "1c456959",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "edbc262e",
+ "id": "5b70af4b",
"metadata": {},
"source": [
"## Overview\n",
@@ -61,7 +61,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "daf14a15",
+ "id": "db9b5f76",
"metadata": {
"hide-output": false
},
@@ -74,7 +74,7 @@
},
{
"cell_type": "markdown",
- "id": "fbea104c",
+ "id": "5deb5cd0",
"metadata": {},
"source": [
"\n",
@@ -83,7 +83,7 @@
},
{
"cell_type": "markdown",
- "id": "30383d85",
+ "id": "6016ff90",
"metadata": {},
"source": [
"## Periodograms\n",
@@ -136,7 +136,7 @@
},
{
"cell_type": "markdown",
- "id": "f0fc1ad5",
+ "id": "e16744b3",
"metadata": {},
"source": [
"### Interpretation\n",
@@ -203,7 +203,7 @@
},
{
"cell_type": "markdown",
- "id": "8f8f8889",
+ "id": "644cc3ae",
"metadata": {},
"source": [
"### Calculation\n",
@@ -261,7 +261,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b55bb8a0",
+ "id": "69524bd2",
"metadata": {
"hide-output": false
},
@@ -283,7 +283,7 @@
},
{
"cell_type": "markdown",
- "id": "4823c600",
+ "id": "36230cfd",
"metadata": {},
"source": [
"This estimate looks rather disappointing, but the data size is only 40, so\n",
@@ -301,7 +301,7 @@
},
{
"cell_type": "markdown",
- "id": "d25d340c",
+ "id": "d8c86d51",
"metadata": {},
"source": [
"## Smoothing\n",
@@ -354,7 +354,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2af98c38",
+ "id": "8b74289b",
"metadata": {
"hide-output": false
},
@@ -376,7 +376,7 @@
},
{
"cell_type": "markdown",
- "id": "07dd8dc7",
+ "id": "cb78c3b7",
"metadata": {},
"source": [
"### Estimation with Smoothing\n",
@@ -422,7 +422,7 @@
},
{
"cell_type": "markdown",
- "id": "6ddb7931",
+ "id": "bc891c5f",
"metadata": {},
"source": [
"### Pre-Filtering and Smoothing\n",
@@ -472,7 +472,7 @@
},
{
"cell_type": "markdown",
- "id": "09541147",
+ "id": "d58dc6f0",
"metadata": {},
"source": [
"### The AR(1) Setting\n",
@@ -548,7 +548,7 @@
},
{
"cell_type": "markdown",
- "id": "2496ad18",
+ "id": "f7bb7651",
"metadata": {},
"source": [
"## Exercises\n",
@@ -559,7 +559,7 @@
},
{
"cell_type": "markdown",
- "id": "153b63df",
+ "id": "7bca53b8",
"metadata": {},
"source": [
"## Exercise 29.1\n",
@@ -573,7 +573,7 @@
},
{
"cell_type": "markdown",
- "id": "6790c8c5",
+ "id": "26580f03",
"metadata": {},
"source": [
"## Solution to[ Exercise 29.1](https://python-advanced.quantecon.org/#est_ex1)"
@@ -582,7 +582,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "34a72e20",
+ "id": "c19f28f4",
"metadata": {
"hide-output": false
},
@@ -615,7 +615,7 @@
},
{
"cell_type": "markdown",
- "id": "9f2c689c",
+ "id": "82706ba3",
"metadata": {},
"source": [
"\n",
@@ -624,7 +624,7 @@
},
{
"cell_type": "markdown",
- "id": "7c5bdfd6",
+ "id": "d5256a2d",
"metadata": {},
"source": [
"## Exercise 29.2\n",
@@ -639,7 +639,7 @@
},
{
"cell_type": "markdown",
- "id": "4e10945f",
+ "id": "057a9f5f",
"metadata": {},
"source": [
"## Solution to[ Exercise 29.2](https://python-advanced.quantecon.org/#est_ex2)"
@@ -648,7 +648,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d042759b",
+ "id": "7d1e105b",
"metadata": {
"hide-output": false
},
@@ -682,7 +682,7 @@
}
],
"metadata": {
- "date": 1723011581.894182,
+ "date": 1723517847.8893352,
"filename": "estspec.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/five_preferences.ipynb b/_notebooks/five_preferences.ipynb
index 82d2bf3c..e72d7119 100644
--- a/_notebooks/five_preferences.ipynb
+++ b/_notebooks/five_preferences.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "635e32ce",
+ "id": "4d8ac013",
"metadata": {},
"source": [
"# Risk and Model Uncertainty"
@@ -10,7 +10,7 @@
},
{
"cell_type": "markdown",
- "id": "3b9300da",
+ "id": "fdb65d05",
"metadata": {},
"source": [
"## Overview\n",
@@ -56,7 +56,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "327057f6",
+ "id": "7c627383",
"metadata": {
"hide-output": false
},
@@ -78,7 +78,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7becb527",
+ "id": "05ad9e4b",
"metadata": {
"hide-output": false
},
@@ -106,7 +106,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "41209159",
+ "id": "bd9eb74e",
"metadata": {
"hide-output": false
},
@@ -164,7 +164,7 @@
},
{
"cell_type": "markdown",
- "id": "7c602af2",
+ "id": "1bb7dde6",
"metadata": {},
"source": [
"## Basic objects\n",
@@ -229,7 +229,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ece2e814",
+ "id": "f18f2002",
"metadata": {
"hide-output": false
},
@@ -261,7 +261,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "582fc626",
+ "id": "0817c77d",
"metadata": {
"hide-output": false
},
@@ -276,7 +276,7 @@
},
{
"cell_type": "markdown",
- "id": "8fe482d9",
+ "id": "f9b106f5",
"metadata": {},
"source": [
"The heat maps in the next two figures vary both $ \\hat{\\pi}_1 $ and $ \\pi_1 $.\n",
@@ -287,7 +287,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "effc8a71",
+ "id": "01534d73",
"metadata": {
"hide-output": false
},
@@ -316,7 +316,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e5ff0320",
+ "id": "25edb598",
"metadata": {
"hide-output": false
},
@@ -334,7 +334,7 @@
},
{
"cell_type": "markdown",
- "id": "f592f2e3",
+ "id": "5cbde348",
"metadata": {},
"source": [
"The next figure plots the logarithm of entropy."
@@ -343,7 +343,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3f003622",
+ "id": "9c0e193d",
"metadata": {
"hide-output": false
},
@@ -358,7 +358,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a0cdc292",
+ "id": "c55ff610",
"metadata": {
"hide-output": false
},
@@ -375,7 +375,7 @@
},
{
"cell_type": "markdown",
- "id": "7f1929ac",
+ "id": "9033f8a0",
"metadata": {},
"source": [
"## Five preference specifications\n",
@@ -400,7 +400,7 @@
},
{
"cell_type": "markdown",
- "id": "c4fb0fc1",
+ "id": "d2d095d0",
"metadata": {},
"source": [
"## Expected utility\n",
@@ -422,7 +422,7 @@
},
{
"cell_type": "markdown",
- "id": "dfddd981",
+ "id": "4cee19c9",
"metadata": {},
"source": [
"## Constraint preferences\n",
@@ -547,7 +547,7 @@
},
{
"cell_type": "markdown",
- "id": "469a8a5c",
+ "id": "f99bf00b",
"metadata": {},
"source": [
"## Multiplier preferences\n",
@@ -610,7 +610,7 @@
},
{
"cell_type": "markdown",
- "id": "c5274cb6",
+ "id": "7bfe023b",
"metadata": {},
"source": [
"## Risk-sensitive preferences\n",
@@ -639,7 +639,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7182efea",
+ "id": "292cbc34",
"metadata": {
"hide-output": false
},
@@ -671,7 +671,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b21eff75",
+ "id": "99ee2e33",
"metadata": {
"hide-output": false
},
@@ -687,7 +687,7 @@
},
{
"cell_type": "markdown",
- "id": "124ad45b",
+ "id": "d9f7238e",
"metadata": {},
"source": [
"For large values of $ \\theta $, $ {\\sf T} u(c) $ is approximately linear in the probability $ \\pi_1 $, but for lower values of $ \\theta $, $ {\\sf T} u(c) $ has considerable curvature as a function of $ \\pi_1 $.\n",
@@ -702,7 +702,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d04df539",
+ "id": "5d02bd57",
"metadata": {
"hide-output": false
},
@@ -745,7 +745,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "53e1f1f8",
+ "id": "99b1df76",
"metadata": {
"hide-output": false
},
@@ -788,7 +788,7 @@
},
{
"cell_type": "markdown",
- "id": "a13cfd9e",
+ "id": "c2fa0c4a",
"metadata": {},
"source": [
"The panel on the right portrays how the transformation $ \\exp\\left(\\frac{-u\\left(c\\right)}{\\theta}\\right) $ sends $ u\\left(c\\right) $ to a new function by (i) flipping the sign, and (ii) increasing curvature in proportion to $ \\theta $.\n",
@@ -809,7 +809,7 @@
},
{
"cell_type": "markdown",
- "id": "f520750b",
+ "id": "279a813c",
"metadata": {},
"source": [
"### Digression on moment generating functions\n",
@@ -861,7 +861,7 @@
},
{
"cell_type": "markdown",
- "id": "47fd107b",
+ "id": "063dc983",
"metadata": {},
"source": [
"## Ex post Bayesian preferences\n",
@@ -881,7 +881,7 @@
},
{
"cell_type": "markdown",
- "id": "6a096368",
+ "id": "2859aeb8",
"metadata": {},
"source": [
"## Comparing preferences\n",
@@ -906,7 +906,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "182ba6b0",
+ "id": "09d5b19a",
"metadata": {
"hide-output": false
},
@@ -936,7 +936,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e7933974",
+ "id": "a5327140",
"metadata": {
"hide-output": false
},
@@ -955,7 +955,7 @@
},
{
"cell_type": "markdown",
- "id": "c411bfef",
+ "id": "a60d680d",
"metadata": {},
"source": [
"The next figure shows the function $ \\sum_{i=1}^I \\pi_i m_i [ u(c_i) + \\theta \\log m_i ] $ that is to be\n",
@@ -967,7 +967,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9b3e3306",
+ "id": "9e8f63e0",
"metadata": {
"hide-output": false
},
@@ -995,7 +995,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5baf9c7b",
+ "id": "96422096",
"metadata": {
"hide-output": false
},
@@ -1033,7 +1033,7 @@
},
{
"cell_type": "markdown",
- "id": "ced8566e",
+ "id": "0370079d",
"metadata": {},
"source": [
"Evidently, from this figure and also from formula [(24.12)](#equation-tom12), lower values of $ \\theta $ lead to lower,\n",
@@ -1061,7 +1061,7 @@
},
{
"cell_type": "markdown",
- "id": "6f1b6421",
+ "id": "0556ef60",
"metadata": {},
"source": [
"## Risk aversion and misspecification aversion\n",
@@ -1112,7 +1112,7 @@
},
{
"cell_type": "markdown",
- "id": "9a963898",
+ "id": "64c12417",
"metadata": {},
"source": [
"## Indifference curves\n",
@@ -1156,7 +1156,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b9e877e3",
+ "id": "1a052bd3",
"metadata": {
"hide-output": false
},
@@ -1277,7 +1277,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a0eacb99",
+ "id": "126a3f98",
"metadata": {
"hide-output": false
},
@@ -1325,7 +1325,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0ff3632c",
+ "id": "2b98f180",
"metadata": {
"hide-output": false
},
@@ -1353,7 +1353,7 @@
},
{
"cell_type": "markdown",
- "id": "8dd5c219",
+ "id": "1361712f",
"metadata": {},
"source": [
"**Kink at 45 degree line**\n",
@@ -1423,7 +1423,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1b8fb10b",
+ "id": "dc23adca",
"metadata": {
"hide-output": false
},
@@ -1472,7 +1472,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "43017574",
+ "id": "1e6c8184",
"metadata": {
"hide-output": false
},
@@ -1500,7 +1500,7 @@
},
{
"cell_type": "markdown",
- "id": "e90aad5e",
+ "id": "1d2313a7",
"metadata": {},
"source": [
"Note that all three lines of the left graph intersect at (1, 3). While the intersection at (3, 1) is hard-coded, the intersection at (1,3) arises from the computation, which confirms that the code seems to be\n",
@@ -1537,7 +1537,7 @@
},
{
"cell_type": "markdown",
- "id": "4bd2d124",
+ "id": "dd0e04f3",
"metadata": {},
"source": [
"## State price deflators\n",
@@ -1577,7 +1577,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ae853d4c",
+ "id": "e6773fc0",
"metadata": {
"hide-output": false
},
@@ -1607,7 +1607,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d58388f2",
+ "id": "b088ec0a",
"metadata": {
"hide-output": false
},
@@ -1630,7 +1630,7 @@
},
{
"cell_type": "markdown",
- "id": "5bd382d8",
+ "id": "ed36ab66",
"metadata": {},
"source": [
"Because budget constraints are linear, asset prices are identical under\n",
@@ -1648,7 +1648,7 @@
},
{
"cell_type": "markdown",
- "id": "d4cd9abe",
+ "id": "e5ee20ee",
"metadata": {},
"source": [
"### Consumption-equivalent measures of uncertainty aversion\n",
@@ -1663,7 +1663,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f9509152",
+ "id": "1b6e5a8c",
"metadata": {
"hide-output": false
},
@@ -1695,7 +1695,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3800533a",
+ "id": "1cc04044",
"metadata": {
"hide-output": false
},
@@ -1732,7 +1732,7 @@
},
{
"cell_type": "markdown",
- "id": "642c6e09",
+ "id": "a9fded17",
"metadata": {},
"source": [
"The figure indicates that the certainty equivalent\n",
@@ -1760,7 +1760,7 @@
},
{
"cell_type": "markdown",
- "id": "a5352e5a",
+ "id": "cdfa7b81",
"metadata": {},
"source": [
"## Iso-utility and iso-entropy curves and expansion paths\n",
@@ -1794,7 +1794,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5d80c921",
+ "id": "bfabdcc8",
"metadata": {
"hide-output": false
},
@@ -1843,7 +1843,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3030f18e",
+ "id": "9ea0b29b",
"metadata": {
"hide-output": false
},
@@ -1918,7 +1918,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "66b91d1c",
+ "id": "6ee8de31",
"metadata": {
"hide-output": false
},
@@ -1932,7 +1932,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a0c79109",
+ "id": "cd62a74d",
"metadata": {
"hide-output": false
},
@@ -1945,7 +1945,7 @@
},
{
"cell_type": "markdown",
- "id": "b9c818b1",
+ "id": "42feee5b",
"metadata": {},
"source": [
"## Bounds on expected utility\n",
@@ -2008,7 +2008,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cece9920",
+ "id": "700d6162",
"metadata": {
"hide-output": false
},
@@ -2074,7 +2074,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eb2f4b7c",
+ "id": "a8a97fb0",
"metadata": {
"hide-output": false
},
@@ -2101,7 +2101,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d31b0ca6",
+ "id": "474c2682",
"metadata": {
"hide-output": false
},
@@ -2117,7 +2117,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c4050682",
+ "id": "61834776",
"metadata": {
"hide-output": false
},
@@ -2134,7 +2134,7 @@
},
{
"cell_type": "markdown",
- "id": "5d6531a4",
+ "id": "7d887ea5",
"metadata": {},
"source": [
"In this figure, expected utility is on the co-ordinate axis\n",
@@ -2184,7 +2184,7 @@
},
{
"cell_type": "markdown",
- "id": "720d7fd1",
+ "id": "138f8d24",
"metadata": {},
"source": [
"## Why entropy?\n",
@@ -2202,7 +2202,7 @@
},
{
"cell_type": "markdown",
- "id": "6f645e74",
+ "id": "ff3f044f",
"metadata": {},
"source": [
"### Entropy and statistical detection\n",
@@ -2250,7 +2250,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "87b8c1f9",
+ "id": "a4fcd52f",
"metadata": {
"hide-output": false
},
@@ -2268,7 +2268,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "16ddb830",
+ "id": "8202589c",
"metadata": {
"hide-output": false
},
@@ -2296,7 +2296,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a79bc5c2",
+ "id": "82cb120c",
"metadata": {
"hide-output": false
},
@@ -2319,7 +2319,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d073bb46",
+ "id": "e05bf4fd",
"metadata": {
"hide-output": false
},
@@ -2330,7 +2330,7 @@
},
{
"cell_type": "markdown",
- "id": "29ac6d46",
+ "id": "43992197",
"metadata": {},
"source": [
"The density for the approximating model is\n",
@@ -2350,7 +2350,7 @@
},
{
"cell_type": "markdown",
- "id": "afe0595f",
+ "id": "07567071",
"metadata": {},
"source": [
"### Axiomatic justifications\n",
@@ -2366,7 +2366,7 @@
}
],
"metadata": {
- "date": 1723011581.9737446,
+ "date": 1723517847.9678419,
"filename": "five_preferences.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/growth_in_dles.ipynb b/_notebooks/growth_in_dles.ipynb
index f23c18c0..c2447c6f 100644
--- a/_notebooks/growth_in_dles.ipynb
+++ b/_notebooks/growth_in_dles.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "db2036e5",
+ "id": "4ea677c5",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "60de0dff",
+ "id": "67b83771",
"metadata": {},
"source": [
"# Growth in Dynamic Linear Economies\n",
@@ -27,7 +27,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d02c42a9",
+ "id": "bd6a4a55",
"metadata": {
"hide-output": false
},
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "d54dfcd7",
+ "id": "6e33d019",
"metadata": {},
"source": [
"This lecture describes several complete market economies having a\n",
@@ -55,7 +55,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7b64f526",
+ "id": "363699ce",
"metadata": {
"hide-output": false
},
@@ -68,7 +68,7 @@
},
{
"cell_type": "markdown",
- "id": "59622683",
+ "id": "ee736471",
"metadata": {},
"source": [
"## Common Structure\n",
@@ -132,7 +132,7 @@
},
{
"cell_type": "markdown",
- "id": "d6dc171a",
+ "id": "ffdd5f59",
"metadata": {},
"source": [
"## A Planning Problem\n",
@@ -215,7 +215,7 @@
},
{
"cell_type": "markdown",
- "id": "dccd5c28",
+ "id": "1a7a3cf5",
"metadata": {},
"source": [
"## Example Economies\n",
@@ -300,7 +300,7 @@
},
{
"cell_type": "markdown",
- "id": "2f129045",
+ "id": "dc41d76a",
"metadata": {},
"source": [
"### Example 1: Hall (1978)\n",
@@ -333,7 +333,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2f7cad21",
+ "id": "aac75fa7",
"metadata": {
"hide-output": false
},
@@ -376,7 +376,7 @@
},
{
"cell_type": "markdown",
- "id": "e79fd6c7",
+ "id": "4d782512",
"metadata": {},
"source": [
"These parameter values are used to define an economy of the DLE class."
@@ -385,7 +385,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "51170cc7",
+ "id": "bc508377",
"metadata": {
"hide-output": false
},
@@ -396,7 +396,7 @@
},
{
"cell_type": "markdown",
- "id": "05402c16",
+ "id": "2ee1ef9a",
"metadata": {},
"source": [
"We can then simulate the economy for a chosen length of time, from our\n",
@@ -406,7 +406,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9e78db36",
+ "id": "030b8f91",
"metadata": {
"hide-output": false
},
@@ -417,7 +417,7 @@
},
{
"cell_type": "markdown",
- "id": "12280004",
+ "id": "307d2097",
"metadata": {},
"source": [
"The economy stores the simulated values for each variable. Below we plot\n",
@@ -427,7 +427,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0ff63037",
+ "id": "55c3664d",
"metadata": {
"hide-output": false
},
@@ -442,7 +442,7 @@
},
{
"cell_type": "markdown",
- "id": "7f62195c",
+ "id": "22cb2404",
"metadata": {},
"source": [
"Inspection of the plot shows that the sample paths of consumption and\n",
@@ -455,7 +455,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "012c186f",
+ "id": "ad8ede5a",
"metadata": {
"hide-output": false
},
@@ -466,7 +466,7 @@
},
{
"cell_type": "markdown",
- "id": "0bcb73a8",
+ "id": "746842f7",
"metadata": {},
"source": [
"The endogenous eigenvalue that appears to be unity reflects the random\n",
@@ -479,7 +479,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2dedfabb",
+ "id": "e19cafb3",
"metadata": {
"hide-output": false
},
@@ -490,7 +490,7 @@
},
{
"cell_type": "markdown",
- "id": "75200f53",
+ "id": "dd168ecd",
"metadata": {},
"source": [
"The fact that the largest endogenous eigenvalue is strictly less than\n",
@@ -501,7 +501,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a2d1621e",
+ "id": "cbef39bd",
"metadata": {
"hide-output": false
},
@@ -514,7 +514,7 @@
},
{
"cell_type": "markdown",
- "id": "2ba68ebe",
+ "id": "5a471961",
"metadata": {},
"source": [
"However, the near-unity endogenous eigenvalue means that these steady\n",
@@ -523,7 +523,7 @@
},
{
"cell_type": "markdown",
- "id": "61544634",
+ "id": "f3351159",
"metadata": {},
"source": [
"### Example 2: Altered Growth Condition\n",
@@ -557,7 +557,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0761c0f9",
+ "id": "40a42800",
"metadata": {
"hide-output": false
},
@@ -576,7 +576,7 @@
},
{
"cell_type": "markdown",
- "id": "eb25f019",
+ "id": "318c83b3",
"metadata": {},
"source": [
"Creating the DLE class and then simulating gives the following plot for\n",
@@ -586,7 +586,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8010c77c",
+ "id": "6f773220",
"metadata": {
"hide-output": false
},
@@ -604,7 +604,7 @@
},
{
"cell_type": "markdown",
- "id": "bbea1224",
+ "id": "630c8df1",
"metadata": {},
"source": [
"Simulating our new economy shows that consumption grows quickly in the\n",
@@ -617,7 +617,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "24075c5f",
+ "id": "42f3e915",
"metadata": {
"hide-output": false
},
@@ -629,7 +629,7 @@
},
{
"cell_type": "markdown",
- "id": "5c874e2e",
+ "id": "dde9c4a4",
"metadata": {},
"source": [
"The economy converges faster to this level than in Example 1 because the\n",
@@ -640,7 +640,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7bcb4b86",
+ "id": "089fe4ac",
"metadata": {
"hide-output": false
},
@@ -651,7 +651,7 @@
},
{
"cell_type": "markdown",
- "id": "06c203a0",
+ "id": "b3585cc1",
"metadata": {},
"source": [
"### Example 3: A Jones-Manuelli (1990) Economy\n",
@@ -699,7 +699,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eeaff1f6",
+ "id": "34586274",
"metadata": {
"hide-output": false
},
@@ -712,7 +712,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "65d1edd7",
+ "id": "f9df1294",
"metadata": {
"hide-output": false
},
@@ -723,7 +723,7 @@
},
{
"cell_type": "markdown",
- "id": "4df48246",
+ "id": "c924f347",
"metadata": {},
"source": [
"We simulate this economy from the original state vector"
@@ -732,7 +732,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d375de52",
+ "id": "ef67d2ac",
"metadata": {
"hide-output": false
},
@@ -749,7 +749,7 @@
},
{
"cell_type": "markdown",
- "id": "ba7db600",
+ "id": "cc29ca15",
"metadata": {},
"source": [
"Thus, adding habit persistence to the Hall model of Example 1 is enough\n",
@@ -762,7 +762,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f19e97f9",
+ "id": "6c10c323",
"metadata": {
"hide-output": false
},
@@ -773,7 +773,7 @@
},
{
"cell_type": "markdown",
- "id": "1967f5ef",
+ "id": "4157058a",
"metadata": {},
"source": [
"We now have two unit endogenous eigenvalues. One stems from satisfying\n",
@@ -787,7 +787,7 @@
},
{
"cell_type": "markdown",
- "id": "78e5a2a3",
+ "id": "ee816850",
"metadata": {},
"source": [
"### Example 3.1: Varying Sensitivity\n",
@@ -798,7 +798,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "61666003",
+ "id": "e8cdab38",
"metadata": {
"hide-output": false
},
@@ -819,7 +819,7 @@
},
{
"cell_type": "markdown",
- "id": "d61574d2",
+ "id": "be4221df",
"metadata": {},
"source": [
"We no longer achieve sustained growth if $ \\lambda $ is raised from -1 to -0.7.\n",
@@ -831,7 +831,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e3f0817b",
+ "id": "e36e39dc",
"metadata": {
"hide-output": false
},
@@ -842,7 +842,7 @@
},
{
"cell_type": "markdown",
- "id": "807e696a",
+ "id": "05976117",
"metadata": {},
"source": [
"### Example 3.2: More Impatience\n",
@@ -853,7 +853,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "763e437d",
+ "id": "4b33e2d2",
"metadata": {
"hide-output": false
},
@@ -874,7 +874,7 @@
},
{
"cell_type": "markdown",
- "id": "0f9bfbe3",
+ "id": "5ada550a",
"metadata": {},
"source": [
"Growth also fails if we lower $ \\beta $, since we now have\n",
@@ -891,7 +891,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c8cc77b9",
+ "id": "530770e9",
"metadata": {
"hide-output": false
},
@@ -902,7 +902,7 @@
}
],
"metadata": {
- "date": 1723011582.0021672,
+ "date": 1723517847.9962149,
"filename": "growth_in_dles.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/hs_invertibility_example.ipynb b/_notebooks/hs_invertibility_example.ipynb
index 71f05e83..d9046f09 100644
--- a/_notebooks/hs_invertibility_example.ipynb
+++ b/_notebooks/hs_invertibility_example.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "fdcc1726",
+ "id": "b6235f3e",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "4ed74f77",
+ "id": "9af4447e",
"metadata": {},
"source": [
"# Shock Non Invertibility"
@@ -21,7 +21,7 @@
},
{
"cell_type": "markdown",
- "id": "d49bdc0e",
+ "id": "06e9ab1d",
"metadata": {},
"source": [
"## Overview\n",
@@ -35,7 +35,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0b5e541e",
+ "id": "008b3df9",
"metadata": {
"hide-output": false
},
@@ -46,7 +46,7 @@
},
{
"cell_type": "markdown",
- "id": "cfcb3e2a",
+ "id": "246c3940",
"metadata": {},
"source": [
"We’ll make these imports:"
@@ -55,7 +55,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dae1ae08",
+ "id": "b1591713",
"metadata": {
"hide-output": false
},
@@ -70,7 +70,7 @@
},
{
"cell_type": "markdown",
- "id": "d0b20e26",
+ "id": "91fe14a7",
"metadata": {},
"source": [
"This lecture describes an early contribution to what is now often called\n",
@@ -96,7 +96,7 @@
},
{
"cell_type": "markdown",
- "id": "438b0db7",
+ "id": "ec6fa233",
"metadata": {},
"source": [
"## Model\n",
@@ -191,7 +191,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "89c1a2d4",
+ "id": "be1f2372",
"metadata": {
"hide-output": false
},
@@ -229,7 +229,7 @@
},
{
"cell_type": "markdown",
- "id": "1dd59318",
+ "id": "9a4ea1a9",
"metadata": {},
"source": [
"We define the household’s net of interest deficit as $ c_t - d_t $.\n",
@@ -300,7 +300,7 @@
},
{
"cell_type": "markdown",
- "id": "787bd3f4",
+ "id": "871e75f9",
"metadata": {},
"source": [
"## Code\n",
@@ -312,7 +312,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "824c639b",
+ "id": "baea6cb4",
"metadata": {
"hide-output": false
},
@@ -340,7 +340,7 @@
},
{
"cell_type": "markdown",
- "id": "139ac2a3",
+ "id": "44051a87",
"metadata": {},
"source": [
"The above figure displays the impulse response of consumption and the\n",
@@ -360,7 +360,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a1b2ca1d",
+ "id": "30fe4e13",
"metadata": {
"hide-output": false
},
@@ -410,7 +410,7 @@
},
{
"cell_type": "markdown",
- "id": "ec7acd3e",
+ "id": "628f2c94",
"metadata": {},
"source": [
"The above figure displays the impulse response of consumption and the\n",
@@ -430,7 +430,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "21cef038",
+ "id": "42345288",
"metadata": {
"hide-output": false
},
@@ -467,7 +467,7 @@
},
{
"cell_type": "markdown",
- "id": "0befc526",
+ "id": "bf2e48bc",
"metadata": {},
"source": [
"The above figure displays the impulse responses of $ u_t $ to\n",
@@ -488,7 +488,7 @@
}
],
"metadata": {
- "date": 1723011582.0193183,
+ "date": 1723517848.0135906,
"filename": "hs_invertibility_example.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/hs_recursive_models.ipynb b/_notebooks/hs_recursive_models.ipynb
index 77bcede0..180232ab 100644
--- a/_notebooks/hs_recursive_models.ipynb
+++ b/_notebooks/hs_recursive_models.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "7404618b",
+ "id": "2bb3bd87",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "5c26223b",
+ "id": "58006cc6",
"metadata": {},
"source": [
"# Recursive Models of Dynamic Linear Economies\n",
@@ -29,7 +29,7 @@
},
{
"cell_type": "markdown",
- "id": "7afca7e0",
+ "id": "8cf8f921",
"metadata": {},
"source": [
"## A Suite of Models\n",
@@ -52,7 +52,7 @@
},
{
"cell_type": "markdown",
- "id": "6e0f6267",
+ "id": "10688a1c",
"metadata": {},
"source": [
"### Overview of the Models\n",
@@ -123,7 +123,7 @@
},
{
"cell_type": "markdown",
- "id": "78b68dd3",
+ "id": "7884f858",
"metadata": {},
"source": [
"### Forecasting?\n",
@@ -140,7 +140,7 @@
},
{
"cell_type": "markdown",
- "id": "b3aa536e",
+ "id": "0afc08af",
"metadata": {},
"source": [
"### Theory and Econometrics\n",
@@ -165,7 +165,7 @@
},
{
"cell_type": "markdown",
- "id": "cde47bea",
+ "id": "8aa7a1e8",
"metadata": {},
"source": [
"### More Details\n",
@@ -248,7 +248,7 @@
},
{
"cell_type": "markdown",
- "id": "16d48808",
+ "id": "4f94305a",
"metadata": {},
"source": [
"### Stochastic Model of Information Flows and Outcomes\n",
@@ -290,7 +290,7 @@
},
{
"cell_type": "markdown",
- "id": "5ea0fca6",
+ "id": "0085be1b",
"metadata": {},
"source": [
"### Information Sets\n",
@@ -304,7 +304,7 @@
},
{
"cell_type": "markdown",
- "id": "1c7406d5",
+ "id": "25f81a28",
"metadata": {},
"source": [
"### Prediction Theory\n",
@@ -380,7 +380,7 @@
},
{
"cell_type": "markdown",
- "id": "6486b52e",
+ "id": "bf1c594e",
"metadata": {},
"source": [
"### Orthogonal Decomposition\n",
@@ -413,7 +413,7 @@
},
{
"cell_type": "markdown",
- "id": "9a716f73",
+ "id": "4c613dfc",
"metadata": {},
"source": [
"### Taste and Technology Shocks\n",
@@ -454,7 +454,7 @@
},
{
"cell_type": "markdown",
- "id": "ab01b79d",
+ "id": "cf16d2d9",
"metadata": {},
"source": [
"### Production Technology\n",
@@ -479,7 +479,7 @@
},
{
"cell_type": "markdown",
- "id": "4ba12eb6",
+ "id": "cdc59fda",
"metadata": {},
"source": [
"### Household Technology\n",
@@ -506,7 +506,7 @@
},
{
"cell_type": "markdown",
- "id": "40b86774",
+ "id": "8de10150",
"metadata": {},
"source": [
"### Preferences\n",
@@ -536,7 +536,7 @@
},
{
"cell_type": "markdown",
- "id": "e944a086",
+ "id": "5c8e2d07",
"metadata": {},
"source": [
"### Endowment Economy\n",
@@ -584,7 +584,7 @@
},
{
"cell_type": "markdown",
- "id": "e2ac81b6",
+ "id": "8868ed3f",
"metadata": {},
"source": [
"### Single-Period Adjustment Costs\n",
@@ -898,7 +898,7 @@
},
{
"cell_type": "markdown",
- "id": "550a1188",
+ "id": "73dc2740",
"metadata": {},
"source": [
"### Optimal Resource Allocation\n",
@@ -951,7 +951,7 @@
},
{
"cell_type": "markdown",
- "id": "ae94b228",
+ "id": "8bd71079",
"metadata": {},
"source": [
"### Lagrangian Formulation\n",
@@ -1070,7 +1070,7 @@
},
{
"cell_type": "markdown",
- "id": "a1da7c86",
+ "id": "1d32b274",
"metadata": {},
"source": [
"### Dynamic Programming\n",
@@ -1286,7 +1286,7 @@
},
{
"cell_type": "markdown",
- "id": "5b345384",
+ "id": "fced01ec",
"metadata": {},
"source": [
"### Other mathematical infrastructure\n",
@@ -1315,7 +1315,7 @@
},
{
"cell_type": "markdown",
- "id": "b3a9e9fc",
+ "id": "4fef42a5",
"metadata": {},
"source": [
"### Representative Household\n",
@@ -1352,7 +1352,7 @@
},
{
"cell_type": "markdown",
- "id": "d22eef5d",
+ "id": "c2d9c4e3",
"metadata": {},
"source": [
"### Type I Firm\n",
@@ -1382,7 +1382,7 @@
},
{
"cell_type": "markdown",
- "id": "378bc4b8",
+ "id": "f3138fe2",
"metadata": {},
"source": [
"### Type II Firm\n",
@@ -1410,7 +1410,7 @@
},
{
"cell_type": "markdown",
- "id": "517d6671",
+ "id": "2076be34",
"metadata": {},
"source": [
"### Competitive Equilibrium: Definition\n",
@@ -1473,7 +1473,7 @@
},
{
"cell_type": "markdown",
- "id": "1f596056",
+ "id": "219512cf",
"metadata": {},
"source": [
"### Asset pricing\n",
@@ -1521,7 +1521,7 @@
},
{
"cell_type": "markdown",
- "id": "9cdc8ebf",
+ "id": "704dcc97",
"metadata": {},
"source": [
"### Re-Opening Markets\n",
@@ -1567,7 +1567,7 @@
},
{
"cell_type": "markdown",
- "id": "d3bc9356",
+ "id": "331bc0f1",
"metadata": {},
"source": [
"## Econometrics\n",
@@ -1680,7 +1680,7 @@
},
{
"cell_type": "markdown",
- "id": "5429e52a",
+ "id": "8f9de5e1",
"metadata": {},
"source": [
"### Factorization of Likelihood Function\n",
@@ -1707,7 +1707,7 @@
},
{
"cell_type": "markdown",
- "id": "9b998269",
+ "id": "e6266a90",
"metadata": {},
"source": [
"### Covariance Generating Functions\n",
@@ -1720,7 +1720,7 @@
},
{
"cell_type": "markdown",
- "id": "51c3e2d2",
+ "id": "2884fd09",
"metadata": {},
"source": [
"### Spectral Factorization Identity\n",
@@ -1764,7 +1764,7 @@
},
{
"cell_type": "markdown",
- "id": "4e732417",
+ "id": "cf50225a",
"metadata": {},
"source": [
"### Wold and Vector Autoregressive Representations\n",
@@ -1806,7 +1806,7 @@
},
{
"cell_type": "markdown",
- "id": "bee32f02",
+ "id": "c2bc908b",
"metadata": {},
"source": [
"## Dynamic Demand Curves and Canonical Household Technologies"
@@ -1814,7 +1814,7 @@
},
{
"cell_type": "markdown",
- "id": "c35d41c0",
+ "id": "7cdf3c18",
"metadata": {},
"source": [
"### Canonical Household Technologies\n",
@@ -1862,7 +1862,7 @@
},
{
"cell_type": "markdown",
- "id": "ca2bec70",
+ "id": "050f130b",
"metadata": {},
"source": [
"### Dynamic Demand Functions\n",
@@ -1915,7 +1915,7 @@
},
{
"cell_type": "markdown",
- "id": "ffc06119",
+ "id": "f05cd082",
"metadata": {},
"source": [
"## Gorman Aggregation and Engel Curves\n",
@@ -1945,7 +1945,7 @@
},
{
"cell_type": "markdown",
- "id": "0acbde52",
+ "id": "e4bd2971",
"metadata": {},
"source": [
"### Re-Opened Markets\n",
@@ -1989,7 +1989,7 @@
},
{
"cell_type": "markdown",
- "id": "4e404f2d",
+ "id": "e6056ed8",
"metadata": {},
"source": [
"### Dynamic Demand\n",
@@ -2017,7 +2017,7 @@
},
{
"cell_type": "markdown",
- "id": "62a99953",
+ "id": "c03cf937",
"metadata": {},
"source": [
"### Attaining a Canonical Household Technology\n",
@@ -2043,7 +2043,7 @@
},
{
"cell_type": "markdown",
- "id": "6b1cfe00",
+ "id": "e17fdaab",
"metadata": {},
"source": [
"## Partial Equilibrium\n",
@@ -2113,7 +2113,7 @@
},
{
"cell_type": "markdown",
- "id": "1850818b",
+ "id": "06e63e32",
"metadata": {},
"source": [
"## Equilibrium Investment Under Uncertainty\n",
@@ -2150,7 +2150,7 @@
},
{
"cell_type": "markdown",
- "id": "b5f6d75f",
+ "id": "ce465765",
"metadata": {},
"source": [
"## A Rosen-Topel Housing Model\n",
@@ -2199,7 +2199,7 @@
},
{
"cell_type": "markdown",
- "id": "0e3feeb2",
+ "id": "6c79232e",
"metadata": {},
"source": [
"## Cattle Cycles\n",
@@ -2269,7 +2269,7 @@
},
{
"cell_type": "markdown",
- "id": "c710a7e8",
+ "id": "6d4842c0",
"metadata": {},
"source": [
"## Models of Occupational Choice and Pay\n",
@@ -2282,7 +2282,7 @@
},
{
"cell_type": "markdown",
- "id": "5ef293e4",
+ "id": "20852628",
"metadata": {},
"source": [
"### Market for Engineers\n",
@@ -2359,7 +2359,7 @@
},
{
"cell_type": "markdown",
- "id": "f57fdcf7",
+ "id": "9c07c187",
"metadata": {},
"source": [
"### Skilled and Unskilled Workers\n",
@@ -2422,7 +2422,7 @@
},
{
"cell_type": "markdown",
- "id": "8a24a989",
+ "id": "253c11ef",
"metadata": {},
"source": [
"## Permanent Income Models\n",
@@ -2500,7 +2500,7 @@
},
{
"cell_type": "markdown",
- "id": "b747b2ee",
+ "id": "11826feb",
"metadata": {},
"source": [
"## Gorman Heterogeneous Households\n",
@@ -2600,7 +2600,7 @@
},
{
"cell_type": "markdown",
- "id": "f1fa7496",
+ "id": "e849fd2c",
"metadata": {},
"source": [
"## Non-Gorman Heterogeneous Households\n",
@@ -2784,7 +2784,7 @@
}
],
"metadata": {
- "date": 1723011582.3153026,
+ "date": 1723517848.0885496,
"filename": "hs_recursive_models.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/intro.ipynb b/_notebooks/intro.ipynb
index 9e7eb684..7300a038 100644
--- a/_notebooks/intro.ipynb
+++ b/_notebooks/intro.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "19595b03",
+ "id": "97348f90",
"metadata": {},
"source": [
"# Advanced Quantitative Economics with Python\n",
@@ -12,7 +12,7 @@
},
{
"cell_type": "markdown",
- "id": "dcb3a5a8",
+ "id": "e313de09",
"metadata": {},
"source": [
"# Tools and Techniques\n",
@@ -25,7 +25,7 @@
},
{
"cell_type": "markdown",
- "id": "81caa974",
+ "id": "7c44ddf0",
"metadata": {},
"source": [
"# LQ Control\n",
@@ -42,7 +42,7 @@
},
{
"cell_type": "markdown",
- "id": "2512a8f9",
+ "id": "f7b571ae",
"metadata": {},
"source": [
"# Multiple Agent Models\n",
@@ -54,7 +54,7 @@
},
{
"cell_type": "markdown",
- "id": "8073a292",
+ "id": "2e88be3d",
"metadata": {},
"source": [
"# Dynamic Linear Economies\n",
@@ -71,7 +71,7 @@
},
{
"cell_type": "markdown",
- "id": "f6b80cf7",
+ "id": "699cd0cd",
"metadata": {},
"source": [
"# Risk, Model Uncertainty, and Robustness\n",
@@ -84,7 +84,7 @@
},
{
"cell_type": "markdown",
- "id": "ce11473f",
+ "id": "8a40d26e",
"metadata": {},
"source": [
"# Time Series Models\n",
@@ -99,7 +99,7 @@
},
{
"cell_type": "markdown",
- "id": "928fcf70",
+ "id": "a79e6e3a",
"metadata": {},
"source": [
"# Asset Pricing and Finance\n",
@@ -113,7 +113,7 @@
},
{
"cell_type": "markdown",
- "id": "68ad524a",
+ "id": "149d1d6c",
"metadata": {},
"source": [
"# Dynamic Programming Squared\n",
@@ -132,7 +132,7 @@
},
{
"cell_type": "markdown",
- "id": "bb8aee61",
+ "id": "f57090c1",
"metadata": {},
"source": [
"# Other\n",
@@ -144,7 +144,7 @@
}
],
"metadata": {
- "date": 1723011582.3491473,
+ "date": 1723517848.3325682,
"filename": "intro.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/irfs_in_hall_model.ipynb b/_notebooks/irfs_in_hall_model.ipynb
index bfce7544..8e140277 100644
--- a/_notebooks/irfs_in_hall_model.ipynb
+++ b/_notebooks/irfs_in_hall_model.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "ebf30747",
+ "id": "4de653a6",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "d24cd979",
+ "id": "88b4fb8f",
"metadata": {},
"source": [
"# IRFs in Hall Models\n",
@@ -27,7 +27,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d9bc8a94",
+ "id": "8e6df55d",
"metadata": {
"hide-output": false
},
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "bcc96659",
+ "id": "ff7da492",
"metadata": {},
"source": [
"We’ll make these imports:"
@@ -47,7 +47,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "08b391df",
+ "id": "4e22b86a",
"metadata": {
"hide-output": false
},
@@ -60,7 +60,7 @@
},
{
"cell_type": "markdown",
- "id": "4c35eb19",
+ "id": "2afb3631",
"metadata": {},
"source": [
"This lecture shows how the DLE class can be used to create impulse\n",
@@ -74,7 +74,7 @@
},
{
"cell_type": "markdown",
- "id": "6c8e5934",
+ "id": "75b812b1",
"metadata": {},
"source": [
"## Example 1: Hall (1978)\n",
@@ -110,7 +110,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e4b7f9ce",
+ "id": "27feec91",
"metadata": {
"hide-output": false
},
@@ -147,7 +147,7 @@
},
{
"cell_type": "markdown",
- "id": "353d1928",
+ "id": "f32393bf",
"metadata": {},
"source": [
"These parameter values are used to define an economy of the DLE class.\n",
@@ -162,7 +162,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e1b70779",
+ "id": "3ea178ad",
"metadata": {
"hide-output": false
},
@@ -180,7 +180,7 @@
},
{
"cell_type": "markdown",
- "id": "1548195c",
+ "id": "5171e6dc",
"metadata": {},
"source": [
"The DLE class can be used to create impulse response functions for each\n",
@@ -197,7 +197,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "59e4fdf9",
+ "id": "c13a5240",
"metadata": {
"hide-output": false
},
@@ -213,7 +213,7 @@
},
{
"cell_type": "markdown",
- "id": "30e49493",
+ "id": "97629229",
"metadata": {},
"source": [
"It can be seen that the endowment shock has permanent effects on the\n",
@@ -226,7 +226,7 @@
},
{
"cell_type": "markdown",
- "id": "4942f859",
+ "id": "645e8254",
"metadata": {},
"source": [
"## Example 2: Higher Adjustment Costs\n",
@@ -242,7 +242,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "40fbe535",
+ "id": "67489b75",
"metadata": {
"hide-output": false
},
@@ -265,7 +265,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "570e29d7",
+ "id": "b45b7e8e",
"metadata": {
"hide-output": false
},
@@ -282,7 +282,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c53e585a",
+ "id": "30d793f2",
"metadata": {
"hide-output": false
},
@@ -294,7 +294,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4450c719",
+ "id": "b2f1e459",
"metadata": {
"hide-output": false
},
@@ -306,7 +306,7 @@
},
{
"cell_type": "markdown",
- "id": "d3b84268",
+ "id": "cd228dac",
"metadata": {},
"source": [
"The first graph shows that there seems to be a downward trend in both\n",
@@ -329,7 +329,7 @@
},
{
"cell_type": "markdown",
- "id": "6526ea8a",
+ "id": "7236e6d0",
"metadata": {},
"source": [
"## Example 3: Durable Consumption Goods\n",
@@ -370,7 +370,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e0ef3e9e",
+ "id": "eaeccb39",
"metadata": {
"hide-output": false
},
@@ -402,7 +402,7 @@
},
{
"cell_type": "markdown",
- "id": "44109ffd",
+ "id": "05757122",
"metadata": {},
"source": [
"In contrast to Hall’s original model of Example 1, it is now investment\n",
@@ -415,7 +415,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5e77d265",
+ "id": "20d16a44",
"metadata": {
"hide-output": false
},
@@ -431,7 +431,7 @@
},
{
"cell_type": "markdown",
- "id": "b8dbb950",
+ "id": "cfab0c51",
"metadata": {},
"source": [
"The impulse response functions confirm that consumption is now much more\n",
@@ -444,7 +444,7 @@
}
],
"metadata": {
- "date": 1723011582.3637125,
+ "date": 1723517848.3468506,
"filename": "irfs_in_hall_model.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/knowing_forecasts_of_others.ipynb b/_notebooks/knowing_forecasts_of_others.ipynb
index 59996e5d..8bcc213b 100644
--- a/_notebooks/knowing_forecasts_of_others.ipynb
+++ b/_notebooks/knowing_forecasts_of_others.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "1b821d68",
+ "id": "4facbf46",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "7a3a1ad5",
+ "id": "f0bdef66",
"metadata": {},
"source": [
"# Knowing the Forecasts of Others\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cfdd392f",
+ "id": "a52e801d",
"metadata": {
"hide-output": false
},
@@ -34,7 +34,7 @@
},
{
"cell_type": "markdown",
- "id": "0bc6f84b",
+ "id": "ee34bcf9",
"metadata": {},
"source": [
"## Introduction\n",
@@ -102,7 +102,7 @@
},
{
"cell_type": "markdown",
- "id": "6474abbb",
+ "id": "caac6fb4",
"metadata": {},
"source": [
"### A Sequence of Models\n",
@@ -135,7 +135,7 @@
},
{
"cell_type": "markdown",
- "id": "45f8ba91",
+ "id": "0b8c1203",
"metadata": {},
"source": [
"## The Setting\n",
@@ -222,7 +222,7 @@
},
{
"cell_type": "markdown",
- "id": "a0d4e19b",
+ "id": "abdf08b6",
"metadata": {},
"source": [
"## Tactics\n",
@@ -322,7 +322,7 @@
},
{
"cell_type": "markdown",
- "id": "b8ca41f9",
+ "id": "1a442fc4",
"metadata": {},
"source": [
"## Equilibrium Conditions\n",
@@ -417,7 +417,7 @@
},
{
"cell_type": "markdown",
- "id": "fe348248",
+ "id": "81f6155e",
"metadata": {},
"source": [
"### Equilibrium under perfect foresight\n",
@@ -497,7 +497,7 @@
},
{
"cell_type": "markdown",
- "id": "01e50ffb",
+ "id": "b9ee9aa9",
"metadata": {},
"source": [
"## Equilibrium with $ \\theta_t $ stochastic but observed at $ t $\n",
@@ -562,7 +562,7 @@
},
{
"cell_type": "markdown",
- "id": "2bca8da5",
+ "id": "5ebba541",
"metadata": {},
"source": [
"### Filtering"
@@ -570,7 +570,7 @@
},
{
"cell_type": "markdown",
- "id": "c3762c4a",
+ "id": "111ad19a",
"metadata": {},
"source": [
"#### One noisy signal\n",
@@ -642,7 +642,7 @@
},
{
"cell_type": "markdown",
- "id": "4b28920f",
+ "id": "d21cc213",
"metadata": {},
"source": [
"#### State-reconstruction error\n",
@@ -721,7 +721,7 @@
},
{
"cell_type": "markdown",
- "id": "b8488fb8",
+ "id": "1b3abbd3",
"metadata": {},
"source": [
"### A new state variable\n",
@@ -760,7 +760,7 @@
},
{
"cell_type": "markdown",
- "id": "cd98bc8d",
+ "id": "366bd38d",
"metadata": {},
"source": [
"### Two Noisy Signals\n",
@@ -853,7 +853,7 @@
},
{
"cell_type": "markdown",
- "id": "a4eb4f7f",
+ "id": "6e135948",
"metadata": {},
"source": [
"## Guess-and-Verify Tactic\n",
@@ -884,7 +884,7 @@
},
{
"cell_type": "markdown",
- "id": "e90fed77",
+ "id": "177149bc",
"metadata": {},
"source": [
"## Equilibrium with One Noisy Signal on $ \\theta_t $"
@@ -892,7 +892,7 @@
},
{
"cell_type": "markdown",
- "id": "0c4da3c5",
+ "id": "6fdbe4ad",
"metadata": {},
"source": [
"### Step 1: Solve for $ \\tilde{\\lambda} $ and $ \\lambda $\n",
@@ -911,7 +911,7 @@
},
{
"cell_type": "markdown",
- "id": "5454861b",
+ "id": "ac9a5883",
"metadata": {},
"source": [
"### Step 2: Solve for $ p $\n",
@@ -944,7 +944,7 @@
},
{
"cell_type": "markdown",
- "id": "e31e8b5b",
+ "id": "91a6dda9",
"metadata": {},
"source": [
"### Step 3: Represent the system using `quantecon.LinearStateSpace`\n",
@@ -1026,7 +1026,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "594fd429",
+ "id": "0ac67476",
"metadata": {
"hide-output": false
},
@@ -1045,7 +1045,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1d4a44d7",
+ "id": "99708cf8",
"metadata": {
"hide-output": false
},
@@ -1061,7 +1061,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1119c3e2",
+ "id": "4fedb8e4",
"metadata": {
"hide-output": false
},
@@ -1077,7 +1077,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3b868823",
+ "id": "79e6e356",
"metadata": {
"hide-output": false
},
@@ -1091,7 +1091,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b8d77bbc",
+ "id": "7bacbe55",
"metadata": {
"hide-output": false
},
@@ -1110,7 +1110,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5f3ae3f6",
+ "id": "d2ad1a63",
"metadata": {
"hide-output": false
},
@@ -1124,7 +1124,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "27975248",
+ "id": "9958f7e1",
"metadata": {
"hide-output": false
},
@@ -1157,7 +1157,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "de3acdcd",
+ "id": "bde45589",
"metadata": {
"hide-output": false
},
@@ -1171,7 +1171,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cb6f59fe",
+ "id": "2086bad3",
"metadata": {
"hide-output": false
},
@@ -1184,7 +1184,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d1a7f865",
+ "id": "bc627c31",
"metadata": {
"hide-output": false
},
@@ -1196,7 +1196,7 @@
},
{
"cell_type": "markdown",
- "id": "93a1d5fa",
+ "id": "bc6bbfa5",
"metadata": {},
"source": [
"### Step 4: Compute impulse response functions\n",
@@ -1208,7 +1208,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3681c75e",
+ "id": "85f2c83a",
"metadata": {
"hide-output": false
},
@@ -1231,7 +1231,7 @@
},
{
"cell_type": "markdown",
- "id": "fd3dca09",
+ "id": "fe08c40b",
"metadata": {},
"source": [
"### Step 5: Compute stationary covariance matrices and population regressions\n",
@@ -1265,7 +1265,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9232c0fa",
+ "id": "f76dbdc2",
"metadata": {
"hide-output": false
},
@@ -1290,7 +1290,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "baf2fdcd",
+ "id": "db5cfc17",
"metadata": {
"hide-output": false
},
@@ -1304,7 +1304,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "41fffd7b",
+ "id": "2daefdb8",
"metadata": {
"hide-output": false
},
@@ -1319,7 +1319,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "134bb0f9",
+ "id": "4acff875",
"metadata": {
"hide-output": false
},
@@ -1332,7 +1332,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dda22c91",
+ "id": "89e9ea06",
"metadata": {
"hide-output": false
},
@@ -1346,7 +1346,7 @@
},
{
"cell_type": "markdown",
- "id": "69e90be7",
+ "id": "46803875",
"metadata": {},
"source": [
"## Equilibrium with Two Noisy Signals on $ \\theta_t $\n",
@@ -1450,7 +1450,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e933403f",
+ "id": "6f8e6a95",
"metadata": {
"hide-output": false
},
@@ -1469,7 +1469,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1fc072e6",
+ "id": "deb0a8e5",
"metadata": {
"hide-output": false
},
@@ -1483,7 +1483,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "30e90e20",
+ "id": "94fc8c06",
"metadata": {
"hide-output": false
},
@@ -1523,7 +1523,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f63beb82",
+ "id": "067cac46",
"metadata": {
"hide-output": false
},
@@ -1537,7 +1537,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "14d2b17b",
+ "id": "48467c1b",
"metadata": {
"hide-output": false
},
@@ -1550,7 +1550,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ab2483e0",
+ "id": "f6d8a068",
"metadata": {
"hide-output": false
},
@@ -1562,7 +1562,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "287edd15",
+ "id": "fcbc1df6",
"metadata": {
"hide-output": false
},
@@ -1586,7 +1586,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ec5cfb9d",
+ "id": "285895ad",
"metadata": {
"hide-output": false
},
@@ -1611,7 +1611,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fcbd864e",
+ "id": "1ffb8b11",
"metadata": {
"hide-output": false
},
@@ -1625,7 +1625,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0ea2eb9e",
+ "id": "c9894902",
"metadata": {
"hide-output": false
},
@@ -1640,7 +1640,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "66a2a95e",
+ "id": "15078298",
"metadata": {
"hide-output": false
},
@@ -1653,7 +1653,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f839fa2c",
+ "id": "458ba362",
"metadata": {
"hide-output": false
},
@@ -1679,7 +1679,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "101d1150",
+ "id": "e7713520",
"metadata": {
"hide-output": false
},
@@ -1692,7 +1692,7 @@
},
{
"cell_type": "markdown",
- "id": "a41fbd6e",
+ "id": "dfe21da3",
"metadata": {},
"source": [
"## Key Step\n",
@@ -1710,7 +1710,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4c453bf8",
+ "id": "94c449ab",
"metadata": {
"hide-output": false
},
@@ -1729,7 +1729,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3062e2f9",
+ "id": "89b1ea92",
"metadata": {
"hide-output": false
},
@@ -1740,7 +1740,7 @@
},
{
"cell_type": "markdown",
- "id": "23a5fe76",
+ "id": "6272a29f",
"metadata": {},
"source": [
"The $ R^2 $ in this regression equals $ 1 $.\n",
@@ -1753,7 +1753,7 @@
},
{
"cell_type": "markdown",
- "id": "f83a3922",
+ "id": "8b7a1006",
"metadata": {},
"source": [
"## An observed common shock benchmark\n",
@@ -1816,7 +1816,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "32e46698",
+ "id": "a3c4cdaf",
"metadata": {
"hide-output": false
},
@@ -1833,7 +1833,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "30b7f4c0",
+ "id": "b12f1ae8",
"metadata": {
"hide-output": false
},
@@ -1846,7 +1846,7 @@
},
{
"cell_type": "markdown",
- "id": "57eebb71",
+ "id": "565a6e6d",
"metadata": {},
"source": [
"Now let’s form and plot an impulse response function of $ k_t^i $ to shocks $ v_t $ to $ \\theta_{t+1} $"
@@ -1855,7 +1855,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "66cbd547",
+ "id": "4232ad6e",
"metadata": {
"hide-output": false
},
@@ -1877,7 +1877,7 @@
},
{
"cell_type": "markdown",
- "id": "9eb60d1a",
+ "id": "c1c7fc88",
"metadata": {},
"source": [
"## Comparison of All Signal Structures\n",
@@ -1892,7 +1892,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2dca1a29",
+ "id": "9326dd66",
"metadata": {
"hide-output": false
},
@@ -1916,7 +1916,7 @@
},
{
"cell_type": "markdown",
- "id": "25131b18",
+ "id": "145180af",
"metadata": {},
"source": [
"The three panels in the graph above show that\n",
@@ -1943,7 +1943,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8add4d00",
+ "id": "f26aa991",
"metadata": {
"hide-output": false
},
@@ -1956,7 +1956,7 @@
},
{
"cell_type": "markdown",
- "id": "01c98bc6",
+ "id": "e4204cd7",
"metadata": {},
"source": [
"Kalman gains for the two\n",
@@ -1966,7 +1966,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "758667d7",
+ "id": "be60fcf2",
"metadata": {
"hide-output": false
},
@@ -1979,7 +1979,7 @@
},
{
"cell_type": "markdown",
- "id": "caa9c553",
+ "id": "6957253c",
"metadata": {},
"source": [
"Another lesson that comes from the preceding three-panel graph is that the presence of iid noise\n",
@@ -1988,7 +1988,7 @@
},
{
"cell_type": "markdown",
- "id": "e1c94171",
+ "id": "8e28ced1",
"metadata": {},
"source": [
"## Notes on History of the Problem\n",
@@ -2048,7 +2048,7 @@
},
{
"cell_type": "markdown",
- "id": "d277fd32",
+ "id": "50983852",
"metadata": {},
"source": [
"### Further historical remarks\n",
@@ -2116,7 +2116,7 @@
}
],
"metadata": {
- "date": 1723011582.4512587,
+ "date": 1723517848.442678,
"filename": "knowing_forecasts_of_others.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/lqramsey.ipynb b/_notebooks/lqramsey.ipynb
index 5f98283e..5d0bc68b 100644
--- a/_notebooks/lqramsey.ipynb
+++ b/_notebooks/lqramsey.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "a174a8e0",
+ "id": "690df557",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "f216006c",
+ "id": "fd6d7b98",
"metadata": {},
"source": [
"# Optimal Taxation in an LQ Economy\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "348cc16d",
+ "id": "3b6fd453",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "5daf67b6",
+ "id": "41a2689a",
"metadata": {},
"source": [
"## Overview\n",
@@ -73,7 +73,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "af680342",
+ "id": "6e0ff6f7",
"metadata": {
"hide-output": false
},
@@ -91,7 +91,7 @@
},
{
"cell_type": "markdown",
- "id": "819db734",
+ "id": "171e55f7",
"metadata": {},
"source": [
"### Model Features\n",
@@ -104,7 +104,7 @@
},
{
"cell_type": "markdown",
- "id": "ce3e35c8",
+ "id": "e98316b8",
"metadata": {},
"source": [
"## The Ramsey Problem\n",
@@ -114,7 +114,7 @@
},
{
"cell_type": "markdown",
- "id": "7dcb72a8",
+ "id": "d84ed7e0",
"metadata": {},
"source": [
"### Technology\n",
@@ -130,7 +130,7 @@
},
{
"cell_type": "markdown",
- "id": "e0d37d8e",
+ "id": "4e7527fa",
"metadata": {},
"source": [
"### Households\n",
@@ -186,7 +186,7 @@
},
{
"cell_type": "markdown",
- "id": "368c479a",
+ "id": "f2d86a15",
"metadata": {},
"source": [
"### Government\n",
@@ -202,7 +202,7 @@
},
{
"cell_type": "markdown",
- "id": "32f20551",
+ "id": "d7321ccc",
"metadata": {},
"source": [
"### Exogenous Variables\n",
@@ -229,7 +229,7 @@
},
{
"cell_type": "markdown",
- "id": "3516d914",
+ "id": "9298cbf2",
"metadata": {},
"source": [
"### Feasibility\n",
@@ -247,7 +247,7 @@
},
{
"cell_type": "markdown",
- "id": "a8bffdc2",
+ "id": "e7fec7f0",
"metadata": {},
"source": [
"### Government Budget Constraint\n",
@@ -264,7 +264,7 @@
},
{
"cell_type": "markdown",
- "id": "09666dc8",
+ "id": "5321ba56",
"metadata": {},
"source": [
"### Equilibrium\n",
@@ -298,7 +298,7 @@
},
{
"cell_type": "markdown",
- "id": "4e657d98",
+ "id": "b6cc0915",
"metadata": {},
"source": [
"### Solution\n",
@@ -419,7 +419,7 @@
},
{
"cell_type": "markdown",
- "id": "7da247f7",
+ "id": "53fe5e88",
"metadata": {},
"source": [
"### Computing the Quadratic Term\n",
@@ -492,7 +492,7 @@
},
{
"cell_type": "markdown",
- "id": "0f332efb",
+ "id": "23876417",
"metadata": {},
"source": [
"### Finite State Markov Case\n",
@@ -534,7 +534,7 @@
},
{
"cell_type": "markdown",
- "id": "7abce316",
+ "id": "d4af0bbb",
"metadata": {},
"source": [
"### Other Variables\n",
@@ -608,7 +608,7 @@
},
{
"cell_type": "markdown",
- "id": "2f5eb5c8",
+ "id": "36581c53",
"metadata": {},
"source": [
"### A Martingale\n",
@@ -672,7 +672,7 @@
},
{
"cell_type": "markdown",
- "id": "d23be1db",
+ "id": "d6faf75e",
"metadata": {},
"source": [
"## Implementation\n",
@@ -689,7 +689,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cae77329",
+ "id": "ee0a2990",
"metadata": {
"hide-output": false
},
@@ -957,7 +957,7 @@
},
{
"cell_type": "markdown",
- "id": "cfa3d54a",
+ "id": "0b4db824",
"metadata": {},
"source": [
"### Comments on the Code\n",
@@ -985,7 +985,7 @@
},
{
"cell_type": "markdown",
- "id": "74475c3f",
+ "id": "40a31278",
"metadata": {},
"source": [
"## Examples\n",
@@ -998,7 +998,7 @@
},
{
"cell_type": "markdown",
- "id": "f7c45135",
+ "id": "d8cf4a08",
"metadata": {},
"source": [
"### The Continuous Case\n",
@@ -1025,7 +1025,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2a647d01",
+ "id": "e98d07ed",
"metadata": {
"hide-output": false
},
@@ -1053,7 +1053,7 @@
},
{
"cell_type": "markdown",
- "id": "35108d37",
+ "id": "763e9791",
"metadata": {},
"source": [
"The legends on the figures indicate the variables being tracked.\n",
@@ -1065,7 +1065,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "45040b98",
+ "id": "182e0312",
"metadata": {
"hide-output": false
},
@@ -1076,7 +1076,7 @@
},
{
"cell_type": "markdown",
- "id": "81b59ff0",
+ "id": "b2b52b84",
"metadata": {},
"source": [
"### The Discrete Case\n",
@@ -1087,7 +1087,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "786b6333",
+ "id": "340392cc",
"metadata": {
"hide-output": false
},
@@ -1122,7 +1122,7 @@
},
{
"cell_type": "markdown",
- "id": "e1cb41d4",
+ "id": "770c0ffb",
"metadata": {},
"source": [
"The call `gen_fig_2(path)` generates"
@@ -1131,7 +1131,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "868dae06",
+ "id": "81c6b383",
"metadata": {
"hide-output": false
},
@@ -1142,7 +1142,7 @@
},
{
"cell_type": "markdown",
- "id": "30f6afab",
+ "id": "21855573",
"metadata": {},
"source": [
"## Exercises\n",
@@ -1153,7 +1153,7 @@
},
{
"cell_type": "markdown",
- "id": "7fa455e1",
+ "id": "284a8df3",
"metadata": {},
"source": [
"## Exercise 12.1\n",
@@ -1171,7 +1171,7 @@
},
{
"cell_type": "markdown",
- "id": "346bdccc",
+ "id": "e1f64097",
"metadata": {},
"source": [
"## Solution to[ Exercise 12.1](https://python-advanced.quantecon.org/#lq_ex1)"
@@ -1180,7 +1180,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "94a60f1a",
+ "id": "ea926b9a",
"metadata": {
"hide-output": false
},
@@ -1214,7 +1214,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d7f271c0",
+ "id": "e86f8f3b",
"metadata": {
"hide-output": false
},
@@ -1225,7 +1225,7 @@
}
],
"metadata": {
- "date": 1723011582.490169,
+ "date": 1723517848.4833317,
"filename": "lqramsey.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/lu_tricks.ipynb b/_notebooks/lu_tricks.ipynb
index d696d134..86953294 100644
--- a/_notebooks/lu_tricks.ipynb
+++ b/_notebooks/lu_tricks.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "4495b227",
+ "id": "7bb0ccaf",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "4830937d",
+ "id": "6919139c",
"metadata": {},
"source": [
"# Classical Control with Linear Algebra"
@@ -19,7 +19,7 @@
},
{
"cell_type": "markdown",
- "id": "129f94fd",
+ "id": "405bd0f1",
"metadata": {},
"source": [
"## Overview\n",
@@ -60,7 +60,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6322c5df",
+ "id": "8948f350",
"metadata": {
"hide-output": false
},
@@ -72,7 +72,7 @@
},
{
"cell_type": "markdown",
- "id": "8686a54c",
+ "id": "0257dcc3",
"metadata": {},
"source": [
"### References\n",
@@ -82,7 +82,7 @@
},
{
"cell_type": "markdown",
- "id": "774b6dcd",
+ "id": "7a135048",
"metadata": {},
"source": [
"## A Control Problem\n",
@@ -123,7 +123,7 @@
},
{
"cell_type": "markdown",
- "id": "6ef58432",
+ "id": "9697d98b",
"metadata": {},
"source": [
"### Example\n",
@@ -165,7 +165,7 @@
},
{
"cell_type": "markdown",
- "id": "d81c9222",
+ "id": "b8440ab0",
"metadata": {},
"source": [
"## Finite Horizon Theory\n",
@@ -295,7 +295,7 @@
},
{
"cell_type": "markdown",
- "id": "a2191996",
+ "id": "c7b51bdd",
"metadata": {},
"source": [
"### Matrix Methods\n",
@@ -305,7 +305,7 @@
},
{
"cell_type": "markdown",
- "id": "9e7f6e45",
+ "id": "8e885691",
"metadata": {},
"source": [
"#### A Single Lag Term\n",
@@ -404,7 +404,7 @@
},
{
"cell_type": "markdown",
- "id": "ca99d3d3",
+ "id": "48cb8eee",
"metadata": {},
"source": [
"#### An Alternative Representation\n",
@@ -497,7 +497,7 @@
},
{
"cell_type": "markdown",
- "id": "54069917",
+ "id": "8585b0bb",
"metadata": {},
"source": [
"#### Additional Lag Terms\n",
@@ -616,7 +616,7 @@
},
{
"cell_type": "markdown",
- "id": "7a07805d",
+ "id": "45c261ca",
"metadata": {},
"source": [
"## Infinite Horizon Limit\n",
@@ -846,7 +846,7 @@
},
{
"cell_type": "markdown",
- "id": "c2f99f1f",
+ "id": "9014458b",
"metadata": {},
"source": [
"## Undiscounted Problems\n",
@@ -888,7 +888,7 @@
},
{
"cell_type": "markdown",
- "id": "59e8c3b8",
+ "id": "c0893dc9",
"metadata": {},
"source": [
"### Transforming Discounted to Undiscounted Problem\n",
@@ -973,7 +973,7 @@
},
{
"cell_type": "markdown",
- "id": "ee82c04e",
+ "id": "d0d54547",
"metadata": {},
"source": [
"## Implementation\n",
@@ -985,7 +985,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "847d65b9",
+ "id": "d014ead8",
"metadata": {
"hide-output": false
},
@@ -1301,7 +1301,7 @@
},
{
"cell_type": "markdown",
- "id": "76916250",
+ "id": "74cddf0a",
"metadata": {},
"source": [
"### Example\n",
@@ -1334,7 +1334,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f5d8ae29",
+ "id": "634ba7b6",
"metadata": {
"hide-output": false
},
@@ -1374,7 +1374,7 @@
},
{
"cell_type": "markdown",
- "id": "6fb8e3d9",
+ "id": "71bef2fd",
"metadata": {},
"source": [
"Here’s what happens when we change $ \\gamma $ to 5.0"
@@ -1383,7 +1383,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5329f299",
+ "id": "4a13b2fb",
"metadata": {
"hide-output": false
},
@@ -1394,7 +1394,7 @@
},
{
"cell_type": "markdown",
- "id": "30e4a36d",
+ "id": "c350f389",
"metadata": {},
"source": [
"And here’s $ \\gamma = 10 $"
@@ -1403,7 +1403,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e9669fbf",
+ "id": "fa7d7fdf",
"metadata": {
"hide-output": false
},
@@ -1414,7 +1414,7 @@
},
{
"cell_type": "markdown",
- "id": "160a05e1",
+ "id": "e4413ac8",
"metadata": {},
"source": [
"## Exercises"
@@ -1422,7 +1422,7 @@
},
{
"cell_type": "markdown",
- "id": "e57dbd73",
+ "id": "843a12d9",
"metadata": {},
"source": [
"## Exercise 31.1\n",
@@ -1468,7 +1468,7 @@
},
{
"cell_type": "markdown",
- "id": "63700671",
+ "id": "2b43390b",
"metadata": {},
"source": [
"## Exercise 31.2\n",
@@ -1492,7 +1492,7 @@
},
{
"cell_type": "markdown",
- "id": "e223dcef",
+ "id": "8db97143",
"metadata": {},
"source": [
"## Exercise 31.3\n",
@@ -1513,7 +1513,7 @@
},
{
"cell_type": "markdown",
- "id": "4fa07411",
+ "id": "4c6bfffe",
"metadata": {},
"source": [
"## Exercise 31.4\n",
@@ -1533,7 +1533,7 @@
}
],
"metadata": {
- "date": 1723011582.537286,
+ "date": 1723517848.5337548,
"filename": "lu_tricks.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/lucas_asset_pricing_dles.ipynb b/_notebooks/lucas_asset_pricing_dles.ipynb
index 5428e50e..8cc6dc67 100644
--- a/_notebooks/lucas_asset_pricing_dles.ipynb
+++ b/_notebooks/lucas_asset_pricing_dles.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "93ae9de3",
+ "id": "4fa3b627",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "d33197bd",
+ "id": "63aee182",
"metadata": {},
"source": [
"# Lucas Asset Pricing Using DLE\n",
@@ -27,7 +27,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3d7f9318",
+ "id": "3aeb2d34",
"metadata": {
"hide-output": false
},
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "ed15498b",
+ "id": "4c98868b",
"metadata": {},
"source": [
"This lecture uses the DLE class to price payout\n",
@@ -58,7 +58,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1749a50e",
+ "id": "1981c4e4",
"metadata": {
"hide-output": false
},
@@ -71,7 +71,7 @@
},
{
"cell_type": "markdown",
- "id": "947f1b3c",
+ "id": "8f9edb2b",
"metadata": {},
"source": [
"We use a linear-quadratic version of an economy that Lucas (1978) [[Lucas, 1978](https://python-advanced.quantecon.org/zreferences.html#id174)] used\n",
@@ -155,7 +155,7 @@
},
{
"cell_type": "markdown",
- "id": "4f75c5ca",
+ "id": "8b473663",
"metadata": {},
"source": [
"## Asset Pricing Equations\n",
@@ -189,7 +189,7 @@
},
{
"cell_type": "markdown",
- "id": "469b14bd",
+ "id": "9219bd73",
"metadata": {},
"source": [
"## Asset Pricing Simulations"
@@ -198,7 +198,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fadc485a",
+ "id": "12e72a52",
"metadata": {
"hide-output": false
},
@@ -235,7 +235,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "03fd2f20",
+ "id": "d131ca14",
"metadata": {
"hide-output": false
},
@@ -246,7 +246,7 @@
},
{
"cell_type": "markdown",
- "id": "1290a90c",
+ "id": "a5bcd47b",
"metadata": {},
"source": [
"After specifying a “Pay” matrix, we simulate the economy.\n",
@@ -258,7 +258,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b5326551",
+ "id": "77b94840",
"metadata": {
"hide-output": false
},
@@ -269,7 +269,7 @@
},
{
"cell_type": "markdown",
- "id": "ccdb1788",
+ "id": "22671f55",
"metadata": {},
"source": [
"The graph below plots the price of this claim over time:"
@@ -278,7 +278,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3c85b6e4",
+ "id": "14420447",
"metadata": {
"hide-output": false
},
@@ -292,7 +292,7 @@
},
{
"cell_type": "markdown",
- "id": "a36942bd",
+ "id": "565450e5",
"metadata": {},
"source": [
"The next plot displays the realized gross rate of return on this “Lucas\n",
@@ -302,7 +302,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6bad6098",
+ "id": "7e330c5b",
"metadata": {
"hide-output": false
},
@@ -318,7 +318,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6f8c9d72",
+ "id": "fa144f48",
"metadata": {
"hide-output": false
},
@@ -329,7 +329,7 @@
},
{
"cell_type": "markdown",
- "id": "d1babcaf",
+ "id": "9cc2d4a1",
"metadata": {},
"source": [
"Above we have also calculated the correlation coefficient between these\n",
@@ -343,7 +343,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c45db7f4",
+ "id": "39b7b266",
"metadata": {
"hide-output": false
},
@@ -358,7 +358,7 @@
},
{
"cell_type": "markdown",
- "id": "bb140670",
+ "id": "dde5e219",
"metadata": {},
"source": [
"From the above plot, we can see the tendency of the term structure to\n",
@@ -376,7 +376,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "df2b5ad2",
+ "id": "f0c02984",
"metadata": {
"hide-output": false
},
@@ -394,7 +394,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bd569ada",
+ "id": "ec1e97c6",
"metadata": {
"hide-output": false
},
@@ -410,7 +410,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f87b6c6c",
+ "id": "07131935",
"metadata": {
"hide-output": false
},
@@ -421,7 +421,7 @@
},
{
"cell_type": "markdown",
- "id": "d974d759",
+ "id": "0b188a19",
"metadata": {},
"source": [
"The correlation between these two gross rates is now more negative.\n",
@@ -433,7 +433,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "493b786a",
+ "id": "eef49482",
"metadata": {
"hide-output": false
},
@@ -448,7 +448,7 @@
},
{
"cell_type": "markdown",
- "id": "9d127a20",
+ "id": "816c2e01",
"metadata": {},
"source": [
"We can see the tendency of the term structure to slope up when rates are\n",
@@ -458,7 +458,7 @@
}
],
"metadata": {
- "date": 1723011582.7654545,
+ "date": 1723517848.5495057,
"filename": "lucas_asset_pricing_dles.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/lucas_model.ipynb b/_notebooks/lucas_model.ipynb
index c272c111..590ac0a3 100644
--- a/_notebooks/lucas_model.ipynb
+++ b/_notebooks/lucas_model.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "34bde94c",
+ "id": "9833ebcc",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "9df6694b",
+ "id": "1d381859",
"metadata": {},
"source": [
"# Asset Pricing II: The Lucas Asset Pricing Model\n",
@@ -22,7 +22,7 @@
},
{
"cell_type": "markdown",
- "id": "883c321d",
+ "id": "4afc051c",
"metadata": {},
"source": [
"## Overview\n",
@@ -45,7 +45,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6ae22c5a",
+ "id": "d9bad3ad",
"metadata": {
"hide-output": false
},
@@ -59,7 +59,7 @@
},
{
"cell_type": "markdown",
- "id": "44ab4cee",
+ "id": "b4edf0c8",
"metadata": {},
"source": [
"## The Lucas Model\n",
@@ -81,7 +81,7 @@
},
{
"cell_type": "markdown",
- "id": "59dbe4ff",
+ "id": "172098b6",
"metadata": {},
"source": [
"### Basic Setup\n",
@@ -91,7 +91,7 @@
},
{
"cell_type": "markdown",
- "id": "5c59420f",
+ "id": "ac09c19b",
"metadata": {},
"source": [
"#### Assets\n",
@@ -121,7 +121,7 @@
},
{
"cell_type": "markdown",
- "id": "ccaa6978",
+ "id": "15ac5c2a",
"metadata": {},
"source": [
"#### Consumers\n",
@@ -145,7 +145,7 @@
},
{
"cell_type": "markdown",
- "id": "77157071",
+ "id": "4e4fcec1",
"metadata": {},
"source": [
"### Pricing a Lucas Tree\n",
@@ -184,7 +184,7 @@
},
{
"cell_type": "markdown",
- "id": "091e07c0",
+ "id": "717d036d",
"metadata": {},
"source": [
"#### The Dynamic Program\n",
@@ -242,7 +242,7 @@
},
{
"cell_type": "markdown",
- "id": "f83ba824",
+ "id": "e3e6a6e9",
"metadata": {},
"source": [
"#### Next Steps\n",
@@ -261,7 +261,7 @@
},
{
"cell_type": "markdown",
- "id": "27269dab",
+ "id": "ca60fdba",
"metadata": {},
"source": [
"#### Equilibrium Constraints\n",
@@ -280,7 +280,7 @@
},
{
"cell_type": "markdown",
- "id": "6dce910f",
+ "id": "e8fef6e4",
"metadata": {},
"source": [
"#### The Equilibrium Price Function\n",
@@ -326,7 +326,7 @@
},
{
"cell_type": "markdown",
- "id": "ebe23130",
+ "id": "82aff839",
"metadata": {},
"source": [
"### Solving the Model\n",
@@ -342,7 +342,7 @@
},
{
"cell_type": "markdown",
- "id": "7e7680aa",
+ "id": "ea4c120a",
"metadata": {},
"source": [
"#### Setting up the Problem\n",
@@ -392,7 +392,7 @@
},
{
"cell_type": "markdown",
- "id": "e1e36320",
+ "id": "81860bc0",
"metadata": {},
"source": [
"#### A Little Fixed Point Theory\n",
@@ -454,7 +454,7 @@
},
{
"cell_type": "markdown",
- "id": "14ffb071",
+ "id": "fb2b790c",
"metadata": {},
"source": [
"### Computation – An Example\n",
@@ -475,7 +475,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5ed643e3",
+ "id": "6e876870",
"metadata": {
"hide-output": false
},
@@ -514,7 +514,7 @@
},
{
"cell_type": "markdown",
- "id": "c2781d6c",
+ "id": "db31ca38",
"metadata": {},
"source": [
"The following function takes an instance of the `LucasTree` and generates a\n",
@@ -524,7 +524,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "97d7fbc0",
+ "id": "ee415248",
"metadata": {
"hide-output": false
},
@@ -566,7 +566,7 @@
},
{
"cell_type": "markdown",
- "id": "1c451f6e",
+ "id": "a8f77b22",
"metadata": {},
"source": [
"To solve the model, we write a function that iterates using the Lucas operator\n",
@@ -576,7 +576,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "83f46f31",
+ "id": "5fe055b9",
"metadata": {
"hide-output": false
},
@@ -612,7 +612,7 @@
},
{
"cell_type": "markdown",
- "id": "4e3ed67e",
+ "id": "c7589292",
"metadata": {},
"source": [
"Solving the model and plotting the resulting price function"
@@ -621,7 +621,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a448de49",
+ "id": "d40f1222",
"metadata": {
"hide-output": false
},
@@ -640,7 +640,7 @@
},
{
"cell_type": "markdown",
- "id": "23d67d56",
+ "id": "cb7ba843",
"metadata": {},
"source": [
"We see that the price is increasing, even if we remove all serial correlation from the endowment process.\n",
@@ -666,7 +666,7 @@
},
{
"cell_type": "markdown",
- "id": "a1eadf83",
+ "id": "0521540d",
"metadata": {},
"source": [
"## Exercises\n",
@@ -677,7 +677,7 @@
},
{
"cell_type": "markdown",
- "id": "6a9db49a",
+ "id": "ead7ce3f",
"metadata": {},
"source": [
"## Exercise 34.1\n",
@@ -687,7 +687,7 @@
},
{
"cell_type": "markdown",
- "id": "bd67b53e",
+ "id": "029e1047",
"metadata": {},
"source": [
"## Solution to[ Exercise 34.1](https://python-advanced.quantecon.org/#lucas_ex1)"
@@ -696,7 +696,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "29dd190c",
+ "id": "55491fd7",
"metadata": {
"hide-output": false
},
@@ -718,7 +718,7 @@
}
],
"metadata": {
- "date": 1723011582.7893145,
+ "date": 1723517848.5744672,
"filename": "lucas_model.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/markov_jump_lq.ipynb b/_notebooks/markov_jump_lq.ipynb
index 88b4c068..e0275725 100644
--- a/_notebooks/markov_jump_lq.ipynb
+++ b/_notebooks/markov_jump_lq.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "5768879d",
+ "id": "c37267e5",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "b19bb330",
+ "id": "1249a0bc",
"metadata": {},
"source": [
"# Markov Jump Linear Quadratic Dynamic Programming\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7ef18b96",
+ "id": "7cf9badb",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "2df5fab8",
+ "id": "c9f7039d",
"metadata": {},
"source": [
"## Overview\n",
@@ -75,7 +75,7 @@
},
{
"cell_type": "markdown",
- "id": "a93c6337",
+ "id": "b295a0e8",
"metadata": {},
"source": [
"## Review of useful LQ dynamic programming formulas\n",
@@ -149,7 +149,7 @@
},
{
"cell_type": "markdown",
- "id": "763098a2",
+ "id": "4d69c0f4",
"metadata": {},
"source": [
"## Linked Riccati equations for Markov LQ dynamic programming\n",
@@ -262,7 +262,7 @@
},
{
"cell_type": "markdown",
- "id": "9f5fb81c",
+ "id": "4b289e73",
"metadata": {},
"source": [
"## Applications\n",
@@ -275,7 +275,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0e548814",
+ "id": "261d031d",
"metadata": {
"hide-output": false
},
@@ -290,7 +290,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "74bfa7b1",
+ "id": "a22dc604",
"metadata": {
"hide-output": false
},
@@ -302,7 +302,7 @@
},
{
"cell_type": "markdown",
- "id": "8b345972",
+ "id": "5e96c7fc",
"metadata": {},
"source": [
"## Example 1\n",
@@ -372,7 +372,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0efb6896",
+ "id": "66ff49eb",
"metadata": {
"hide-output": false
},
@@ -417,7 +417,7 @@
},
{
"cell_type": "markdown",
- "id": "0716e3f4",
+ "id": "3196e17d",
"metadata": {},
"source": [
"The continuous part of the state $ x_t $ consists of two variables,\n",
@@ -427,7 +427,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0d6d53a9",
+ "id": "d0f31612",
"metadata": {
"hide-output": false
},
@@ -438,7 +438,7 @@
},
{
"cell_type": "markdown",
- "id": "e3a6b31a",
+ "id": "2ee7a28e",
"metadata": {},
"source": [
"We start with a Markov transition matrix that makes the Markov state be\n",
@@ -478,7 +478,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "38bf66f9",
+ "id": "cd46d402",
"metadata": {
"hide-output": false
},
@@ -492,7 +492,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cf3d7cbc",
+ "id": "1d80cfc8",
"metadata": {
"hide-output": false
},
@@ -505,7 +505,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d811e43b",
+ "id": "2e170e40",
"metadata": {
"hide-output": false
},
@@ -519,7 +519,7 @@
},
{
"cell_type": "markdown",
- "id": "f6d9de2d",
+ "id": "ca923d98",
"metadata": {},
"source": [
"Let’s look at the value function matrices and the decision rules for\n",
@@ -529,7 +529,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b2ad2795",
+ "id": "5f543834",
"metadata": {
"hide-output": false
},
@@ -542,7 +542,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ce08f369",
+ "id": "cebb2f01",
"metadata": {
"hide-output": false
},
@@ -555,7 +555,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7705b5c6",
+ "id": "97f2f027",
"metadata": {
"hide-output": false
},
@@ -567,7 +567,7 @@
},
{
"cell_type": "markdown",
- "id": "5a682bde",
+ "id": "b4eb0663",
"metadata": {},
"source": [
"Now we’ll plot the decision rules and see if they make sense"
@@ -576,7 +576,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4c6a158f",
+ "id": "1d69d9ff",
"metadata": {
"hide-output": false
},
@@ -608,7 +608,7 @@
},
{
"cell_type": "markdown",
- "id": "00506129",
+ "id": "39b75646",
"metadata": {},
"source": [
"The above graph plots $ k_{t+1}= k_t + u_t = k_t - F x_t $ as an affine\n",
@@ -634,7 +634,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1d7737b6",
+ "id": "b018ee46",
"metadata": {
"hide-output": false
},
@@ -655,7 +655,7 @@
},
{
"cell_type": "markdown",
- "id": "78625f73",
+ "id": "88a908a9",
"metadata": {},
"source": [
"Now we’ll depart from the preceding transition matrix that made the\n",
@@ -674,7 +674,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d214ee70",
+ "id": "90e1ffdd",
"metadata": {
"hide-output": false
},
@@ -692,7 +692,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "30f7feb8",
+ "id": "1f696094",
"metadata": {
"hide-output": false
},
@@ -709,7 +709,7 @@
},
{
"cell_type": "markdown",
- "id": "26558532",
+ "id": "0006f0f8",
"metadata": {},
"source": [
"We can plot optimal decision rules associated with different\n",
@@ -719,7 +719,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "41bbc955",
+ "id": "2e7192a8",
"metadata": {
"hide-output": false
},
@@ -742,7 +742,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d25427d0",
+ "id": "52fc774c",
"metadata": {
"hide-output": false
},
@@ -762,7 +762,7 @@
},
{
"cell_type": "markdown",
- "id": "bb9dcec0",
+ "id": "6a7dd8da",
"metadata": {},
"source": [
"Notice how the decision rules’ constants and slopes behave as functions\n",
@@ -787,7 +787,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5cb238fe",
+ "id": "2ab7758f",
"metadata": {
"hide-output": false
},
@@ -804,7 +804,7 @@
},
{
"cell_type": "markdown",
- "id": "a0feacdc",
+ "id": "c56d94d5",
"metadata": {},
"source": [
"We can plot optimal decision rules for different $ \\lambda $ and\n",
@@ -814,7 +814,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "564cba68",
+ "id": "a50f38a9",
"metadata": {
"hide-output": false
},
@@ -844,7 +844,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c75bdb50",
+ "id": "a57fb53e",
"metadata": {
"hide-output": false
},
@@ -866,7 +866,7 @@
},
{
"cell_type": "markdown",
- "id": "6185e977",
+ "id": "779a4086",
"metadata": {},
"source": [
"The following code defines a wrapper function that computes optimal\n",
@@ -876,7 +876,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "71c67eb9",
+ "id": "3ec0a41f",
"metadata": {
"hide-output": false
},
@@ -977,7 +977,7 @@
},
{
"cell_type": "markdown",
- "id": "19b863ac",
+ "id": "f484dfbe",
"metadata": {},
"source": [
"To illustrate the code with another example, we shall set\n",
@@ -1029,7 +1029,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "12a53e17",
+ "id": "eb5362e5",
"metadata": {
"hide-output": false
},
@@ -1040,7 +1040,7 @@
},
{
"cell_type": "markdown",
- "id": "cddd8961",
+ "id": "8bfcc353",
"metadata": {},
"source": [
"Set $ f_{1,{s_t}} $ and $ d_{s_t} $ as constant functions and\n",
@@ -1053,7 +1053,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "80a3261d",
+ "id": "d35ba263",
"metadata": {
"hide-output": false
},
@@ -1064,7 +1064,7 @@
},
{
"cell_type": "markdown",
- "id": "3a95eae8",
+ "id": "f6401b7e",
"metadata": {},
"source": [
"## Example 2\n",
@@ -1134,7 +1134,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "74bd47e1",
+ "id": "7d739a34",
"metadata": {
"hide-output": false
},
@@ -1187,7 +1187,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cee5e419",
+ "id": "9655e781",
"metadata": {
"hide-output": false
},
@@ -1198,7 +1198,7 @@
},
{
"cell_type": "markdown",
- "id": "75ead5b6",
+ "id": "1304a227",
"metadata": {},
"source": [
"Only $ d_{s_t} $ depends on $ s_t $."
@@ -1207,7 +1207,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e7ce5545",
+ "id": "e64ab84e",
"metadata": {
"hide-output": false
},
@@ -1218,7 +1218,7 @@
},
{
"cell_type": "markdown",
- "id": "7a1d2fcd",
+ "id": "cd9714a3",
"metadata": {},
"source": [
"Only $ f_{1,{s_t}} $ depends on $ s_t $."
@@ -1227,7 +1227,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e14426d1",
+ "id": "73b0d179",
"metadata": {
"hide-output": false
},
@@ -1238,7 +1238,7 @@
},
{
"cell_type": "markdown",
- "id": "2ee7b33e",
+ "id": "650551cf",
"metadata": {},
"source": [
"Only $ f_{2,{s_t}} $ depends on $ s_t $."
@@ -1247,7 +1247,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "42a48ad4",
+ "id": "77ed613c",
"metadata": {
"hide-output": false
},
@@ -1258,7 +1258,7 @@
},
{
"cell_type": "markdown",
- "id": "cc173250",
+ "id": "08fa4f46",
"metadata": {},
"source": [
"Only $ \\alpha_0(s_t) $ depends on $ s_t $."
@@ -1267,7 +1267,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "77a37b66",
+ "id": "89d849a3",
"metadata": {
"hide-output": false
},
@@ -1278,7 +1278,7 @@
},
{
"cell_type": "markdown",
- "id": "c5bcca7b",
+ "id": "ae2ed4c0",
"metadata": {},
"source": [
"Only $ \\rho_{s_t} $ depends on $ s_t $."
@@ -1287,7 +1287,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a9df7a77",
+ "id": "b9bb3d09",
"metadata": {
"hide-output": false
},
@@ -1298,7 +1298,7 @@
},
{
"cell_type": "markdown",
- "id": "469523b1",
+ "id": "2e70842c",
"metadata": {},
"source": [
"Only $ \\sigma_{s_t} $ depends on $ s_t $."
@@ -1307,7 +1307,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "debf315d",
+ "id": "7f5637cb",
"metadata": {
"hide-output": false
},
@@ -1318,7 +1318,7 @@
},
{
"cell_type": "markdown",
- "id": "1dec6fc5",
+ "id": "5cd4fcec",
"metadata": {},
"source": [
"## More examples\n",
@@ -1333,7 +1333,7 @@
}
],
"metadata": {
- "date": 1723011582.8311577,
+ "date": 1723517848.6165621,
"filename": "markov_jump_lq.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/matsuyama.ipynb b/_notebooks/matsuyama.ipynb
index 2f71ac28..e2f17bc2 100644
--- a/_notebooks/matsuyama.ipynb
+++ b/_notebooks/matsuyama.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "88a901d2",
+ "id": "2e3ba0ae",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "cf7b2141",
+ "id": "b3120d9c",
"metadata": {},
"source": [
"# Globalization and Cycles"
@@ -19,7 +19,7 @@
},
{
"cell_type": "markdown",
- "id": "9a79cf23",
+ "id": "3e126508",
"metadata": {},
"source": [
"## Overview\n",
@@ -44,7 +44,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "03384489",
+ "id": "4bbd9fb4",
"metadata": {
"hide-output": false
},
@@ -58,7 +58,7 @@
},
{
"cell_type": "markdown",
- "id": "5f0b17e3",
+ "id": "047c8515",
"metadata": {},
"source": [
"### Background\n",
@@ -74,7 +74,7 @@
},
{
"cell_type": "markdown",
- "id": "2d745605",
+ "id": "c47dd3bd",
"metadata": {},
"source": [
"## Key Ideas\n",
@@ -84,7 +84,7 @@
},
{
"cell_type": "markdown",
- "id": "a0ecbefb",
+ "id": "42a26429",
"metadata": {},
"source": [
"### Innovation Cycles\n",
@@ -112,7 +112,7 @@
},
{
"cell_type": "markdown",
- "id": "4e285cf1",
+ "id": "406a87b1",
"metadata": {},
"source": [
"### Synchronization\n",
@@ -128,7 +128,7 @@
},
{
"cell_type": "markdown",
- "id": "8c6df7ad",
+ "id": "c75c1486",
"metadata": {},
"source": [
"## Model\n",
@@ -176,7 +176,7 @@
},
{
"cell_type": "markdown",
- "id": "86b31f4d",
+ "id": "21fb3d42",
"metadata": {},
"source": [
"### Prices\n",
@@ -266,7 +266,7 @@
},
{
"cell_type": "markdown",
- "id": "fb95617a",
+ "id": "440cd1ae",
"metadata": {},
"source": [
"### New Varieties\n",
@@ -298,7 +298,7 @@
},
{
"cell_type": "markdown",
- "id": "bb6b5908",
+ "id": "c3dd0a33",
"metadata": {},
"source": [
"### Law of Motion\n",
@@ -377,7 +377,7 @@
},
{
"cell_type": "markdown",
- "id": "746bae50",
+ "id": "356ffa01",
"metadata": {},
"source": [
"## Simulation\n",
@@ -404,7 +404,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "33962199",
+ "id": "4b91a1c7",
"metadata": {
"hide-output": false
},
@@ -717,7 +717,7 @@
},
{
"cell_type": "markdown",
- "id": "9a0ce0a8",
+ "id": "ae040dce",
"metadata": {},
"source": [
"### Time Series of Firm Measures\n",
@@ -734,7 +734,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6cbe4599",
+ "id": "9dc71a35",
"metadata": {
"hide-output": false
},
@@ -774,7 +774,7 @@
},
{
"cell_type": "markdown",
- "id": "36782165",
+ "id": "7dd03424",
"metadata": {},
"source": [
"In the first case, innovation in the two countries does not synchronize.\n",
@@ -785,7 +785,7 @@
},
{
"cell_type": "markdown",
- "id": "ed60e3af",
+ "id": "966db403",
"metadata": {},
"source": [
"### Basin of Attraction\n",
@@ -820,7 +820,7 @@
},
{
"cell_type": "markdown",
- "id": "44058d4b",
+ "id": "aa707ef4",
"metadata": {},
"source": [
"## Exercises"
@@ -828,7 +828,7 @@
},
{
"cell_type": "markdown",
- "id": "7e2a8e7a",
+ "id": "4c367a87",
"metadata": {},
"source": [
"## Exercise 14.1\n",
@@ -838,7 +838,7 @@
},
{
"cell_type": "markdown",
- "id": "23baf340",
+ "id": "2d3aa945",
"metadata": {},
"source": [
"## Solution to[ Exercise 14.1](https://python-advanced.quantecon.org/#matsuyama_ex1)"
@@ -847,7 +847,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4b1aab45",
+ "id": "ef11c3f3",
"metadata": {
"hide-output": false
},
@@ -903,7 +903,7 @@
},
{
"cell_type": "markdown",
- "id": "be224093",
+ "id": "f47c6276",
"metadata": {},
"source": [
"Additionally, instead of just seeing 4 plots at once, we might want to\n",
@@ -916,7 +916,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1715548c",
+ "id": "fd94c463",
"metadata": {
"hide-output": false
},
@@ -943,7 +943,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1ae622e1",
+ "id": "65989cf6",
"metadata": {
"hide-output": false
},
@@ -957,7 +957,7 @@
}
],
"metadata": {
- "date": 1723011582.8532298,
+ "date": 1723517848.8948047,
"filename": "matsuyama.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/muth_kalman.ipynb b/_notebooks/muth_kalman.ipynb
index a8510dda..9cc0f7dc 100644
--- a/_notebooks/muth_kalman.ipynb
+++ b/_notebooks/muth_kalman.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "149c85ef",
+ "id": "c97c29c3",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "edd649df",
+ "id": "6aca6129",
"metadata": {},
"source": [
"# Reverse Engineering a la Muth\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c41f1e02",
+ "id": "f9835494",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "864d68ff",
+ "id": "50b62a6f",
"metadata": {},
"source": [
"We’ll also need the following imports:"
@@ -44,7 +44,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "767dcd5b",
+ "id": "44e9d88f",
"metadata": {
"hide-output": false
},
@@ -60,7 +60,7 @@
},
{
"cell_type": "markdown",
- "id": "a83c0e03",
+ "id": "08f11aef",
"metadata": {},
"source": [
"This lecture uses the Kalman filter to reformulate John F. Muth’s first\n",
@@ -73,7 +73,7 @@
},
{
"cell_type": "markdown",
- "id": "151af35e",
+ "id": "9eef315c",
"metadata": {},
"source": [
"## Friedman (1956) and Muth (1960)\n",
@@ -124,7 +124,7 @@
},
{
"cell_type": "markdown",
- "id": "081508e2",
+ "id": "a1cb5a4a",
"metadata": {},
"source": [
"## A Process for Which Adaptive Expectations are Optimal\n",
@@ -192,7 +192,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cbf83b09",
+ "id": "b5f6e860",
"metadata": {
"hide-output": false
},
@@ -225,7 +225,7 @@
},
{
"cell_type": "markdown",
- "id": "1f1916fe",
+ "id": "f123a591",
"metadata": {},
"source": [
"## Some Useful State-Space Math\n",
@@ -282,7 +282,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0133fb2e",
+ "id": "2fa681aa",
"metadata": {
"hide-output": false
},
@@ -315,7 +315,7 @@
},
{
"cell_type": "markdown",
- "id": "8bcae517",
+ "id": "19c9af16",
"metadata": {},
"source": [
"Now that we have simulated our joint system, we have $ x_t $,\n",
@@ -327,7 +327,7 @@
},
{
"cell_type": "markdown",
- "id": "6f6c3f2f",
+ "id": "2f85191a",
"metadata": {},
"source": [
"## Estimates of Unobservables\n",
@@ -340,7 +340,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8720c839",
+ "id": "d428da7d",
"metadata": {
"hide-output": false
},
@@ -357,7 +357,7 @@
},
{
"cell_type": "markdown",
- "id": "748e654e",
+ "id": "4d4d211c",
"metadata": {},
"source": [
"Note how $ x_t $ and $ \\hat{x_t} $ differ.\n",
@@ -368,7 +368,7 @@
},
{
"cell_type": "markdown",
- "id": "919a41b0",
+ "id": "392b542a",
"metadata": {},
"source": [
"## Relationship of Unobservables to Observables\n",
@@ -381,7 +381,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9eb09493",
+ "id": "f9344fcb",
"metadata": {
"hide-output": false
},
@@ -398,7 +398,7 @@
},
{
"cell_type": "markdown",
- "id": "1eda023e",
+ "id": "f2a46f0b",
"metadata": {},
"source": [
"We see above that $ y $ seems to look like white noise around the\n",
@@ -407,7 +407,7 @@
},
{
"cell_type": "markdown",
- "id": "6a2cba50",
+ "id": "7c3a4826",
"metadata": {},
"source": [
"### Innovations\n",
@@ -419,7 +419,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "778b59af",
+ "id": "abc92b1d",
"metadata": {
"hide-output": false
},
@@ -435,7 +435,7 @@
},
{
"cell_type": "markdown",
- "id": "25264646",
+ "id": "da4d0f15",
"metadata": {},
"source": [
"## MA and AR Representations\n",
@@ -456,7 +456,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a2b9e2a2",
+ "id": "5df630ad",
"metadata": {
"hide-output": false
},
@@ -482,7 +482,7 @@
},
{
"cell_type": "markdown",
- "id": "3de2c038",
+ "id": "0dacf8c3",
"metadata": {},
"source": [
"The **moving average** coefficients in the top panel show tell-tale\n",
@@ -499,7 +499,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7d753b6b",
+ "id": "a7269cc6",
"metadata": {
"hide-output": false
},
@@ -510,7 +510,7 @@
}
],
"metadata": {
- "date": 1723011582.874031,
+ "date": 1723517848.9146514,
"filename": "muth_kalman.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/opt_tax_recur.ipynb b/_notebooks/opt_tax_recur.ipynb
index 7d1bdc6a..a8f3ceee 100644
--- a/_notebooks/opt_tax_recur.ipynb
+++ b/_notebooks/opt_tax_recur.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "209ad4aa",
+ "id": "a6775d2a",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "346545c8",
+ "id": "b9986833",
"metadata": {},
"source": [
"# Optimal Taxation with State-Contingent Debt\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ef3c2a49",
+ "id": "49bf2c2d",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "5ecf9057",
+ "id": "074f8ed4",
"metadata": {},
"source": [
"## Overview\n",
@@ -74,7 +74,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "57c87067",
+ "id": "132e9911",
"metadata": {
"hide-output": false
},
@@ -91,7 +91,7 @@
},
{
"cell_type": "markdown",
- "id": "5616c575",
+ "id": "e954ecbf",
"metadata": {},
"source": [
"## A Competitive Equilibrium with Distorting Taxes\n",
@@ -208,7 +208,7 @@
},
{
"cell_type": "markdown",
- "id": "cf1b11d5",
+ "id": "1d5a4579",
"metadata": {},
"source": [
"### Arrow-Debreu Version of Price System\n",
@@ -236,7 +236,7 @@
},
{
"cell_type": "markdown",
- "id": "d0856c1c",
+ "id": "c3591c4d",
"metadata": {},
"source": [
"### Primal Approach\n",
@@ -268,7 +268,7 @@
},
{
"cell_type": "markdown",
- "id": "31f9d42f",
+ "id": "250de7e9",
"metadata": {},
"source": [
"### The Implementability Constraint\n",
@@ -344,7 +344,7 @@
},
{
"cell_type": "markdown",
- "id": "0967395b",
+ "id": "bc46bbe2",
"metadata": {},
"source": [
"### Solution Details\n",
@@ -486,7 +486,7 @@
},
{
"cell_type": "markdown",
- "id": "fb3abc93",
+ "id": "7e8cbc66",
"metadata": {},
"source": [
"### The Ramsey Allocation for a Given Multiplier\n",
@@ -522,7 +522,7 @@
},
{
"cell_type": "markdown",
- "id": "bc10e14c",
+ "id": "ebbc29ef",
"metadata": {},
"source": [
"### Further Specialization\n",
@@ -544,7 +544,7 @@
},
{
"cell_type": "markdown",
- "id": "7d9368d5",
+ "id": "77f74f0b",
"metadata": {},
"source": [
"### Determining the Lagrange Multiplier\n",
@@ -680,7 +680,7 @@
},
{
"cell_type": "markdown",
- "id": "97a861ff",
+ "id": "4690425a",
"metadata": {},
"source": [
"### Time Inconsistency\n",
@@ -711,7 +711,7 @@
},
{
"cell_type": "markdown",
- "id": "6891bc1a",
+ "id": "7c68e0c2",
"metadata": {},
"source": [
"### Specification with CRRA Utility\n",
@@ -796,7 +796,7 @@
},
{
"cell_type": "markdown",
- "id": "2088e789",
+ "id": "190f81a1",
"metadata": {},
"source": [
"### Sequence Implementation\n",
@@ -807,7 +807,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "704c17cd",
+ "id": "b6715240",
"metadata": {
"hide-output": false
},
@@ -1015,7 +1015,7 @@
},
{
"cell_type": "markdown",
- "id": "4e5fca3b",
+ "id": "c2e24e7d",
"metadata": {},
"source": [
"## Recursive Formulation of the Ramsey Problem\n",
@@ -1032,7 +1032,7 @@
},
{
"cell_type": "markdown",
- "id": "3a6e94e3",
+ "id": "450828db",
"metadata": {},
"source": [
"### Intertemporal Delegation\n",
@@ -1081,7 +1081,7 @@
},
{
"cell_type": "markdown",
- "id": "44d727d1",
+ "id": "33ed0533",
"metadata": {},
"source": [
"### Two Bellman Equations\n",
@@ -1100,7 +1100,7 @@
},
{
"cell_type": "markdown",
- "id": "242a4c44",
+ "id": "4ede52ec",
"metadata": {},
"source": [
"### The Continuation Ramsey Problem\n",
@@ -1145,7 +1145,7 @@
},
{
"cell_type": "markdown",
- "id": "df91bb1e",
+ "id": "bb67d226",
"metadata": {},
"source": [
"### The Ramsey Problem\n",
@@ -1198,7 +1198,7 @@
},
{
"cell_type": "markdown",
- "id": "7ad37ad8",
+ "id": "90ef4b0b",
"metadata": {},
"source": [
"### First-Order Conditions\n",
@@ -1282,7 +1282,7 @@
},
{
"cell_type": "markdown",
- "id": "6c6b1c66",
+ "id": "70917e91",
"metadata": {},
"source": [
"### State Variable Degeneracy\n",
@@ -1310,7 +1310,7 @@
},
{
"cell_type": "markdown",
- "id": "ef757499",
+ "id": "7bcdfb9c",
"metadata": {},
"source": [
"### Manifestations of Time Inconsistency\n",
@@ -1360,7 +1360,7 @@
},
{
"cell_type": "markdown",
- "id": "9b845cad",
+ "id": "6279323e",
"metadata": {},
"source": [
"### Recursive Implementation\n",
@@ -1371,7 +1371,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a93fa75e",
+ "id": "2723e0fc",
"metadata": {
"hide-output": false
},
@@ -1625,7 +1625,7 @@
},
{
"cell_type": "markdown",
- "id": "a3af99f6",
+ "id": "37b9d752",
"metadata": {},
"source": [
"## Examples\n",
@@ -1635,7 +1635,7 @@
},
{
"cell_type": "markdown",
- "id": "bead6f1d",
+ "id": "8a5918ed",
"metadata": {},
"source": [
"### Anticipated One-Period War\n",
@@ -1691,7 +1691,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a135c324",
+ "id": "79c0f233",
"metadata": {
"hide-output": false
},
@@ -1747,7 +1747,7 @@
},
{
"cell_type": "markdown",
- "id": "5ffa1180",
+ "id": "f71f91ce",
"metadata": {},
"source": [
"We set initial government debt $ b_0 = 1 $.\n",
@@ -1761,7 +1761,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d235a9ba",
+ "id": "9762be15",
"metadata": {
"hide-output": false
},
@@ -1802,7 +1802,7 @@
},
{
"cell_type": "markdown",
- "id": "a6f76adc",
+ "id": "ec7fa2ba",
"metadata": {},
"source": [
"**Tax smoothing**\n",
@@ -1848,7 +1848,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c430f832",
+ "id": "e95d9476",
"metadata": {
"hide-output": false
},
@@ -1863,7 +1863,7 @@
},
{
"cell_type": "markdown",
- "id": "3a585fd5",
+ "id": "fd61b6c4",
"metadata": {},
"source": [
"### Government Saving\n",
@@ -1899,7 +1899,7 @@
},
{
"cell_type": "markdown",
- "id": "2b581cba",
+ "id": "50667519",
"metadata": {},
"source": [
"### Time 0 Manipulation of Interest Rate\n",
@@ -1917,7 +1917,7 @@
},
{
"cell_type": "markdown",
- "id": "56a82a12",
+ "id": "bb0a098e",
"metadata": {},
"source": [
"### Time 0 and Time-Inconsistency\n",
@@ -1937,7 +1937,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "af80ec07",
+ "id": "ef10d994",
"metadata": {
"hide-output": false
},
@@ -1971,7 +1971,7 @@
},
{
"cell_type": "markdown",
- "id": "a5bf9e64",
+ "id": "d0bee249",
"metadata": {},
"source": [
"The figure indicates that if the government enters with positive debt, it sets\n",
@@ -2021,7 +2021,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "53d92b82",
+ "id": "abe8ec78",
"metadata": {
"hide-output": false
},
@@ -2051,7 +2051,7 @@
},
{
"cell_type": "markdown",
- "id": "3de64b8e",
+ "id": "8fb5716d",
"metadata": {},
"source": [
"The tax rates in the figure are equal for only two values of initial government debt."
@@ -2059,7 +2059,7 @@
},
{
"cell_type": "markdown",
- "id": "64a37cb4",
+ "id": "17e87da2",
"metadata": {},
"source": [
"### Tax Smoothing and non-CRRA Preferences\n",
@@ -2096,7 +2096,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "742c81b0",
+ "id": "315f9af5",
"metadata": {
"hide-output": false
},
@@ -2142,7 +2142,7 @@
},
{
"cell_type": "markdown",
- "id": "5563d1ca",
+ "id": "0d6e8903",
"metadata": {},
"source": [
"Also, suppose that $ g_t $ follows a two-state IID process with equal\n",
@@ -2156,7 +2156,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3e1a9f39",
+ "id": "7634ede0",
"metadata": {
"hide-output": false
},
@@ -2198,7 +2198,7 @@
},
{
"cell_type": "markdown",
- "id": "41e83d76",
+ "id": "b2199cf1",
"metadata": {},
"source": [
"As should be expected, the recursive and sequential solutions produce almost\n",
@@ -2211,7 +2211,7 @@
},
{
"cell_type": "markdown",
- "id": "23e98336",
+ "id": "2d70ef23",
"metadata": {},
"source": [
"### Further Comments\n",
@@ -2232,7 +2232,7 @@
}
],
"metadata": {
- "date": 1723011582.944608,
+ "date": 1723517848.9845448,
"filename": "opt_tax_recur.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/orth_proj.ipynb b/_notebooks/orth_proj.ipynb
index 27172b72..0f2741cb 100644
--- a/_notebooks/orth_proj.ipynb
+++ b/_notebooks/orth_proj.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "e8c84ec9",
+ "id": "3042364b",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "7162447c",
+ "id": "405995ad",
"metadata": {},
"source": [
"# Orthogonal Projections and Their Applications\n",
@@ -22,7 +22,7 @@
},
{
"cell_type": "markdown",
- "id": "29639753",
+ "id": "8434da21",
"metadata": {},
"source": [
"## Overview\n",
@@ -51,7 +51,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5b3d5cb3",
+ "id": "0b5aaba8",
"metadata": {
"hide-output": false
},
@@ -63,7 +63,7 @@
},
{
"cell_type": "markdown",
- "id": "1d23ef96",
+ "id": "5c501a93",
"metadata": {},
"source": [
"### Further Reading\n",
@@ -79,7 +79,7 @@
},
{
"cell_type": "markdown",
- "id": "bc557ba3",
+ "id": "5382a1e0",
"metadata": {},
"source": [
"## Key Definitions\n",
@@ -143,7 +143,7 @@
},
{
"cell_type": "markdown",
- "id": "f59dafed",
+ "id": "50ba5139",
"metadata": {},
"source": [
"### Linear Independence vs Orthogonality\n",
@@ -157,7 +157,7 @@
},
{
"cell_type": "markdown",
- "id": "b2babb18",
+ "id": "3e8b1ca9",
"metadata": {},
"source": [
"## The Orthogonal Projection Theorem\n",
@@ -188,7 +188,7 @@
},
{
"cell_type": "markdown",
- "id": "fe430c75",
+ "id": "8f2b5ce2",
"metadata": {},
"source": [
"### Proof of Sufficiency\n",
@@ -214,7 +214,7 @@
},
{
"cell_type": "markdown",
- "id": "2624d087",
+ "id": "7f8ec3fe",
"metadata": {},
"source": [
"### Orthogonal Projection as a Mapping\n",
@@ -255,7 +255,7 @@
},
{
"cell_type": "markdown",
- "id": "eee73d7d",
+ "id": "1c28f173",
"metadata": {},
"source": [
"#### Orthogonal Complement\n",
@@ -296,7 +296,7 @@
},
{
"cell_type": "markdown",
- "id": "0c2dd684",
+ "id": "fa4a3eea",
"metadata": {},
"source": [
"## Orthonormal Basis\n",
@@ -342,7 +342,7 @@
},
{
"cell_type": "markdown",
- "id": "52cd03e9",
+ "id": "8e78196b",
"metadata": {},
"source": [
"### Projection onto an Orthonormal Basis\n",
@@ -380,7 +380,7 @@
},
{
"cell_type": "markdown",
- "id": "f41b8bd7",
+ "id": "a985a313",
"metadata": {},
"source": [
"## Projection Via Matrix Algebra\n",
@@ -442,7 +442,7 @@
},
{
"cell_type": "markdown",
- "id": "8dee1ef5",
+ "id": "2cb4a662",
"metadata": {},
"source": [
"### Starting with the Basis\n",
@@ -464,7 +464,7 @@
},
{
"cell_type": "markdown",
- "id": "6b0ebbf8",
+ "id": "99153e79",
"metadata": {},
"source": [
"### The Orthonormal Case\n",
@@ -495,7 +495,7 @@
},
{
"cell_type": "markdown",
- "id": "4cb4dc31",
+ "id": "23477475",
"metadata": {},
"source": [
"### Application: Overdetermined Systems of Equations\n",
@@ -552,7 +552,7 @@
},
{
"cell_type": "markdown",
- "id": "e99182a4",
+ "id": "0dd6ce53",
"metadata": {},
"source": [
"## Least Squares Regression\n",
@@ -566,7 +566,7 @@
},
{
"cell_type": "markdown",
- "id": "289c2159",
+ "id": "5c0dd140",
"metadata": {},
"source": [
"### Squared Risk Measures\n",
@@ -604,7 +604,7 @@
},
{
"cell_type": "markdown",
- "id": "2050876a",
+ "id": "56441f1e",
"metadata": {},
"source": [
"### Solution\n",
@@ -713,7 +713,7 @@
},
{
"cell_type": "markdown",
- "id": "1e1397cc",
+ "id": "22fd45f6",
"metadata": {},
"source": [
"## Orthogonalization and Decomposition\n",
@@ -730,7 +730,7 @@
},
{
"cell_type": "markdown",
- "id": "fb40a91c",
+ "id": "78d98d11",
"metadata": {},
"source": [
"### Gram-Schmidt Orthogonalization\n",
@@ -763,7 +763,7 @@
},
{
"cell_type": "markdown",
- "id": "b1668183",
+ "id": "a15f94c9",
"metadata": {},
"source": [
"### QR Decomposition\n",
@@ -795,7 +795,7 @@
},
{
"cell_type": "markdown",
- "id": "3abc3123",
+ "id": "712930c6",
"metadata": {},
"source": [
"### Linear Regression via QR Decomposition\n",
@@ -820,7 +820,7 @@
},
{
"cell_type": "markdown",
- "id": "1dcdff3f",
+ "id": "7a3bc307",
"metadata": {},
"source": [
"## Exercises"
@@ -828,7 +828,7 @@
},
{
"cell_type": "markdown",
- "id": "13e07d57",
+ "id": "46a64211",
"metadata": {},
"source": [
"## Exercise 1.1\n",
@@ -838,7 +838,7 @@
},
{
"cell_type": "markdown",
- "id": "f1ddc6be",
+ "id": "d0dd1684",
"metadata": {},
"source": [
"## Solution to[ Exercise 1.1](https://python-advanced.quantecon.org/#op_ex1)\n",
@@ -849,7 +849,7 @@
},
{
"cell_type": "markdown",
- "id": "5952beee",
+ "id": "2e28847a",
"metadata": {},
"source": [
"## Exercise 1.2\n",
@@ -861,7 +861,7 @@
},
{
"cell_type": "markdown",
- "id": "7e29c379",
+ "id": "68563db5",
"metadata": {},
"source": [
"## Solution to[ Exercise 1.2](https://python-advanced.quantecon.org/#op_ex2)\n",
@@ -877,7 +877,7 @@
},
{
"cell_type": "markdown",
- "id": "92172734",
+ "id": "17bc7546",
"metadata": {},
"source": [
"## Exercise 1.3\n",
@@ -912,7 +912,7 @@
},
{
"cell_type": "markdown",
- "id": "47ed1b0b",
+ "id": "747021ea",
"metadata": {},
"source": [
"## Solution to[ Exercise 1.3](https://python-advanced.quantecon.org/#op_ex3)\n",
@@ -924,7 +924,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3a93c73c",
+ "id": "ab9d32bb",
"metadata": {
"hide-output": false
},
@@ -970,7 +970,7 @@
},
{
"cell_type": "markdown",
- "id": "a6ed7254",
+ "id": "3f66a098",
"metadata": {},
"source": [
"Here are the arrays we’ll work with"
@@ -979,7 +979,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fa6d9c4d",
+ "id": "03e6597d",
"metadata": {
"hide-output": false
},
@@ -996,7 +996,7 @@
},
{
"cell_type": "markdown",
- "id": "0baec4f7",
+ "id": "77a43071",
"metadata": {},
"source": [
"First, let’s try projection of $ y $ onto the column space of\n",
@@ -1006,7 +1006,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "74a989a1",
+ "id": "99569080",
"metadata": {
"hide-output": false
},
@@ -1018,7 +1018,7 @@
},
{
"cell_type": "markdown",
- "id": "81fdb42b",
+ "id": "1a4d8d28",
"metadata": {},
"source": [
"Now let’s do the same using an orthonormal basis created from our\n",
@@ -1028,7 +1028,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1c46d588",
+ "id": "22d3e992",
"metadata": {
"hide-output": false
},
@@ -1041,7 +1041,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1b606148",
+ "id": "0962c318",
"metadata": {
"hide-output": false
},
@@ -1053,7 +1053,7 @@
},
{
"cell_type": "markdown",
- "id": "4cf7f225",
+ "id": "4029ae1e",
"metadata": {},
"source": [
"This is the same answer. So far so good. Finally, let’s try the same\n",
@@ -1063,7 +1063,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "571cb28d",
+ "id": "f50c2ba4",
"metadata": {
"hide-output": false
},
@@ -1076,7 +1076,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4d4c1cc2",
+ "id": "8429a649",
"metadata": {
"hide-output": false
},
@@ -1088,7 +1088,7 @@
},
{
"cell_type": "markdown",
- "id": "18ea6e78",
+ "id": "54455448",
"metadata": {},
"source": [
"Again, we obtain the same answer."
@@ -1096,7 +1096,7 @@
}
],
"metadata": {
- "date": 1723011582.9845464,
+ "date": 1723517849.0265186,
"filename": "orth_proj.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/permanent_income_dles.ipynb b/_notebooks/permanent_income_dles.ipynb
index 944a9888..06a00683 100644
--- a/_notebooks/permanent_income_dles.ipynb
+++ b/_notebooks/permanent_income_dles.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "3d623563",
+ "id": "7371c61d",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "adf622be",
+ "id": "5a4bd726",
"metadata": {},
"source": [
"# Permanent Income Model using the DLE Class\n",
@@ -27,7 +27,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "775e9bcc",
+ "id": "43ca516f",
"metadata": {
"hide-output": false
},
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "c9d1a1b7",
+ "id": "779bbc77",
"metadata": {},
"source": [
"This lecture adds a third solution method for the\n",
@@ -59,7 +59,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "188bdda5",
+ "id": "bd3740d8",
"metadata": {
"hide-output": false
},
@@ -74,7 +74,7 @@
},
{
"cell_type": "markdown",
- "id": "6aeea410",
+ "id": "a24ea60b",
"metadata": {},
"source": [
"## The Permanent Income Model\n",
@@ -174,7 +174,7 @@
},
{
"cell_type": "markdown",
- "id": "8efc59cd",
+ "id": "1d3d1c17",
"metadata": {},
"source": [
"### Solution with the DLE Class\n",
@@ -233,7 +233,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "03bd89c1",
+ "id": "3fe6815f",
"metadata": {
"hide-output": false
},
@@ -273,7 +273,7 @@
},
{
"cell_type": "markdown",
- "id": "cd7b7e49",
+ "id": "91bf25d6",
"metadata": {},
"source": [
"To check the solution of this model with that from the **LQ** problem,\n",
@@ -290,7 +290,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3aede370",
+ "id": "2a469ec5",
"metadata": {
"hide-output": false
},
@@ -301,7 +301,7 @@
},
{
"cell_type": "markdown",
- "id": "85f81d2d",
+ "id": "cbdf5718",
"metadata": {},
"source": [
"The state vector in the DLE class is:\n",
@@ -331,7 +331,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3707ed9b",
+ "id": "34db73f9",
"metadata": {
"hide-output": false
},
@@ -357,7 +357,7 @@
}
],
"metadata": {
- "date": 1723011583.0005496,
+ "date": 1723517849.043094,
"filename": "permanent_income_dles.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/rob_markov_perf.ipynb b/_notebooks/rob_markov_perf.ipynb
index 48460bf9..bbe7dfc6 100644
--- a/_notebooks/rob_markov_perf.ipynb
+++ b/_notebooks/rob_markov_perf.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "67760e41",
+ "id": "dfc2f879",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "532a20d1",
+ "id": "5bcdc61c",
"metadata": {},
"source": [
"# Robust Markov Perfect Equilibrium\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a1779e22",
+ "id": "4896c52a",
"metadata": {
"hide-output": false
},
@@ -33,7 +33,7 @@
},
{
"cell_type": "markdown",
- "id": "0d0df582",
+ "id": "e36bf2f9",
"metadata": {},
"source": [
"## Overview\n",
@@ -60,7 +60,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fc05172f",
+ "id": "1a842767",
"metadata": {
"hide-output": false
},
@@ -74,7 +74,7 @@
},
{
"cell_type": "markdown",
- "id": "6041597d",
+ "id": "f3f763d6",
"metadata": {},
"source": [
"### Basic Setup\n",
@@ -108,7 +108,7 @@
},
{
"cell_type": "markdown",
- "id": "be762ff1",
+ "id": "78310dd6",
"metadata": {},
"source": [
"## Linear Markov Perfect Equilibria with Robust Agents\n",
@@ -123,7 +123,7 @@
},
{
"cell_type": "markdown",
- "id": "a0dc30e1",
+ "id": "3046b554",
"metadata": {},
"source": [
"### Modified Coupled Linear Regulator Problems\n",
@@ -200,7 +200,7 @@
},
{
"cell_type": "markdown",
- "id": "c275f77a",
+ "id": "48219a74",
"metadata": {},
"source": [
"### Computing Equilibrium\n",
@@ -317,7 +317,7 @@
},
{
"cell_type": "markdown",
- "id": "8f31bd47",
+ "id": "1f9f23c0",
"metadata": {},
"source": [
"### Key Insight\n",
@@ -337,7 +337,7 @@
},
{
"cell_type": "markdown",
- "id": "0d65b9a6",
+ "id": "9eefa9a1",
"metadata": {},
"source": [
"### Worst-case Shocks\n",
@@ -357,7 +357,7 @@
},
{
"cell_type": "markdown",
- "id": "c9b3b78d",
+ "id": "b4612f83",
"metadata": {},
"source": [
"### Infinite Horizon\n",
@@ -371,7 +371,7 @@
},
{
"cell_type": "markdown",
- "id": "55166091",
+ "id": "0a44534c",
"metadata": {},
"source": [
"### Implementation\n",
@@ -383,7 +383,7 @@
},
{
"cell_type": "markdown",
- "id": "e94a382d",
+ "id": "34a5f7eb",
"metadata": {},
"source": [
"## Application\n",
@@ -394,7 +394,7 @@
},
{
"cell_type": "markdown",
- "id": "e2245547",
+ "id": "24760002",
"metadata": {},
"source": [
"### A Duopoly Model\n",
@@ -524,7 +524,7 @@
},
{
"cell_type": "markdown",
- "id": "888b8f12",
+ "id": "59fbf575",
"metadata": {},
"source": [
"### Parameters and Solution\n",
@@ -543,7 +543,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e516e286",
+ "id": "f3618dcf",
"metadata": {
"hide-output": false
},
@@ -589,7 +589,7 @@
},
{
"cell_type": "markdown",
- "id": "c7d2dbb0",
+ "id": "9d824c8c",
"metadata": {},
"source": [
"#### Markov Perfect Equilibrium with Robustness\n",
@@ -608,7 +608,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "60235df5",
+ "id": "b2f1468e",
"metadata": {
"hide-output": false
},
@@ -780,7 +780,7 @@
},
{
"cell_type": "markdown",
- "id": "2b1f381e",
+ "id": "a10d241e",
"metadata": {},
"source": [
"### Some Details\n",
@@ -854,7 +854,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3c8186ee",
+ "id": "9af60eb4",
"metadata": {
"hide-output": false
},
@@ -887,7 +887,7 @@
},
{
"cell_type": "markdown",
- "id": "0a96121e",
+ "id": "643aa00d",
"metadata": {},
"source": [
"#### Consistency Check\n",
@@ -899,7 +899,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4df40caa",
+ "id": "d8d146d1",
"metadata": {
"hide-output": false
},
@@ -923,7 +923,7 @@
},
{
"cell_type": "markdown",
- "id": "4deda07c",
+ "id": "891a05d5",
"metadata": {},
"source": [
"We can see that the results are consistent across the two functions."
@@ -931,7 +931,7 @@
},
{
"cell_type": "markdown",
- "id": "cc0d64b2",
+ "id": "86f630b1",
"metadata": {},
"source": [
"#### Comparative Dynamics under Baseline Transition Dynamics\n",
@@ -975,7 +975,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d0ada675",
+ "id": "e3ada672",
"metadata": {
"hide-output": false
},
@@ -1046,7 +1046,7 @@
},
{
"cell_type": "markdown",
- "id": "77ce7b3d",
+ "id": "8ec945fa",
"metadata": {},
"source": [
"The following code prepares graphs that compare market-wide output $ q_{1t} + q_{2t} $ and the price of the good\n",
@@ -1060,7 +1060,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "241fcb6c",
+ "id": "7283ea54",
"metadata": {
"hide-output": false
},
@@ -1084,7 +1084,7 @@
},
{
"cell_type": "markdown",
- "id": "be383f08",
+ "id": "6f713d9b",
"metadata": {},
"source": [
"Under the dynamics associated with the baseline model, the price path is higher with the Markov perfect equilibrium robust decision rules\n",
@@ -1100,7 +1100,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "45d9dc12",
+ "id": "495decfd",
"metadata": {
"hide-output": false
},
@@ -1124,7 +1124,7 @@
},
{
"cell_type": "markdown",
- "id": "d14795dc",
+ "id": "65b2ac06",
"metadata": {},
"source": [
"Evidently, firm 1’s output path is substantially lower when firms are robust firms while\n",
@@ -1147,7 +1147,7 @@
},
{
"cell_type": "markdown",
- "id": "f4536145",
+ "id": "b20f8d53",
"metadata": {},
"source": [
"#### Heterogeneous Beliefs\n",
@@ -1178,7 +1178,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "75f101bd",
+ "id": "d7d04fd7",
"metadata": {
"hide-output": false
},
@@ -1194,7 +1194,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "be41b4b3",
+ "id": "3a32e675",
"metadata": {
"hide-output": false
},
@@ -1225,7 +1225,7 @@
},
{
"cell_type": "markdown",
- "id": "85158ee7",
+ "id": "917a2ae6",
"metadata": {},
"source": [
"We see from the above graph that under robustness concerns, player 1 and\n",
@@ -1245,7 +1245,7 @@
}
],
"metadata": {
- "date": 1723011583.0330455,
+ "date": 1723517849.0774796,
"filename": "rob_markov_perf.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/robustness.ipynb b/_notebooks/robustness.ipynb
index 06a43faf..585c60b0 100644
--- a/_notebooks/robustness.ipynb
+++ b/_notebooks/robustness.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "517e0bae",
+ "id": "6a0637cd",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "4b6641a1",
+ "id": "821b4f0e",
"metadata": {},
"source": [
"# Robustness\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f95b14f4",
+ "id": "36d4a061",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "0b888a68",
+ "id": "eed04cbc",
"metadata": {},
"source": [
"## Overview\n",
@@ -84,7 +84,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4ef203da",
+ "id": "6c7cb971",
"metadata": {
"hide-output": false
},
@@ -99,7 +99,7 @@
},
{
"cell_type": "markdown",
- "id": "3d2988c7",
+ "id": "9f2014fe",
"metadata": {},
"source": [
"\n",
@@ -108,7 +108,7 @@
},
{
"cell_type": "markdown",
- "id": "8095d7d0",
+ "id": "01ae0238",
"metadata": {},
"source": [
"### Sets of Models Imply Sets Of Values\n",
@@ -175,7 +175,7 @@
},
{
"cell_type": "markdown",
- "id": "9776b7c8",
+ "id": "6b186fd5",
"metadata": {},
"source": [
"### Inspiring Video\n",
@@ -185,7 +185,7 @@
},
{
"cell_type": "markdown",
- "id": "040b97e7",
+ "id": "53c73111",
"metadata": {},
"source": [
"### Other References\n",
@@ -198,7 +198,7 @@
},
{
"cell_type": "markdown",
- "id": "f4b8b9e8",
+ "id": "306a8da2",
"metadata": {},
"source": [
"## The Model\n",
@@ -252,7 +252,7 @@
},
{
"cell_type": "markdown",
- "id": "b3900973",
+ "id": "f6687fde",
"metadata": {},
"source": [
"## Constructing More Robust Policies\n",
@@ -301,7 +301,7 @@
},
{
"cell_type": "markdown",
- "id": "3ab0d598",
+ "id": "d5dea253",
"metadata": {},
"source": [
"### Analyzing the Bellman Equation\n",
@@ -407,7 +407,7 @@
},
{
"cell_type": "markdown",
- "id": "712fb471",
+ "id": "06e40cc8",
"metadata": {},
"source": [
"## Robustness as Outcome of a Two-Person Zero-Sum Game\n",
@@ -428,7 +428,7 @@
},
{
"cell_type": "markdown",
- "id": "7c5691a2",
+ "id": "ad54f31d",
"metadata": {},
"source": [
"### Agent 2’s Problem\n",
@@ -535,7 +535,7 @@
},
{
"cell_type": "markdown",
- "id": "43ac65e8",
+ "id": "6841747e",
"metadata": {},
"source": [
"### Using Agent 2’s Problem to Construct Bounds on the Value Sets"
@@ -543,7 +543,7 @@
},
{
"cell_type": "markdown",
- "id": "6b697579",
+ "id": "44d70469",
"metadata": {},
"source": [
"#### The Lower Bound\n",
@@ -602,7 +602,7 @@
},
{
"cell_type": "markdown",
- "id": "bba99d67",
+ "id": "73e3b4b3",
"metadata": {},
"source": [
"#### The Upper Bound\n",
@@ -665,7 +665,7 @@
},
{
"cell_type": "markdown",
- "id": "146b855d",
+ "id": "9be83232",
"metadata": {},
"source": [
"#### Reshaping the Set of Values\n",
@@ -675,7 +675,7 @@
},
{
"cell_type": "markdown",
- "id": "f77518c9",
+ "id": "a91c3cb2",
"metadata": {},
"source": [
"### Agent 1’s Problem\n",
@@ -722,7 +722,7 @@
},
{
"cell_type": "markdown",
- "id": "130d4a29",
+ "id": "26f03522",
"metadata": {},
"source": [
"### Nash Equilibrium\n",
@@ -756,7 +756,7 @@
},
{
"cell_type": "markdown",
- "id": "6b990b0e",
+ "id": "8d391b32",
"metadata": {},
"source": [
"## The Stochastic Case\n",
@@ -805,7 +805,7 @@
},
{
"cell_type": "markdown",
- "id": "ba18b03f",
+ "id": "7aa8a819",
"metadata": {},
"source": [
"### Solving the Model\n",
@@ -903,7 +903,7 @@
},
{
"cell_type": "markdown",
- "id": "0b6bbdd2",
+ "id": "8f1ab62e",
"metadata": {},
"source": [
"### Computing Other Quantities\n",
@@ -913,7 +913,7 @@
},
{
"cell_type": "markdown",
- "id": "0b2b5986",
+ "id": "a81ec981",
"metadata": {},
"source": [
"#### Worst-Case Value of a Policy\n",
@@ -971,7 +971,7 @@
},
{
"cell_type": "markdown",
- "id": "6922894e",
+ "id": "a9338b54",
"metadata": {},
"source": [
"## Implementation\n",
@@ -997,7 +997,7 @@
},
{
"cell_type": "markdown",
- "id": "4a855320",
+ "id": "c687a0f5",
"metadata": {},
"source": [
"## Application\n",
@@ -1097,7 +1097,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4485302a",
+ "id": "fdb16976",
"metadata": {
"hide-output": false
},
@@ -1274,7 +1274,7 @@
},
{
"cell_type": "markdown",
- "id": "9ae83604",
+ "id": "e93f4cad",
"metadata": {},
"source": [
"Here’s another such figure, with $ \\theta = 0.002 $ instead of $ 0.02 $\n",
@@ -1290,7 +1290,7 @@
},
{
"cell_type": "markdown",
- "id": "4bca3471",
+ "id": "58844cd1",
"metadata": {},
"source": [
"## Appendix\n",
@@ -1364,7 +1364,7 @@
}
],
"metadata": {
- "date": 1723011583.3028057,
+ "date": 1723517849.1248803,
"filename": "robustness.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/rosen_schooling_model.ipynb b/_notebooks/rosen_schooling_model.ipynb
index 57b56a2e..518df1b3 100644
--- a/_notebooks/rosen_schooling_model.ipynb
+++ b/_notebooks/rosen_schooling_model.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "11abfeab",
+ "id": "e74a5d4a",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "b7146b0e",
+ "id": "8302e213",
"metadata": {},
"source": [
"# Rosen Schooling Model\n",
@@ -27,7 +27,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fa1c3586",
+ "id": "d80d1dec",
"metadata": {
"hide-output": false
},
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "8befb393",
+ "id": "2445848a",
"metadata": {},
"source": [
"We’ll also need the following imports:"
@@ -47,7 +47,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "314f58ab",
+ "id": "7a398e01",
"metadata": {
"hide-output": false
},
@@ -61,7 +61,7 @@
},
{
"cell_type": "markdown",
- "id": "a798408e",
+ "id": "6304ecb8",
"metadata": {},
"source": [
"## A One-Occupation Model\n",
@@ -109,7 +109,7 @@
},
{
"cell_type": "markdown",
- "id": "22156d4b",
+ "id": "b6785104",
"metadata": {},
"source": [
"## Mapping into HS2013 Framework\n",
@@ -124,7 +124,7 @@
},
{
"cell_type": "markdown",
- "id": "a66bcdaf",
+ "id": "959f9519",
"metadata": {},
"source": [
"### Preferences\n",
@@ -156,7 +156,7 @@
},
{
"cell_type": "markdown",
- "id": "52cd3eb2",
+ "id": "c38411ef",
"metadata": {},
"source": [
"### Technology\n",
@@ -177,7 +177,7 @@
},
{
"cell_type": "markdown",
- "id": "dc0059be",
+ "id": "977e2503",
"metadata": {},
"source": [
"### Information\n",
@@ -210,7 +210,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cdac857c",
+ "id": "84308187",
"metadata": {
"hide-output": false
},
@@ -223,7 +223,7 @@
},
{
"cell_type": "markdown",
- "id": "22cb35ff",
+ "id": "091821cf",
"metadata": {},
"source": [
"### Effects of Changes in Education Technology and Demand\n",
@@ -242,7 +242,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "952890ac",
+ "id": "2c8104cc",
"metadata": {
"hide-output": false
},
@@ -297,7 +297,7 @@
},
{
"cell_type": "markdown",
- "id": "bb819622",
+ "id": "8d915c30",
"metadata": {},
"source": [
"We create three other instances by:\n",
@@ -310,7 +310,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "633bb8f7",
+ "id": "497e0674",
"metadata": {
"hide-output": false
},
@@ -357,7 +357,7 @@
},
{
"cell_type": "markdown",
- "id": "47a39f8c",
+ "id": "a77b6721",
"metadata": {},
"source": [
"The first figure plots the impulse response of $ n_t $ (on the left)\n",
@@ -385,7 +385,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5d57514a",
+ "id": "8d807638",
"metadata": {
"hide-output": false
},
@@ -406,7 +406,7 @@
},
{
"cell_type": "markdown",
- "id": "3f9ac194",
+ "id": "cc2156df",
"metadata": {},
"source": [
"The next figure plots the impulse response of $ n_t $ (on the left)\n",
@@ -417,7 +417,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3f52d9eb",
+ "id": "94e57276",
"metadata": {
"hide-output": false
},
@@ -440,7 +440,7 @@
},
{
"cell_type": "markdown",
- "id": "560a748b",
+ "id": "daf555fe",
"metadata": {},
"source": [
"Both panels in the above figure show that raising $ k $ lowers the effect of\n",
@@ -454,7 +454,7 @@
}
],
"metadata": {
- "date": 1723011583.3198574,
+ "date": 1723517849.1409554,
"filename": "rosen_schooling_model.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/smoothing.ipynb b/_notebooks/smoothing.ipynb
index a782452f..bf2f4698 100644
--- a/_notebooks/smoothing.ipynb
+++ b/_notebooks/smoothing.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "27ec404b",
+ "id": "7b444905",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "2504280d",
+ "id": "b456f890",
"metadata": {},
"source": [
"# Consumption Smoothing with Complete and Incomplete Markets\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8037db9b",
+ "id": "a672d652",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "ac4addc4",
+ "id": "2c37af9d",
"metadata": {},
"source": [
"## Overview\n",
@@ -87,7 +87,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ffda8df3",
+ "id": "740ee0ea",
"metadata": {
"hide-output": false
},
@@ -101,7 +101,7 @@
},
{
"cell_type": "markdown",
- "id": "63a6b27b",
+ "id": "81541c25",
"metadata": {},
"source": [
"### Relationship to Other Lectures\n",
@@ -113,7 +113,7 @@
},
{
"cell_type": "markdown",
- "id": "4ffacadc",
+ "id": "51710c2a",
"metadata": {},
"source": [
"## Background\n",
@@ -148,7 +148,7 @@
},
{
"cell_type": "markdown",
- "id": "b77bb25b",
+ "id": "c79e7298",
"metadata": {},
"source": [
"## Linear State Space Version of Complete Markets Model\n",
@@ -309,7 +309,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6f240355",
+ "id": "b56ae595",
"metadata": {
"hide-output": false
},
@@ -392,7 +392,7 @@
},
{
"cell_type": "markdown",
- "id": "300fb0c6",
+ "id": "5e2753de",
"metadata": {},
"source": [
"### Interpretation of Graph\n",
@@ -410,7 +410,7 @@
},
{
"cell_type": "markdown",
- "id": "1c0d41a4",
+ "id": "3a4326b7",
"metadata": {},
"source": [
"### Incomplete Markets Version\n",
@@ -423,7 +423,7 @@
},
{
"cell_type": "markdown",
- "id": "f91ad9d8",
+ "id": "aaa3afca",
"metadata": {},
"source": [
"### Finite State Markov Income Process\n",
@@ -474,7 +474,7 @@
},
{
"cell_type": "markdown",
- "id": "f5854798",
+ "id": "cabde6ce",
"metadata": {},
"source": [
"### Market Structure\n",
@@ -493,7 +493,7 @@
},
{
"cell_type": "markdown",
- "id": "b3c07631",
+ "id": "28acc28c",
"metadata": {},
"source": [
"## Model 1 (Complete Markets)\n",
@@ -672,7 +672,7 @@
},
{
"cell_type": "markdown",
- "id": "330fd7d6",
+ "id": "93364dc8",
"metadata": {},
"source": [
"### Key Outcomes\n",
@@ -700,7 +700,7 @@
},
{
"cell_type": "markdown",
- "id": "f4cdf431",
+ "id": "55a50ffc",
"metadata": {},
"source": [
"### Code\n",
@@ -714,7 +714,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4a0d9ab7",
+ "id": "e542baca",
"metadata": {
"hide-output": false
},
@@ -844,7 +844,7 @@
},
{
"cell_type": "markdown",
- "id": "e05ef638",
+ "id": "2913ae40",
"metadata": {},
"source": [
"Let’s test by checking that $ \\bar c $ and $ b_2 $ satisfy the budget constraint"
@@ -853,7 +853,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "40086964",
+ "id": "71457f47",
"metadata": {
"hide-output": false
},
@@ -866,7 +866,7 @@
},
{
"cell_type": "markdown",
- "id": "17da4d7c",
+ "id": "847c5c45",
"metadata": {},
"source": [
"Below, we’ll take the outcomes produced by this code – in particular the implied\n",
@@ -876,7 +876,7 @@
},
{
"cell_type": "markdown",
- "id": "a3ac8285",
+ "id": "782923af",
"metadata": {},
"source": [
"## Model 2 (One-Period Risk-Free Debt Only)\n",
@@ -1005,7 +1005,7 @@
},
{
"cell_type": "markdown",
- "id": "013a7a78",
+ "id": "375aacfa",
"metadata": {},
"source": [
"### Summary of Outcomes\n",
@@ -1027,7 +1027,7 @@
},
{
"cell_type": "markdown",
- "id": "2640feed",
+ "id": "bfdf8877",
"metadata": {},
"source": [
"### The Incomplete Markets Model\n",
@@ -1044,7 +1044,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cead1d3b",
+ "id": "c815a8da",
"metadata": {
"hide-output": false
},
@@ -1082,7 +1082,7 @@
},
{
"cell_type": "markdown",
- "id": "7d811246",
+ "id": "2ca47066",
"metadata": {},
"source": [
"In the graph on the left, for the same sample path of nonfinancial\n",
@@ -1097,7 +1097,7 @@
},
{
"cell_type": "markdown",
- "id": "48ab23b3",
+ "id": "54316971",
"metadata": {},
"source": [
"### A sequel\n",
@@ -1108,7 +1108,7 @@
}
],
"metadata": {
- "date": 1723011583.3565788,
+ "date": 1723517849.363196,
"filename": "smoothing.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/smoothing_tax.ipynb b/_notebooks/smoothing_tax.ipynb
index 68c8ab48..ea99d861 100644
--- a/_notebooks/smoothing_tax.ipynb
+++ b/_notebooks/smoothing_tax.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "4b680051",
+ "id": "a799158d",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "4e1f2e50",
+ "id": "769af08c",
"metadata": {},
"source": [
"# Tax Smoothing with Complete and Incomplete Markets\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e4259c0f",
+ "id": "22e16e09",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "d47c7ab9",
+ "id": "cf210ec2",
"metadata": {},
"source": [
"## Overview\n",
@@ -73,7 +73,7 @@
},
{
"cell_type": "markdown",
- "id": "c00fa380",
+ "id": "ba94114c",
"metadata": {},
"source": [
"### Isomorphism between Consumption and Tax Smoothing\n",
@@ -99,7 +99,7 @@
},
{
"cell_type": "markdown",
- "id": "5b9519a4",
+ "id": "fa38ec87",
"metadata": {},
"source": [
"#### Link to History\n",
@@ -113,7 +113,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "14b67a21",
+ "id": "e1ab9937",
"metadata": {
"hide-output": false
},
@@ -126,7 +126,7 @@
},
{
"cell_type": "markdown",
- "id": "e2e96b92",
+ "id": "b4b9f412",
"metadata": {},
"source": [
"To exploit the isomorphism between consumption-smoothing and tax-smoothing models, we simply use code from [Consumption Smoothing with Complete and Incomplete Markets](https://python-advanced.quantecon.org/smoothing.html)"
@@ -134,7 +134,7 @@
},
{
"cell_type": "markdown",
- "id": "45a41049",
+ "id": "d2006586",
"metadata": {},
"source": [
"### Code\n",
@@ -148,7 +148,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d409cf1e",
+ "id": "7cdb0b09",
"metadata": {
"hide-output": false
},
@@ -278,7 +278,7 @@
},
{
"cell_type": "markdown",
- "id": "9b9c1eb9",
+ "id": "ee2c9c08",
"metadata": {},
"source": [
"### Revisiting the consumption-smoothing model\n",
@@ -295,7 +295,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f0a561b1",
+ "id": "214c49d4",
"metadata": {
"hide-output": false
},
@@ -331,7 +331,7 @@
},
{
"cell_type": "markdown",
- "id": "054ba475",
+ "id": "e9de2271",
"metadata": {},
"source": [
"In the graph on the left, for the same sample path of nonfinancial\n",
@@ -346,7 +346,7 @@
},
{
"cell_type": "markdown",
- "id": "b9fe6459",
+ "id": "c0812400",
"metadata": {},
"source": [
"#### Relabeling variables to create tax-smoothing models\n",
@@ -357,7 +357,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5fbc090c",
+ "id": "e73977d2",
"metadata": {
"hide-output": false
},
@@ -386,7 +386,7 @@
},
{
"cell_type": "markdown",
- "id": "1630d8a4",
+ "id": "94774dba",
"metadata": {},
"source": [
"## Tax Smoothing with Complete Markets\n",
@@ -437,7 +437,7 @@
},
{
"cell_type": "markdown",
- "id": "e9e551a5",
+ "id": "cfe82411",
"metadata": {},
"source": [
"## Returns on State-Contingent Debt\n",
@@ -469,7 +469,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d54c0401",
+ "id": "44baa8cf",
"metadata": {
"hide-output": false
},
@@ -509,7 +509,7 @@
},
{
"cell_type": "markdown",
- "id": "76fb6c7f",
+ "id": "cbc150e9",
"metadata": {},
"source": [
"### An Example of Tax Smoothing\n",
@@ -538,7 +538,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d746df14",
+ "id": "70f8be6f",
"metadata": {
"hide-output": false
},
@@ -617,7 +617,7 @@
},
{
"cell_type": "markdown",
- "id": "eaa474f0",
+ "id": "41e75255",
"metadata": {},
"source": [
"### Explanation\n",
@@ -643,7 +643,7 @@
},
{
"cell_type": "markdown",
- "id": "03e1a2a9",
+ "id": "aaf760ed",
"metadata": {},
"source": [
"### Exercise 7.1\n",
@@ -664,7 +664,7 @@
},
{
"cell_type": "markdown",
- "id": "e1ef5e72",
+ "id": "20669dc7",
"metadata": {},
"source": [
"## More Finite Markov Chain Tax-Smoothing Examples\n",
@@ -682,7 +682,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "44b520a4",
+ "id": "9f60be3d",
"metadata": {
"hide-output": false
},
@@ -801,7 +801,7 @@
},
{
"cell_type": "markdown",
- "id": "9a2ec382",
+ "id": "be2fb455",
"metadata": {},
"source": [
"### Parameters"
@@ -810,7 +810,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "61de5549",
+ "id": "7ec2e93d",
"metadata": {
"hide-output": false
},
@@ -829,7 +829,7 @@
},
{
"cell_type": "markdown",
- "id": "09975006",
+ "id": "e762d872",
"metadata": {},
"source": [
"### Example 1\n",
@@ -861,7 +861,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e3d55973",
+ "id": "822e2f50",
"metadata": {
"hide-output": false
},
@@ -878,7 +878,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5ea09de9",
+ "id": "214b0a06",
"metadata": {
"hide-output": false
},
@@ -891,7 +891,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "79c2abd1",
+ "id": "9b5fa47d",
"metadata": {
"hide-output": false
},
@@ -905,7 +905,7 @@
},
{
"cell_type": "markdown",
- "id": "f7477e0c",
+ "id": "a5391a50",
"metadata": {},
"source": [
"### Example 2\n",
@@ -931,7 +931,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ce520451",
+ "id": "b0020320",
"metadata": {
"hide-output": false
},
@@ -948,7 +948,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "34dbb891",
+ "id": "eec30211",
"metadata": {
"hide-output": false
},
@@ -960,7 +960,7 @@
},
{
"cell_type": "markdown",
- "id": "64235103",
+ "id": "d19af046",
"metadata": {},
"source": [
"### Example 3\n",
@@ -989,7 +989,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "10cb65d4",
+ "id": "1f3f5a3c",
"metadata": {
"hide-output": false
},
@@ -1007,7 +1007,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e6435235",
+ "id": "7b4e637e",
"metadata": {
"hide-output": false
},
@@ -1019,7 +1019,7 @@
},
{
"cell_type": "markdown",
- "id": "3de44fcb",
+ "id": "c99318d5",
"metadata": {},
"source": [
"### Example 4\n",
@@ -1046,7 +1046,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "19c6a1c4",
+ "id": "ef54ce45",
"metadata": {
"hide-output": false
},
@@ -1065,7 +1065,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a1e26b7a",
+ "id": "b1a041c8",
"metadata": {
"hide-output": false
},
@@ -1077,7 +1077,7 @@
},
{
"cell_type": "markdown",
- "id": "9e66cb67",
+ "id": "3486fc34",
"metadata": {},
"source": [
"### Example 5\n",
@@ -1109,7 +1109,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2053c0fb",
+ "id": "065b4805",
"metadata": {
"hide-output": false
},
@@ -1130,7 +1130,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "25349abd",
+ "id": "86b48648",
"metadata": {
"hide-output": false
},
@@ -1142,7 +1142,7 @@
},
{
"cell_type": "markdown",
- "id": "c7d23fa5",
+ "id": "5635e05d",
"metadata": {},
"source": [
"### Continuous-State Gaussian Model\n",
@@ -1192,7 +1192,7 @@
},
{
"cell_type": "markdown",
- "id": "863b9794",
+ "id": "ea99c7ba",
"metadata": {},
"source": [
"#### Related Lectures\n",
@@ -1218,7 +1218,7 @@
}
],
"metadata": {
- "date": 1723011583.3944843,
+ "date": 1723517849.3995714,
"filename": "smoothing_tax.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/stationary_densities.ipynb b/_notebooks/stationary_densities.ipynb
index fb3a9041..eb038d70 100644
--- a/_notebooks/stationary_densities.ipynb
+++ b/_notebooks/stationary_densities.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "19f007eb",
+ "id": "b66b67f9",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "7e9467f3",
+ "id": "3c9d58af",
"metadata": {},
"source": [
"# Continuous State Markov Chains\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "69ef3195",
+ "id": "e40c46d9",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "d1ecc91f",
+ "id": "a4027b39",
"metadata": {},
"source": [
"## Overview\n",
@@ -83,7 +83,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "be895e5d",
+ "id": "3184fd0e",
"metadata": {
"hide-output": false
},
@@ -98,7 +98,7 @@
},
{
"cell_type": "markdown",
- "id": "a49a5327",
+ "id": "98471c10",
"metadata": {},
"source": [
"\n",
@@ -107,7 +107,7 @@
},
{
"cell_type": "markdown",
- "id": "f3dca5e3",
+ "id": "e39aee50",
"metadata": {},
"source": [
"## The Density Case\n",
@@ -127,7 +127,7 @@
},
{
"cell_type": "markdown",
- "id": "3c299ac0",
+ "id": "cbae9f13",
"metadata": {},
"source": [
"### Definitions and Basic Properties\n",
@@ -205,7 +205,7 @@
},
{
"cell_type": "markdown",
- "id": "31f5669d",
+ "id": "643f0510",
"metadata": {},
"source": [
"### Connection to Stochastic Difference Equations\n",
@@ -327,7 +327,7 @@
},
{
"cell_type": "markdown",
- "id": "9f2e459e",
+ "id": "de3e73b0",
"metadata": {},
"source": [
"### Distribution Dynamics\n",
@@ -414,7 +414,7 @@
},
{
"cell_type": "markdown",
- "id": "c92bea56",
+ "id": "3aeed251",
"metadata": {},
"source": [
"### Computation\n",
@@ -495,7 +495,7 @@
},
{
"cell_type": "markdown",
- "id": "393f2053",
+ "id": "cd06e01c",
"metadata": {},
"source": [
"### Implementation\n",
@@ -520,7 +520,7 @@
},
{
"cell_type": "markdown",
- "id": "57e9b494",
+ "id": "4b6829bb",
"metadata": {},
"source": [
"### Example\n",
@@ -534,7 +534,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a0458b37",
+ "id": "c1e86a68",
"metadata": {
"hide-output": false
},
@@ -584,7 +584,7 @@
},
{
"cell_type": "markdown",
- "id": "91ac51c9",
+ "id": "cc039447",
"metadata": {},
"source": [
"The figure shows part of the density sequence $ \\{\\psi_t\\} $, with each\n",
@@ -599,7 +599,7 @@
},
{
"cell_type": "markdown",
- "id": "8642857e",
+ "id": "9537a6c6",
"metadata": {},
"source": [
"## Beyond Densities\n",
@@ -621,7 +621,7 @@
},
{
"cell_type": "markdown",
- "id": "402e3012",
+ "id": "0baa8e00",
"metadata": {},
"source": [
"### Example and Definitions\n",
@@ -678,7 +678,7 @@
},
{
"cell_type": "markdown",
- "id": "bf9042ea",
+ "id": "3d68a209",
"metadata": {},
"source": [
"### Computation\n",
@@ -693,7 +693,7 @@
},
{
"cell_type": "markdown",
- "id": "498f96e5",
+ "id": "14341d4e",
"metadata": {},
"source": [
"## Stability\n",
@@ -709,7 +709,7 @@
},
{
"cell_type": "markdown",
- "id": "181b8121",
+ "id": "c65f0e52",
"metadata": {},
"source": [
"### Theoretical Results\n",
@@ -792,7 +792,7 @@
},
{
"cell_type": "markdown",
- "id": "a0404fd3",
+ "id": "5e047bb8",
"metadata": {},
"source": [
"### An Example of Stability\n",
@@ -819,7 +819,7 @@
},
{
"cell_type": "markdown",
- "id": "2464798c",
+ "id": "c9562169",
"metadata": {},
"source": [
"### Computing Stationary Densities\n",
@@ -871,7 +871,7 @@
},
{
"cell_type": "markdown",
- "id": "389ac9bd",
+ "id": "7ecf2e25",
"metadata": {},
"source": [
"## Exercises\n",
@@ -882,7 +882,7 @@
},
{
"cell_type": "markdown",
- "id": "88936987",
+ "id": "40941700",
"metadata": {},
"source": [
"## Exercise 2.1\n",
@@ -937,7 +937,7 @@
},
{
"cell_type": "markdown",
- "id": "461b76f7",
+ "id": "a32710ad",
"metadata": {},
"source": [
"## Solution to[ Exercise 2.1](https://python-advanced.quantecon.org/#sd_ex1)\n",
@@ -957,7 +957,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0ba1fb35",
+ "id": "0be6e8be",
"metadata": {
"hide-output": false
},
@@ -996,7 +996,7 @@
},
{
"cell_type": "markdown",
- "id": "669bacc8",
+ "id": "5e1e7a08",
"metadata": {},
"source": [
"\n",
@@ -1005,7 +1005,7 @@
},
{
"cell_type": "markdown",
- "id": "7243cfe0",
+ "id": "e3eeb1be",
"metadata": {},
"source": [
"## Exercise 2.2\n",
@@ -1024,7 +1024,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1d1c227d",
+ "id": "2958d1c2",
"metadata": {
"hide-output": false
},
@@ -1035,7 +1035,7 @@
},
{
"cell_type": "markdown",
- "id": "aa2c7d5a",
+ "id": "faf27e25",
"metadata": {},
"source": [
"## Solution to[ Exercise 2.2](https://python-advanced.quantecon.org/#sd_ex2)\n",
@@ -1046,7 +1046,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4173af32",
+ "id": "ccc2b35b",
"metadata": {
"hide-output": false
},
@@ -1098,7 +1098,7 @@
},
{
"cell_type": "markdown",
- "id": "4c95bcb3",
+ "id": "f2e61708",
"metadata": {},
"source": [
"\n",
@@ -1107,7 +1107,7 @@
},
{
"cell_type": "markdown",
- "id": "f58e15d6",
+ "id": "f2d6f7b8",
"metadata": {},
"source": [
"## Exercise 2.3\n",
@@ -1131,7 +1131,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1b6b133c",
+ "id": "81d9143f",
"metadata": {
"hide-output": false
},
@@ -1153,7 +1153,7 @@
},
{
"cell_type": "markdown",
- "id": "c43ca29a",
+ "id": "8b5b92d8",
"metadata": {},
"source": [
"Each data set is represented by a box, where the top and bottom of the box are the third and first quartiles of the data, and the red line in the center is the median.\n",
@@ -1179,7 +1179,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b8aaf524",
+ "id": "66b391dd",
"metadata": {
"hide-output": false
},
@@ -1190,7 +1190,7 @@
},
{
"cell_type": "markdown",
- "id": "534fd055",
+ "id": "aef936af",
"metadata": {},
"source": [
"For each $ X_0 $ in this set,\n",
@@ -1204,7 +1204,7 @@
},
{
"cell_type": "markdown",
- "id": "c2a093ab",
+ "id": "d05b39f3",
"metadata": {},
"source": [
"## Solution to[ Exercise 2.3](https://python-advanced.quantecon.org/#sd_ex3)\n",
@@ -1218,7 +1218,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1b344810",
+ "id": "e5b8a215",
"metadata": {
"hide-output": false
},
@@ -1252,7 +1252,7 @@
},
{
"cell_type": "markdown",
- "id": "2efce9d3",
+ "id": "6ebfbfb2",
"metadata": {},
"source": [
"## Appendix\n",
@@ -1272,7 +1272,7 @@
}
],
"metadata": {
- "date": 1723011583.4483817,
+ "date": 1723517849.451061,
"filename": "stationary_densities.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/status.ipynb b/_notebooks/status.ipynb
index bee401f2..36704b50 100644
--- a/_notebooks/status.ipynb
+++ b/_notebooks/status.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "2d4a4301",
+ "id": "d33511fe",
"metadata": {},
"source": [
"# Execution Statistics\n",
@@ -11,65 +11,65 @@
"\n",
"[](https://python-advanced.quantecon.org/BCG_complete_mkts.html)[](https://python-advanced.quantecon.org/BCG_incomplete_mkts.html)[](https://python-advanced.quantecon.org/additive_functionals.html)[](https://python-advanced.quantecon.org/amss.html)[](https://python-advanced.quantecon.org/amss2.html)[](https://python-advanced.quantecon.org/amss3.html)[](https://python-advanced.quantecon.org/arellano.html)[](https://python-advanced.quantecon.org/arma.html)[](https://python-advanced.quantecon.org/asset_pricing_lph.html)[](https://python-advanced.quantecon.org/black_litterman.html)[](https://python-advanced.quantecon.org/calvo.html)[](https://python-advanced.quantecon.org/calvo_machine_learn.html)[](https://python-advanced.quantecon.org/cattle_cycles.html)[](https://python-advanced.quantecon.org/chang_credible.html)[](https://python-advanced.quantecon.org/chang_ramsey.html)[](https://python-advanced.quantecon.org/classical_filtering.html)[](https://python-advanced.quantecon.org/coase.html)[](https://python-advanced.quantecon.org/cons_news.html)[](https://python-advanced.quantecon.org/discrete_dp.html)[](https://python-advanced.quantecon.org/dyn_stack.html)[](https://python-advanced.quantecon.org/entropy.html)[](https://python-advanced.quantecon.org/estspec.html)[](https://python-advanced.quantecon.org/five_preferences.html)[](https://python-advanced.quantecon.org/growth_in_dles.html)[](https://python-advanced.quantecon.org/hs_invertibility_example.html)[](https://python-advanced.quantecon.org/hs_recursive_models.html)[](https://python-advanced.quantecon.org/intro.html)[](https://python-advanced.quantecon.org/irfs_in_hall_model.html)[](https://python-advanced.quantecon.org/knowing_forecasts_of_others.html)[](https://python-advanced.quantecon.org/lqramsey.html)[](https://python-advanced.quantecon.org/lu_tricks.html)[](https://python-advanced.quantecon.org/lucas_asset_pricing_dles.html)[](https://python-advanced.quantecon.org/lucas_model.html)[](https://python-advanced.quantecon.org/markov_jump_lq.html)[](https://python-advanced.quantecon.org/matsuyama.html)[](https://python-advanced.quantecon.org/muth_kalman.html)[](https://python-advanced.quantecon.org/opt_tax_recur.html)[](https://python-advanced.quantecon.org/orth_proj.html)[](https://python-advanced.quantecon.org/permanent_income_dles.html)[](https://python-advanced.quantecon.org/rob_markov_perf.html)[](https://python-advanced.quantecon.org/robustness.html)[](https://python-advanced.quantecon.org/rosen_schooling_model.html)[](https://python-advanced.quantecon.org/smoothing.html)[](https://python-advanced.quantecon.org/smoothing_tax.html)[](https://python-advanced.quantecon.org/stationary_densities.html)[](https://python-advanced.quantecon.org/.html)[](https://python-advanced.quantecon.org/tax_smoothing_1.html)[](https://python-advanced.quantecon.org/tax_smoothing_2.html)[](https://python-advanced.quantecon.org/tax_smoothing_3.html)[](https://python-advanced.quantecon.org/troubleshooting.html)[](https://python-advanced.quantecon.org/un_insure.html)[](https://python-advanced.quantecon.org/zreferences.html)|Document|Modified|Method|Run Time (s)|Status|\n",
"|:------------------:|:------------------:|:------------------:|:------------------:|:------------------:|\n",
- "|BCG_complete_mkts|2024-08-07 02:06|cache|52.69|✅|\n",
- "|BCG_incomplete_mkts|2024-08-07 02:07|cache|91.31|✅|\n",
- "|additive_functionals|2024-08-07 02:08|cache|14.59|✅|\n",
- "|amss|2024-08-07 02:12|cache|288.73|✅|\n",
- "|amss2|2024-08-07 02:13|cache|55.36|✅|\n",
- "|amss3|2024-08-07 02:17|cache|244.02|✅|\n",
- "|arellano|2024-08-07 02:19|cache|86.37|✅|\n",
- "|arma|2024-08-07 02:19|cache|9.1|✅|\n",
- "|asset_pricing_lph|2024-08-07 02:19|cache|2.6|✅|\n",
- "|black_litterman|2024-08-07 02:20|cache|32.41|✅|\n",
- "|calvo|2024-08-07 02:20|cache|13.31|✅|\n",
- "|calvo_machine_learn|2024-08-07 02:20|cache|23.95|✅|\n",
- "|cattle_cycles|2024-08-07 02:20|cache|5.91|✅|\n",
- "|chang_credible|2024-08-07 02:23|cache|172.5|✅|\n",
- "|chang_ramsey|2024-08-07 02:29|cache|338.19|✅|\n",
- "|classical_filtering|2024-08-07 02:29|cache|1.3|✅|\n",
- "|coase|2024-08-07 02:29|cache|3.65|✅|\n",
- "|cons_news|2024-08-07 02:29|cache|6.24|✅|\n",
- "|discrete_dp|2024-08-07 02:30|cache|31.49|✅|\n",
- "|dyn_stack|2024-08-07 02:30|cache|7.63|✅|\n",
- "|entropy|2024-08-07 02:30|cache|0.84|✅|\n",
- "|estspec|2024-08-07 02:30|cache|6.6|✅|\n",
- "|five_preferences|2024-08-07 02:30|cache|39.01|✅|\n",
- "|growth_in_dles|2024-08-07 02:31|cache|5.66|✅|\n",
- "|hs_invertibility_example|2024-08-07 02:31|cache|6.08|✅|\n",
- "|hs_recursive_models|2024-08-07 02:31|cache|0.78|✅|\n",
- "|intro|2024-08-07 02:31|cache|0.78|✅|\n",
- "|irfs_in_hall_model|2024-08-07 02:31|cache|5.95|✅|\n",
- "|knowing_forecasts_of_others|2024-08-07 02:31|cache|26.04|✅|\n",
- "|lqramsey|2024-08-07 02:31|cache|7.42|✅|\n",
- "|lu_tricks|2024-08-07 02:31|cache|2.29|✅|\n",
- "|lucas_asset_pricing_dles|2024-08-07 02:31|cache|5.82|✅|\n",
- "|lucas_model|2024-08-07 02:32|cache|16.91|✅|\n",
- "|markov_jump_lq|2024-08-07 02:33|cache|74.99|✅|\n",
- "|matsuyama|2024-08-07 04:33|cache|7206.94|✅|\n",
- "|muth_kalman|2024-08-07 04:33|cache|6.19|✅|\n",
- "|opt_tax_recur|2024-08-07 04:35|cache|111.82|✅|\n",
- "|orth_proj|2024-08-07 04:35|cache|1.17|✅|\n",
- "|permanent_income_dles|2024-08-07 04:35|cache|5.74|✅|\n",
- "|rob_markov_perf|2024-08-07 04:35|cache|5.73|✅|\n",
- "|robustness|2024-08-07 04:35|cache|7.07|✅|\n",
- "|rosen_schooling_model|2024-08-07 04:36|cache|5.87|✅|\n",
- "|smoothing|2024-08-07 04:36|cache|6.15|✅|\n",
- "|smoothing_tax|2024-08-07 04:36|cache|8.64|✅|\n",
- "|stationary_densities|2024-08-07 04:36|cache|10.48|✅|\n",
- "|status|2024-08-07 02:31|cache|0.78|✅|\n",
- "|tax_smoothing_1|2024-08-07 04:36|cache|12.25|✅|\n",
- "|tax_smoothing_2|2024-08-07 04:36|cache|6.6|✅|\n",
- "|tax_smoothing_3|2024-08-07 04:36|cache|6.48|✅|\n",
- "|troubleshooting|2024-08-07 02:31|cache|0.78|✅|\n",
- "|un_insure|2024-08-07 04:37|cache|11.39|✅|\n",
- "|zreferences|2024-08-07 02:31|cache|0.78|✅|\n",
+ "|BCG_complete_mkts|2024-08-11 19:47|cache|47.2|✅|\n",
+ "|BCG_incomplete_mkts|2024-08-11 19:49|cache|87.14|✅|\n",
+ "|additive_functionals|2024-08-11 19:49|cache|14.03|✅|\n",
+ "|amss|2024-08-11 19:54|cache|280.82|✅|\n",
+ "|amss2|2024-08-11 19:54|cache|55.24|✅|\n",
+ "|amss3|2024-08-11 19:59|cache|246.99|✅|\n",
+ "|arellano|2024-08-11 20:00|cache|85.52|✅|\n",
+ "|arma|2024-08-11 20:00|cache|8.23|✅|\n",
+ "|asset_pricing_lph|2024-08-11 20:00|cache|2.39|✅|\n",
+ "|black_litterman|2024-08-11 20:01|cache|31.97|✅|\n",
+ "|calvo|2024-08-11 20:01|cache|12.08|✅|\n",
+ "|calvo_machine_learn|2024-08-11 20:01|cache|22.2|✅|\n",
+ "|cattle_cycles|2024-08-11 20:01|cache|5.48|✅|\n",
+ "|chang_credible|2024-08-11 20:04|cache|168.21|✅|\n",
+ "|chang_ramsey|2024-08-11 20:10|cache|334.02|✅|\n",
+ "|classical_filtering|2024-08-11 20:10|cache|1.42|✅|\n",
+ "|coase|2024-08-11 20:10|cache|3.66|✅|\n",
+ "|cons_news|2024-08-11 20:10|cache|5.68|✅|\n",
+ "|discrete_dp|2024-08-11 20:11|cache|30.72|✅|\n",
+ "|dyn_stack|2024-08-11 20:11|cache|7.3|✅|\n",
+ "|entropy|2024-08-11 20:11|cache|0.87|✅|\n",
+ "|estspec|2024-08-11 20:11|cache|6.2|✅|\n",
+ "|five_preferences|2024-08-11 20:11|cache|37.74|✅|\n",
+ "|growth_in_dles|2024-08-11 20:11|cache|5.5|✅|\n",
+ "|hs_invertibility_example|2024-08-11 20:12|cache|5.44|✅|\n",
+ "|hs_recursive_models|2024-08-11 20:12|cache|0.79|✅|\n",
+ "|intro|2024-08-11 20:12|cache|0.79|✅|\n",
+ "|irfs_in_hall_model|2024-08-11 20:12|cache|5.52|✅|\n",
+ "|knowing_forecasts_of_others|2024-08-11 20:12|cache|44.8|✅|\n",
+ "|lqramsey|2024-08-11 20:13|cache|6.96|✅|\n",
+ "|lu_tricks|2024-08-11 20:13|cache|2.09|✅|\n",
+ "|lucas_asset_pricing_dles|2024-08-11 20:13|cache|5.5|✅|\n",
+ "|lucas_model|2024-08-11 20:13|cache|16.39|✅|\n",
+ "|markov_jump_lq|2024-08-11 20:14|cache|73.73|✅|\n",
+ "|matsuyama|2024-08-11 22:14|cache|7206.61|✅|\n",
+ "|muth_kalman|2024-08-11 22:14|cache|5.77|✅|\n",
+ "|opt_tax_recur|2024-08-11 22:16|cache|107.83|✅|\n",
+ "|orth_proj|2024-08-11 22:16|cache|0.94|✅|\n",
+ "|permanent_income_dles|2024-08-11 22:16|cache|5.39|✅|\n",
+ "|rob_markov_perf|2024-08-11 22:16|cache|5.39|✅|\n",
+ "|robustness|2024-08-11 22:17|cache|6.69|✅|\n",
+ "|rosen_schooling_model|2024-08-11 22:17|cache|5.47|✅|\n",
+ "|smoothing|2024-08-11 22:17|cache|5.93|✅|\n",
+ "|smoothing_tax|2024-08-11 22:17|cache|7.95|✅|\n",
+ "|stationary_densities|2024-08-11 22:17|cache|10.0|✅|\n",
+ "|status|2024-08-11 20:12|cache|0.79|✅|\n",
+ "|tax_smoothing_1|2024-08-11 22:17|cache|11.83|✅|\n",
+ "|tax_smoothing_2|2024-08-11 22:17|cache|5.99|✅|\n",
+ "|tax_smoothing_3|2024-08-11 22:17|cache|5.77|✅|\n",
+ "|troubleshooting|2024-08-11 20:12|cache|0.79|✅|\n",
+ "|un_insure|2024-08-11 22:18|cache|11.25|✅|\n",
+ "|zreferences|2024-08-11 20:12|cache|0.79|✅|\n",
"These lectures are built on `linux` instances through `github actions` so are\n",
"executed using the following [hardware specifications](https://docs.github.com/en/actions/reference/specifications-for-github-hosted-runners#supported-runners-and-hardware-resources)"
]
}
],
"metadata": {
- "date": 1723011583.4708538,
+ "date": 1723517849.4731183,
"filename": "status.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/tax_smoothing_1.ipynb b/_notebooks/tax_smoothing_1.ipynb
index d2c44ebe..8bf9d496 100644
--- a/_notebooks/tax_smoothing_1.ipynb
+++ b/_notebooks/tax_smoothing_1.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "b61ed7a7",
+ "id": "62e6e0f5",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "c1192347",
+ "id": "e6e7d518",
"metadata": {},
"source": [
"# How to Pay for a War: Part 1\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "39da5214",
+ "id": "c7cd41ec",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "8966e32d",
+ "id": "761389d3",
"metadata": {},
"source": [
"## Reader’s Guide\n",
@@ -46,7 +46,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "49bba91b",
+ "id": "cc82a6ba",
"metadata": {
"hide-output": false
},
@@ -59,7 +59,7 @@
},
{
"cell_type": "markdown",
- "id": "80f7ca15",
+ "id": "b8775931",
"metadata": {},
"source": [
"This lecture uses the method of **Markov jump linear quadratic dynamic programming** that is described in lecture\n",
@@ -163,7 +163,7 @@
},
{
"cell_type": "markdown",
- "id": "00955d1a",
+ "id": "24ffa492",
"metadata": {},
"source": [
"## Public Finance Questions\n",
@@ -208,7 +208,7 @@
},
{
"cell_type": "markdown",
- "id": "313c36ac",
+ "id": "02af331d",
"metadata": {},
"source": [
"## Barro (1979) Model\n",
@@ -325,7 +325,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5842387c",
+ "id": "ddadc112",
"metadata": {
"hide-output": false
},
@@ -370,7 +370,7 @@
},
{
"cell_type": "markdown",
- "id": "714830d7",
+ "id": "0a7d3854",
"metadata": {},
"source": [
"We can now create an instance of `LQ`:"
@@ -379,7 +379,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ba13c3af",
+ "id": "cb7370b6",
"metadata": {
"hide-output": false
},
@@ -392,7 +392,7 @@
},
{
"cell_type": "markdown",
- "id": "792072e6",
+ "id": "2dd6ce00",
"metadata": {},
"source": [
"We can see the isomorphism by noting that consumption is a martingale in\n",
@@ -432,7 +432,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ed87a94f",
+ "id": "85b20a69",
"metadata": {
"hide-output": false
},
@@ -443,7 +443,7 @@
},
{
"cell_type": "markdown",
- "id": "8fed3ab2",
+ "id": "7e743fef",
"metadata": {},
"source": [
"This explains the fanning out of the conditional empirical distribution of taxation across time, computing\n",
@@ -454,7 +454,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "555cb804",
+ "id": "5d4328e0",
"metadata": {
"hide-output": false
},
@@ -471,7 +471,7 @@
},
{
"cell_type": "markdown",
- "id": "50620b55",
+ "id": "9a409ec4",
"metadata": {},
"source": [
"We can see a similar, but a smoother pattern, if we plot government debt\n",
@@ -481,7 +481,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "80b8a167",
+ "id": "11dbb8f5",
"metadata": {
"hide-output": false
},
@@ -498,7 +498,7 @@
},
{
"cell_type": "markdown",
- "id": "3144e248",
+ "id": "68d6235e",
"metadata": {},
"source": [
"## Python Class to Solve Markov Jump Linear Quadratic Control Problems\n",
@@ -527,7 +527,7 @@
},
{
"cell_type": "markdown",
- "id": "cbc17b53",
+ "id": "95f0f465",
"metadata": {},
"source": [
"## Barro Model with a Time-varying Interest Rate\n",
@@ -569,7 +569,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ad317ec2",
+ "id": "d9885f38",
"metadata": {
"hide-output": false
},
@@ -601,7 +601,7 @@
},
{
"cell_type": "markdown",
- "id": "f07d76b0",
+ "id": "f844c774",
"metadata": {},
"source": [
"The decision rules are now dependent on the Markov state:"
@@ -610,7 +610,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "09551a3d",
+ "id": "706dc7e1",
"metadata": {
"hide-output": false
},
@@ -622,7 +622,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "57faef42",
+ "id": "dc29bc0b",
"metadata": {
"hide-output": false
},
@@ -633,7 +633,7 @@
},
{
"cell_type": "markdown",
- "id": "e30e1488",
+ "id": "a6b9f451",
"metadata": {},
"source": [
"Simulating a large number of such economies over time reveals\n",
@@ -646,7 +646,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c3401b52",
+ "id": "a306c1e3",
"metadata": {
"hide-output": false
},
@@ -664,7 +664,7 @@
}
],
"metadata": {
- "date": 1723011583.500223,
+ "date": 1723517849.5030415,
"filename": "tax_smoothing_1.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/tax_smoothing_2.ipynb b/_notebooks/tax_smoothing_2.ipynb
index 897f1032..2ef0a48a 100644
--- a/_notebooks/tax_smoothing_2.ipynb
+++ b/_notebooks/tax_smoothing_2.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "967152d2",
+ "id": "9151bed4",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "b9661545",
+ "id": "7ca8d0b7",
"metadata": {},
"source": [
"# How to Pay for a War: Part 2\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9b68af52",
+ "id": "94eea565",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "56b5b01b",
+ "id": "e034ff26",
"metadata": {},
"source": [
"## An Application of Markov Jump Linear Quadratic Dynamic Programming\n",
@@ -83,7 +83,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bd553650",
+ "id": "4aa023a8",
"metadata": {
"hide-output": false
},
@@ -96,7 +96,7 @@
},
{
"cell_type": "markdown",
- "id": "859186bb",
+ "id": "29f85d9a",
"metadata": {},
"source": [
"## Two example specifications\n",
@@ -113,7 +113,7 @@
},
{
"cell_type": "markdown",
- "id": "c2b99bd6",
+ "id": "678cd865",
"metadata": {},
"source": [
"## One- and Two-period Bonds but No Restructuring\n",
@@ -186,7 +186,7 @@
},
{
"cell_type": "markdown",
- "id": "2e8d484d",
+ "id": "be1b361c",
"metadata": {},
"source": [
"## Mapping into an LQ Markov Jump Problem\n",
@@ -351,7 +351,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "56ceccda",
+ "id": "565b17bc",
"metadata": {
"hide-output": false
},
@@ -412,7 +412,7 @@
},
{
"cell_type": "markdown",
- "id": "87a450b4",
+ "id": "866d0ca5",
"metadata": {},
"source": [
"With the above function, we can proceed to solve the model in two steps:\n",
@@ -426,7 +426,7 @@
},
{
"cell_type": "markdown",
- "id": "ae918db6",
+ "id": "842af821",
"metadata": {},
"source": [
"## Penalty on Different Issuance Across Maturities\n",
@@ -479,7 +479,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d9dd2a69",
+ "id": "4c16a139",
"metadata": {
"hide-output": false
},
@@ -533,7 +533,7 @@
},
{
"cell_type": "markdown",
- "id": "32e81555",
+ "id": "1a6b89f3",
"metadata": {},
"source": [
"The above simulations show that when no penalty is imposed on different\n",
@@ -550,7 +550,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a890d8de",
+ "id": "5a157e8d",
"metadata": {
"hide-output": false
},
@@ -594,7 +594,7 @@
},
{
"cell_type": "markdown",
- "id": "47ddefb1",
+ "id": "cf1fa8c5",
"metadata": {},
"source": [
"## A Model with Restructuring\n",
@@ -771,7 +771,7 @@
},
{
"cell_type": "markdown",
- "id": "db71da49",
+ "id": "bb769f04",
"metadata": {},
"source": [
"## Restructuring as a Markov Jump Linear Quadratic Control Problem\n",
@@ -784,7 +784,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b58f04da",
+ "id": "749a79a4",
"metadata": {
"hide-output": false
},
@@ -839,7 +839,7 @@
},
{
"cell_type": "markdown",
- "id": "15b9b582",
+ "id": "1e94d86b",
"metadata": {},
"source": [
"### Example with Restructuring\n",
@@ -870,7 +870,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "44586a20",
+ "id": "c25027f5",
"metadata": {
"hide-output": false
},
@@ -915,7 +915,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4cba06c3",
+ "id": "21d9a6c4",
"metadata": {
"hide-output": false
},
@@ -943,7 +943,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c045fad2",
+ "id": "fd35a4ef",
"metadata": {
"hide-output": false
},
@@ -960,7 +960,7 @@
}
],
"metadata": {
- "date": 1723011583.525245,
+ "date": 1723517849.5289707,
"filename": "tax_smoothing_2.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/tax_smoothing_3.ipynb b/_notebooks/tax_smoothing_3.ipynb
index 91292c57..ca88df95 100644
--- a/_notebooks/tax_smoothing_3.ipynb
+++ b/_notebooks/tax_smoothing_3.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "eae43c49",
+ "id": "2b853ad7",
"metadata": {},
"source": [
"\n",
@@ -13,7 +13,7 @@
},
{
"cell_type": "markdown",
- "id": "3024eff6",
+ "id": "f55bf453",
"metadata": {},
"source": [
"# How to Pay for a War: Part 3\n",
@@ -24,7 +24,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bcd64bdf",
+ "id": "8769f137",
"metadata": {
"hide-output": false
},
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "8fba4baf",
+ "id": "d8861320",
"metadata": {},
"source": [
"## Another Application of Markov Jump Linear Quadratic Dynamic Programming\n",
@@ -64,7 +64,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "31281518",
+ "id": "3a11a1ce",
"metadata": {
"hide-output": false
},
@@ -77,7 +77,7 @@
},
{
"cell_type": "markdown",
- "id": "f0760b35",
+ "id": "6436813f",
"metadata": {},
"source": [
"## Roll-Over Risk\n",
@@ -129,7 +129,7 @@
},
{
"cell_type": "markdown",
- "id": "e568c8ec",
+ "id": "a94267b5",
"metadata": {},
"source": [
"## A Dead End\n",
@@ -167,7 +167,7 @@
},
{
"cell_type": "markdown",
- "id": "fdb73a38",
+ "id": "96c9236f",
"metadata": {},
"source": [
"## Better Representation of Roll-Over Risk\n",
@@ -221,7 +221,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "61245e39",
+ "id": "79ff4b67",
"metadata": {
"hide-output": false
},
@@ -281,7 +281,7 @@
},
{
"cell_type": "markdown",
- "id": "3e4a0558",
+ "id": "5136c3b8",
"metadata": {},
"source": [
"This model is simulated below, using the same process for $ G_t $ as\n",
@@ -304,7 +304,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3db19301",
+ "id": "96a57598",
"metadata": {
"hide-output": false
},
@@ -332,7 +332,7 @@
},
{
"cell_type": "markdown",
- "id": "d547670d",
+ "id": "52b5f7b4",
"metadata": {},
"source": [
"We can adjust the model so that, rather than having debt fluctuate\n",
@@ -346,7 +346,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a34deefe",
+ "id": "5070b462",
"metadata": {
"hide-output": false
},
@@ -387,7 +387,7 @@
},
{
"cell_type": "markdown",
- "id": "7477a2f1",
+ "id": "57f41346",
"metadata": {},
"source": [
"With a lower interest rate, the government has an incentive to\n",
@@ -403,7 +403,7 @@
}
],
"metadata": {
- "date": 1723011583.539983,
+ "date": 1723517849.5434592,
"filename": "tax_smoothing_3.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/troubleshooting.ipynb b/_notebooks/troubleshooting.ipynb
index 1bdad675..b0de6b4e 100644
--- a/_notebooks/troubleshooting.ipynb
+++ b/_notebooks/troubleshooting.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "a66ce247",
+ "id": "5565ac3b",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "ac92818d",
+ "id": "6181f994",
"metadata": {},
"source": [
"# Troubleshooting\n",
@@ -21,7 +21,7 @@
},
{
"cell_type": "markdown",
- "id": "f1b9445c",
+ "id": "2dbb94a8",
"metadata": {},
"source": [
"## Fixing Your Local Environment\n",
@@ -63,7 +63,7 @@
},
{
"cell_type": "markdown",
- "id": "c2bc18e7",
+ "id": "5a088326",
"metadata": {},
"source": [
"## Reporting an Issue\n",
@@ -80,7 +80,7 @@
}
],
"metadata": {
- "date": 1723011583.5446067,
+ "date": 1723517849.547474,
"filename": "troubleshooting.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/un_insure.ipynb b/_notebooks/un_insure.ipynb
index 8aaf284f..c369be62 100644
--- a/_notebooks/un_insure.ipynb
+++ b/_notebooks/un_insure.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "452cb78e",
+ "id": "4d197987",
"metadata": {},
"source": [
"# Optimal Unemployment Insurance"
@@ -10,7 +10,7 @@
},
{
"cell_type": "markdown",
- "id": "318702f0",
+ "id": "f8d667cb",
"metadata": {},
"source": [
"## Overview\n",
@@ -28,7 +28,7 @@
},
{
"cell_type": "markdown",
- "id": "9de9af06",
+ "id": "4e053857",
"metadata": {},
"source": [
"## Shavell and Weiss’s Model\n",
@@ -88,7 +88,7 @@
},
{
"cell_type": "markdown",
- "id": "d76276c8",
+ "id": "dd4f8cac",
"metadata": {},
"source": [
"### Autarky\n",
@@ -160,7 +160,7 @@
},
{
"cell_type": "markdown",
- "id": "b5e9fea9",
+ "id": "2270158f",
"metadata": {},
"source": [
"### Full Information\n",
@@ -274,7 +274,7 @@
},
{
"cell_type": "markdown",
- "id": "4fe52eee",
+ "id": "5113e814",
"metadata": {},
"source": [
"### Incentive Problem\n",
@@ -340,7 +340,7 @@
},
{
"cell_type": "markdown",
- "id": "eadf3cc8",
+ "id": "fca560d4",
"metadata": {},
"source": [
"## Private Information\n",
@@ -445,7 +445,7 @@
},
{
"cell_type": "markdown",
- "id": "54f89ef2",
+ "id": "f27387a8",
"metadata": {},
"source": [
"### Computational Details\n",
@@ -534,7 +534,7 @@
},
{
"cell_type": "markdown",
- "id": "6e8ec14d",
+ "id": "876ec1d2",
"metadata": {},
"source": [
"### Python Computations\n",
@@ -547,7 +547,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cb0afd39",
+ "id": "26a4adcd",
"metadata": {
"hide-output": false
},
@@ -560,7 +560,7 @@
},
{
"cell_type": "markdown",
- "id": "c47c33dc",
+ "id": "485489f4",
"metadata": {},
"source": [
"We first create a class to set up a particular parametrization."
@@ -569,7 +569,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e07cafb1",
+ "id": "b5e2d057",
"metadata": {
"hide-output": false
},
@@ -592,7 +592,7 @@
},
{
"cell_type": "markdown",
- "id": "717fcc21",
+ "id": "712367b1",
"metadata": {},
"source": [
"### Parameter Values\n",
@@ -607,7 +607,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2a8b8d21",
+ "id": "23efb8b3",
"metadata": {
"hide-output": false
},
@@ -633,7 +633,7 @@
},
{
"cell_type": "markdown",
- "id": "13b000eb",
+ "id": "cf518561",
"metadata": {},
"source": [
"Recall that under autarky the value for an unemployed worker\n",
@@ -672,7 +672,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fac0a3d5",
+ "id": "3fa64ea8",
"metadata": {
"hide-output": false
},
@@ -691,7 +691,7 @@
},
{
"cell_type": "markdown",
- "id": "5855f673",
+ "id": "449e3f19",
"metadata": {},
"source": [
"Since the calibration exercise is to match the hazard rate under autarky to the data, we must find an interest rate $ r $ to match `p(a,r) = 0.1`.\n",
@@ -704,7 +704,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6a4fb9ff",
+ "id": "ffb3c6c1",
"metadata": {
"hide-output": false
},
@@ -722,7 +722,7 @@
},
{
"cell_type": "markdown",
- "id": "d597ec64",
+ "id": "a9c7b452",
"metadata": {},
"source": [
"Now, let us create an instance of the model with our parametrization"
@@ -731,7 +731,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3ac9846f",
+ "id": "74e13a8e",
"metadata": {
"hide-output": false
},
@@ -745,7 +745,7 @@
},
{
"cell_type": "markdown",
- "id": "6f43eead",
+ "id": "6644dd10",
"metadata": {},
"source": [
"We want to compute an $ r $ that is consistent with the hazard rate 0.1 in autarky.\n",
@@ -756,7 +756,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2cd0dab5",
+ "id": "0b36bed6",
"metadata": {
"hide-output": false
},
@@ -773,7 +773,7 @@
},
{
"cell_type": "markdown",
- "id": "aad65c57",
+ "id": "2681aca4",
"metadata": {},
"source": [
"Now that we have calibrated our interest rate $ r $, we can continue with solving the model with private information."
@@ -781,7 +781,7 @@
},
{
"cell_type": "markdown",
- "id": "60dc8357",
+ "id": "251ba17c",
"metadata": {},
"source": [
"### Computation under Private Information\n",
@@ -806,7 +806,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a720ad4e",
+ "id": "46ff367c",
"metadata": {
"hide-output": false
},
@@ -836,7 +836,7 @@
},
{
"cell_type": "markdown",
- "id": "5ccd4d80",
+ "id": "b9fdbcbb",
"metadata": {},
"source": [
"With these analytical solutions for optimal $ c $ and $ a $ in hand, we can reduce the minimization to [(39.12)](#equation-eq-hugo23) in the single variable\n",
@@ -847,7 +847,7 @@
},
{
"cell_type": "markdown",
- "id": "aa4c35a7",
+ "id": "d7acc99d",
"metadata": {},
"source": [
"### Algorithm\n",
@@ -866,7 +866,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "68773b7b",
+ "id": "d3f56aa6",
"metadata": {
"hide-output": false
},
@@ -919,7 +919,7 @@
},
{
"cell_type": "markdown",
- "id": "10566abd",
+ "id": "abc2e043",
"metadata": {},
"source": [
"The below code executes steps 4 and 5 in the Algorithm until convergence to a function $ C^*(V) $."
@@ -928,7 +928,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "97d83089",
+ "id": "5a4458bf",
"metadata": {
"hide-output": false
},
@@ -956,7 +956,7 @@
},
{
"cell_type": "markdown",
- "id": "fdaea53f",
+ "id": "a32a7ab2",
"metadata": {},
"source": [
"## Outcomes\n",
@@ -967,7 +967,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4410981c",
+ "id": "29b472d7",
"metadata": {
"hide-output": false
},
@@ -993,7 +993,7 @@
},
{
"cell_type": "markdown",
- "id": "65966112",
+ "id": "c1dff72f",
"metadata": {},
"source": [
"### Replacement Ratios and Continuation Values\n",
@@ -1008,7 +1008,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "040aa7d4",
+ "id": "f1f01523",
"metadata": {
"hide-output": false
},
@@ -1028,7 +1028,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0375576c",
+ "id": "06a6dfb0",
"metadata": {
"hide-output": false
},
@@ -1045,7 +1045,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c3933275",
+ "id": "232fb4f6",
"metadata": {
"hide-output": false
},
@@ -1081,7 +1081,7 @@
},
{
"cell_type": "markdown",
- "id": "0e34f309",
+ "id": "b935a57d",
"metadata": {},
"source": [
"For an initial promised value $ V^u = V_{\\rm aut} $, the planner chooses the autarky level of $ 0 $ for the replacement ratio and instructs the worker to search at the autarky search intensity, regardless of the duration of unemployment\n",
@@ -1091,7 +1091,7 @@
},
{
"cell_type": "markdown",
- "id": "fe7cc8fb",
+ "id": "b7bb6f07",
"metadata": {},
"source": [
"### Interpretations\n",
@@ -1145,7 +1145,7 @@
}
],
"metadata": {
- "date": 1723011583.8332434,
+ "date": 1723517849.5894141,
"filename": "un_insure.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_notebooks/zreferences.ipynb b/_notebooks/zreferences.ipynb
index a9922d98..c9260ab2 100644
--- a/_notebooks/zreferences.ipynb
+++ b/_notebooks/zreferences.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "5e9b054a",
+ "id": "da145b7b",
"metadata": {},
"source": [
"\n",
@@ -11,7 +11,7 @@
},
{
"cell_type": "markdown",
- "id": "09f9da81",
+ "id": "a90887a3",
"metadata": {},
"source": [
"# References\n",
@@ -325,7 +325,7 @@
}
],
"metadata": {
- "date": 1723011583.8656945,
+ "date": 1723517849.6177776,
"filename": "zreferences.md",
"kernelspec": {
"display_name": "Python",
diff --git a/_pdf/quantecon-python-advanced.pdf b/_pdf/quantecon-python-advanced.pdf
index 2655fcdd..1329f83f 100644
Binary files a/_pdf/quantecon-python-advanced.pdf and b/_pdf/quantecon-python-advanced.pdf differ
diff --git a/_sources/BCG_complete_mkts.ipynb b/_sources/BCG_complete_mkts.ipynb
index 4f43fbea..3f1b1dab 100644
--- a/_sources/BCG_complete_mkts.ipynb
+++ b/_sources/BCG_complete_mkts.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "779acb85",
+ "id": "749339a8",
"metadata": {},
"source": [
"(bcg_complete_mkts_final)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f8c74d16",
+ "id": "a83fa03e",
"metadata": {
"tags": [
"hide-output"
@@ -36,7 +36,7 @@
},
{
"cell_type": "markdown",
- "id": "18f7bb1e",
+ "id": "f4fd4aba",
"metadata": {},
"source": [
"## Introduction\n",
@@ -875,7 +875,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "81f800b8",
+ "id": "4e44b88d",
"metadata": {},
"outputs": [],
"source": [
@@ -889,7 +889,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1aa4b0ab",
+ "id": "acad2b36",
"metadata": {},
"outputs": [],
"source": [
@@ -1082,7 +1082,7 @@
},
{
"cell_type": "markdown",
- "id": "9bf102b9",
+ "id": "b4e97bad",
"metadata": {},
"source": [
"### Examples\n",
@@ -1105,7 +1105,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f7daac4a",
+ "id": "6d5562fd",
"metadata": {},
"outputs": [],
"source": [
@@ -1116,7 +1116,7 @@
},
{
"cell_type": "markdown",
- "id": "0630b976",
+ "id": "5a7bc3b7",
"metadata": {},
"source": [
"Let’s plot the agents’ time-1 endowments with respect to shocks to see\n",
@@ -1126,7 +1126,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "20a2fc2e",
+ "id": "f26ebc1f",
"metadata": {},
"outputs": [],
"source": [
@@ -1161,7 +1161,7 @@
},
{
"cell_type": "markdown",
- "id": "7b0fd273",
+ "id": "bbb1f5da",
"metadata": {},
"source": [
"Let’s also compare the optimal capital stock, $k$, and optimal\n",
@@ -1171,7 +1171,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f175bfbd",
+ "id": "5293c1e9",
"metadata": {},
"outputs": [],
"source": [
@@ -1192,7 +1192,7 @@
},
{
"cell_type": "markdown",
- "id": "87c7e7ca",
+ "id": "e0f94d09",
"metadata": {},
"source": [
"#### 2nd example\n",
@@ -1207,7 +1207,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "985f353b",
+ "id": "3b07ac6e",
"metadata": {},
"outputs": [],
"source": [
@@ -1237,7 +1237,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "905231dd",
+ "id": "3e258a63",
"metadata": {},
"outputs": [],
"source": [
@@ -1248,7 +1248,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6ab89070",
+ "id": "5dda0e74",
"metadata": {},
"outputs": [],
"source": [
@@ -1260,7 +1260,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f248698e",
+ "id": "b5671ff5",
"metadata": {},
"outputs": [],
"source": [
diff --git a/_sources/BCG_incomplete_mkts.ipynb b/_sources/BCG_incomplete_mkts.ipynb
index 93878189..31488169 100644
--- a/_sources/BCG_incomplete_mkts.ipynb
+++ b/_sources/BCG_incomplete_mkts.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "de1add4d",
+ "id": "d8ad31de",
"metadata": {},
"source": [
"(bcg_incomplete_final)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "594d5349",
+ "id": "d5ff7d93",
"metadata": {
"tags": [
"hide-output"
@@ -36,7 +36,7 @@
},
{
"cell_type": "markdown",
- "id": "1a535621",
+ "id": "b1c9c964",
"metadata": {},
"source": [
"## Introduction\n",
@@ -711,7 +711,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0b404259",
+ "id": "d539cea5",
"metadata": {},
"outputs": [],
"source": [
@@ -724,7 +724,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d9d89698",
+ "id": "4e8bac26",
"metadata": {},
"outputs": [],
"source": [
@@ -1215,7 +1215,7 @@
},
{
"cell_type": "markdown",
- "id": "71515d6d",
+ "id": "85f8840b",
"metadata": {},
"source": [
"## Examples\n",
@@ -1231,7 +1231,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "66a11d75",
+ "id": "90f1bf33",
"metadata": {
"tags": [
"hide-output"
@@ -1246,7 +1246,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "93b26633",
+ "id": "f326fe6c",
"metadata": {},
"outputs": [],
"source": [
@@ -1257,7 +1257,7 @@
},
{
"cell_type": "markdown",
- "id": "60b378a4",
+ "id": "25edbe98",
"metadata": {},
"source": [
"Python reports to us that the equilibrium firm value is $V=0.101$,\n",
@@ -1274,7 +1274,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "84c15ed0",
+ "id": "44564834",
"metadata": {},
"outputs": [],
"source": [
@@ -1286,7 +1286,7 @@
},
{
"cell_type": "markdown",
- "id": "2ac4d392",
+ "id": "05632a2d",
"metadata": {},
"source": [
"Up to the approximation involved in using a discrete grid, these numbers\n",
@@ -1303,7 +1303,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "86bb1b7c",
+ "id": "d8691d58",
"metadata": {},
"outputs": [],
"source": [
@@ -1342,7 +1342,7 @@
},
{
"cell_type": "markdown",
- "id": "d40f7581",
+ "id": "386cd465",
"metadata": {},
"source": [
"#### A Modigliani-Miller theorem?\n",
@@ -1436,7 +1436,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a7954aea",
+ "id": "39402312",
"metadata": {},
"outputs": [],
"source": [
@@ -1658,7 +1658,7 @@
},
{
"cell_type": "markdown",
- "id": "2eead774",
+ "id": "54d4e969",
"metadata": {},
"source": [
"Here is our strategy for checking *stability* of an equilibrium.\n",
@@ -1684,7 +1684,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "baa52bb3",
+ "id": "cd10cfdf",
"metadata": {},
"outputs": [],
"source": [
@@ -1730,7 +1730,7 @@
},
{
"cell_type": "markdown",
- "id": "2920e2d9",
+ "id": "ce321d03",
"metadata": {},
"source": [
"In the above 3D surface of prospective firm valuations, the perturbed\n",
@@ -1748,7 +1748,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d3f942c1",
+ "id": "d788af52",
"metadata": {},
"outputs": [],
"source": [
@@ -1793,7 +1793,7 @@
},
{
"cell_type": "markdown",
- "id": "9b790d8d",
+ "id": "4069ff02",
"metadata": {},
"source": [
"In contrast to $(k^*,b^* - e)$, the 3D surface for\n",
@@ -1813,7 +1813,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b3d0f0fc",
+ "id": "c82567c4",
"metadata": {},
"outputs": [],
"source": [
@@ -1822,7 +1822,7 @@
},
{
"cell_type": "markdown",
- "id": "30bf1454",
+ "id": "26af5a43",
"metadata": {},
"source": [
"Our two *stability experiments* suggest that the equilibrium capital\n",
@@ -1843,7 +1843,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0d0a3eb2",
+ "id": "155031e5",
"metadata": {},
"outputs": [],
"source": [
@@ -1879,7 +1879,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e3768799",
+ "id": "055d9050",
"metadata": {},
"outputs": [],
"source": [
@@ -1914,7 +1914,7 @@
},
{
"cell_type": "markdown",
- "id": "69e7490d",
+ "id": "5368d859",
"metadata": {},
"source": [
"### Comments on equilibrium pricing functions\n",
@@ -1950,7 +1950,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ca080300",
+ "id": "97d892b0",
"metadata": {
"tags": [
"hide-output"
@@ -2007,7 +2007,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b37f6f7b",
+ "id": "4e350bf3",
"metadata": {},
"outputs": [],
"source": [
@@ -2044,7 +2044,7 @@
},
{
"cell_type": "markdown",
- "id": "96993cb6",
+ "id": "cd8c3713",
"metadata": {},
"source": [
"## A picture worth a thousand words\n",
@@ -2064,7 +2064,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "185b2033",
+ "id": "1eb8f1b8",
"metadata": {},
"outputs": [],
"source": [
@@ -2094,7 +2094,7 @@
},
{
"cell_type": "markdown",
- "id": "69c8bb7c",
+ "id": "a7a41356",
"metadata": {},
"source": [
"It is rewarding to stare at the above plots too.\n",
diff --git a/_sources/additive_functionals.ipynb b/_sources/additive_functionals.ipynb
index 47daf0bf..0df009e7 100644
--- a/_sources/additive_functionals.ipynb
+++ b/_sources/additive_functionals.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "1e24a6e5",
+ "id": "26e87da7",
"metadata": {},
"source": [
"(additive_functionals)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ea936ddc",
+ "id": "87e475bd",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "5c18957c",
+ "id": "597e29b4",
"metadata": {},
"source": [
"## Overview\n",
@@ -81,7 +81,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6e436d16",
+ "id": "284c3c70",
"metadata": {},
"outputs": [],
"source": [
@@ -94,7 +94,7 @@
},
{
"cell_type": "markdown",
- "id": "47677740",
+ "id": "e4aa390c",
"metadata": {},
"source": [
"## A Particular Additive Functional\n",
@@ -263,7 +263,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b59ef329",
+ "id": "4563e2b3",
"metadata": {},
"outputs": [],
"source": [
@@ -421,7 +421,7 @@
},
{
"cell_type": "markdown",
- "id": "a6002908",
+ "id": "0dec838e",
"metadata": {},
"source": [
"#### Plotting\n",
@@ -432,7 +432,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1575036a",
+ "id": "a8583b03",
"metadata": {
"tags": [
"collapse-20"
@@ -717,7 +717,7 @@
},
{
"cell_type": "markdown",
- "id": "f549bc41",
+ "id": "60deda43",
"metadata": {},
"source": [
"For now, we just plot $y_t$ and $x_t$, postponing until later a description of exactly how we compute them.\n",
@@ -728,7 +728,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "859121c8",
+ "id": "f7af44c7",
"metadata": {},
"outputs": [],
"source": [
@@ -765,7 +765,7 @@
},
{
"cell_type": "markdown",
- "id": "7fbca530",
+ "id": "39f9f7cb",
"metadata": {},
"source": [
"Notice the irregular but persistent growth in $y_t$.\n",
@@ -918,7 +918,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d7d3bcc5",
+ "id": "63f5200d",
"metadata": {},
"outputs": [],
"source": [
@@ -928,7 +928,7 @@
},
{
"cell_type": "markdown",
- "id": "36befdd7",
+ "id": "12249c0c",
"metadata": {},
"source": [
"When we plot multiple realizations of a component in the 2nd, 3rd, and 4th panels, we also plot the population 95% probability coverage sets computed using the LinearStateSpace class.\n",
@@ -986,7 +986,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ff8ddf20",
+ "id": "a21eb9b2",
"metadata": {},
"outputs": [],
"source": [
@@ -996,7 +996,7 @@
},
{
"cell_type": "markdown",
- "id": "37c0a81c",
+ "id": "e83e4e6e",
"metadata": {},
"source": [
"As before, when we plotted multiple realizations of a component in the 2nd, 3rd, and 4th panels, we also plotted population 95% confidence bands computed using the LinearStateSpace class.\n",
@@ -1032,7 +1032,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e2b23822",
+ "id": "945f355f",
"metadata": {},
"outputs": [],
"source": [
@@ -1043,7 +1043,7 @@
},
{
"cell_type": "markdown",
- "id": "2eb72e45",
+ "id": "79421901",
"metadata": {},
"source": [
"The dotted line in the above graph is the mean $E \\tilde M_t = 1$ of the martingale.\n",
@@ -1088,7 +1088,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "06fe64c0",
+ "id": "49befe4d",
"metadata": {},
"outputs": [],
"source": [
@@ -1198,7 +1198,7 @@
},
{
"cell_type": "markdown",
- "id": "19fd06c3",
+ "id": "eea5e5ac",
"metadata": {},
"source": [
"The heavy lifting is done inside the `AMF_LSS_VAR` class.\n",
@@ -1209,7 +1209,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b2cb13e7",
+ "id": "2853e402",
"metadata": {},
"outputs": [],
"source": [
@@ -1257,7 +1257,7 @@
},
{
"cell_type": "markdown",
- "id": "438fa761",
+ "id": "a4477d3c",
"metadata": {},
"source": [
"Now that we have these functions in our toolkit, let's apply them to run some\n",
@@ -1267,7 +1267,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d871e66a",
+ "id": "e3809ddb",
"metadata": {},
"outputs": [],
"source": [
@@ -1308,7 +1308,7 @@
},
{
"cell_type": "markdown",
- "id": "a7ee7f70",
+ "id": "2927b9cd",
"metadata": {},
"source": [
"Let's plot the probability density functions for $\\log {\\widetilde M}_t$ for\n",
@@ -1334,7 +1334,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9c1d74b0",
+ "id": "7fcfb814",
"metadata": {},
"outputs": [],
"source": [
@@ -1387,7 +1387,7 @@
},
{
"cell_type": "markdown",
- "id": "e8565b20",
+ "id": "f3f01893",
"metadata": {},
"source": [
"These probability density functions help us understand mechanics underlying the **peculiar property** of our multiplicative martingale\n",
diff --git a/_sources/amss.ipynb b/_sources/amss.ipynb
index 59ebff1d..18bbae8b 100644
--- a/_sources/amss.ipynb
+++ b/_sources/amss.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "fa2358c5",
+ "id": "e03205a2",
"metadata": {},
"source": [
"(opt_tax_amss)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2a8778d6",
+ "id": "c97ac204",
"metadata": {
"tags": [
"hide-output"
@@ -36,7 +36,7 @@
},
{
"cell_type": "markdown",
- "id": "92bc0805",
+ "id": "e598ead2",
"metadata": {},
"source": [
"## Overview\n",
@@ -47,7 +47,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fca561a4",
+ "id": "40e92476",
"metadata": {},
"outputs": [],
"source": [
@@ -62,7 +62,7 @@
},
{
"cell_type": "markdown",
- "id": "5ea712c5",
+ "id": "a4745a1f",
"metadata": {},
"source": [
"In {doc}`an earlier lecture `, we described a model of\n",
@@ -423,7 +423,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fa01dc69",
+ "id": "33ac16de",
"metadata": {
"load": "_static/lecture_specific/opt_tax_recur/sequential_allocation.py",
"tags": [
@@ -634,7 +634,7 @@
},
{
"cell_type": "markdown",
- "id": "a4928817",
+ "id": "aee5afff",
"metadata": {},
"source": [
"To analyze the AMSS model, we find it useful to adopt a recursive formulation\n",
@@ -913,7 +913,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a52563b2",
+ "id": "c75541b5",
"metadata": {
"load": "_static/lecture_specific/amss/recursive_allocation.py",
"tags": [
@@ -1138,7 +1138,7 @@
},
{
"cell_type": "markdown",
- "id": "b8ae9cc0",
+ "id": "c9443b9e",
"metadata": {},
"source": [
"## Examples\n",
@@ -1207,7 +1207,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "394706f4",
+ "id": "2e420811",
"metadata": {
"load": "_static/lecture_specific/opt_tax_recur/crra_utility.py"
},
@@ -1263,7 +1263,7 @@
},
{
"cell_type": "markdown",
- "id": "3a7bcb4b",
+ "id": "a173f69e",
"metadata": {},
"source": [
"The following figure plots Ramsey plans under complete and incomplete\n",
@@ -1279,7 +1279,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7d0cf48a",
+ "id": "ed74421f",
"metadata": {},
"outputs": [],
"source": [
@@ -1313,7 +1313,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "45de144b",
+ "id": "64f0f3a2",
"metadata": {},
"outputs": [],
"source": [
@@ -1333,7 +1333,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8705379a",
+ "id": "97a9261c",
"metadata": {
"tags": [
"scroll-output"
@@ -1349,7 +1349,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "340e34f3",
+ "id": "4fc7cd77",
"metadata": {},
"outputs": [],
"source": [
@@ -1360,7 +1360,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "12d4463d",
+ "id": "f1681094",
"metadata": {},
"outputs": [],
"source": [
@@ -1392,7 +1392,7 @@
},
{
"cell_type": "markdown",
- "id": "4a6e8195",
+ "id": "5d5acba8",
"metadata": {},
"source": [
"How a Ramsey planner responds to war depends on the structure of the asset market.\n",
@@ -1453,7 +1453,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6b30daa2",
+ "id": "350b8331",
"metadata": {
"load": "_static/lecture_specific/opt_tax_recur/log_utility.py"
},
@@ -1499,7 +1499,7 @@
},
{
"cell_type": "markdown",
- "id": "05a919c4",
+ "id": "dd29378a",
"metadata": {},
"source": [
"With these preferences, Ramsey tax rates will vary even in the Lucas-Stokey\n",
@@ -1513,7 +1513,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "167fab1d",
+ "id": "fb24ae27",
"metadata": {},
"outputs": [],
"source": [
@@ -1548,7 +1548,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e74816a4",
+ "id": "c0d13f71",
"metadata": {
"tags": [
"scroll-output"
@@ -1565,7 +1565,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5caea7c7",
+ "id": "f21a0b63",
"metadata": {},
"outputs": [],
"source": [
@@ -1575,7 +1575,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f2f03da3",
+ "id": "e0c37af3",
"metadata": {},
"outputs": [],
"source": [
@@ -1605,7 +1605,7 @@
},
{
"cell_type": "markdown",
- "id": "033a10c0",
+ "id": "9828a35b",
"metadata": {},
"source": [
"When the government experiences a prolonged period of peace, it is able to reduce\n",
@@ -1627,7 +1627,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1605ec33",
+ "id": "e6c97a3e",
"metadata": {},
"outputs": [],
"source": [
@@ -1641,7 +1641,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f3a2d448",
+ "id": "aeb0dbb9",
"metadata": {},
"outputs": [],
"source": [
@@ -1667,7 +1667,7 @@
},
{
"cell_type": "markdown",
- "id": "3a0f92af",
+ "id": "06603420",
"metadata": {},
"source": [
"[^fn_a]: In an allocation that solves the Ramsey problem and that levies distorting\n",
diff --git a/_sources/amss2.ipynb b/_sources/amss2.ipynb
index ecc2937b..272a537f 100644
--- a/_sources/amss2.ipynb
+++ b/_sources/amss2.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "f4f77419",
+ "id": "1a7e8746",
"metadata": {},
"source": [
"(amss2)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f4ed42fc",
+ "id": "02f630fc",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "d38b0489",
+ "id": "45850cc8",
"metadata": {},
"source": [
"## Overview\n",
@@ -96,7 +96,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d4aee38e",
+ "id": "ba3a81ff",
"metadata": {},
"outputs": [],
"source": [
@@ -106,7 +106,7 @@
},
{
"cell_type": "markdown",
- "id": "04635bf9",
+ "id": "312a1262",
"metadata": {},
"source": [
"## Forces at Work\n",
@@ -265,7 +265,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "56543598",
+ "id": "269f9af8",
"metadata": {
"load": "_static/lecture_specific/amss2/crra_utility.py"
},
@@ -313,7 +313,7 @@
},
{
"cell_type": "markdown",
- "id": "9148475e",
+ "id": "5a5e5017",
"metadata": {},
"source": [
"## Example Economy\n",
@@ -347,7 +347,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4b9dcb7c",
+ "id": "4b3df325",
"metadata": {
"load": "_static/lecture_specific/amss2/sequential_allocation.py",
"tags": [
@@ -519,7 +519,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "817ecae6",
+ "id": "85a61bea",
"metadata": {
"load": "_static/lecture_specific/amss2/recursive_allocation.py",
"tags": [
@@ -831,7 +831,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2687b2fc",
+ "id": "25dafc71",
"metadata": {
"load": "_static/lecture_specific/amss2/utilities.py",
"tags": [
@@ -913,7 +913,7 @@
},
{
"cell_type": "markdown",
- "id": "8ed1545f",
+ "id": "59a5d4ae",
"metadata": {},
"source": [
"## Reverse Engineering Strategy\n",
@@ -969,7 +969,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "501925a9",
+ "id": "46d31725",
"metadata": {},
"outputs": [],
"source": [
@@ -1013,7 +1013,7 @@
},
{
"cell_type": "markdown",
- "id": "cd6818fc",
+ "id": "70d83da0",
"metadata": {},
"source": [
"To recover and print out $\\bar b$"
@@ -1022,7 +1022,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c98bfb81",
+ "id": "9c6afb1f",
"metadata": {},
"outputs": [],
"source": [
@@ -1032,7 +1032,7 @@
},
{
"cell_type": "markdown",
- "id": "de80beb1",
+ "id": "2bfdb104",
"metadata": {},
"source": [
"To complete the reverse engineering exercise by jointly determining $c_0, b_0$, we\n",
@@ -1042,7 +1042,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c0dfb707",
+ "id": "4d592d13",
"metadata": {},
"outputs": [],
"source": [
@@ -1067,7 +1067,7 @@
},
{
"cell_type": "markdown",
- "id": "786cbdaa",
+ "id": "b1553f05",
"metadata": {},
"source": [
"To solve the equations for $c_0, b_0$, we use SciPy's fsolve function"
@@ -1076,7 +1076,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2515b609",
+ "id": "8fc855b1",
"metadata": {},
"outputs": [],
"source": [
@@ -1087,7 +1087,7 @@
},
{
"cell_type": "markdown",
- "id": "0397a388",
+ "id": "419506c4",
"metadata": {},
"source": [
"Thus, we have reverse engineered an initial $b0 = -1.038698407551764$ that ought to render the AMSS measurability constraints slack.\n",
@@ -1103,7 +1103,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cca6f276",
+ "id": "e67a16ac",
"metadata": {
"tags": [
"scroll-output"
@@ -1153,7 +1153,7 @@
},
{
"cell_type": "markdown",
- "id": "8bd36b76",
+ "id": "934f3710",
"metadata": {},
"source": [
"The Ramsey allocations and Ramsey outcomes are **identical** for the Lucas-Stokey and AMSS economies.\n",
@@ -1193,7 +1193,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2b8c20f4",
+ "id": "fa4c8501",
"metadata": {},
"outputs": [],
"source": [
@@ -1219,7 +1219,7 @@
},
{
"cell_type": "markdown",
- "id": "bfed32b6",
+ "id": "f78fc07c",
"metadata": {},
"source": [
"### Remarks about Long Simulation\n",
@@ -1363,7 +1363,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c556cefd",
+ "id": "9d566833",
"metadata": {},
"outputs": [],
"source": [
@@ -1383,7 +1383,7 @@
},
{
"cell_type": "markdown",
- "id": "56e673f9",
+ "id": "37d031bc",
"metadata": {},
"source": [
"Now let's form the two random variables ${\\mathcal R}, {\\mathcal X}$ appearing in the BEGS approximating formulas"
@@ -1392,7 +1392,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "908bd75f",
+ "id": "901c9f8e",
"metadata": {},
"outputs": [],
"source": [
@@ -1416,7 +1416,7 @@
},
{
"cell_type": "markdown",
- "id": "b3af9679",
+ "id": "2b907e78",
"metadata": {},
"source": [
"Now let's compute the ingredient of the approximating limit and the approximating rate of convergence"
@@ -1425,7 +1425,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "37bfd7db",
+ "id": "84d9db86",
"metadata": {},
"outputs": [],
"source": [
@@ -1437,7 +1437,7 @@
},
{
"cell_type": "markdown",
- "id": "fc9f1e8f",
+ "id": "7261ddac",
"metadata": {},
"source": [
"Print out $\\hat b$ and $\\bar b$"
@@ -1446,7 +1446,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1eb3eefa",
+ "id": "d7bf5bea",
"metadata": {},
"outputs": [],
"source": [
@@ -1455,7 +1455,7 @@
},
{
"cell_type": "markdown",
- "id": "371db272",
+ "id": "2f9b51ce",
"metadata": {},
"source": [
"So we have"
@@ -1464,7 +1464,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6cc1f817",
+ "id": "03272f0d",
"metadata": {},
"outputs": [],
"source": [
@@ -1473,7 +1473,7 @@
},
{
"cell_type": "markdown",
- "id": "37dba9e6",
+ "id": "5c3c133f",
"metadata": {},
"source": [
"These outcomes show that $\\hat b$ does a remarkably good job of approximating $\\bar b$.\n",
@@ -1484,7 +1484,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0c3820e8",
+ "id": "21993766",
"metadata": {},
"outputs": [],
"source": [
@@ -1494,7 +1494,7 @@
},
{
"cell_type": "markdown",
- "id": "d22929c0",
+ "id": "20abd5a5",
"metadata": {},
"source": [
"This is *machine zero*, a verification that $\\hat b$ succeeds in minimizing the nonnegative fiscal cost criterion $J ( {\\mathcal B}^*)$ defined in\n",
@@ -1506,7 +1506,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "38a3c4a2",
+ "id": "889948fb",
"metadata": {},
"outputs": [],
"source": [
@@ -1517,7 +1517,7 @@
},
{
"cell_type": "markdown",
- "id": "b16c0ca9",
+ "id": "2ce6f527",
"metadata": {},
"source": [
"Now let's compute the implied meantime to get to within 0.01 of the limit"
@@ -1526,7 +1526,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dd58af0d",
+ "id": "c9751db4",
"metadata": {},
"outputs": [],
"source": [
@@ -1536,7 +1536,7 @@
},
{
"cell_type": "markdown",
- "id": "1eaaefd9",
+ "id": "83685fc7",
"metadata": {},
"source": [
"The slow rate of convergence and the implied time of getting within one percent of the limiting value do a good job of approximating\n",
diff --git a/_sources/amss3.ipynb b/_sources/amss3.ipynb
index 5b27734c..ebad9843 100644
--- a/_sources/amss3.ipynb
+++ b/_sources/amss3.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "a8379ff2",
+ "id": "95533143",
"metadata": {},
"source": [
"(amss3)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c8934b19",
+ "id": "76bac312",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "475f72c8",
+ "id": "05af20e3",
"metadata": {},
"source": [
"## Overview\n",
@@ -81,7 +81,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "11cf2d60",
+ "id": "3b4eae96",
"metadata": {},
"outputs": [],
"source": [
@@ -91,7 +91,7 @@
},
{
"cell_type": "markdown",
- "id": "d5990e14",
+ "id": "ee1fd6c3",
"metadata": {},
"source": [
"## The Economy\n",
@@ -136,7 +136,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "20f68e1d",
+ "id": "6fd0e7d6",
"metadata": {
"load": "_static/lecture_specific/amss2/crra_utility.py"
},
@@ -184,7 +184,7 @@
},
{
"cell_type": "markdown",
- "id": "1b8880f1",
+ "id": "f379ab3b",
"metadata": {},
"source": [
"### First and Second Moments\n",
@@ -197,7 +197,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "86084738",
+ "id": "63f6f4b7",
"metadata": {},
"outputs": [],
"source": [
@@ -217,7 +217,7 @@
},
{
"cell_type": "markdown",
- "id": "b12b8bc4",
+ "id": "93aa683b",
"metadata": {},
"source": [
"## Long Simulation\n",
@@ -232,7 +232,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e8f8b742",
+ "id": "dd5c5e54",
"metadata": {
"load": "_static/lecture_specific/amss2/sequential_allocation.py",
"tags": [
@@ -404,7 +404,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8b6fcb8f",
+ "id": "812bea3c",
"metadata": {
"load": "_static/lecture_specific/amss2/recursive_allocation.py",
"tags": [
@@ -716,7 +716,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f8e2744e",
+ "id": "7699755e",
"metadata": {
"load": "_static/lecture_specific/amss2/utilities.py",
"tags": [
@@ -798,7 +798,7 @@
},
{
"cell_type": "markdown",
- "id": "da048c58",
+ "id": "fd8fcf69",
"metadata": {},
"source": [
"Next, we show the code that we use to generate a very long simulation starting from initial\n",
@@ -810,7 +810,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "17c9749f",
+ "id": "9a4cc7ca",
"metadata": {
"tags": [
"scroll-output"
@@ -853,7 +853,7 @@
},
{
"cell_type": "markdown",
- "id": "74bc0768",
+ "id": "c243f728",
"metadata": {},
"source": [
"```{figure} /_static/lecture_specific/amss3/amss3_g1.png\n",
@@ -886,7 +886,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8494282c",
+ "id": "345d437b",
"metadata": {},
"outputs": [],
"source": [
@@ -912,7 +912,7 @@
},
{
"cell_type": "markdown",
- "id": "38f0ac4d",
+ "id": "bbe00db3",
"metadata": {},
"source": [
"```{figure} /_static/lecture_specific/amss3/amss3_g2.png\n",
@@ -1200,7 +1200,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2009fcc2",
+ "id": "f227d0ed",
"metadata": {},
"outputs": [],
"source": [
@@ -1222,7 +1222,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3bfe0522",
+ "id": "96fbb63f",
"metadata": {},
"outputs": [],
"source": [
@@ -1231,7 +1231,7 @@
},
{
"cell_type": "markdown",
- "id": "38ef7d09",
+ "id": "b893b62d",
"metadata": {},
"source": [
"#### Step 2"
@@ -1240,7 +1240,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ff38164a",
+ "id": "0423f0ea",
"metadata": {},
"outputs": [],
"source": [
@@ -1249,7 +1249,7 @@
},
{
"cell_type": "markdown",
- "id": "28f16c3f",
+ "id": "631f9b4f",
"metadata": {},
"source": [
"### Note about Code\n",
@@ -1274,7 +1274,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ab44acb6",
+ "id": "34ba0900",
"metadata": {},
"outputs": [],
"source": [
@@ -1291,7 +1291,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ad6389c9",
+ "id": "743a3782",
"metadata": {},
"outputs": [],
"source": [
@@ -1301,7 +1301,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f27e90b6",
+ "id": "97c53d22",
"metadata": {},
"outputs": [],
"source": [
@@ -1310,7 +1310,7 @@
},
{
"cell_type": "markdown",
- "id": "61aecf8a",
+ "id": "667abbe7",
"metadata": {},
"source": [
"We only want unconditional expectations because we are in an IID case.\n",
@@ -1322,7 +1322,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4d5a0bb4",
+ "id": "0498adce",
"metadata": {},
"outputs": [],
"source": [
@@ -1333,7 +1333,7 @@
},
{
"cell_type": "markdown",
- "id": "b74447c2",
+ "id": "93dd8baa",
"metadata": {},
"source": [
"Let's look at the random variables ${\\mathcal R}, {\\mathcal X}$"
@@ -1342,7 +1342,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a93014a1",
+ "id": "4363b13d",
"metadata": {},
"outputs": [],
"source": [
@@ -1352,7 +1352,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c3dd5d93",
+ "id": "791c759a",
"metadata": {},
"outputs": [],
"source": [
@@ -1362,7 +1362,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "df6374a0",
+ "id": "c5be8cb5",
"metadata": {},
"outputs": [],
"source": [
@@ -1372,7 +1372,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "017ff3fc",
+ "id": "9c7b669f",
"metadata": {},
"outputs": [],
"source": [
@@ -1382,7 +1382,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "467d5613",
+ "id": "99a5f80e",
"metadata": {},
"outputs": [],
"source": [
@@ -1391,7 +1391,7 @@
},
{
"cell_type": "markdown",
- "id": "49dfc7d2",
+ "id": "751c125a",
"metadata": {},
"source": [
"#### Step 3"
@@ -1400,7 +1400,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "133facfd",
+ "id": "7785a1e7",
"metadata": {},
"outputs": [],
"source": [
@@ -1411,7 +1411,7 @@
},
{
"cell_type": "markdown",
- "id": "223de16d",
+ "id": "eae70e34",
"metadata": {},
"source": [
"Note that $B$ is a scalar.\n",
@@ -1422,7 +1422,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8faf28d1",
+ "id": "abbec7a1",
"metadata": {},
"outputs": [],
"source": [
@@ -1435,7 +1435,7 @@
},
{
"cell_type": "markdown",
- "id": "5f97a433",
+ "id": "78a6ddb1",
"metadata": {},
"source": [
"In the above cell, B is fixed at 1 and $\\tau$ is to be computed as\n",
@@ -1450,7 +1450,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "919c0073",
+ "id": "97520325",
"metadata": {},
"outputs": [],
"source": [
@@ -1464,7 +1464,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "54a90118",
+ "id": "09e7600b",
"metadata": {},
"outputs": [],
"source": [
@@ -1473,7 +1473,7 @@
},
{
"cell_type": "markdown",
- "id": "b9ad4107",
+ "id": "4e1381a7",
"metadata": {},
"source": [
"#### Step 6"
@@ -1482,7 +1482,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f58722fd",
+ "id": "bed62f05",
"metadata": {},
"outputs": [],
"source": [
@@ -1493,7 +1493,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d9b6bf5e",
+ "id": "ee4506ab",
"metadata": {},
"outputs": [],
"source": [
@@ -1503,7 +1503,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b1a4a74a",
+ "id": "1ee87400",
"metadata": {},
"outputs": [],
"source": [
@@ -1515,7 +1515,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b0d25afd",
+ "id": "ac741228",
"metadata": {},
"outputs": [],
"source": [
@@ -1526,7 +1526,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1103031e",
+ "id": "f744ecc5",
"metadata": {},
"outputs": [],
"source": [
@@ -1537,7 +1537,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "20e238f3",
+ "id": "e8e6a8b2",
"metadata": {},
"outputs": [],
"source": [
@@ -1548,7 +1548,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "368903ef",
+ "id": "ded35a67",
"metadata": {},
"outputs": [],
"source": [
@@ -1559,7 +1559,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f5210d64",
+ "id": "b83fff64",
"metadata": {},
"outputs": [],
"source": [
diff --git a/_sources/arellano.ipynb b/_sources/arellano.ipynb
index 25244bcd..eb6d0655 100644
--- a/_sources/arellano.ipynb
+++ b/_sources/arellano.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "f68624cf",
+ "id": "8fdc243f",
"metadata": {},
"source": [
"(arellano)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0d573b34",
+ "id": "7c43b257",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "9ddc2cff",
+ "id": "0b446d41",
"metadata": {},
"source": [
"## Overview\n",
@@ -85,7 +85,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "41d622cf",
+ "id": "37cad224",
"metadata": {},
"outputs": [],
"source": [
@@ -97,7 +97,7 @@
},
{
"cell_type": "markdown",
- "id": "e6119461",
+ "id": "d0ca04cb",
"metadata": {},
"source": [
"## Structure\n",
@@ -365,7 +365,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5f827d77",
+ "id": "dfde75de",
"metadata": {},
"outputs": [],
"source": [
@@ -410,7 +410,7 @@
},
{
"cell_type": "markdown",
- "id": "0bcf052f",
+ "id": "6a823348",
"metadata": {},
"source": [
"Notice how the class returns the data it stores as simple numerical values and\n",
@@ -426,7 +426,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "08eba63e",
+ "id": "aac2756c",
"metadata": {},
"outputs": [],
"source": [
@@ -437,7 +437,7 @@
},
{
"cell_type": "markdown",
- "id": "3714ab77",
+ "id": "887454be",
"metadata": {},
"source": [
"Here is a function to compute the bond price at each state, given $v_c$ and\n",
@@ -447,7 +447,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0ad039b9",
+ "id": "00a742a7",
"metadata": {},
"outputs": [],
"source": [
@@ -472,7 +472,7 @@
},
{
"cell_type": "markdown",
- "id": "c7ab08b1",
+ "id": "f79db8ee",
"metadata": {},
"source": [
"Next we introduce Bellman operators that updated $v_d$ and $v_c$."
@@ -481,7 +481,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "05f2207f",
+ "id": "48d644c7",
"metadata": {},
"outputs": [],
"source": [
@@ -531,7 +531,7 @@
},
{
"cell_type": "markdown",
- "id": "c7273117",
+ "id": "7210f5c2",
"metadata": {},
"source": [
"Here is a fast function that calls these operators in the right sequence."
@@ -540,7 +540,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "316d10be",
+ "id": "c8ef68a3",
"metadata": {},
"outputs": [],
"source": [
@@ -575,7 +575,7 @@
},
{
"cell_type": "markdown",
- "id": "4ff00946",
+ "id": "9a1d2544",
"metadata": {},
"source": [
"We can now write a function that will use the `Arellano_Economy` class and the\n",
@@ -592,7 +592,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a3e04769",
+ "id": "7f4b0d27",
"metadata": {},
"outputs": [],
"source": [
@@ -634,7 +634,7 @@
},
{
"cell_type": "markdown",
- "id": "84de91f8",
+ "id": "2fc3be6a",
"metadata": {},
"source": [
"Finally, we write a function that will allow us to simulate the economy once\n",
@@ -644,7 +644,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "77fc0646",
+ "id": "5144f326",
"metadata": {},
"outputs": [],
"source": [
@@ -712,7 +712,7 @@
},
{
"cell_type": "markdown",
- "id": "b8f9c774",
+ "id": "157ad4ed",
"metadata": {},
"source": [
"## Results\n",
@@ -808,7 +808,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e45e2593",
+ "id": "7050bce0",
"metadata": {},
"outputs": [],
"source": [
@@ -818,7 +818,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eef41e3a",
+ "id": "40ce25c5",
"metadata": {},
"outputs": [],
"source": [
@@ -827,7 +827,7 @@
},
{
"cell_type": "markdown",
- "id": "44478997",
+ "id": "02ac1891",
"metadata": {},
"source": [
"Compute the bond price schedule as seen in figure 3 of Arellano (2008)"
@@ -836,7 +836,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cd9842da",
+ "id": "fc32f1c7",
"metadata": {},
"outputs": [],
"source": [
@@ -870,7 +870,7 @@
},
{
"cell_type": "markdown",
- "id": "f06f4224",
+ "id": "e7e4d607",
"metadata": {},
"source": [
"Draw a plot of the value functions"
@@ -879,7 +879,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "05c131eb",
+ "id": "b3305fc9",
"metadata": {},
"outputs": [],
"source": [
@@ -897,7 +897,7 @@
},
{
"cell_type": "markdown",
- "id": "9379bd69",
+ "id": "5a601cdc",
"metadata": {},
"source": [
"Draw a heat map for default probability"
@@ -906,7 +906,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "23c3e760",
+ "id": "534abe0e",
"metadata": {},
"outputs": [],
"source": [
@@ -929,7 +929,7 @@
},
{
"cell_type": "markdown",
- "id": "88689ac3",
+ "id": "83fbead1",
"metadata": {},
"source": [
"Plot a time series of major variables simulated from the model"
@@ -938,7 +938,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8fef58ef",
+ "id": "57e6f2e8",
"metadata": {},
"outputs": [],
"source": [
@@ -985,7 +985,7 @@
},
{
"cell_type": "markdown",
- "id": "477646ed",
+ "id": "b45f163a",
"metadata": {},
"source": [
"```{solution-end}\n",
diff --git a/_sources/arma.ipynb b/_sources/arma.ipynb
index 4c77f551..da20ddf0 100644
--- a/_sources/arma.ipynb
+++ b/_sources/arma.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "1e6290d4",
+ "id": "645631c0",
"metadata": {},
"source": [
"(arma)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d1d847dd",
+ "id": "6c966de7",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "348e4175",
+ "id": "2506a4ce",
"metadata": {},
"source": [
"## Overview\n",
@@ -101,7 +101,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "79e8c8a2",
+ "id": "35da0be6",
"metadata": {},
"outputs": [],
"source": [
@@ -112,7 +112,7 @@
},
{
"cell_type": "markdown",
- "id": "f2e2dc95",
+ "id": "3c12bb54",
"metadata": {},
"source": [
"## Introduction\n",
@@ -256,7 +256,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bfe0581a",
+ "id": "5235768f",
"metadata": {},
"outputs": [],
"source": [
@@ -278,7 +278,7 @@
},
{
"cell_type": "markdown",
- "id": "c0ea5737",
+ "id": "90b394b2",
"metadata": {},
"source": [
"Another very simple process is the MA(1) process (here MA means \"moving average\")\n",
@@ -502,7 +502,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7d966d38",
+ "id": "a2eb8356",
"metadata": {},
"outputs": [],
"source": [
@@ -527,7 +527,7 @@
},
{
"cell_type": "markdown",
- "id": "b854d7fb",
+ "id": "fdbebbbe",
"metadata": {},
"source": [
"These spectral densities correspond to the autocovariance functions for the\n",
@@ -561,7 +561,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f3997a27",
+ "id": "ae02eef6",
"metadata": {},
"outputs": [],
"source": [
@@ -602,7 +602,7 @@
},
{
"cell_type": "markdown",
- "id": "f151ebb4",
+ "id": "c082e09c",
"metadata": {},
"source": [
"On the other hand, if we evaluate $f(\\omega)$ at $\\omega = \\pi / 3$, then the cycles are\n",
@@ -613,7 +613,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "10d55e15",
+ "id": "6dc59f78",
"metadata": {},
"outputs": [],
"source": [
@@ -654,7 +654,7 @@
},
{
"cell_type": "markdown",
- "id": "30c5e90c",
+ "id": "da74da59",
"metadata": {},
"source": [
"In summary, the spectral density is large at frequencies $\\omega$ where the autocovariance function exhibits damped cycles.\n",
@@ -784,7 +784,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c079fed5",
+ "id": "304eda34",
"metadata": {},
"outputs": [],
"source": [
@@ -843,7 +843,7 @@
},
{
"cell_type": "markdown",
- "id": "66370264",
+ "id": "ceacd6ea",
"metadata": {},
"source": [
"Now let's call these functions to generate plots.\n",
@@ -854,7 +854,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "16a527f3",
+ "id": "f327a2f6",
"metadata": {},
"outputs": [],
"source": [
@@ -866,7 +866,7 @@
},
{
"cell_type": "markdown",
- "id": "5b0fd08c",
+ "id": "30ae1a95",
"metadata": {},
"source": [
"If we look carefully, things look good: the spectrum is the flat line at $10^0$ at the very top of the spectrum graphs,\n",
@@ -887,7 +887,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a22e5895",
+ "id": "103a28c7",
"metadata": {},
"outputs": [],
"source": [
@@ -899,7 +899,7 @@
},
{
"cell_type": "markdown",
- "id": "60d4f820",
+ "id": "771e1377",
"metadata": {},
"source": [
"Ljungqvist and Sargent's second model is $X_t = .9 X_{t-1} + \\epsilon_t$"
@@ -908,7 +908,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9d532598",
+ "id": "a2184c2b",
"metadata": {},
"outputs": [],
"source": [
@@ -920,7 +920,7 @@
},
{
"cell_type": "markdown",
- "id": "c4f51af0",
+ "id": "a29f6e7e",
"metadata": {},
"source": [
"Ljungqvist and Sargent's third model is $X_t = .8 X_{t-4} + \\epsilon_t$"
@@ -929,7 +929,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f17ef028",
+ "id": "2cd990a4",
"metadata": {},
"outputs": [],
"source": [
@@ -941,7 +941,7 @@
},
{
"cell_type": "markdown",
- "id": "77921156",
+ "id": "e1b6a5fb",
"metadata": {},
"source": [
"Ljungqvist and Sargent's fourth model is $X_t = .98 X_{t-1} + \\epsilon_t -.7 \\epsilon_{t-1}$"
@@ -950,7 +950,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f06d6ae8",
+ "id": "6c5ff002",
"metadata": {},
"outputs": [],
"source": [
@@ -962,7 +962,7 @@
},
{
"cell_type": "markdown",
- "id": "fbca8634",
+ "id": "a9ccc7f9",
"metadata": {},
"source": [
"### Explanation\n",
diff --git a/_sources/asset_pricing_lph.ipynb b/_sources/asset_pricing_lph.ipynb
index 5de99dd7..4e3ad891 100644
--- a/_sources/asset_pricing_lph.ipynb
+++ b/_sources/asset_pricing_lph.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "0cba2890",
+ "id": "ff5c5a53",
"metadata": {},
"source": [
"# Elementary Asset Pricing Theory\n",
@@ -347,7 +347,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "20bf2c5d",
+ "id": "f7cd119d",
"metadata": {},
"outputs": [],
"source": [
@@ -393,7 +393,7 @@
},
{
"cell_type": "markdown",
- "id": "fa26440a",
+ "id": "57e38965",
"metadata": {},
"source": [
"The figure shows two straight lines, the blue upper one being the locus of $( \\sigma(R^i), E(R^i)$ pairs that are on\n",
@@ -484,7 +484,7 @@
},
{
"cell_type": "markdown",
- "id": "b6607c59",
+ "id": "8ee5962f",
"metadata": {},
"source": [
"## Multi-factor Models\n",
@@ -543,7 +543,7 @@
},
{
"cell_type": "markdown",
- "id": "fb056cb5",
+ "id": "3287d693",
"metadata": {},
"source": [
"**Testing strategies:**\n",
@@ -596,7 +596,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "660fb48a",
+ "id": "05c0a36e",
"metadata": {},
"outputs": [],
"source": [
@@ -607,7 +607,7 @@
},
{
"cell_type": "markdown",
- "id": "d6c035bd",
+ "id": "9fb62206",
"metadata": {},
"source": [
"Lots of our calculations will involve computing population and sample OLS regressions.\n",
@@ -618,7 +618,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b56e3882",
+ "id": "83ddda71",
"metadata": {},
"outputs": [],
"source": [
@@ -638,7 +638,7 @@
},
{
"cell_type": "markdown",
- "id": "54bb64a4",
+ "id": "2b7de87e",
"metadata": {},
"source": [
"```{exercise-start}\n",
@@ -763,7 +763,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "73c0ea54",
+ "id": "8c349591",
"metadata": {},
"outputs": [],
"source": [
@@ -781,7 +781,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d3cc7df4",
+ "id": "c4f01fe7",
"metadata": {},
"outputs": [],
"source": [
@@ -794,7 +794,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b365fd05",
+ "id": "b1b489eb",
"metadata": {},
"outputs": [],
"source": [
@@ -807,7 +807,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "871f3d02",
+ "id": "c2ab6ca7",
"metadata": {},
"outputs": [],
"source": [
@@ -826,7 +826,7 @@
},
{
"cell_type": "markdown",
- "id": "983d9fa4",
+ "id": "b9b6cebd",
"metadata": {},
"source": [
"Now that we have a panel of data, we'd like to solve the inverse problem by assuming the theory specified above and estimating the coefficients given above."
@@ -835,7 +835,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ea7ceb29",
+ "id": "3779d94a",
"metadata": {},
"outputs": [],
"source": [
@@ -844,7 +844,7 @@
},
{
"cell_type": "markdown",
- "id": "0860d014",
+ "id": "f4b4f41a",
"metadata": {},
"source": [
"**Inverse Problem:**\n",
@@ -857,7 +857,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d5e21667",
+ "id": "b63ea9bb",
"metadata": {},
"outputs": [],
"source": [
@@ -867,7 +867,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "47ae3035",
+ "id": "ccfba536",
"metadata": {},
"outputs": [],
"source": [
@@ -876,7 +876,7 @@
},
{
"cell_type": "markdown",
- "id": "9c337408",
+ "id": "68a0c8c6",
"metadata": {},
"source": [
"Let's compare these with the _true_ population parameter values."
@@ -885,7 +885,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "43dce0a1",
+ "id": "babe9760",
"metadata": {},
"outputs": [],
"source": [
@@ -894,7 +894,7 @@
},
{
"cell_type": "markdown",
- "id": "5b5fb255",
+ "id": "b9fab451",
"metadata": {},
"source": [
"2. $\\xi$ and $\\lambda$"
@@ -903,7 +903,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "aac65f87",
+ "id": "61495e3e",
"metadata": {},
"outputs": [],
"source": [
@@ -913,7 +913,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7836b459",
+ "id": "636be7bf",
"metadata": {},
"outputs": [],
"source": [
@@ -923,7 +923,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a6e3ac70",
+ "id": "142d3ecc",
"metadata": {},
"outputs": [],
"source": [
@@ -932,7 +932,7 @@
},
{
"cell_type": "markdown",
- "id": "29aebd90",
+ "id": "6fe6d793",
"metadata": {},
"source": [
"3. $\\beta_{i, R^m}$ and $\\sigma_i$"
@@ -941,7 +941,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "632797d4",
+ "id": "b5ca0ee6",
"metadata": {},
"outputs": [],
"source": [
@@ -955,7 +955,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b91e358d",
+ "id": "41290d9c",
"metadata": {},
"outputs": [],
"source": [
@@ -965,7 +965,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d341a167",
+ "id": "4d1c53cc",
"metadata": {},
"outputs": [],
"source": [
@@ -974,7 +974,7 @@
},
{
"cell_type": "markdown",
- "id": "cae003a3",
+ "id": "909c7fda",
"metadata": {},
"source": [
"Q: How close did your estimates come to the parameters we specified?\n",
@@ -1013,7 +1013,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ef2110b1",
+ "id": "ebe59f3e",
"metadata": {},
"outputs": [],
"source": [
@@ -1034,7 +1034,7 @@
},
{
"cell_type": "markdown",
- "id": "b62890a2",
+ "id": "8a1ffedb",
"metadata": {},
"source": [
"Let's try to solve $a$ and $b$ using the actual model parameters."
@@ -1043,7 +1043,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "92c5c678",
+ "id": "88b49179",
"metadata": {},
"outputs": [],
"source": [
@@ -1053,7 +1053,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cbb1ea7d",
+ "id": "3286ff6c",
"metadata": {},
"outputs": [],
"source": [
@@ -1062,7 +1062,7 @@
},
{
"cell_type": "markdown",
- "id": "b3ee1cb6",
+ "id": "19973a02",
"metadata": {},
"source": [
"```{solution-end}\n",
@@ -1087,7 +1087,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "608920f4",
+ "id": "9b697d2d",
"metadata": {},
"outputs": [],
"source": [
@@ -1097,7 +1097,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7f1c2d87",
+ "id": "66711ab2",
"metadata": {},
"outputs": [],
"source": [
@@ -1106,7 +1106,7 @@
},
{
"cell_type": "markdown",
- "id": "f61454dd",
+ "id": "c072f62e",
"metadata": {},
"source": [
"```{solution-end}\n",
diff --git a/_sources/black_litterman.ipynb b/_sources/black_litterman.ipynb
index a7b51351..b150cf06 100644
--- a/_sources/black_litterman.ipynb
+++ b/_sources/black_litterman.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "353de149",
+ "id": "d35cb867",
"metadata": {},
"source": [
"(black_litterman)=\n",
@@ -79,7 +79,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f717138e",
+ "id": "dd77780a",
"metadata": {},
"outputs": [],
"source": [
@@ -91,7 +91,7 @@
},
{
"cell_type": "markdown",
- "id": "2c2447b9",
+ "id": "53949343",
"metadata": {},
"source": [
"## Mean-Variance Portfolio Choice\n",
@@ -179,7 +179,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0832c42e",
+ "id": "d0af3391",
"metadata": {},
"outputs": [],
"source": [
@@ -230,7 +230,7 @@
},
{
"cell_type": "markdown",
- "id": "96adb548",
+ "id": "fc3d539d",
"metadata": {},
"source": [
"Black and Litterman's responded to this situation in the following way:\n",
@@ -322,7 +322,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c6fed18f",
+ "id": "1dc0eba6",
"metadata": {},
"outputs": [],
"source": [
@@ -355,7 +355,7 @@
},
{
"cell_type": "markdown",
- "id": "3b3fef01",
+ "id": "c385a921",
"metadata": {},
"source": [
"## Adding Views\n",
@@ -418,7 +418,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "640fa42a",
+ "id": "c018aab8",
"metadata": {},
"outputs": [],
"source": [
@@ -480,7 +480,7 @@
},
{
"cell_type": "markdown",
- "id": "313210c4",
+ "id": "50190b24",
"metadata": {},
"source": [
"## Bayesian Interpretation\n",
@@ -653,7 +653,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ccc73279",
+ "id": "905770e5",
"metadata": {},
"outputs": [],
"source": [
@@ -729,7 +729,7 @@
},
{
"cell_type": "markdown",
- "id": "e3e741e1",
+ "id": "4c0b9ebe",
"metadata": {},
"source": [
"Note that the line that connects the two points\n",
@@ -750,7 +750,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b5cc9a49",
+ "id": "9b2cdd39",
"metadata": {},
"outputs": [],
"source": [
@@ -798,7 +798,7 @@
},
{
"cell_type": "markdown",
- "id": "f4e95499",
+ "id": "fc3b581f",
"metadata": {},
"source": [
"## Black-Litterman Recommendation as Regularization\n",
@@ -1317,7 +1317,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "72a43f38",
+ "id": "ed0e093e",
"metadata": {},
"outputs": [],
"source": [
@@ -1346,7 +1346,7 @@
},
{
"cell_type": "markdown",
- "id": "3606b86c",
+ "id": "2474797a",
"metadata": {},
"source": [
"## Frequency and the Mean Estimator\n",
@@ -1428,7 +1428,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7b9cd8c8",
+ "id": "0d93fdfe",
"metadata": {},
"outputs": [],
"source": [
@@ -1454,7 +1454,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "abab23c5",
+ "id": "b8eeb957",
"metadata": {},
"outputs": [],
"source": [
@@ -1498,7 +1498,7 @@
},
{
"cell_type": "markdown",
- "id": "f2668e3a",
+ "id": "863b41c0",
"metadata": {},
"source": [
"The above figure illustrates the relationship between the asymptotic\n",
diff --git a/_sources/calvo.ipynb b/_sources/calvo.ipynb
index 904d1bd2..c927292b 100644
--- a/_sources/calvo.ipynb
+++ b/_sources/calvo.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "32bd945b",
+ "id": "444358eb",
"metadata": {},
"source": [
"(calvo)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3ddef781",
+ "id": "af69fb14",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "b6ae53ea",
+ "id": "c577b7ea",
"metadata": {},
"source": [
"## Overview\n",
@@ -85,7 +85,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d7817d18",
+ "id": "7adb5973",
"metadata": {
"tags": [
"hide-output"
@@ -98,7 +98,7 @@
},
{
"cell_type": "markdown",
- "id": "3b47dc22",
+ "id": "9db8e8ad",
"metadata": {},
"source": [
"We'll start with some imports:"
@@ -107,7 +107,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6ffdcdd2",
+ "id": "eab2bc7b",
"metadata": {},
"outputs": [],
"source": [
@@ -121,7 +121,7 @@
},
{
"cell_type": "markdown",
- "id": "6a567a61",
+ "id": "aa07c1f5",
"metadata": {},
"source": [
"## Model components\n",
@@ -930,7 +930,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eff3b62b",
+ "id": "1a9271a3",
"metadata": {},
"outputs": [],
"source": [
@@ -1049,7 +1049,7 @@
},
{
"cell_type": "markdown",
- "id": "1c623067",
+ "id": "a86c8122",
"metadata": {},
"source": [
"Let's create an instance of ChangLQ with the following parameters:"
@@ -1058,7 +1058,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "509d7c53",
+ "id": "3b823d82",
"metadata": {},
"outputs": [],
"source": [
@@ -1067,7 +1067,7 @@
},
{
"cell_type": "markdown",
- "id": "d1e85ab8",
+ "id": "f0667beb",
"metadata": {},
"source": [
"The following code plots value functions for a continuation Ramsey\n",
@@ -1077,7 +1077,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fde871ba",
+ "id": "b08af211",
"metadata": {
"tags": [
"hide-input"
@@ -1149,7 +1149,7 @@
},
{
"cell_type": "markdown",
- "id": "755354bf",
+ "id": "b6b45ee4",
"metadata": {},
"source": [
"The dotted line in the above graph is the 45-degree line.\n",
@@ -1183,7 +1183,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b40e76ac",
+ "id": "dc745a92",
"metadata": {
"tags": [
"hide-input"
@@ -1226,7 +1226,7 @@
},
{
"cell_type": "markdown",
- "id": "b46544fc",
+ "id": "f782ceb9",
"metadata": {},
"source": [
"In the above graph, notice that $\\theta^* < \\theta_\\infty^R < \\theta^{CR} < \\theta_0^R < \\theta^{MPE} .$\n",
@@ -1264,7 +1264,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "57132b77",
+ "id": "5e21a410",
"metadata": {},
"outputs": [],
"source": [
@@ -1275,7 +1275,7 @@
},
{
"cell_type": "markdown",
- "id": "a9898d83",
+ "id": "ecdc878e",
"metadata": {},
"source": [
"So our claim that $J(\\theta_\\infty^R) = V^{CR}(\\theta_\\infty^R)$is verified numerically.\n",
@@ -1300,7 +1300,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c0aa43b4",
+ "id": "25307bf8",
"metadata": {
"tags": [
"hide-input"
@@ -1416,7 +1416,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "24368dd3",
+ "id": "49b7c190",
"metadata": {},
"outputs": [],
"source": [
@@ -1431,7 +1431,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e4efe126",
+ "id": "b505536a",
"metadata": {},
"outputs": [],
"source": [
@@ -1440,7 +1440,7 @@
},
{
"cell_type": "markdown",
- "id": "6be9bd87",
+ "id": "300ebc7f",
"metadata": {},
"source": [
"The above graphs and table convey many useful things.\n",
@@ -1472,7 +1472,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f0d6b7ce",
+ "id": "6e304f13",
"metadata": {},
"outputs": [],
"source": [
@@ -1487,7 +1487,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1f597083",
+ "id": "6a4d1057",
"metadata": {},
"outputs": [],
"source": [
@@ -1496,7 +1496,7 @@
},
{
"cell_type": "markdown",
- "id": "f16ec335",
+ "id": "4f0e019a",
"metadata": {},
"source": [
"The above table and figures show how \n",
@@ -1514,7 +1514,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4ed0c0d0",
+ "id": "1daabdd6",
"metadata": {},
"outputs": [],
"source": [
@@ -1528,7 +1528,7 @@
},
{
"cell_type": "markdown",
- "id": "c8205efb",
+ "id": "b5859d99",
"metadata": {},
"source": [
"The above graphs indicate that as $c$ approaches zero, $\\theta_\\infty^R, \\theta_0^R, \\theta^{CR}$,\n",
@@ -1552,7 +1552,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9f8303c2",
+ "id": "ef13c21a",
"metadata": {
"tags": [
"hide-input"
@@ -1621,7 +1621,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5af8c98d",
+ "id": "6e931b0a",
"metadata": {},
"outputs": [],
"source": [
@@ -1633,7 +1633,7 @@
},
{
"cell_type": "markdown",
- "id": "78d02e69",
+ "id": "fe93eed6",
"metadata": {},
"source": [
"Notice how $d_1$ changes as we raise the discount factor parameter $\\beta$.\n",
@@ -1644,7 +1644,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9193dd15",
+ "id": "c1ea4550",
"metadata": {},
"outputs": [],
"source": [
@@ -1657,7 +1657,7 @@
},
{
"cell_type": "markdown",
- "id": "bf3fbda9",
+ "id": "a76bb430",
"metadata": {},
"source": [
"Evidently, increasing $c$ causes the decay factor $d_1$ to increase.\n",
@@ -1670,7 +1670,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "36ae406a",
+ "id": "0c8bc6f5",
"metadata": {},
"outputs": [],
"source": [
@@ -1683,7 +1683,7 @@
},
{
"cell_type": "markdown",
- "id": "c1e92ee2",
+ "id": "d8af95d6",
"metadata": {},
"source": [
"The above panels for an $\\alpha = 4$ setting indicate that $\\alpha$ and $c$ affect outcomes \n",
@@ -1969,7 +1969,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "36d8052f",
+ "id": "5d030560",
"metadata": {
"tags": [
"hide-input"
@@ -2029,7 +2029,7 @@
},
{
"cell_type": "markdown",
- "id": "3fd0478e",
+ "id": "07bb2e8f",
"metadata": {},
"source": [
"To confirm that the plan $\\vec \\mu^A$ is **self-enforcing**, we\n",
@@ -2052,7 +2052,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ce0144ec",
+ "id": "cfd9ee04",
"metadata": {},
"outputs": [],
"source": [
@@ -2061,7 +2061,7 @@
},
{
"cell_type": "markdown",
- "id": "e7a977ac",
+ "id": "a34811d2",
"metadata": {},
"source": [
"Given that plan $\\vec \\mu^A$ is self-enforcing, we can check that\n",
@@ -2075,7 +2075,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a607ef35",
+ "id": "5d3eae73",
"metadata": {},
"outputs": [],
"source": [
@@ -2094,7 +2094,7 @@
},
{
"cell_type": "markdown",
- "id": "bf348b5f",
+ "id": "119adf94",
"metadata": {},
"source": [
"### Recursive representation of a sustainable plan\n",
@@ -2165,7 +2165,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5fbc4da8",
+ "id": "323c6d83",
"metadata": {},
"outputs": [],
"source": [
@@ -2175,7 +2175,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "02345dc8",
+ "id": "e5ad79af",
"metadata": {},
"outputs": [],
"source": [
@@ -2185,7 +2185,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ab2cf315",
+ "id": "bcaf1f03",
"metadata": {},
"outputs": [],
"source": [
@@ -2194,7 +2194,7 @@
},
{
"cell_type": "markdown",
- "id": "4be388c1",
+ "id": "74ec336a",
"metadata": {},
"source": [
"We have also computed **credible plans** for a government or sequence\n",
diff --git a/_sources/calvo_machine_learn.ipynb b/_sources/calvo_machine_learn.ipynb
index b939785e..3f21e97f 100644
--- a/_sources/calvo_machine_learn.ipynb
+++ b/_sources/calvo_machine_learn.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "c3adab2c",
+ "id": "f7b65bcc",
"metadata": {},
"source": [
"# Machine Learning a Ramsey Plan\n",
@@ -383,7 +383,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "27e4fe1e",
+ "id": "a548e851",
"metadata": {
"tags": [
"hide-output"
@@ -399,7 +399,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "23b5e7df",
+ "id": "dd2fea87",
"metadata": {},
"outputs": [],
"source": [
@@ -414,7 +414,7 @@
},
{
"cell_type": "markdown",
- "id": "8d369166",
+ "id": "a9dd4c64",
"metadata": {},
"source": [
"First, because we'll want to compare the results we obtain here with those obtained with another, more structured, approach, we copy the class `ChangLQ` to solve the LQ Chang model in this quantecon lecture {doc}`calvo`.\n",
@@ -425,7 +425,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5adc0dc3",
+ "id": "5bb657af",
"metadata": {
"tags": [
"hide-input"
@@ -548,7 +548,7 @@
},
{
"cell_type": "markdown",
- "id": "cb6c6a3b",
+ "id": "0becb39a",
"metadata": {},
"source": [
"Now we compute the value of $V$ under this setup, and compare it against those obtained in {ref}`compute_lq`."
@@ -557,7 +557,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "66f939ee",
+ "id": "b36c83ba",
"metadata": {},
"outputs": [],
"source": [
@@ -569,7 +569,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2be31152",
+ "id": "65536c5d",
"metadata": {},
"outputs": [],
"source": [
@@ -625,7 +625,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7b9579db",
+ "id": "0b0e8877",
"metadata": {},
"outputs": [],
"source": [
@@ -637,7 +637,7 @@
},
{
"cell_type": "markdown",
- "id": "0529f6dd",
+ "id": "2b93a161",
"metadata": {},
"source": [
"Now we want to maximize the function $V$ by choice of $\\mu$.\n",
@@ -648,7 +648,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3554af0c",
+ "id": "9575502c",
"metadata": {},
"outputs": [],
"source": [
@@ -686,7 +686,7 @@
},
{
"cell_type": "markdown",
- "id": "5f0d905f",
+ "id": "2723567d",
"metadata": {},
"source": [
"Here we use automatic differentiation functionality in JAX with `grad`."
@@ -695,7 +695,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9cf90b54",
+ "id": "5989fc24",
"metadata": {
"tags": [
"scroll-output"
@@ -714,7 +714,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3f7c2bcb",
+ "id": "3de35ed6",
"metadata": {},
"outputs": [],
"source": [
@@ -729,7 +729,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cc79cf02",
+ "id": "98399bb6",
"metadata": {},
"outputs": [],
"source": [
@@ -739,7 +739,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e3c123dc",
+ "id": "be4f564c",
"metadata": {},
"outputs": [],
"source": [
@@ -749,7 +749,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "32c7afcf",
+ "id": "0662e751",
"metadata": {},
"outputs": [],
"source": [
@@ -759,7 +759,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "607daf76",
+ "id": "5d5a4471",
"metadata": {},
"outputs": [],
"source": [
@@ -768,7 +768,7 @@
},
{
"cell_type": "markdown",
- "id": "8165ca54",
+ "id": "fd6ba402",
"metadata": {},
"source": [
" \n",
@@ -788,7 +788,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "56fb72a1",
+ "id": "e5a134a2",
"metadata": {},
"outputs": [],
"source": [
@@ -807,7 +807,7 @@
},
{
"cell_type": "markdown",
- "id": "982b0c1b",
+ "id": "80f899b2",
"metadata": {},
"source": [
"Compare it to $\\mu^{CR}$ in {doc}`calvo`, we again obtained a close estimate."
@@ -816,7 +816,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ca46d3b3",
+ "id": "1e6b7361",
"metadata": {},
"outputs": [],
"source": [
@@ -826,7 +826,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1f7ff94b",
+ "id": "c78162a6",
"metadata": {},
"outputs": [],
"source": [
@@ -837,7 +837,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "865b1e75",
+ "id": "39e644ed",
"metadata": {},
"outputs": [],
"source": [
@@ -846,7 +846,7 @@
},
{
"cell_type": "markdown",
- "id": "1ab70434",
+ "id": "c7a47b81",
"metadata": {},
"source": [
"## A more structured ML algorithm\n",
@@ -933,7 +933,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7cc88f51",
+ "id": "72791de0",
"metadata": {},
"outputs": [],
"source": [
@@ -950,7 +950,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6fcc668f",
+ "id": "7db28c8a",
"metadata": {},
"outputs": [],
"source": [
@@ -962,7 +962,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b5e7ce89",
+ "id": "11342fc6",
"metadata": {},
"outputs": [],
"source": [
@@ -974,7 +974,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "330ccd21",
+ "id": "bd1fc508",
"metadata": {},
"outputs": [],
"source": [
@@ -983,7 +983,7 @@
},
{
"cell_type": "markdown",
- "id": "57b6d0c8",
+ "id": "7be1f22c",
"metadata": {},
"source": [
"As before, the Ramsey planner's criterion is\n",
@@ -1072,7 +1072,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8bcb3350",
+ "id": "b71592af",
"metadata": {},
"outputs": [],
"source": [
@@ -1098,7 +1098,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0a65965e",
+ "id": "61c58e09",
"metadata": {},
"outputs": [],
"source": [
@@ -1113,7 +1113,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c12bc8d8",
+ "id": "9ca544de",
"metadata": {},
"outputs": [],
"source": [
@@ -1128,7 +1128,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3e4ef167",
+ "id": "2befe95a",
"metadata": {},
"outputs": [],
"source": [
@@ -1138,7 +1138,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "269609ac",
+ "id": "d2e76752",
"metadata": {},
"outputs": [],
"source": [
@@ -1148,7 +1148,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5f977709",
+ "id": "0652d04f",
"metadata": {},
"outputs": [],
"source": [
@@ -1158,7 +1158,7 @@
},
{
"cell_type": "markdown",
- "id": "5124c2e0",
+ "id": "e9da6b84",
"metadata": {},
"source": [
"We find that by exploiting more knowledge about the structure of the problem, we can significantly speed up our computation.\n",
@@ -1169,7 +1169,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ad9f5f6d",
+ "id": "cf42990e",
"metadata": {},
"outputs": [],
"source": [
@@ -1194,7 +1194,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "16b5315d",
+ "id": "14f93cdd",
"metadata": {},
"outputs": [],
"source": [
@@ -1204,7 +1204,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a56b735f",
+ "id": "40b95a14",
"metadata": {},
"outputs": [],
"source": [
@@ -1214,7 +1214,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3717586e",
+ "id": "e9cc7f44",
"metadata": {},
"outputs": [],
"source": [
@@ -1223,7 +1223,7 @@
},
{
"cell_type": "markdown",
- "id": "2579f750",
+ "id": "4ec89a40",
"metadata": {},
"source": [
"We can check the gradient of the analytical solution against the `JAX` computed version"
@@ -1232,7 +1232,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "29bb03eb",
+ "id": "d1912e1d",
"metadata": {},
"outputs": [],
"source": [
@@ -1258,7 +1258,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "86369b82",
+ "id": "e617f287",
"metadata": {},
"outputs": [],
"source": [
@@ -1268,7 +1268,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "946f76dd",
+ "id": "aaae2260",
"metadata": {},
"outputs": [],
"source": [
@@ -1278,7 +1278,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "856fbcf3",
+ "id": "a0c1f2a9",
"metadata": {},
"outputs": [],
"source": [
@@ -1287,7 +1287,7 @@
},
{
"cell_type": "markdown",
- "id": "8a7d8034",
+ "id": "0683b3cc",
"metadata": {},
"source": [
"## Some Exploratory Regressions\n",
@@ -1320,7 +1320,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "39bbb982",
+ "id": "57c12a21",
"metadata": {},
"outputs": [],
"source": [
@@ -1340,7 +1340,7 @@
},
{
"cell_type": "markdown",
- "id": "292e80af",
+ "id": "2e16668b",
"metadata": {},
"source": [
"We notice that $\\theta_t$ is less than $\\mu_t$for low $t$'s but that it eventually converges to\n",
@@ -1358,7 +1358,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c4180963",
+ "id": "8043adb5",
"metadata": {},
"outputs": [],
"source": [
@@ -1374,7 +1374,7 @@
},
{
"cell_type": "markdown",
- "id": "842fbff5",
+ "id": "2e9ce3c0",
"metadata": {},
"source": [
"Our regression tells us that along the Ramsey outcome $\\vec \\mu, \\vec \\theta$ the linear function\n",
@@ -1396,7 +1396,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c15c7d24",
+ "id": "9a67ede1",
"metadata": {},
"outputs": [],
"source": [
@@ -1410,7 +1410,7 @@
},
{
"cell_type": "markdown",
- "id": "5f5dd3be",
+ "id": "459cd667",
"metadata": {},
"source": [
"The time $0$ pair $(\\theta_0, \\mu_0)$ appears as the point on the upper right. \n",
@@ -1426,7 +1426,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "df65a538",
+ "id": "4add57f6",
"metadata": {},
"outputs": [],
"source": [
@@ -1444,7 +1444,7 @@
},
{
"cell_type": "markdown",
- "id": "077352c2",
+ "id": "48bfb4d8",
"metadata": {},
"source": [
"We find that the regression line fits perfectly and thus discover the affine relationship\n",
@@ -1461,7 +1461,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bb45131b",
+ "id": "b8e3f165",
"metadata": {},
"outputs": [],
"source": [
@@ -1477,7 +1477,7 @@
},
{
"cell_type": "markdown",
- "id": "1cda109a",
+ "id": "d7f1840c",
"metadata": {},
"source": [
"Points for succeeding times appear further and further to the lower left and eventually converge to\n",
@@ -1505,7 +1505,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "835468ee",
+ "id": "0b13d26e",
"metadata": {},
"outputs": [],
"source": [
@@ -1540,7 +1540,7 @@
},
{
"cell_type": "markdown",
- "id": "a674d1ec",
+ "id": "af439705",
"metadata": {},
"source": [
"The initial continuation value $v_0$ should equals the optimized value of the Ramsey planner's criterion $V$ defined\n",
@@ -1553,7 +1553,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "44964af8",
+ "id": "d1cc2967",
"metadata": {},
"outputs": [],
"source": [
@@ -1562,7 +1562,7 @@
},
{
"cell_type": "markdown",
- "id": "8bc24b36",
+ "id": "ded4e93a",
"metadata": {},
"source": [
"We can also verify approximate equality by inspecting a graph of $v_t$ against $t$ for $t=0, \\ldots, T$ along with the value attained by a restricted Ramsey planner $V^{CR}$ and the optimized value of the ordinary Ramsey planner $V^R$"
@@ -1571,7 +1571,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "557acf44",
+ "id": "9a5dce6b",
"metadata": {
"mystnb": {
"figure": {
@@ -1603,7 +1603,7 @@
},
{
"cell_type": "markdown",
- "id": "d0585cca",
+ "id": "0547723c",
"metadata": {},
"source": [
"Figure {numref}`continuation_values` shows several striking patterns:\n",
@@ -1630,7 +1630,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3551d492",
+ "id": "99752ddc",
"metadata": {},
"outputs": [],
"source": [
@@ -1647,7 +1647,7 @@
},
{
"cell_type": "markdown",
- "id": "c61ed3ba",
+ "id": "62c92508",
"metadata": {},
"source": [
"The regression has an $R^2$ equal to $1$ and so fits perfectly.\n",
@@ -1661,7 +1661,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8a266dd1",
+ "id": "01f248c2",
"metadata": {},
"outputs": [],
"source": [
@@ -1670,7 +1670,7 @@
},
{
"cell_type": "markdown",
- "id": "aacfb0d5",
+ "id": "5f8dc183",
"metadata": {},
"source": [
"Let's plot $v_t$ against $\\theta_t$ along with the nonlinear regression line."
@@ -1679,7 +1679,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b829d1fa",
+ "id": "1cbefde0",
"metadata": {},
"outputs": [],
"source": [
@@ -1704,7 +1704,7 @@
},
{
"cell_type": "markdown",
- "id": "dff31d79",
+ "id": "b647f567",
"metadata": {},
"source": [
"The highest continuation value $v_0$ at $t=0$ appears at the peak of the function quadratic function\n",
@@ -1805,7 +1805,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e67a7ec3",
+ "id": "79cd3370",
"metadata": {},
"outputs": [],
"source": [
@@ -1814,7 +1814,7 @@
},
{
"cell_type": "markdown",
- "id": "74773c79",
+ "id": "4aab6725",
"metadata": {},
"source": [
"Now let's print out the decision rule for $\\mu_t$ uncovered by applying dynamic programming squared."
@@ -1823,7 +1823,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "28b4885a",
+ "id": "d617d0a6",
"metadata": {},
"outputs": [],
"source": [
@@ -1833,7 +1833,7 @@
},
{
"cell_type": "markdown",
- "id": "a2c80174",
+ "id": "94072e23",
"metadata": {},
"source": [
"Now let's print out the decision rule for $\\theta_{t+1} $ uncovered by applying dynamic programming squared."
@@ -1842,7 +1842,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9e7a44c8",
+ "id": "bf16560f",
"metadata": {},
"outputs": [],
"source": [
@@ -1852,7 +1852,7 @@
},
{
"cell_type": "markdown",
- "id": "f918de7a",
+ "id": "d742fcf5",
"metadata": {},
"source": [
"Evidently, these agree with the relationships that we discovered by running regressions on the Ramsey outcomes $\\vec \\mu^R, \\vec \\theta^R$ that we constructed with either of our machine learning algorithms.\n",
diff --git a/_sources/cattle_cycles.ipynb b/_sources/cattle_cycles.ipynb
index 3bff4639..925b5b70 100644
--- a/_sources/cattle_cycles.ipynb
+++ b/_sources/cattle_cycles.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "912de34c",
+ "id": "81aeb8c5",
"metadata": {},
"source": [
"(cattle_cycles)=\n",
@@ -28,7 +28,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b85a5e29",
+ "id": "22c5ce58",
"metadata": {
"tags": [
"hide-output"
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "6760e17e",
+ "id": "471c8b20",
"metadata": {},
"source": [
"This lecture uses the DLE class to construct instances of the \"Cattle Cycles\" model\n",
@@ -56,7 +56,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8f14e65c",
+ "id": "a32a7437",
"metadata": {},
"outputs": [],
"source": [
@@ -69,7 +69,7 @@
},
{
"cell_type": "markdown",
- "id": "e36415b5",
+ "id": "25749843",
"metadata": {},
"source": [
"## The Model\n",
@@ -219,7 +219,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8aebb62c",
+ "id": "49fa51e1",
"metadata": {},
"outputs": [],
"source": [
@@ -233,7 +233,7 @@
},
{
"cell_type": "markdown",
- "id": "adbdfbaa",
+ "id": "2ea4385f",
"metadata": {},
"source": [
"We set parameters to those used by {cite}`rosen1994cattle`"
@@ -242,7 +242,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "58526141",
+ "id": "78ef0834",
"metadata": {},
"outputs": [],
"source": [
@@ -314,7 +314,7 @@
},
{
"cell_type": "markdown",
- "id": "8633b0f5",
+ "id": "5193f381",
"metadata": {},
"source": [
"Notice that we have set $\\rho_1 = \\rho_2 = 0$, so $h_t$ and\n",
@@ -331,7 +331,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0884018e",
+ "id": "278719cd",
"metadata": {},
"outputs": [],
"source": [
@@ -362,7 +362,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bcad1e28",
+ "id": "97e00bc6",
"metadata": {},
"outputs": [],
"source": [
@@ -379,7 +379,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "881f9f2d",
+ "id": "2a79632a",
"metadata": {},
"outputs": [],
"source": [
@@ -388,7 +388,7 @@
},
{
"cell_type": "markdown",
- "id": "1c793da4",
+ "id": "7a0156cb",
"metadata": {},
"source": [
"{cite}`rosen1994cattle` use the model to understand the\n",
@@ -401,7 +401,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d42f1f0b",
+ "id": "9da3c59d",
"metadata": {},
"outputs": [],
"source": [
@@ -416,7 +416,7 @@
},
{
"cell_type": "markdown",
- "id": "5746764b",
+ "id": "be47376a",
"metadata": {},
"source": [
"In their Figure 3, {cite}`rosen1994cattle` plot the impulse response functions\n",
@@ -429,7 +429,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "92a984ca",
+ "id": "20918464",
"metadata": {},
"outputs": [],
"source": [
@@ -456,7 +456,7 @@
},
{
"cell_type": "markdown",
- "id": "5e1334bb",
+ "id": "70922671",
"metadata": {},
"source": [
"The above figures show how consumption patterns differ markedly,\n",
@@ -478,7 +478,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "349729a3",
+ "id": "b5f4309a",
"metadata": {},
"outputs": [],
"source": [
@@ -498,7 +498,7 @@
},
{
"cell_type": "markdown",
- "id": "e0199696",
+ "id": "3318f41e",
"metadata": {},
"source": [
"The fact that $y_t$ is a weighted moving average of $x_t$\n",
diff --git a/_sources/chang_credible.ipynb b/_sources/chang_credible.ipynb
index 8e9803cf..c68180ec 100644
--- a/_sources/chang_credible.ipynb
+++ b/_sources/chang_credible.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "f5e1f52f",
+ "id": "63d1d482",
"metadata": {},
"source": [
"(chang_credible)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a3e2ba53",
+ "id": "f2aa2d41",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "48141169",
+ "id": "3b890904",
"metadata": {},
"source": [
"## Overview\n",
@@ -93,7 +93,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f8863ba9",
+ "id": "fa5d557f",
"metadata": {},
"outputs": [],
"source": [
@@ -104,7 +104,7 @@
},
{
"cell_type": "markdown",
- "id": "f660bded",
+ "id": "e874f29b",
"metadata": {},
"source": [
"## The Setting\n",
@@ -247,11 +247,9 @@
"\n",
"y_t = f(x_t)\n",
"```\n",
- "\n",
- "where $f: \\mathbb{R}\\rightarrow \\mathbb{R}$ satisfies $f(x) > 0$,\n",
- "is twice continuously differentiable, $f''(x) < 0$, and\n",
- "$f(x) = f(-x)$ for all $x \\in\n",
- "\\mathbb{R}$, so that subsidies and taxes are equally distorting.\n",
+ "where $f: \\mathbb{R}\\rightarrow \\mathbb{R}$ satisfies $f(x) > 0$, $f(x)$\n",
+ "is twice continuously differentiable, $f''(x) < 0$, $f'(0) = 0$, and\n",
+ "$f(x) = f(-x)$ for all $x \\in \\mathbb{R}$, so that subsidies and taxes are equally distorting.\n",
"\n",
"The purpose is not to model the causes of tax distortions in any detail but simply to summarize\n",
"the *outcome* of those distortions via the function $f(x)$.\n",
@@ -798,7 +796,7 @@
"following functional forms:\n",
"\n",
"$$\n",
- "u(c) = log(c)\n",
+ "u(c) = \\log(c)\n",
"$$\n",
"\n",
"$$\n",
@@ -826,7 +824,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "85977b5e",
+ "id": "e60a43e3",
"metadata": {
"load": "_static/lecture_specific/chang_credible/changecon.py",
"tags": [
@@ -1337,7 +1335,7 @@
},
{
"cell_type": "markdown",
- "id": "3c016c6f",
+ "id": "74c3b357",
"metadata": {},
"source": [
"### Comparison of Sets\n",
@@ -1352,7 +1350,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a1d0b261",
+ "id": "fa210b09",
"metadata": {},
"outputs": [],
"source": [
@@ -1362,7 +1360,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9bb976d5",
+ "id": "6a9ce69d",
"metadata": {},
"outputs": [],
"source": [
@@ -1371,7 +1369,7 @@
},
{
"cell_type": "markdown",
- "id": "a442a823",
+ "id": "7065df9a",
"metadata": {},
"source": [
"The following plot shows both the set of $w,\\theta$ pairs associated with competitive equilibria (in red)\n",
@@ -1381,7 +1379,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0f7b8993",
+ "id": "f88d9a6a",
"metadata": {},
"outputs": [],
"source": [
@@ -1421,7 +1419,7 @@
},
{
"cell_type": "markdown",
- "id": "f9408915",
+ "id": "f44f04b5",
"metadata": {},
"source": [
"Evidently, the Ramsey plan, denoted by the $R$, is not sustainable.\n",
@@ -1432,7 +1430,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e3e0b1aa",
+ "id": "f3f126ef",
"metadata": {},
"outputs": [],
"source": [
@@ -1443,7 +1441,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e0ce0d7c",
+ "id": "8ca72302",
"metadata": {},
"outputs": [],
"source": [
@@ -1452,7 +1450,7 @@
},
{
"cell_type": "markdown",
- "id": "ee990e3a",
+ "id": "c9eb4b46",
"metadata": {},
"source": [
"Let's plot both sets"
@@ -1461,7 +1459,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bfd5af94",
+ "id": "18a92fca",
"metadata": {},
"outputs": [],
"source": [
@@ -1470,7 +1468,7 @@
},
{
"cell_type": "markdown",
- "id": "d7701d83",
+ "id": "37110c35",
"metadata": {},
"source": [
"Evidently, the Ramsey plan is now sustainable."
@@ -1495,18 +1493,18 @@
30,
83,
87,
- 804,
- 809,
- 819,
+ 802,
+ 807,
+ 817,
+ 821,
823,
- 825,
- 830,
- 863,
- 869,
+ 828,
+ 861,
+ 867,
+ 872,
874,
- 876,
- 880,
- 882
+ 878,
+ 880
]
},
"nbformat": 4,
diff --git a/_sources/chang_credible.md b/_sources/chang_credible.md
index 0340aa4f..42cc9156 100644
--- a/_sources/chang_credible.md
+++ b/_sources/chang_credible.md
@@ -226,11 +226,9 @@ assumption about outcomes for per capita output:
y_t = f(x_t)
```
-
-where $f: \mathbb{R}\rightarrow \mathbb{R}$ satisfies $f(x) > 0$,
-is twice continuously differentiable, $f''(x) < 0$, and
-$f(x) = f(-x)$ for all $x \in
-\mathbb{R}$, so that subsidies and taxes are equally distorting.
+where $f: \mathbb{R}\rightarrow \mathbb{R}$ satisfies $f(x) > 0$, $f(x)$
+is twice continuously differentiable, $f''(x) < 0$, $f'(0) = 0$, and
+$f(x) = f(-x)$ for all $x \in \mathbb{R}$, so that subsidies and taxes are equally distorting.
The purpose is not to model the causes of tax distortions in any detail but simply to summarize
the *outcome* of those distortions via the function $f(x)$.
@@ -777,7 +775,7 @@ We have created a Python class that solves the model assuming the
following functional forms:
$$
-u(c) = log(c)
+u(c) = \log(c)
$$
$$
diff --git a/_sources/chang_ramsey.ipynb b/_sources/chang_ramsey.ipynb
index 8af34ad8..d190a9f2 100644
--- a/_sources/chang_ramsey.ipynb
+++ b/_sources/chang_ramsey.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "937e28b4",
+ "id": "440fd6dd",
"metadata": {},
"source": [
"(chang_ramsey)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b95be5f1",
+ "id": "27f500ca",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "5a4f6393",
+ "id": "52e81c93",
"metadata": {},
"source": [
"## Overview\n",
@@ -81,7 +81,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8f5a3104",
+ "id": "3c9d14e4",
"metadata": {},
"outputs": [],
"source": [
@@ -92,7 +92,7 @@
},
{
"cell_type": "markdown",
- "id": "7b85bdf2",
+ "id": "ba25c324",
"metadata": {},
"source": [
"### The Setting\n",
@@ -146,7 +146,7 @@
"effects into account in designing a plan of government actions for\n",
"$t \\geq 0$.\n",
"\n",
- "## Setting\n",
+ "## Decisions\n",
"\n",
"### The Household’s Problem\n",
"\n",
@@ -154,7 +154,7 @@
"$\\vec q$ and sequences $\\vec y, \\vec x$ of income and total\n",
"tax collections, respectively.\n",
"\n",
- "The household chooses nonnegative\n",
+ "Facing vector $\\vec q$ as a price taker, the representative household chooses nonnegative\n",
"sequences $\\vec c, \\vec M$ of consumption and nominal balances,\n",
"respectively, to maximize\n",
"\n",
@@ -195,8 +195,8 @@
"Inequality {eq}`eqn_chang_ramsey2` is the household’s time $t$ budget constraint.\n",
"\n",
"It tells how real balances $q_t M_t$ carried out of period $t$ depend\n",
- "on income, consumption, taxes, and real balances $q_t M_{t-1}$\n",
- "carried into the period.\n",
+ "on real balances $q_t M_{t-1}$\n",
+ "carried into period $t$, income, consumption, taxes.\n",
"\n",
"Equation {eq}`eqn_chang_ramsey3` imposes an exogenous upper bound\n",
"$\\bar m$ on the household's choice of real balances, where\n",
@@ -210,13 +210,35 @@
"[ \\underline \\pi, \\overline \\pi]$, where\n",
"$0 < \\underline \\pi < 1 < { 1 \\over \\beta } \\leq \\overline \\pi$.\n",
"\n",
- "The government faces a sequence of budget constraints with time\n",
- "$t$ component\n",
+ "The government purchases no goods.\n",
+ "\n",
+ "It taxes only to acquire paper currency that it will withdraw from circulation (e.g., by burning it).\n",
+ "\n",
+ "Let $p_t $ be the price level at time $t$, measured as time $t$ dollars per unit of the consumption good.\n",
+ "\n",
+ "Evidently, the value of paper currency meassured in units of the consumption good at time $t$ is \n",
"\n",
"$$\n",
- "-x_t = q_t (M_t - M_{t-1})\n",
+ "q_t = \\frac{1}{p_t} .\n",
+ "$$\n",
+ "\n",
+ "The government faces a sequence of budget constraints with time $t$ component \n",
+ "\n",
+ "$$\n",
+ "x_t + \\frac{M_{t} - M_{t-1}}{p_t} = 0,\n",
"$$\n",
"\n",
+ "where $x_t$ is the real value of revenue that the government raises from taxes and $\\frac{M_{t} - M_{t-1}}{p_t}$ is\n",
+ "the real value of revenue that the government raises by printing new paper currency. \n",
+ "\n",
+ "Evidently, this budget constraint can be rewritten as\n",
+ "\n",
+ "\n",
+ "\n",
+ "$$\n",
+ "-x_t = q_t (M_t - M_{t-1})\n",
+ "$$ \n",
+ "\n",
"which by using the definitions of $m_t$ and $h_t$ can also\n",
"be expressed as\n",
"\n",
@@ -226,7 +248,8 @@
"-x_t = m_t (1-h_t)\n",
"```\n",
"\n",
- "The restrictions $m_t \\in [0, \\bar m]$ and $h_t \\in \\Pi$ evidently\n",
+ "\n",
+ "The restrictions $m_t \\in [0, \\bar m]$ and $h_t \\in \\Pi = [\\underline \\pi, \\overline \\pi]$ evidently\n",
"imply that $x_t \\in X \\equiv [(\\underline \\pi -1)\\bar m,\n",
"(\\overline \\pi -1) \\bar m]$.\n",
"\n",
@@ -242,10 +265,27 @@
"y_t = f(x_t),\n",
"```\n",
"\n",
- "where $f: \\mathbb{R}\\rightarrow \\mathbb{R}$ satisfies $f(x) > 0$,\n",
- "is twice continuously differentiable, $f''(x) < 0$, and\n",
- "$f(x) = f(-x)$ for all $x \\in\n",
- "\\mathbb{R}$, so that subsidies and taxes are equally distorting.\n",
+ "where $f: \\mathbb{R}\\rightarrow \\mathbb{R}$ satisfies $f(x) > 0$, $f(x)$\n",
+ "is twice continuously differentiable, $f''(x) < 0$, $f'(0) = 0$, and\n",
+ "$f(x) = f(-x)$ for all $x \\in \\mathbb{R}$, so that subsidies and taxes are equally distorting.\n",
+ "\n",
+ "**Example parameterizations**\n",
+ "\n",
+ "In some of our Python code deployed later in this lecture, we'll assume the following functional forms:\n",
+ "\n",
+ "$$\n",
+ "u(c) = \\log(c)\n",
+ "$$\n",
+ "\n",
+ "$$\n",
+ "v(m) = \\frac{1}{500}(m \\bar m - 0.5m^2)^{0.5}\n",
+ "$$\n",
+ "\n",
+ "$$\n",
+ "f(x) = 180 - (0.4x)^2\n",
+ "$$\n",
+ "\n",
+ "**The tax distortion function** \n",
"\n",
"Calvo's and Chang's purpose is not to model the causes of tax distortions in\n",
"any detail but simply to summarize\n",
@@ -876,7 +916,7 @@
"following functional forms:\n",
"\n",
"$$\n",
- "u(c) = log(c)\n",
+ "u(c) = \\log(c)\n",
"$$\n",
"\n",
"$$\n",
@@ -901,7 +941,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "65a05b7b",
+ "id": "1841b2ae",
"metadata": {
"load": "_static/lecture_specific/chang_credible/changecon.py"
},
@@ -1410,7 +1450,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f93bcffe",
+ "id": "5924787b",
"metadata": {},
"outputs": [],
"source": [
@@ -1421,7 +1461,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e6dc6344",
+ "id": "37a66c4a",
"metadata": {},
"outputs": [],
"source": [
@@ -1460,7 +1500,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "54966ff6",
+ "id": "b1a3d478",
"metadata": {},
"outputs": [],
"source": [
@@ -1472,7 +1512,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f1b2593c",
+ "id": "fcdbbf33",
"metadata": {},
"outputs": [],
"source": [
@@ -1481,7 +1521,7 @@
},
{
"cell_type": "markdown",
- "id": "bcc3ff9b",
+ "id": "cd93d58d",
"metadata": {},
"source": [
"## Solving a Continuation Ramsey Planner's Bellman Equation\n",
@@ -1541,7 +1581,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a678f20e",
+ "id": "bc96edd4",
"metadata": {},
"outputs": [],
"source": [
@@ -1554,7 +1594,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bfe2b01c",
+ "id": "7dc225bc",
"metadata": {},
"outputs": [],
"source": [
@@ -1564,7 +1604,7 @@
},
{
"cell_type": "markdown",
- "id": "804a5e6d",
+ "id": "4267a606",
"metadata": {},
"source": [
"First, a quick check that our approximations of the value functions are\n",
@@ -1576,7 +1616,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6273ef3c",
+ "id": "3425756f",
"metadata": {},
"outputs": [],
"source": [
@@ -1585,7 +1625,7 @@
},
{
"cell_type": "markdown",
- "id": "c0dfb9ae",
+ "id": "8bf1d83a",
"metadata": {},
"source": [
"The value functions plotted below trace out the right edges of the sets\n",
@@ -1595,7 +1635,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "88cf8618",
+ "id": "5fff2dfa",
"metadata": {},
"outputs": [],
"source": [
@@ -1612,7 +1652,7 @@
},
{
"cell_type": "markdown",
- "id": "c021b2d1",
+ "id": "a8981b1d",
"metadata": {},
"source": [
"The next figure plots the optimal policy functions; values of\n",
@@ -1622,7 +1662,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8cef9af0",
+ "id": "8e6809d4",
"metadata": {},
"outputs": [],
"source": [
@@ -1645,7 +1685,7 @@
},
{
"cell_type": "markdown",
- "id": "91efd604",
+ "id": "9588015c",
"metadata": {},
"source": [
"With the first set of parameter values, the value of $\\theta'$ chosen by the Ramsey\n",
@@ -1666,7 +1706,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ad906cf6",
+ "id": "62ed1b8c",
"metadata": {},
"outputs": [],
"source": [
@@ -1683,7 +1723,7 @@
},
{
"cell_type": "markdown",
- "id": "010ef62a",
+ "id": "e2786d12",
"metadata": {},
"source": [
"Subproblem 2 is equivalent to the planner choosing the initial value of\n",
@@ -1699,7 +1739,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f7d3c065",
+ "id": "330b3206",
"metadata": {},
"outputs": [],
"source": [
@@ -1720,7 +1760,7 @@
},
{
"cell_type": "markdown",
- "id": "35d0b2f4",
+ "id": "9785c4fc",
"metadata": {},
"source": [
"### Next Steps\n",
@@ -1753,25 +1793,25 @@
30,
71,
75,
- 879,
- 883,
- 888,
- 921,
- 927,
- 929,
- 984,
- 991,
- 994,
- 1001,
- 1003,
- 1008,
- 1018,
- 1023,
- 1039,
- 1055,
- 1065,
- 1076,
- 1090
+ 919,
+ 923,
+ 928,
+ 961,
+ 967,
+ 969,
+ 1024,
+ 1031,
+ 1034,
+ 1041,
+ 1043,
+ 1048,
+ 1058,
+ 1063,
+ 1079,
+ 1095,
+ 1105,
+ 1116,
+ 1130
]
},
"nbformat": 4,
diff --git a/_sources/chang_ramsey.md b/_sources/chang_ramsey.md
index 792e6550..dbf111d8 100644
--- a/_sources/chang_ramsey.md
+++ b/_sources/chang_ramsey.md
@@ -125,7 +125,7 @@ time $0$ Ramsey planner takes these
effects into account in designing a plan of government actions for
$t \geq 0$.
-## Setting
+## Decisions
### The Household’s Problem
@@ -133,7 +133,7 @@ A representative household faces a nonnegative value of money sequence
$\vec q$ and sequences $\vec y, \vec x$ of income and total
tax collections, respectively.
-The household chooses nonnegative
+Facing vector $\vec q$ as a price taker, the representative household chooses nonnegative
sequences $\vec c, \vec M$ of consumption and nominal balances,
respectively, to maximize
@@ -174,8 +174,8 @@ The household carries real balances out of a period equal to $m_t = q_t M_t$.
Inequality {eq}`eqn_chang_ramsey2` is the household’s time $t$ budget constraint.
It tells how real balances $q_t M_t$ carried out of period $t$ depend
-on income, consumption, taxes, and real balances $q_t M_{t-1}$
-carried into the period.
+on real balances $q_t M_{t-1}$
+carried into period $t$, income, consumption, taxes.
Equation {eq}`eqn_chang_ramsey3` imposes an exogenous upper bound
$\bar m$ on the household's choice of real balances, where
@@ -189,13 +189,35 @@ $h_t \equiv {M_{t-1}\over M_t} \in \Pi \equiv
[ \underline \pi, \overline \pi]$, where
$0 < \underline \pi < 1 < { 1 \over \beta } \leq \overline \pi$.
-The government faces a sequence of budget constraints with time
-$t$ component
+The government purchases no goods.
+
+It taxes only to acquire paper currency that it will withdraw from circulation (e.g., by burning it).
+
+Let $p_t $ be the price level at time $t$, measured as time $t$ dollars per unit of the consumption good.
+
+Evidently, the value of paper currency meassured in units of the consumption good at time $t$ is
$$
--x_t = q_t (M_t - M_{t-1})
+q_t = \frac{1}{p_t} .
+$$
+
+The government faces a sequence of budget constraints with time $t$ component
+
+$$
+x_t + \frac{M_{t} - M_{t-1}}{p_t} = 0,
$$
+where $x_t$ is the real value of revenue that the government raises from taxes and $\frac{M_{t} - M_{t-1}}{p_t}$ is
+the real value of revenue that the government raises by printing new paper currency.
+
+Evidently, this budget constraint can be rewritten as
+
+
+
+$$
+-x_t = q_t (M_t - M_{t-1})
+$$
+
which by using the definitions of $m_t$ and $h_t$ can also
be expressed as
@@ -205,7 +227,8 @@ be expressed as
-x_t = m_t (1-h_t)
```
-The restrictions $m_t \in [0, \bar m]$ and $h_t \in \Pi$ evidently
+
+The restrictions $m_t \in [0, \bar m]$ and $h_t \in \Pi = [\underline \pi, \overline \pi]$ evidently
imply that $x_t \in X \equiv [(\underline \pi -1)\bar m,
(\overline \pi -1) \bar m]$.
@@ -221,10 +244,27 @@ assumption about outcomes for per capita output:
y_t = f(x_t),
```
-where $f: \mathbb{R}\rightarrow \mathbb{R}$ satisfies $f(x) > 0$,
-is twice continuously differentiable, $f''(x) < 0$, and
-$f(x) = f(-x)$ for all $x \in
-\mathbb{R}$, so that subsidies and taxes are equally distorting.
+where $f: \mathbb{R}\rightarrow \mathbb{R}$ satisfies $f(x) > 0$, $f(x)$
+is twice continuously differentiable, $f''(x) < 0$, $f'(0) = 0$, and
+$f(x) = f(-x)$ for all $x \in \mathbb{R}$, so that subsidies and taxes are equally distorting.
+
+**Example parameterizations**
+
+In some of our Python code deployed later in this lecture, we'll assume the following functional forms:
+
+$$
+u(c) = \log(c)
+$$
+
+$$
+v(m) = \frac{1}{500}(m \bar m - 0.5m^2)^{0.5}
+$$
+
+$$
+f(x) = 180 - (0.4x)^2
+$$
+
+**The tax distortion function**
Calvo's and Chang's purpose is not to model the causes of tax distortions in
any detail but simply to summarize
@@ -855,7 +895,7 @@ We have created a Python class that solves the model assuming the
following functional forms:
$$
-u(c) = log(c)
+u(c) = \log(c)
$$
$$
diff --git a/_sources/classical_filtering.ipynb b/_sources/classical_filtering.ipynb
index 0251bf68..87b6fd6b 100644
--- a/_sources/classical_filtering.ipynb
+++ b/_sources/classical_filtering.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "9c431fa1",
+ "id": "06af96bd",
"metadata": {},
"source": [
"(classical_filtering)=\n",
@@ -64,7 +64,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c3635455",
+ "id": "524d35c0",
"metadata": {},
"outputs": [],
"source": [
@@ -73,7 +73,7 @@
},
{
"cell_type": "markdown",
- "id": "531a602c",
+ "id": "a706f8de",
"metadata": {},
"source": [
"### References\n",
@@ -233,7 +233,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d69a44a9",
+ "id": "1f78ce8a",
"metadata": {
"load": "_static/lecture_specific/lu_tricks/control_and_filter.py"
},
@@ -549,7 +549,7 @@
},
{
"cell_type": "markdown",
- "id": "a11b1ede",
+ "id": "fcbcfb97",
"metadata": {},
"source": [
"Let's use this code to tackle two interesting examples.\n",
@@ -574,7 +574,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8d25d9a9",
+ "id": "103cae88",
"metadata": {},
"outputs": [],
"source": [
@@ -588,7 +588,7 @@
},
{
"cell_type": "markdown",
- "id": "0ca2dcce",
+ "id": "83aa0b62",
"metadata": {},
"source": [
"The Wold representation is computed by `example.coeffs_of_c()`.\n",
@@ -599,7 +599,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "520df49b",
+ "id": "eff23291",
"metadata": {},
"outputs": [],
"source": [
@@ -609,7 +609,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d3f0f37e",
+ "id": "db35bcf0",
"metadata": {},
"outputs": [],
"source": [
@@ -618,7 +618,7 @@
},
{
"cell_type": "markdown",
- "id": "e6c88806",
+ "id": "8a3399eb",
"metadata": {},
"source": [
"Now let's form the covariance matrix of a time series vector of length $N$\n",
@@ -631,7 +631,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "77550c2a",
+ "id": "89a69936",
"metadata": {},
"outputs": [],
"source": [
@@ -641,7 +641,7 @@
},
{
"cell_type": "markdown",
- "id": "88856d93",
+ "id": "4a3daccb",
"metadata": {},
"source": [
"Notice how the lower rows of the \"moving average representations\" are converging to the appropriate infinite history Wold representation\n",
@@ -651,7 +651,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "592daaac",
+ "id": "580b7a35",
"metadata": {},
"outputs": [],
"source": [
@@ -661,7 +661,7 @@
},
{
"cell_type": "markdown",
- "id": "bea13066",
+ "id": "3313a896",
"metadata": {},
"source": [
"Notice how the lower rows of the \"autoregressive representations\" are converging to the appropriate infinite-history\n",
@@ -671,7 +671,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7cdbcd59",
+ "id": "a7b1430c",
"metadata": {},
"outputs": [],
"source": [
@@ -681,7 +681,7 @@
},
{
"cell_type": "markdown",
- "id": "986a8c93",
+ "id": "0e28d082",
"metadata": {},
"source": [
"### Example 2\n",
@@ -708,7 +708,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "63d18b28",
+ "id": "cdfe027c",
"metadata": {},
"outputs": [],
"source": [
@@ -724,7 +724,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "056ac86b",
+ "id": "ee724f0c",
"metadata": {},
"outputs": [],
"source": [
@@ -734,7 +734,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c3c6a089",
+ "id": "0f1ab736",
"metadata": {},
"outputs": [],
"source": [
@@ -745,7 +745,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "428e24f5",
+ "id": "2d2a6257",
"metadata": {},
"outputs": [],
"source": [
@@ -756,7 +756,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ed0ca468",
+ "id": "9ae9e91e",
"metadata": {},
"outputs": [],
"source": [
@@ -766,7 +766,7 @@
},
{
"cell_type": "markdown",
- "id": "78b8d1b1",
+ "id": "8cae18cc",
"metadata": {},
"source": [
"### Prediction\n",
diff --git a/_sources/coase.ipynb b/_sources/coase.ipynb
index 21930cbc..4307354a 100644
--- a/_sources/coase.ipynb
+++ b/_sources/coase.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "af8f75cb",
+ "id": "7c884de5",
"metadata": {},
"source": [
"(coase)=\n",
@@ -44,7 +44,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8a0cedc6",
+ "id": "ea20760b",
"metadata": {},
"outputs": [],
"source": [
@@ -55,7 +55,7 @@
},
{
"cell_type": "markdown",
- "id": "6cca0b05",
+ "id": "3ee52c30",
"metadata": {},
"source": [
"### Why Firms Exist\n",
@@ -444,7 +444,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9c0b6cb1",
+ "id": "434d4864",
"metadata": {},
"outputs": [],
"source": [
@@ -461,7 +461,7 @@
},
{
"cell_type": "markdown",
- "id": "c70fc2ca",
+ "id": "ee6e5268",
"metadata": {},
"source": [
"Now let's implement and iterate with $T$ until convergence.\n",
@@ -473,7 +473,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d50d4899",
+ "id": "1187e084",
"metadata": {},
"outputs": [],
"source": [
@@ -510,7 +510,7 @@
},
{
"cell_type": "markdown",
- "id": "f216c895",
+ "id": "be07e900",
"metadata": {},
"source": [
"The next function computes optimal choice of upstream boundary and range of\n",
@@ -520,7 +520,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0c6b5494",
+ "id": "ec22e858",
"metadata": {},
"outputs": [],
"source": [
@@ -545,7 +545,7 @@
},
{
"cell_type": "markdown",
- "id": "6dae2689",
+ "id": "351481fa",
"metadata": {},
"source": [
"The allocation of firms can be computed by recursively stepping through firms' choices of\n",
@@ -557,7 +557,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a9a2b578",
+ "id": "566c1fa4",
"metadata": {},
"outputs": [],
"source": [
@@ -572,7 +572,7 @@
},
{
"cell_type": "markdown",
- "id": "a58abfdd",
+ "id": "6e437b4b",
"metadata": {},
"source": [
"Let's try this at the default parameters.\n",
@@ -584,7 +584,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "788bad8a",
+ "id": "1cb13ce7",
"metadata": {},
"outputs": [],
"source": [
@@ -605,7 +605,7 @@
},
{
"cell_type": "markdown",
- "id": "f0d61564",
+ "id": "6ecabbe4",
"metadata": {},
"source": [
"Here's the function $\\ell^*$, which shows how large a firm with\n",
@@ -615,7 +615,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9ee1ca54",
+ "id": "e0d4580c",
"metadata": {},
"outputs": [],
"source": [
@@ -632,7 +632,7 @@
},
{
"cell_type": "markdown",
- "id": "620ed944",
+ "id": "4c855843",
"metadata": {},
"source": [
"Note that downstream firms choose to be larger, a point we return to below.\n",
@@ -661,7 +661,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a282e3d5",
+ "id": "13642013",
"metadata": {},
"outputs": [],
"source": [
@@ -676,7 +676,7 @@
},
{
"cell_type": "markdown",
- "id": "3a24b65c",
+ "id": "d20a0421",
"metadata": {},
"source": [
"```{solution-end}\n",
@@ -718,7 +718,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cf4e9e9f",
+ "id": "8017c79c",
"metadata": {},
"outputs": [],
"source": [
@@ -740,7 +740,7 @@
},
{
"cell_type": "markdown",
- "id": "90c60ca1",
+ "id": "5871cda4",
"metadata": {},
"source": [
"```{solution-end}\n",
diff --git a/_sources/cons_news.ipynb b/_sources/cons_news.ipynb
index 401811d7..42c398be 100644
--- a/_sources/cons_news.ipynb
+++ b/_sources/cons_news.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "87067e1d",
+ "id": "f73dcb87",
"metadata": {},
"source": [
"(information_consumption_smoothing-v3)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "31857e8d",
+ "id": "751a5d2f",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "b1a60416",
+ "id": "7f43bb39",
"metadata": {},
"source": [
"## Overview\n",
@@ -612,7 +612,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "89610fd8",
+ "id": "8c5ed14f",
"metadata": {},
"outputs": [],
"source": [
@@ -624,7 +624,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c212ceea",
+ "id": "5ff8b7cd",
"metadata": {},
"outputs": [],
"source": [
@@ -644,7 +644,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6ae32bef",
+ "id": "8f5f4411",
"metadata": {},
"outputs": [],
"source": [
@@ -663,7 +663,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1c00cd0f",
+ "id": "38e40cb4",
"metadata": {},
"outputs": [],
"source": [
@@ -673,7 +673,7 @@
},
{
"cell_type": "markdown",
- "id": "7c382be9",
+ "id": "c8d21a83",
"metadata": {},
"source": [
"Evidently, optimal consumption and debt decision rules for the consumer\n",
@@ -692,7 +692,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "49210823",
+ "id": "f0f0736c",
"metadata": {},
"outputs": [],
"source": [
@@ -710,7 +710,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "be7d4d14",
+ "id": "f28e47db",
"metadata": {},
"outputs": [],
"source": [
@@ -719,7 +719,7 @@
},
{
"cell_type": "markdown",
- "id": "3e1b9c57",
+ "id": "5a21cf4e",
"metadata": {},
"source": [
"For a consumer having access only to the information associated with the\n",
@@ -772,7 +772,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "af093d48",
+ "id": "a534b6d2",
"metadata": {},
"outputs": [],
"source": [
@@ -790,7 +790,7 @@
},
{
"cell_type": "markdown",
- "id": "9311437a",
+ "id": "a730b8ea",
"metadata": {},
"source": [
"The following code computes impulse response functions of\n",
@@ -800,7 +800,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0670196f",
+ "id": "806ebb56",
"metadata": {},
"outputs": [],
"source": [
@@ -818,7 +818,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "536125ea",
+ "id": "dbf18e98",
"metadata": {},
"outputs": [],
"source": [
@@ -828,7 +828,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "276b5587",
+ "id": "8d776038",
"metadata": {},
"outputs": [],
"source": [
@@ -840,7 +840,7 @@
},
{
"cell_type": "markdown",
- "id": "432948c6",
+ "id": "2a0d09d2",
"metadata": {},
"source": [
"The above two impulse response functions show that when the consumer has\n",
@@ -856,7 +856,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ed2bfbfe",
+ "id": "6af1ed1e",
"metadata": {},
"outputs": [],
"source": [
@@ -866,7 +866,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "257442c0",
+ "id": "d813e848",
"metadata": {},
"outputs": [],
"source": [
@@ -879,7 +879,7 @@
},
{
"cell_type": "markdown",
- "id": "f57b80d1",
+ "id": "4efb215a",
"metadata": {},
"source": [
"The above impulse responses show that when the consumer has only the\n",
@@ -903,7 +903,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bca0f5cf",
+ "id": "f464a9f8",
"metadata": {},
"outputs": [],
"source": [
@@ -914,7 +914,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f46e4e88",
+ "id": "d6e85f17",
"metadata": {},
"outputs": [],
"source": [
@@ -929,7 +929,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4c2bfaec",
+ "id": "6664f48f",
"metadata": {},
"outputs": [],
"source": [
@@ -943,7 +943,7 @@
},
{
"cell_type": "markdown",
- "id": "bb5d7da3",
+ "id": "dd75ec53",
"metadata": {},
"source": [
"## Simulating Income Process and Two Associated Shock Processes\n",
diff --git a/_sources/discrete_dp.ipynb b/_sources/discrete_dp.ipynb
index 31eafe1a..ee886189 100644
--- a/_sources/discrete_dp.ipynb
+++ b/_sources/discrete_dp.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "c1d5a483",
+ "id": "fff53ad1",
"metadata": {},
"source": [
"(discrete_dp)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ba765a93",
+ "id": "2c32839a",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "c9f65998",
+ "id": "07fbd544",
"metadata": {},
"source": [
"## Overview\n",
@@ -72,7 +72,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9ae56028",
+ "id": "33944873",
"metadata": {},
"outputs": [],
"source": [
@@ -86,7 +86,7 @@
},
{
"cell_type": "markdown",
- "id": "f5d297fb",
+ "id": "695c5a73",
"metadata": {},
"source": [
"### How to Read this Lecture\n",
@@ -467,7 +467,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b6014c31",
+ "id": "3a233750",
"metadata": {},
"outputs": [],
"source": [
@@ -516,7 +516,7 @@
},
{
"cell_type": "markdown",
- "id": "af864b0a",
+ "id": "98349f97",
"metadata": {},
"source": [
"Let's run this code and create an instance of `SimpleOG`."
@@ -525,7 +525,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2bc6bfb9",
+ "id": "3db774b8",
"metadata": {},
"outputs": [],
"source": [
@@ -534,7 +534,7 @@
},
{
"cell_type": "markdown",
- "id": "7cde5da8",
+ "id": "d07cdaab",
"metadata": {},
"source": [
"Instances of `DiscreteDP` are created using the signature `DiscreteDP(R, Q, β)`.\n",
@@ -545,7 +545,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "446b859b",
+ "id": "6933f27c",
"metadata": {},
"outputs": [],
"source": [
@@ -554,7 +554,7 @@
},
{
"cell_type": "markdown",
- "id": "aa2dff7d",
+ "id": "356f22d6",
"metadata": {},
"source": [
"Now that we have an instance `ddp` of `DiscreteDP` we can solve it as follows"
@@ -563,7 +563,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6ad3ed1b",
+ "id": "784c50cd",
"metadata": {},
"outputs": [],
"source": [
@@ -572,7 +572,7 @@
},
{
"cell_type": "markdown",
- "id": "edae7371",
+ "id": "7c8d5939",
"metadata": {},
"source": [
"Let's see what we've got here"
@@ -581,7 +581,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "389afe3b",
+ "id": "6ce81380",
"metadata": {},
"outputs": [],
"source": [
@@ -590,7 +590,7 @@
},
{
"cell_type": "markdown",
- "id": "15eba211",
+ "id": "c9ab1e3d",
"metadata": {},
"source": [
"(In IPython version 4.0 and above you can also type `results.` and hit the tab key)\n",
@@ -601,7 +601,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "922a931c",
+ "id": "0b765a12",
"metadata": {},
"outputs": [],
"source": [
@@ -611,7 +611,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6e97104c",
+ "id": "f058d3bd",
"metadata": {},
"outputs": [],
"source": [
@@ -620,7 +620,7 @@
},
{
"cell_type": "markdown",
- "id": "6fecfa4f",
+ "id": "b8ff158a",
"metadata": {},
"source": [
"Since we've used policy iteration, these results will be exact unless we hit the iteration bound `max_iter`.\n",
@@ -631,7 +631,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f4cda746",
+ "id": "c1832ce2",
"metadata": {},
"outputs": [],
"source": [
@@ -641,7 +641,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "718b3df6",
+ "id": "9d555012",
"metadata": {},
"outputs": [],
"source": [
@@ -650,7 +650,7 @@
},
{
"cell_type": "markdown",
- "id": "90a755e8",
+ "id": "bcc48942",
"metadata": {},
"source": [
"Another interesting object is `results.mc`, which is the controlled chain defined by $Q_{\\sigma^*}$, where $\\sigma^*$ is the optimal policy.\n",
@@ -664,7 +664,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "863b9dea",
+ "id": "6e561773",
"metadata": {},
"outputs": [],
"source": [
@@ -673,7 +673,7 @@
},
{
"cell_type": "markdown",
- "id": "265caa95",
+ "id": "2f67c7a7",
"metadata": {},
"source": [
"Here's the same information in a bar graph\n",
@@ -688,7 +688,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "211e0b54",
+ "id": "10d3b542",
"metadata": {},
"outputs": [],
"source": [
@@ -699,7 +699,7 @@
},
{
"cell_type": "markdown",
- "id": "a201d57d",
+ "id": "3e2b28cb",
"metadata": {},
"source": [
"If we look at the bar graph we can see the rightward shift in probability mass\n",
@@ -728,7 +728,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "072e2d1d",
+ "id": "795dd576",
"metadata": {},
"outputs": [],
"source": [
@@ -759,7 +759,7 @@
},
{
"cell_type": "markdown",
- "id": "251d4e81",
+ "id": "5f0a65fe",
"metadata": {},
"source": [
"For larger problems, you might need to write this code more efficiently by vectorizing or using Numba.\n",
@@ -783,7 +783,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "14960fbe",
+ "id": "8591698c",
"metadata": {},
"outputs": [],
"source": [
@@ -795,7 +795,7 @@
},
{
"cell_type": "markdown",
- "id": "481b7c78",
+ "id": "341ac17e",
"metadata": {},
"source": [
"Here we want to solve a finite state version of the continuous state model above.\n",
@@ -806,7 +806,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5257ae18",
+ "id": "82d3bcd2",
"metadata": {},
"outputs": [],
"source": [
@@ -817,7 +817,7 @@
},
{
"cell_type": "markdown",
- "id": "5a0f093c",
+ "id": "8a07f737",
"metadata": {},
"source": [
"We choose the action to be the amount of capital to save for the next\n",
@@ -846,7 +846,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "663d50cb",
+ "id": "5c6e6863",
"metadata": {},
"outputs": [],
"source": [
@@ -866,7 +866,7 @@
},
{
"cell_type": "markdown",
- "id": "d690106e",
+ "id": "53eb276a",
"metadata": {},
"source": [
"Reward vector `R` (of length `L`):"
@@ -875,7 +875,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2174f0b1",
+ "id": "fd2607e5",
"metadata": {},
"outputs": [],
"source": [
@@ -884,7 +884,7 @@
},
{
"cell_type": "markdown",
- "id": "039d4d78",
+ "id": "38041923",
"metadata": {},
"source": [
"(Degenerate) transition probability matrix `Q` (of shape `(L, grid_size)`), where we choose the [scipy.sparse.lil_matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.lil_matrix.html) format, while any format will do (internally it will be converted to the csr format):"
@@ -893,7 +893,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "737191a1",
+ "id": "f911f896",
"metadata": {},
"outputs": [],
"source": [
@@ -903,7 +903,7 @@
},
{
"cell_type": "markdown",
- "id": "6d631e69",
+ "id": "e96b281a",
"metadata": {},
"source": [
"(If you are familiar with the data structure of [scipy.sparse.csr_matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csr_matrix.html), the following is the most efficient way to create the `Q` matrix in\n",
@@ -913,7 +913,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4b60f243",
+ "id": "92523482",
"metadata": {},
"outputs": [],
"source": [
@@ -924,7 +924,7 @@
},
{
"cell_type": "markdown",
- "id": "67f52acb",
+ "id": "61d9f456",
"metadata": {},
"source": [
"Discrete growth model:"
@@ -933,7 +933,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5fa29bd3",
+ "id": "84bbf239",
"metadata": {},
"outputs": [],
"source": [
@@ -942,7 +942,7 @@
},
{
"cell_type": "markdown",
- "id": "8ff96d07",
+ "id": "25fd3ab1",
"metadata": {},
"source": [
"**Notes**\n",
@@ -959,7 +959,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ce5fb67a",
+ "id": "acf548c4",
"metadata": {},
"outputs": [],
"source": [
@@ -970,7 +970,7 @@
},
{
"cell_type": "markdown",
- "id": "9e9c5d48",
+ "id": "eb17155b",
"metadata": {},
"source": [
"Note that `sigma` contains the *indices* of the optimal *capital\n",
@@ -981,7 +981,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "faf92c34",
+ "id": "053dd492",
"metadata": {},
"outputs": [],
"source": [
@@ -1002,7 +1002,7 @@
},
{
"cell_type": "markdown",
- "id": "183b0c76",
+ "id": "18d08a9c",
"metadata": {},
"source": [
"Let us compare the solution of the discrete model with that of the\n",
@@ -1012,7 +1012,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c03d1a4a",
+ "id": "62302cd3",
"metadata": {},
"outputs": [],
"source": [
@@ -1039,7 +1039,7 @@
},
{
"cell_type": "markdown",
- "id": "844b2bf3",
+ "id": "7f23c017",
"metadata": {},
"source": [
"The outcomes appear very close to those of the continuous version.\n",
@@ -1050,7 +1050,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a86d728e",
+ "id": "677aa3eb",
"metadata": {},
"outputs": [],
"source": [
@@ -1060,7 +1060,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4dbb3456",
+ "id": "aca2953d",
"metadata": {},
"outputs": [],
"source": [
@@ -1069,7 +1069,7 @@
},
{
"cell_type": "markdown",
- "id": "fa830855",
+ "id": "ad9190e0",
"metadata": {},
"source": [
"The optimal consumption functions are close as well:"
@@ -1078,7 +1078,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dc8e338b",
+ "id": "cce942d0",
"metadata": {},
"outputs": [],
"source": [
@@ -1087,7 +1087,7 @@
},
{
"cell_type": "markdown",
- "id": "4f59b5fa",
+ "id": "c8b1b9ba",
"metadata": {},
"source": [
"In fact, the optimal consumption obtained in the discrete version is not\n",
@@ -1097,7 +1097,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cdf501e6",
+ "id": "1faa6761",
"metadata": {},
"outputs": [],
"source": [
@@ -1108,7 +1108,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a5d7ee84",
+ "id": "243f2dfb",
"metadata": {},
"outputs": [],
"source": [
@@ -1119,7 +1119,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9971ace0",
+ "id": "29b3b437",
"metadata": {},
"outputs": [],
"source": [
@@ -1128,7 +1128,7 @@
},
{
"cell_type": "markdown",
- "id": "5bb65408",
+ "id": "5411be95",
"metadata": {},
"source": [
"The value function is monotone:"
@@ -1137,7 +1137,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2bcd77a9",
+ "id": "4891201e",
"metadata": {},
"outputs": [],
"source": [
@@ -1146,7 +1146,7 @@
},
{
"cell_type": "markdown",
- "id": "716503b9",
+ "id": "292c1fb4",
"metadata": {},
"source": [
"### Comparison of the Solution Methods\n",
@@ -1159,7 +1159,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6713504e",
+ "id": "b7fefba4",
"metadata": {},
"outputs": [],
"source": [
@@ -1172,7 +1172,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ac5f0b03",
+ "id": "da902014",
"metadata": {},
"outputs": [],
"source": [
@@ -1181,7 +1181,7 @@
},
{
"cell_type": "markdown",
- "id": "162ecbbe",
+ "id": "19a33759",
"metadata": {},
"source": [
"#### Modified Policy Iteration"
@@ -1190,7 +1190,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b621312d",
+ "id": "e612ab94",
"metadata": {},
"outputs": [],
"source": [
@@ -1201,7 +1201,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6069b687",
+ "id": "67cfa316",
"metadata": {},
"outputs": [],
"source": [
@@ -1210,7 +1210,7 @@
},
{
"cell_type": "markdown",
- "id": "d1435a03",
+ "id": "022c930c",
"metadata": {},
"source": [
"#### Speed Comparison"
@@ -1219,7 +1219,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bb432c4a",
+ "id": "9a8a88d8",
"metadata": {},
"outputs": [],
"source": [
@@ -1230,7 +1230,7 @@
},
{
"cell_type": "markdown",
- "id": "e564cddf",
+ "id": "1aa774fb",
"metadata": {},
"source": [
"As is often the case, policy iteration and modified policy iteration are\n",
@@ -1250,7 +1250,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1db6fadb",
+ "id": "53d7f7c9",
"metadata": {},
"outputs": [],
"source": [
@@ -1273,7 +1273,7 @@
},
{
"cell_type": "markdown",
- "id": "c9b7dfed",
+ "id": "802ea8e6",
"metadata": {},
"source": [
"We next plot the consumption policies along with the value iteration"
@@ -1282,7 +1282,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b0645e18",
+ "id": "fcdf0516",
"metadata": {},
"outputs": [],
"source": [
@@ -1313,7 +1313,7 @@
},
{
"cell_type": "markdown",
- "id": "432db4d2",
+ "id": "1da07974",
"metadata": {},
"source": [
"#### Dynamics of the Capital Stock\n",
@@ -1328,7 +1328,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "022863a7",
+ "id": "6ddebd68",
"metadata": {},
"outputs": [],
"source": [
@@ -1361,7 +1361,7 @@
},
{
"cell_type": "markdown",
- "id": "5c6e9b82",
+ "id": "5d895277",
"metadata": {},
"source": [
"(ddp_algorithms)=\n",
diff --git a/_sources/dyn_stack.ipynb b/_sources/dyn_stack.ipynb
index 689c39e5..89d8f087 100644
--- a/_sources/dyn_stack.ipynb
+++ b/_sources/dyn_stack.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "63ae96e3",
+ "id": "0729d8af",
"metadata": {},
"source": [
"(dyn_stack)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5c84a4dd",
+ "id": "7d6ab478",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "484675cd",
+ "id": "cf38c570",
"metadata": {},
"source": [
"## Overview\n",
@@ -60,7 +60,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8708a591",
+ "id": "b33605c7",
"metadata": {},
"outputs": [],
"source": [
@@ -73,7 +73,7 @@
},
{
"cell_type": "markdown",
- "id": "8808df5a",
+ "id": "caaa0e9e",
"metadata": {},
"source": [
"## Duopoly\n",
@@ -968,7 +968,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ffb578ac",
+ "id": "5e8f2f12",
"metadata": {},
"outputs": [],
"source": [
@@ -990,7 +990,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d142dd53",
+ "id": "abd444f4",
"metadata": {},
"outputs": [],
"source": [
@@ -1048,7 +1048,7 @@
},
{
"cell_type": "markdown",
- "id": "6d5e99a4",
+ "id": "e63f9ccf",
"metadata": {},
"source": [
"## Time Series for Price and Quantities\n",
@@ -1061,7 +1061,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "52a9ac0a",
+ "id": "53f34d33",
"metadata": {},
"outputs": [],
"source": [
@@ -1082,7 +1082,7 @@
},
{
"cell_type": "markdown",
- "id": "bf54f940",
+ "id": "38b975e0",
"metadata": {},
"source": [
"### Value of Stackelberg Leader\n",
@@ -1097,7 +1097,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d295f2a8",
+ "id": "3e481d76",
"metadata": {},
"outputs": [],
"source": [
@@ -1113,7 +1113,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7fc3cf13",
+ "id": "2f5dac98",
"metadata": {},
"outputs": [],
"source": [
@@ -1125,7 +1125,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fd0328af",
+ "id": "9ab3c481",
"metadata": {},
"outputs": [],
"source": [
@@ -1138,7 +1138,7 @@
},
{
"cell_type": "markdown",
- "id": "d891c2c3",
+ "id": "8ce953c7",
"metadata": {},
"source": [
"## Time Inconsistency of Stackelberg Plan\n",
@@ -1157,7 +1157,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2d31dcd2",
+ "id": "6ac91c53",
"metadata": {},
"outputs": [],
"source": [
@@ -1176,7 +1176,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "95cc613e",
+ "id": "af8d2b24",
"metadata": {},
"outputs": [],
"source": [
@@ -1203,7 +1203,7 @@
},
{
"cell_type": "markdown",
- "id": "1f2338f4",
+ "id": "4880664b",
"metadata": {},
"source": [
"The figure above shows\n",
@@ -1226,7 +1226,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0e208ad4",
+ "id": "606acd57",
"metadata": {},
"outputs": [],
"source": [
@@ -1252,7 +1252,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c4718105",
+ "id": "9bec5460",
"metadata": {},
"outputs": [],
"source": [
@@ -1267,7 +1267,7 @@
},
{
"cell_type": "markdown",
- "id": "aaa0ebe5",
+ "id": "11dcd64b",
"metadata": {},
"source": [
"Note: Variables with `_tilde` are obtained from solving the follower's\n",
@@ -1277,7 +1277,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "15ccc73b",
+ "id": "597415af",
"metadata": {},
"outputs": [],
"source": [
@@ -1289,7 +1289,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ee3a6def",
+ "id": "7d2ac7d4",
"metadata": {},
"outputs": [],
"source": [
@@ -1299,7 +1299,7 @@
},
{
"cell_type": "markdown",
- "id": "cfeba79e",
+ "id": "608bd979",
"metadata": {},
"source": [
"### Explanation of Alignment\n",
@@ -1319,7 +1319,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "55cc3e1a",
+ "id": "fb8e1f46",
"metadata": {},
"outputs": [],
"source": [
@@ -1330,7 +1330,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "19d8fa60",
+ "id": "25d132de",
"metadata": {},
"outputs": [],
"source": [
@@ -1341,7 +1341,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5495f614",
+ "id": "ddc32e65",
"metadata": {},
"outputs": [],
"source": [
@@ -1352,7 +1352,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bcde2478",
+ "id": "6992ff73",
"metadata": {},
"outputs": [],
"source": [
@@ -1363,7 +1363,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0ab5540d",
+ "id": "6276c951",
"metadata": {},
"outputs": [],
"source": [
@@ -1380,7 +1380,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8486c0e7",
+ "id": "113b19a6",
"metadata": {},
"outputs": [],
"source": [
@@ -1391,7 +1391,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "be609941",
+ "id": "efbda16b",
"metadata": {},
"outputs": [],
"source": [
@@ -1402,7 +1402,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7adb0511",
+ "id": "5b8dd53a",
"metadata": {},
"outputs": [],
"source": [
@@ -1443,7 +1443,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "281b9551",
+ "id": "298c489d",
"metadata": {},
"outputs": [],
"source": [
@@ -1467,7 +1467,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "390da07b",
+ "id": "c8ff40c2",
"metadata": {},
"outputs": [],
"source": [
@@ -1477,7 +1477,7 @@
},
{
"cell_type": "markdown",
- "id": "68cf7816",
+ "id": "f35d6815",
"metadata": {},
"source": [
"## Markov Perfect Equilibrium\n",
@@ -1517,7 +1517,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "865d392d",
+ "id": "f9b24d31",
"metadata": {},
"outputs": [],
"source": [
@@ -1558,7 +1558,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cfa25ed9",
+ "id": "3bddddfa",
"metadata": {},
"outputs": [],
"source": [
@@ -1579,7 +1579,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cc4db7fb",
+ "id": "872097b4",
"metadata": {},
"outputs": [],
"source": [
@@ -1590,7 +1590,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e1efc114",
+ "id": "cbace0b8",
"metadata": {},
"outputs": [],
"source": [
@@ -1616,7 +1616,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0a9a4822",
+ "id": "039034a0",
"metadata": {},
"outputs": [],
"source": [
@@ -1632,7 +1632,7 @@
},
{
"cell_type": "markdown",
- "id": "8e3753f5",
+ "id": "8d2f8f76",
"metadata": {},
"source": [
"## Comparing Markov Perfect Equilibrium and Stackelberg Outcome\n",
@@ -1649,7 +1649,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e1e8da01",
+ "id": "fd39f500",
"metadata": {},
"outputs": [],
"source": [
@@ -1673,7 +1673,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6301823a",
+ "id": "896eea1e",
"metadata": {},
"outputs": [],
"source": [
@@ -1687,7 +1687,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "87a5f560",
+ "id": "2b33b1f1",
"metadata": {},
"outputs": [],
"source": [
diff --git a/_sources/entropy.ipynb b/_sources/entropy.ipynb
index 624d9ef2..7bb100f6 100644
--- a/_sources/entropy.ipynb
+++ b/_sources/entropy.ipynb
@@ -3,14 +3,14 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "50096e8f",
+ "id": "60000d2c",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
- "id": "f1dccd60",
+ "id": "fc17fefb",
"metadata": {},
"source": [
"# Etymology of Entropy\n",
diff --git a/_sources/estspec.ipynb b/_sources/estspec.ipynb
index d68a5cbe..b45315fc 100644
--- a/_sources/estspec.ipynb
+++ b/_sources/estspec.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "647722ba",
+ "id": "3c99fbfa",
"metadata": {},
"source": [
"(estspec)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "387c0e28",
+ "id": "bc46cd45",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "dba57738",
+ "id": "8abab764",
"metadata": {},
"source": [
"## Overview\n",
@@ -65,7 +65,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8134b262",
+ "id": "6ff460fd",
"metadata": {},
"outputs": [],
"source": [
@@ -76,7 +76,7 @@
},
{
"cell_type": "markdown",
- "id": "c53de35b",
+ "id": "c195704e",
"metadata": {},
"source": [
"(periodograms)=\n",
@@ -245,7 +245,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cde1e63d",
+ "id": "3a0921c7",
"metadata": {},
"outputs": [],
"source": [
@@ -265,7 +265,7 @@
},
{
"cell_type": "markdown",
- "id": "402e877d",
+ "id": "74b28d43",
"metadata": {},
"source": [
"This estimate looks rather disappointing, but the data size is only 40, so\n",
@@ -333,7 +333,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ccbd6952",
+ "id": "42f286d3",
"metadata": {},
"outputs": [],
"source": [
@@ -353,7 +353,7 @@
},
{
"cell_type": "markdown",
- "id": "fb84e25f",
+ "id": "ffce6904",
"metadata": {},
"source": [
"### Estimation with Smoothing\n",
@@ -533,7 +533,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e673c3aa",
+ "id": "06f48db6",
"metadata": {},
"outputs": [],
"source": [
@@ -564,7 +564,7 @@
},
{
"cell_type": "markdown",
- "id": "3fc0814e",
+ "id": "acb62d0e",
"metadata": {},
"source": [
"```{solution-end}\n",
@@ -594,7 +594,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "03758f52",
+ "id": "a09478ce",
"metadata": {},
"outputs": [],
"source": [
@@ -626,7 +626,7 @@
},
{
"cell_type": "markdown",
- "id": "50070ecf",
+ "id": "2686e64d",
"metadata": {},
"source": [
"```{solution-end}\n",
diff --git a/_sources/five_preferences.ipynb b/_sources/five_preferences.ipynb
index 0e43dce7..64741a55 100644
--- a/_sources/five_preferences.ipynb
+++ b/_sources/five_preferences.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "6645d09a",
+ "id": "7625ad92",
"metadata": {},
"source": [
"# Risk and Model Uncertainty\n",
@@ -50,7 +50,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1197e379",
+ "id": "360fb71b",
"metadata": {},
"outputs": [],
"source": [
@@ -70,7 +70,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "869859ff",
+ "id": "2d99c875",
"metadata": {
"tags": [
"hide-input"
@@ -100,7 +100,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0278e0c3",
+ "id": "711712dc",
"metadata": {
"tags": [
"hide-input"
@@ -160,7 +160,7 @@
},
{
"cell_type": "markdown",
- "id": "21724223",
+ "id": "6a927deb",
"metadata": {},
"source": [
"## Basic objects\n",
@@ -227,7 +227,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "48a109a5",
+ "id": "19a4dca6",
"metadata": {
"tags": [
"hide-input"
@@ -261,7 +261,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eb454b08",
+ "id": "d949b13f",
"metadata": {
"mystnb": {
"figure": {
@@ -284,7 +284,7 @@
},
{
"cell_type": "markdown",
- "id": "e33aa288",
+ "id": "48d9aa25",
"metadata": {},
"source": [
"The heat maps in the next two figures vary both $\\hat{\\pi}_1$ and $\\pi_1$.\n",
@@ -295,7 +295,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9ea1b6a9",
+ "id": "96ee2185",
"metadata": {
"tags": [
"hide-input"
@@ -326,7 +326,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ac2c4b9b",
+ "id": "f25651f6",
"metadata": {
"tags": [
"hide-input"
@@ -346,7 +346,7 @@
},
{
"cell_type": "markdown",
- "id": "4ef38a6b",
+ "id": "40907979",
"metadata": {},
"source": [
"The next figure plots the logarithm of entropy."
@@ -355,7 +355,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2d0a27ac",
+ "id": "9b838e4e",
"metadata": {
"tags": [
"hide-input"
@@ -372,7 +372,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ce8772d8",
+ "id": "15e7f01c",
"metadata": {
"tags": [
"hide-input"
@@ -391,7 +391,7 @@
},
{
"cell_type": "markdown",
- "id": "d10712cf",
+ "id": "8680ccdd",
"metadata": {},
"source": [
"## Five preference specifications\n",
@@ -606,7 +606,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0e310b17",
+ "id": "50c6beab",
"metadata": {
"tags": [
"hide-input"
@@ -640,7 +640,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cb781b0f",
+ "id": "38a38680",
"metadata": {
"tags": [
"hide-input"
@@ -658,7 +658,7 @@
},
{
"cell_type": "markdown",
- "id": "da34145e",
+ "id": "a3c56403",
"metadata": {},
"source": [
"For large values of $\\theta$, ${\\sf T} u(c)$ is approximately linear in the probability $\\pi_1$, but for lower values of $\\theta$, ${\\sf T} u(c)$ has considerable curvature as a function of $\\pi_1$.\n",
@@ -673,7 +673,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ca7e4858",
+ "id": "d46adcde",
"metadata": {
"tags": [
"hide-input"
@@ -718,7 +718,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cc17fc5c",
+ "id": "2ee4e687",
"metadata": {
"tags": [
"hide-input"
@@ -763,7 +763,7 @@
},
{
"cell_type": "markdown",
- "id": "5bdfd912",
+ "id": "d9a72e98",
"metadata": {},
"source": [
"The panel on the right portrays how the transformation $\\exp\\left(\\frac{-u\\left(c\\right)}{\\theta}\\right)$ sends $u\\left(c\\right)$ to a new function by (i) flipping the sign, and (ii) increasing curvature in proportion to $\\theta$.\n",
@@ -859,7 +859,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "02e8ed6b",
+ "id": "23a3ee2c",
"metadata": {
"tags": [
"hide-input"
@@ -891,7 +891,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bb0c4b4a",
+ "id": "a50777d1",
"metadata": {
"tags": [
"hide-input"
@@ -912,7 +912,7 @@
},
{
"cell_type": "markdown",
- "id": "e328156f",
+ "id": "759ee886",
"metadata": {},
"source": [
"The next figure shows the function $\\sum_{i=1}^I \\pi_i m_i [ u(c_i) + \\theta \\log m_i ]$ that is to be\n",
@@ -924,7 +924,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1f35df6f",
+ "id": "7662ed88",
"metadata": {
"tags": [
"hide-input"
@@ -954,7 +954,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9bfc87e2",
+ "id": "22f4a203",
"metadata": {
"tags": [
"hide-input"
@@ -994,7 +994,7 @@
},
{
"cell_type": "markdown",
- "id": "8b50a304",
+ "id": "f0efc200",
"metadata": {},
"source": [
"Evidently, from this figure and also from formula {eq}`tom12`, lower values of $\\theta$ lead to lower,\n",
@@ -1111,7 +1111,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d8f3d6bd",
+ "id": "87c38e78",
"metadata": {
"tags": [
"hide-input"
@@ -1234,7 +1234,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0bfdd9dc",
+ "id": "33381966",
"metadata": {
"tags": [
"hide-input"
@@ -1284,7 +1284,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b894e375",
+ "id": "b93876a3",
"metadata": {
"tags": [
"hide-input"
@@ -1314,7 +1314,7 @@
},
{
"cell_type": "markdown",
- "id": "8ee6688d",
+ "id": "97f8547f",
"metadata": {},
"source": [
"**Kink at 45 degree line**\n",
@@ -1384,7 +1384,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c26ac736",
+ "id": "0fc9a36e",
"metadata": {
"tags": [
"hide-input"
@@ -1435,7 +1435,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d6555f39",
+ "id": "d7f2e9bb",
"metadata": {
"tags": [
"hide-input"
@@ -1465,7 +1465,7 @@
},
{
"cell_type": "markdown",
- "id": "f971c618",
+ "id": "4c0465b2",
"metadata": {},
"source": [
"Note that all three lines of the left graph intersect at (1, 3). While the intersection at (3, 1) is hard-coded, the intersection at (1,3) arises from the computation, which confirms that the code seems to be\n",
@@ -1536,7 +1536,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3d3dc947",
+ "id": "810bb3bf",
"metadata": {
"tags": [
"hide-input"
@@ -1568,7 +1568,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c3db4bc4",
+ "id": "bb2d50cf",
"metadata": {
"tags": [
"hide-input"
@@ -1593,7 +1593,7 @@
},
{
"cell_type": "markdown",
- "id": "a8955e36",
+ "id": "b376d4f2",
"metadata": {},
"source": [
"Because budget constraints are linear, asset prices are identical under\n",
@@ -1621,7 +1621,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "85142755",
+ "id": "174cca24",
"metadata": {
"tags": [
"hide-input"
@@ -1655,7 +1655,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "723f3fa9",
+ "id": "55355056",
"metadata": {
"tags": [
"hide-input"
@@ -1694,7 +1694,7 @@
},
{
"cell_type": "markdown",
- "id": "ab7e7145",
+ "id": "22014b60",
"metadata": {},
"source": [
"The figure indicates that the certainty equivalent\n",
@@ -1751,7 +1751,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "462c489c",
+ "id": "a18bf322",
"metadata": {
"tags": [
"hide-input"
@@ -1802,7 +1802,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5e0b88cd",
+ "id": "7a160a7c",
"metadata": {
"tags": [
"hide-input"
@@ -1879,7 +1879,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3a1f9e31",
+ "id": "335a18da",
"metadata": {
"tags": [
"hide-input"
@@ -1895,7 +1895,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d6adfd7a",
+ "id": "7f677165",
"metadata": {
"tags": [
"hide-input"
@@ -1910,7 +1910,7 @@
},
{
"cell_type": "markdown",
- "id": "d6c9fc0b",
+ "id": "3af0467c",
"metadata": {},
"source": [
"## Bounds on expected utility\n",
@@ -1972,7 +1972,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7450f7d9",
+ "id": "25845864",
"metadata": {
"tags": [
"hide-input"
@@ -2040,7 +2040,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "653c1bf6",
+ "id": "5ae38623",
"metadata": {
"tags": [
"hide-input"
@@ -2069,7 +2069,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "397ab656",
+ "id": "2bcbd42f",
"metadata": {
"tags": [
"hide-input"
@@ -2087,7 +2087,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eb61155b",
+ "id": "1f748310",
"metadata": {
"tags": [
"hide-input"
@@ -2106,7 +2106,7 @@
},
{
"cell_type": "markdown",
- "id": "1c7fce39",
+ "id": "b4d5e5e8",
"metadata": {},
"source": [
"In this figure, expected utility is on the co-ordinate axis\n",
@@ -2211,7 +2211,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "555170d7",
+ "id": "ac2b1d63",
"metadata": {
"tags": [
"hide-input"
@@ -2231,7 +2231,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "205cbbe9",
+ "id": "d9989bf3",
"metadata": {
"tags": [
"hide-input"
@@ -2261,7 +2261,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0ccb4e43",
+ "id": "a1550ab0",
"metadata": {
"tags": [
"hide-input"
@@ -2286,7 +2286,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "143546fe",
+ "id": "69375dcb",
"metadata": {
"tags": [
"hide-input"
@@ -2299,7 +2299,7 @@
},
{
"cell_type": "markdown",
- "id": "4ca4b9c9",
+ "id": "f5ff4b44",
"metadata": {},
"source": [
"The density for the approximating model is\n",
diff --git a/_sources/growth_in_dles.ipynb b/_sources/growth_in_dles.ipynb
index 586ad1a6..84224938 100644
--- a/_sources/growth_in_dles.ipynb
+++ b/_sources/growth_in_dles.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "d0d7b6ee",
+ "id": "e32ae8bf",
"metadata": {},
"source": [
"(growth_in_dles)=\n",
@@ -28,7 +28,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8322349e",
+ "id": "3aa813f3",
"metadata": {
"tags": [
"hide-output"
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "5c5e6a71",
+ "id": "840b2cb5",
"metadata": {},
"source": [
"This lecture describes several complete market economies having a\n",
@@ -58,7 +58,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c91d1eeb",
+ "id": "28815ca0",
"metadata": {},
"outputs": [],
"source": [
@@ -69,7 +69,7 @@
},
{
"cell_type": "markdown",
- "id": "ed103cc7",
+ "id": "c0458696",
"metadata": {},
"source": [
"## Common Structure\n",
@@ -321,7 +321,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "93bf6583",
+ "id": "f1ab63e7",
"metadata": {},
"outputs": [],
"source": [
@@ -362,7 +362,7 @@
},
{
"cell_type": "markdown",
- "id": "d49ae89b",
+ "id": "ea4d65bd",
"metadata": {},
"source": [
"These parameter values are used to define an economy of the DLE class."
@@ -371,7 +371,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1ba96186",
+ "id": "35354c76",
"metadata": {},
"outputs": [],
"source": [
@@ -380,7 +380,7 @@
},
{
"cell_type": "markdown",
- "id": "a0a87b51",
+ "id": "fd6147fc",
"metadata": {},
"source": [
"We can then simulate the economy for a chosen length of time, from our\n",
@@ -390,7 +390,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1d6dc2b5",
+ "id": "6942df2a",
"metadata": {},
"outputs": [],
"source": [
@@ -399,7 +399,7 @@
},
{
"cell_type": "markdown",
- "id": "d94b7a67",
+ "id": "b3b1ae6b",
"metadata": {},
"source": [
"The economy stores the simulated values for each variable. Below we plot\n",
@@ -409,7 +409,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "141c81b6",
+ "id": "9e212271",
"metadata": {},
"outputs": [],
"source": [
@@ -422,7 +422,7 @@
},
{
"cell_type": "markdown",
- "id": "1d70499c",
+ "id": "8cc9e110",
"metadata": {},
"source": [
"Inspection of the plot shows that the sample paths of consumption and\n",
@@ -435,7 +435,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f478c465",
+ "id": "dc7dfe3e",
"metadata": {},
"outputs": [],
"source": [
@@ -444,7 +444,7 @@
},
{
"cell_type": "markdown",
- "id": "502276c3",
+ "id": "f2879bcb",
"metadata": {},
"source": [
"The endogenous eigenvalue that appears to be unity reflects the random\n",
@@ -457,7 +457,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6abfc34f",
+ "id": "92e4b082",
"metadata": {},
"outputs": [],
"source": [
@@ -466,7 +466,7 @@
},
{
"cell_type": "markdown",
- "id": "44830295",
+ "id": "f2f10360",
"metadata": {},
"source": [
"The fact that the largest endogenous eigenvalue is strictly less than\n",
@@ -477,7 +477,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ba7f2e4c",
+ "id": "77bdd7b0",
"metadata": {},
"outputs": [],
"source": [
@@ -488,7 +488,7 @@
},
{
"cell_type": "markdown",
- "id": "497f80fd",
+ "id": "04ce6db8",
"metadata": {},
"source": [
"However, the near-unity endogenous eigenvalue means that these steady\n",
@@ -524,7 +524,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0e9efdbd",
+ "id": "d6d31418",
"metadata": {},
"outputs": [],
"source": [
@@ -541,7 +541,7 @@
},
{
"cell_type": "markdown",
- "id": "94a19070",
+ "id": "17aeb8ed",
"metadata": {},
"source": [
"Creating the DLE class and then simulating gives the following plot for\n",
@@ -551,7 +551,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "52bc740c",
+ "id": "61e57b81",
"metadata": {},
"outputs": [],
"source": [
@@ -567,7 +567,7 @@
},
{
"cell_type": "markdown",
- "id": "1d3c25ef",
+ "id": "b2773e69",
"metadata": {},
"source": [
"Simulating our new economy shows that consumption grows quickly in the\n",
@@ -580,7 +580,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "21e26eee",
+ "id": "512351d1",
"metadata": {},
"outputs": [],
"source": [
@@ -590,7 +590,7 @@
},
{
"cell_type": "markdown",
- "id": "10bd7da3",
+ "id": "61f61119",
"metadata": {},
"source": [
"The economy converges faster to this level than in Example 1 because the\n",
@@ -601,7 +601,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7ed3fd8c",
+ "id": "fdadd59e",
"metadata": {},
"outputs": [],
"source": [
@@ -610,7 +610,7 @@
},
{
"cell_type": "markdown",
- "id": "f054c7f5",
+ "id": "14da2aa5",
"metadata": {},
"source": [
"### Example 3: A Jones-Manuelli (1990) Economy\n",
@@ -657,7 +657,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "acfd7e46",
+ "id": "e052b61f",
"metadata": {},
"outputs": [],
"source": [
@@ -668,7 +668,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4e027051",
+ "id": "1e8a015b",
"metadata": {},
"outputs": [],
"source": [
@@ -677,7 +677,7 @@
},
{
"cell_type": "markdown",
- "id": "ec7709a9",
+ "id": "62dc61a0",
"metadata": {},
"source": [
"We simulate this economy from the original state vector"
@@ -686,7 +686,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0b3eab23",
+ "id": "ad31805a",
"metadata": {},
"outputs": [],
"source": [
@@ -701,7 +701,7 @@
},
{
"cell_type": "markdown",
- "id": "fac38174",
+ "id": "63d2029e",
"metadata": {},
"source": [
"Thus, adding habit persistence to the Hall model of Example 1 is enough\n",
@@ -714,7 +714,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b56b550a",
+ "id": "260f5bda",
"metadata": {},
"outputs": [],
"source": [
@@ -723,7 +723,7 @@
},
{
"cell_type": "markdown",
- "id": "3f9411d6",
+ "id": "6ae78637",
"metadata": {},
"source": [
"We now have two unit endogenous eigenvalues. One stems from satisfying\n",
@@ -742,7 +742,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ccaf4b43",
+ "id": "3298e778",
"metadata": {},
"outputs": [],
"source": [
@@ -761,7 +761,7 @@
},
{
"cell_type": "markdown",
- "id": "e2d793cd",
+ "id": "c8d197d1",
"metadata": {},
"source": [
"We no longer achieve sustained growth if $\\lambda$ is raised from -1 to -0.7.\n",
@@ -773,7 +773,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "935cd722",
+ "id": "ce4b3f92",
"metadata": {},
"outputs": [],
"source": [
@@ -782,7 +782,7 @@
},
{
"cell_type": "markdown",
- "id": "903750c1",
+ "id": "e0d1b42e",
"metadata": {},
"source": [
"### Example 3.2: More Impatience\n",
@@ -793,7 +793,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c5fc1508",
+ "id": "f860b099",
"metadata": {},
"outputs": [],
"source": [
@@ -812,7 +812,7 @@
},
{
"cell_type": "markdown",
- "id": "156cd4a4",
+ "id": "5e6ee43d",
"metadata": {},
"source": [
"Growth also fails if we lower $\\beta$, since we now have\n",
@@ -829,7 +829,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c4ed2132",
+ "id": "87bd1b30",
"metadata": {},
"outputs": [],
"source": [
diff --git a/_sources/hs_invertibility_example.ipynb b/_sources/hs_invertibility_example.ipynb
index e88a50fd..9a50a0c6 100644
--- a/_sources/hs_invertibility_example.ipynb
+++ b/_sources/hs_invertibility_example.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "08503ec0",
+ "id": "da3e8bb3",
"metadata": {},
"source": [
"(hs_invertibility_example)=\n",
@@ -30,7 +30,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ae913f01",
+ "id": "1e33055e",
"metadata": {
"tags": [
"hide-output"
@@ -43,7 +43,7 @@
},
{
"cell_type": "markdown",
- "id": "8e14d5e2",
+ "id": "29fe9ab6",
"metadata": {},
"source": [
"We'll make these imports:"
@@ -52,7 +52,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e43e5556",
+ "id": "c58881c5",
"metadata": {},
"outputs": [],
"source": [
@@ -65,7 +65,7 @@
},
{
"cell_type": "markdown",
- "id": "3fbb8cab",
+ "id": "f91f222e",
"metadata": {},
"source": [
"This lecture describes an early contribution to what is now often called\n",
@@ -180,7 +180,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "698971e0",
+ "id": "68c53f72",
"metadata": {},
"outputs": [],
"source": [
@@ -216,7 +216,7 @@
},
{
"cell_type": "markdown",
- "id": "eafa0eaa",
+ "id": "72215085",
"metadata": {},
"source": [
"We define the household's net of interest deficit as $c_t - d_t$.\n",
@@ -294,7 +294,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9c7ab020",
+ "id": "b8b4e98d",
"metadata": {},
"outputs": [],
"source": [
@@ -320,7 +320,7 @@
},
{
"cell_type": "markdown",
- "id": "608f13a8",
+ "id": "94945351",
"metadata": {},
"source": [
"The above figure displays the impulse response of consumption and the\n",
@@ -340,7 +340,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "503b0249",
+ "id": "e2482216",
"metadata": {},
"outputs": [],
"source": [
@@ -388,7 +388,7 @@
},
{
"cell_type": "markdown",
- "id": "fdb117b3",
+ "id": "6b4414b9",
"metadata": {},
"source": [
"The above figure displays the impulse response of consumption and the\n",
@@ -407,7 +407,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "64f90994",
+ "id": "77addde3",
"metadata": {},
"outputs": [],
"source": [
@@ -442,7 +442,7 @@
},
{
"cell_type": "markdown",
- "id": "e1474a79",
+ "id": "8f8e006c",
"metadata": {},
"source": [
"The above figure displays the impulse responses of $u_t$ to\n",
diff --git a/_sources/hs_recursive_models.ipynb b/_sources/hs_recursive_models.ipynb
index 27070951..ecf01201 100644
--- a/_sources/hs_recursive_models.ipynb
+++ b/_sources/hs_recursive_models.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "b1cf830f",
+ "id": "731307de",
"metadata": {},
"source": [
"(hs_recursive_models)=\n",
diff --git a/_sources/intro.ipynb b/_sources/intro.ipynb
index ac576f1d..eb9b8cf1 100644
--- a/_sources/intro.ipynb
+++ b/_sources/intro.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "24911726",
+ "id": "a8cbd67b",
"metadata": {},
"source": [
"# Advanced Quantitative Economics with Python\n",
diff --git a/_sources/irfs_in_hall_model.ipynb b/_sources/irfs_in_hall_model.ipynb
index 87772fa5..1f6a0c55 100644
--- a/_sources/irfs_in_hall_model.ipynb
+++ b/_sources/irfs_in_hall_model.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "76b0abe5",
+ "id": "908d4fa9",
"metadata": {},
"source": [
"(irfs_in_hall_model)=\n",
@@ -28,7 +28,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "31e896c6",
+ "id": "8ff041a6",
"metadata": {
"tags": [
"hide-output"
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "d054716a",
+ "id": "8d76d79c",
"metadata": {},
"source": [
"We'll make these imports:"
@@ -50,7 +50,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "46b5a03f",
+ "id": "2bb0f6c1",
"metadata": {},
"outputs": [],
"source": [
@@ -61,7 +61,7 @@
},
{
"cell_type": "markdown",
- "id": "780d7e93",
+ "id": "e0ca4390",
"metadata": {},
"source": [
"This lecture shows how the DLE class can be used to create impulse\n",
@@ -105,7 +105,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "41b10f67",
+ "id": "4f2a232e",
"metadata": {},
"outputs": [],
"source": [
@@ -140,7 +140,7 @@
},
{
"cell_type": "markdown",
- "id": "7641da34",
+ "id": "f6d33fc6",
"metadata": {},
"source": [
"These parameter values are used to define an economy of the DLE class.\n",
@@ -155,7 +155,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0c3347e8",
+ "id": "e20a8f4a",
"metadata": {},
"outputs": [],
"source": [
@@ -171,7 +171,7 @@
},
{
"cell_type": "markdown",
- "id": "99fdd2ac",
+ "id": "a892bb05",
"metadata": {},
"source": [
"The DLE class can be used to create impulse response functions for each\n",
@@ -188,7 +188,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "14a70cdb",
+ "id": "386499f0",
"metadata": {},
"outputs": [],
"source": [
@@ -202,7 +202,7 @@
},
{
"cell_type": "markdown",
- "id": "c48538f8",
+ "id": "68465b1d",
"metadata": {},
"source": [
"It can be seen that the endowment shock has permanent effects on the\n",
@@ -225,7 +225,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3db8b44d",
+ "id": "ad967e95",
"metadata": {},
"outputs": [],
"source": [
@@ -246,7 +246,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3faf58c6",
+ "id": "f94c3dfc",
"metadata": {},
"outputs": [],
"source": [
@@ -261,7 +261,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8f88cf2e",
+ "id": "a5357996",
"metadata": {},
"outputs": [],
"source": [
@@ -271,7 +271,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fa700fee",
+ "id": "d8285b27",
"metadata": {},
"outputs": [],
"source": [
@@ -281,7 +281,7 @@
},
{
"cell_type": "markdown",
- "id": "f13670ce",
+ "id": "93219788",
"metadata": {},
"source": [
"The first graph shows that there seems to be a downward trend in both\n",
@@ -339,7 +339,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d7e22970",
+ "id": "46b96266",
"metadata": {},
"outputs": [],
"source": [
@@ -369,7 +369,7 @@
},
{
"cell_type": "markdown",
- "id": "8409af9b",
+ "id": "d00e41d2",
"metadata": {},
"source": [
"In contrast to Hall's original model of Example 1, it is now investment\n",
@@ -382,7 +382,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e686946e",
+ "id": "48861ddb",
"metadata": {},
"outputs": [],
"source": [
@@ -396,7 +396,7 @@
},
{
"cell_type": "markdown",
- "id": "eb5f740b",
+ "id": "159a9b97",
"metadata": {},
"source": [
"The impulse response functions confirm that consumption is now much more\n",
diff --git a/_sources/knowing_forecasts_of_others.ipynb b/_sources/knowing_forecasts_of_others.ipynb
index 1348fa64..0b85110e 100644
--- a/_sources/knowing_forecasts_of_others.ipynb
+++ b/_sources/knowing_forecasts_of_others.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "1033218e",
+ "id": "35ea8614",
"metadata": {},
"source": [
"(knowing_the_forecast_of_others_v3)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bdc600fd",
+ "id": "d551d0c0",
"metadata": {
"tags": [
"hide-output"
@@ -36,7 +36,7 @@
},
{
"cell_type": "markdown",
- "id": "82fb2adc",
+ "id": "d7388218",
"metadata": {},
"source": [
"## Introduction\n",
@@ -926,7 +926,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4f5809a9",
+ "id": "1f7c1714",
"metadata": {},
"outputs": [],
"source": [
@@ -943,7 +943,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "59157549",
+ "id": "37514315",
"metadata": {},
"outputs": [],
"source": [
@@ -957,7 +957,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ef0b14ff",
+ "id": "59190b4a",
"metadata": {},
"outputs": [],
"source": [
@@ -971,7 +971,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4e00acdd",
+ "id": "6673fb65",
"metadata": {},
"outputs": [],
"source": [
@@ -983,7 +983,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d332f188",
+ "id": "62aa96e2",
"metadata": {},
"outputs": [],
"source": [
@@ -1000,7 +1000,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5c988556",
+ "id": "8c10ddb1",
"metadata": {},
"outputs": [],
"source": [
@@ -1012,7 +1012,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b79ab8ec",
+ "id": "bda55eac",
"metadata": {},
"outputs": [],
"source": [
@@ -1043,7 +1043,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "833d0ef0",
+ "id": "fa8b0f18",
"metadata": {},
"outputs": [],
"source": [
@@ -1055,7 +1055,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "46a16a13",
+ "id": "a9b76445",
"metadata": {},
"outputs": [],
"source": [
@@ -1066,7 +1066,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "acbdf5de",
+ "id": "e1a70daa",
"metadata": {},
"outputs": [],
"source": [
@@ -1076,7 +1076,7 @@
},
{
"cell_type": "markdown",
- "id": "d68126d4",
+ "id": "4a5dbab7",
"metadata": {},
"source": [
"### Step 4: Compute impulse response functions\n",
@@ -1088,7 +1088,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4a2e4d1c",
+ "id": "c99d4fa2",
"metadata": {},
"outputs": [],
"source": [
@@ -1109,7 +1109,7 @@
},
{
"cell_type": "markdown",
- "id": "a2ee7afa",
+ "id": "3319792f",
"metadata": {},
"source": [
"### Step 5: Compute stationary covariance matrices and population regressions\n",
@@ -1143,7 +1143,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1aef74f0",
+ "id": "44d26619",
"metadata": {},
"outputs": [],
"source": [
@@ -1166,7 +1166,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1bc2c4b9",
+ "id": "1ca92399",
"metadata": {},
"outputs": [],
"source": [
@@ -1178,7 +1178,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dfabb4e2",
+ "id": "4c9bd2ac",
"metadata": {},
"outputs": [],
"source": [
@@ -1191,7 +1191,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "60499b61",
+ "id": "aa37540d",
"metadata": {},
"outputs": [],
"source": [
@@ -1202,7 +1202,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5237e744",
+ "id": "2600baa4",
"metadata": {},
"outputs": [],
"source": [
@@ -1214,7 +1214,7 @@
},
{
"cell_type": "markdown",
- "id": "08f57974",
+ "id": "a5c21364",
"metadata": {},
"source": [
"## Equilibrium with Two Noisy Signals on $\\theta_t$\n",
@@ -1318,7 +1318,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "90da85b0",
+ "id": "2f395a94",
"metadata": {},
"outputs": [],
"source": [
@@ -1335,7 +1335,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5c1b865e",
+ "id": "6d00a528",
"metadata": {},
"outputs": [],
"source": [
@@ -1347,7 +1347,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "078cc7aa",
+ "id": "84715b99",
"metadata": {},
"outputs": [],
"source": [
@@ -1385,7 +1385,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a0b2e491",
+ "id": "de9e230b",
"metadata": {},
"outputs": [],
"source": [
@@ -1397,7 +1397,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "355822fe",
+ "id": "32139974",
"metadata": {},
"outputs": [],
"source": [
@@ -1408,7 +1408,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4a6535c4",
+ "id": "14640618",
"metadata": {},
"outputs": [],
"source": [
@@ -1418,7 +1418,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7fab61d8",
+ "id": "413558e3",
"metadata": {},
"outputs": [],
"source": [
@@ -1440,7 +1440,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fea11698",
+ "id": "01ff6b58",
"metadata": {},
"outputs": [],
"source": [
@@ -1463,7 +1463,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d9081c09",
+ "id": "84d9e3b6",
"metadata": {},
"outputs": [],
"source": [
@@ -1475,7 +1475,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7ee85c8a",
+ "id": "ba33cf9e",
"metadata": {},
"outputs": [],
"source": [
@@ -1488,7 +1488,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eb2837f1",
+ "id": "c61920d2",
"metadata": {},
"outputs": [],
"source": [
@@ -1499,7 +1499,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "53970d6e",
+ "id": "a4e28b8c",
"metadata": {},
"outputs": [],
"source": [
@@ -1523,7 +1523,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5187aca0",
+ "id": "943d8cbe",
"metadata": {},
"outputs": [],
"source": [
@@ -1534,7 +1534,7 @@
},
{
"cell_type": "markdown",
- "id": "62567097",
+ "id": "8cb15099",
"metadata": {},
"source": [
"## Key Step\n",
@@ -1552,7 +1552,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f0e59cf6",
+ "id": "8b0301a9",
"metadata": {},
"outputs": [],
"source": [
@@ -1569,7 +1569,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "95a3f5d6",
+ "id": "aae08d27",
"metadata": {},
"outputs": [],
"source": [
@@ -1578,7 +1578,7 @@
},
{
"cell_type": "markdown",
- "id": "024cfadb",
+ "id": "8ff7bd70",
"metadata": {},
"source": [
"The $R^2$ in this regression equals $1$.\n",
@@ -1654,7 +1654,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "930d84e5",
+ "id": "cfb243ff",
"metadata": {},
"outputs": [],
"source": [
@@ -1669,7 +1669,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fb1a62b1",
+ "id": "deb5e6a1",
"metadata": {},
"outputs": [],
"source": [
@@ -1680,7 +1680,7 @@
},
{
"cell_type": "markdown",
- "id": "446f00d0",
+ "id": "1c524709",
"metadata": {},
"source": [
"Now let's form and plot an impulse response function of $k_t^i$ to shocks $v_t$ to $\\theta_{t+1}$"
@@ -1689,7 +1689,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c2f2de6e",
+ "id": "beb48a7f",
"metadata": {},
"outputs": [],
"source": [
@@ -1709,7 +1709,7 @@
},
{
"cell_type": "markdown",
- "id": "86041a76",
+ "id": "d8886cdb",
"metadata": {},
"source": [
"## Comparison of All Signal Structures\n",
@@ -1724,7 +1724,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5b450ed3",
+ "id": "ee8944e0",
"metadata": {
"hide-output": false
},
@@ -1748,7 +1748,7 @@
},
{
"cell_type": "markdown",
- "id": "49d49da7",
+ "id": "130330be",
"metadata": {},
"source": [
"The three panels in the graph above show that\n",
@@ -1776,7 +1776,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9cf55606",
+ "id": "814db42a",
"metadata": {
"hide-output": false
},
@@ -1789,7 +1789,7 @@
},
{
"cell_type": "markdown",
- "id": "65a15cc6",
+ "id": "1d0bb225",
"metadata": {},
"source": [
"Kalman gains for the two\n",
@@ -1799,7 +1799,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fe8edad6",
+ "id": "f487fd21",
"metadata": {
"hide-output": false
},
@@ -1812,7 +1812,7 @@
},
{
"cell_type": "markdown",
- "id": "d11bf774",
+ "id": "c3687bd2",
"metadata": {},
"source": [
"Another lesson that comes from the preceding three-panel graph is that the presence of iid noise\n",
diff --git a/_sources/lqramsey.ipynb b/_sources/lqramsey.ipynb
index c066294c..68d2eb30 100644
--- a/_sources/lqramsey.ipynb
+++ b/_sources/lqramsey.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "f3847b95",
+ "id": "eb0941c4",
"metadata": {},
"source": [
"(lqramsey)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "faa2e649",
+ "id": "6503ae24",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "06e8f5af",
+ "id": "de580066",
"metadata": {},
"source": [
"## Overview\n",
@@ -86,7 +86,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0a65f93c",
+ "id": "38a5d6bc",
"metadata": {},
"outputs": [],
"source": [
@@ -102,7 +102,7 @@
},
{
"cell_type": "markdown",
- "id": "7d6c5ecf",
+ "id": "54668154",
"metadata": {},
"source": [
"### Model Features\n",
@@ -608,7 +608,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "94c2bd5f",
+ "id": "dc2847d1",
"metadata": {},
"outputs": [],
"source": [
@@ -874,7 +874,7 @@
},
{
"cell_type": "markdown",
- "id": "28a073b5",
+ "id": "ed5986db",
"metadata": {},
"source": [
"### Comments on the Code\n",
@@ -926,7 +926,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "63aef06e",
+ "id": "8ead4042",
"metadata": {},
"outputs": [],
"source": [
@@ -952,7 +952,7 @@
},
{
"cell_type": "markdown",
- "id": "567628dc",
+ "id": "62f14388",
"metadata": {},
"source": [
"The legends on the figures indicate the variables being tracked.\n",
@@ -964,7 +964,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "db5fa374",
+ "id": "34a18bd2",
"metadata": {},
"outputs": [],
"source": [
@@ -973,7 +973,7 @@
},
{
"cell_type": "markdown",
- "id": "88a5c2c6",
+ "id": "e4d45267",
"metadata": {},
"source": [
"```{only} html\n",
@@ -992,7 +992,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d159efe4",
+ "id": "5799bb66",
"metadata": {},
"outputs": [],
"source": [
@@ -1025,7 +1025,7 @@
},
{
"cell_type": "markdown",
- "id": "7d33bc8c",
+ "id": "487c4e85",
"metadata": {},
"source": [
"The call `gen_fig_2(path)` generates"
@@ -1034,7 +1034,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b65171d3",
+ "id": "d0babf06",
"metadata": {},
"outputs": [],
"source": [
@@ -1043,7 +1043,7 @@
},
{
"cell_type": "markdown",
- "id": "e4969d3e",
+ "id": "3bd16d00",
"metadata": {},
"source": [
"```{only} html\n",
@@ -1082,7 +1082,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "171da54e",
+ "id": "3e130a82",
"metadata": {},
"outputs": [],
"source": [
@@ -1114,7 +1114,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5932ea35",
+ "id": "a06d9bec",
"metadata": {},
"outputs": [],
"source": [
@@ -1123,7 +1123,7 @@
},
{
"cell_type": "markdown",
- "id": "a533e2e3",
+ "id": "ff24effd",
"metadata": {},
"source": [
"```{solution-end}\n",
diff --git a/_sources/lu_tricks.ipynb b/_sources/lu_tricks.ipynb
index 19963df6..eae97c5e 100644
--- a/_sources/lu_tricks.ipynb
+++ b/_sources/lu_tricks.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "7295d55e",
+ "id": "f13fdd5f",
"metadata": {},
"source": [
"(lu_tricks)=\n",
@@ -52,7 +52,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3f47875b",
+ "id": "101df759",
"metadata": {},
"outputs": [],
"source": [
@@ -62,7 +62,7 @@
},
{
"cell_type": "markdown",
- "id": "03ac9d57",
+ "id": "242bd8b4",
"metadata": {},
"source": [
"### References\n",
@@ -899,7 +899,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "092d722d",
+ "id": "31e65c53",
"metadata": {
"load": "_static/lecture_specific/lu_tricks/control_and_filter.py"
},
@@ -1215,7 +1215,7 @@
},
{
"cell_type": "markdown",
- "id": "cda1922b",
+ "id": "b4cbd319",
"metadata": {},
"source": [
"### Example\n",
@@ -1248,7 +1248,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9d9f799e",
+ "id": "9094ae03",
"metadata": {},
"outputs": [],
"source": [
@@ -1286,7 +1286,7 @@
},
{
"cell_type": "markdown",
- "id": "dfe36e1e",
+ "id": "03e29698",
"metadata": {},
"source": [
"Here's what happens when we change $\\gamma$ to 5.0"
@@ -1295,7 +1295,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c9221675",
+ "id": "0ddc9c63",
"metadata": {},
"outputs": [],
"source": [
@@ -1304,7 +1304,7 @@
},
{
"cell_type": "markdown",
- "id": "3041b953",
+ "id": "7cb8ce79",
"metadata": {},
"source": [
"And here's $\\gamma = 10$"
@@ -1313,7 +1313,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3ce29908",
+ "id": "5ccd2b22",
"metadata": {},
"outputs": [],
"source": [
@@ -1322,7 +1322,7 @@
},
{
"cell_type": "markdown",
- "id": "aabee344",
+ "id": "8f13f1ff",
"metadata": {},
"source": [
"## Exercises\n",
diff --git a/_sources/lucas_asset_pricing_dles.ipynb b/_sources/lucas_asset_pricing_dles.ipynb
index 4c0aa2a8..5491e039 100644
--- a/_sources/lucas_asset_pricing_dles.ipynb
+++ b/_sources/lucas_asset_pricing_dles.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "718ab6e7",
+ "id": "3b0ac8fe",
"metadata": {},
"source": [
"(lucas_asset_pricing_dles)=\n",
@@ -28,7 +28,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "76de50ea",
+ "id": "5a6f8054",
"metadata": {
"tags": [
"hide-output"
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "f69709bc",
+ "id": "a02ba1cf",
"metadata": {},
"source": [
"This lecture uses the DLE class to price payout\n",
@@ -61,7 +61,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "88ddbd73",
+ "id": "9adc216e",
"metadata": {},
"outputs": [],
"source": [
@@ -72,7 +72,7 @@
},
{
"cell_type": "markdown",
- "id": "76bbc257",
+ "id": "887c31b8",
"metadata": {},
"source": [
"We use a linear-quadratic version of an economy that Lucas (1978) {cite}`Lucas1978` used\n",
@@ -187,7 +187,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8f87e492",
+ "id": "b94fd00a",
"metadata": {},
"outputs": [],
"source": [
@@ -222,7 +222,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "423adabe",
+ "id": "c2ea9e7c",
"metadata": {},
"outputs": [],
"source": [
@@ -231,7 +231,7 @@
},
{
"cell_type": "markdown",
- "id": "dabbdec4",
+ "id": "5575cbb4",
"metadata": {},
"source": [
"After specifying a \"Pay\" matrix, we simulate the economy.\n",
@@ -243,7 +243,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "137be8e5",
+ "id": "cd2b0d29",
"metadata": {},
"outputs": [],
"source": [
@@ -252,7 +252,7 @@
},
{
"cell_type": "markdown",
- "id": "cc82a95d",
+ "id": "c787b621",
"metadata": {},
"source": [
"The graph below plots the price of this claim over time:"
@@ -261,7 +261,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dbadefcf",
+ "id": "29b90a52",
"metadata": {},
"outputs": [],
"source": [
@@ -273,7 +273,7 @@
},
{
"cell_type": "markdown",
- "id": "cc4e8fc8",
+ "id": "5eadede3",
"metadata": {},
"source": [
"The next plot displays the realized gross rate of return on this \"Lucas\n",
@@ -283,7 +283,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8812258f",
+ "id": "1a8f2799",
"metadata": {},
"outputs": [],
"source": [
@@ -297,7 +297,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f76b892d",
+ "id": "58ba0379",
"metadata": {},
"outputs": [],
"source": [
@@ -306,7 +306,7 @@
},
{
"cell_type": "markdown",
- "id": "adb27895",
+ "id": "6058129f",
"metadata": {},
"source": [
"Above we have also calculated the correlation coefficient between these\n",
@@ -320,7 +320,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "43d9feff",
+ "id": "18883540",
"metadata": {},
"outputs": [],
"source": [
@@ -333,7 +333,7 @@
},
{
"cell_type": "markdown",
- "id": "e51dc310",
+ "id": "042bc7f6",
"metadata": {},
"source": [
"From the above plot, we can see the tendency of the term structure to\n",
@@ -351,7 +351,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "476022b6",
+ "id": "841f1691",
"metadata": {},
"outputs": [],
"source": [
@@ -367,7 +367,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "995b2729",
+ "id": "0f15f3cd",
"metadata": {},
"outputs": [],
"source": [
@@ -381,7 +381,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bab86a30",
+ "id": "6db6696a",
"metadata": {},
"outputs": [],
"source": [
@@ -390,7 +390,7 @@
},
{
"cell_type": "markdown",
- "id": "c18b4254",
+ "id": "94ca7537",
"metadata": {},
"source": [
"The correlation between these two gross rates is now more negative.\n",
@@ -402,7 +402,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a22f31d6",
+ "id": "06ac6eeb",
"metadata": {},
"outputs": [],
"source": [
@@ -415,7 +415,7 @@
},
{
"cell_type": "markdown",
- "id": "cac74bdb",
+ "id": "8dc8685d",
"metadata": {},
"source": [
"We can see the tendency of the term structure to slope up when rates are\n",
diff --git a/_sources/lucas_model.ipynb b/_sources/lucas_model.ipynb
index 71c04233..f67b5e56 100644
--- a/_sources/lucas_model.ipynb
+++ b/_sources/lucas_model.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "f7663caf",
+ "id": "143aa869",
"metadata": {},
"source": [
"(lucas_asset)=\n",
@@ -39,7 +39,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f1889209",
+ "id": "283f19fa",
"metadata": {},
"outputs": [],
"source": [
@@ -51,7 +51,7 @@
},
{
"cell_type": "markdown",
- "id": "e11e340b",
+ "id": "6448ff27",
"metadata": {},
"source": [
"## The Lucas Model\n",
@@ -398,7 +398,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4442d6de",
+ "id": "16ad6476",
"metadata": {},
"outputs": [],
"source": [
@@ -435,7 +435,7 @@
},
{
"cell_type": "markdown",
- "id": "a727b072",
+ "id": "fb0de1b4",
"metadata": {},
"source": [
"The following function takes an instance of the `LucasTree` and generates a\n",
@@ -445,7 +445,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8bac3b11",
+ "id": "dca65f64",
"metadata": {},
"outputs": [],
"source": [
@@ -485,7 +485,7 @@
},
{
"cell_type": "markdown",
- "id": "a41a1c89",
+ "id": "e4a2838e",
"metadata": {},
"source": [
"To solve the model, we write a function that iterates using the Lucas operator\n",
@@ -495,7 +495,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "90b9e9b8",
+ "id": "f1f5ab2e",
"metadata": {},
"outputs": [],
"source": [
@@ -529,7 +529,7 @@
},
{
"cell_type": "markdown",
- "id": "1778022b",
+ "id": "e795c8eb",
"metadata": {},
"source": [
"Solving the model and plotting the resulting price function"
@@ -538,7 +538,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e421eac3",
+ "id": "f7689b45",
"metadata": {},
"outputs": [],
"source": [
@@ -555,7 +555,7 @@
},
{
"cell_type": "markdown",
- "id": "afa49a3d",
+ "id": "4878df1d",
"metadata": {},
"source": [
"We see that the price is increasing, even if we remove all serial correlation from the endowment process.\n",
@@ -598,7 +598,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "66b32c33",
+ "id": "43f7222a",
"metadata": {},
"outputs": [],
"source": [
@@ -618,7 +618,7 @@
},
{
"cell_type": "markdown",
- "id": "81016c04",
+ "id": "8e5faeb8",
"metadata": {},
"source": [
"```{solution-end}\n",
diff --git a/_sources/markov_jump_lq.ipynb b/_sources/markov_jump_lq.ipynb
index 660a51c5..e43fbb61 100644
--- a/_sources/markov_jump_lq.ipynb
+++ b/_sources/markov_jump_lq.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "71136858",
+ "id": "7f468c5f",
"metadata": {},
"source": [
"(markov_jump_lq)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f4dfb146",
+ "id": "45250236",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "ceeed896",
+ "id": "88856710",
"metadata": {},
"source": [
"## Overview\n",
@@ -257,7 +257,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c0b296f0",
+ "id": "d8ba2cc8",
"metadata": {},
"outputs": [],
"source": [
@@ -270,7 +270,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b139e2cf",
+ "id": "649ecbeb",
"metadata": {},
"outputs": [],
"source": [
@@ -280,7 +280,7 @@
},
{
"cell_type": "markdown",
- "id": "15ce1a51",
+ "id": "9af2481d",
"metadata": {},
"source": [
"## Example 1\n",
@@ -350,7 +350,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ec09dc8e",
+ "id": "5f5fc9c6",
"metadata": {},
"outputs": [],
"source": [
@@ -393,7 +393,7 @@
},
{
"cell_type": "markdown",
- "id": "5c37a687",
+ "id": "6f469ca1",
"metadata": {},
"source": [
"The continuous part of the state $x_t$ consists of two variables,\n",
@@ -403,7 +403,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a2ca0ca5",
+ "id": "4301bd53",
"metadata": {},
"outputs": [],
"source": [
@@ -412,7 +412,7 @@
},
{
"cell_type": "markdown",
- "id": "214c8462",
+ "id": "acfbfedb",
"metadata": {},
"source": [
"We start with a Markov transition matrix that makes the Markov state be\n",
@@ -452,7 +452,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7677ed0d",
+ "id": "1ce767bb",
"metadata": {},
"outputs": [],
"source": [
@@ -464,7 +464,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8075a44e",
+ "id": "9ea8ac31",
"metadata": {},
"outputs": [],
"source": [
@@ -475,7 +475,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a245d86e",
+ "id": "3b887e17",
"metadata": {},
"outputs": [],
"source": [
@@ -487,7 +487,7 @@
},
{
"cell_type": "markdown",
- "id": "811eae62",
+ "id": "3f7dd634",
"metadata": {},
"source": [
"Let’s look at the value function matrices and the decision rules for\n",
@@ -497,7 +497,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a7e815cd",
+ "id": "c68cca16",
"metadata": {},
"outputs": [],
"source": [
@@ -508,7 +508,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6a6b1140",
+ "id": "e0288aa4",
"metadata": {},
"outputs": [],
"source": [
@@ -519,7 +519,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f80e06b2",
+ "id": "6783cd0c",
"metadata": {},
"outputs": [],
"source": [
@@ -529,7 +529,7 @@
},
{
"cell_type": "markdown",
- "id": "e1e26f13",
+ "id": "b30e2772",
"metadata": {},
"source": [
"Now we’ll plot the decision rules and see if they make sense"
@@ -538,7 +538,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "97c9f968",
+ "id": "ad7c6f52",
"metadata": {},
"outputs": [],
"source": [
@@ -568,7 +568,7 @@
},
{
"cell_type": "markdown",
- "id": "b5a68fdf",
+ "id": "3bc69e68",
"metadata": {},
"source": [
"The above graph plots $k_{t+1}= k_t + u_t = k_t - F x_t$ as an affine\n",
@@ -594,7 +594,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0845fb38",
+ "id": "13906747",
"metadata": {},
"outputs": [],
"source": [
@@ -613,7 +613,7 @@
},
{
"cell_type": "markdown",
- "id": "e91f7c58",
+ "id": "c662744c",
"metadata": {},
"source": [
"Now we’ll depart from the preceding transition matrix that made the\n",
@@ -632,7 +632,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f3bdbf86",
+ "id": "9d9759a2",
"metadata": {},
"outputs": [],
"source": [
@@ -648,7 +648,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6e274b3e",
+ "id": "6de4ab86",
"metadata": {},
"outputs": [],
"source": [
@@ -663,7 +663,7 @@
},
{
"cell_type": "markdown",
- "id": "6118bf41",
+ "id": "a134bee8",
"metadata": {},
"source": [
"We can plot optimal decision rules associated with different\n",
@@ -673,7 +673,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8bc98aaf",
+ "id": "92e29d8d",
"metadata": {},
"outputs": [],
"source": [
@@ -694,7 +694,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ef319a4e",
+ "id": "7aa834c3",
"metadata": {},
"outputs": [],
"source": [
@@ -712,7 +712,7 @@
},
{
"cell_type": "markdown",
- "id": "65901585",
+ "id": "10d4cf59",
"metadata": {},
"source": [
"Notice how the decision rules’ constants and slopes behave as functions\n",
@@ -737,7 +737,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "31d8b8d1",
+ "id": "8681e280",
"metadata": {},
"outputs": [],
"source": [
@@ -752,7 +752,7 @@
},
{
"cell_type": "markdown",
- "id": "88e49a2c",
+ "id": "19281f6f",
"metadata": {},
"source": [
"We can plot optimal decision rules for different $\\lambda$ and\n",
@@ -762,7 +762,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0b07e9ba",
+ "id": "fde00640",
"metadata": {},
"outputs": [],
"source": [
@@ -790,7 +790,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8451359c",
+ "id": "c5fd79cb",
"metadata": {},
"outputs": [],
"source": [
@@ -810,7 +810,7 @@
},
{
"cell_type": "markdown",
- "id": "0d9a1df7",
+ "id": "b6452313",
"metadata": {},
"source": [
"The following code defines a wrapper function that computes optimal\n",
@@ -820,7 +820,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "201ea1d0",
+ "id": "8cd88e66",
"metadata": {},
"outputs": [],
"source": [
@@ -919,7 +919,7 @@
},
{
"cell_type": "markdown",
- "id": "315b9339",
+ "id": "74c69b05",
"metadata": {},
"source": [
"To illustrate the code with another example, we shall set\n",
@@ -971,7 +971,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a94c6f52",
+ "id": "3f03598e",
"metadata": {},
"outputs": [],
"source": [
@@ -980,7 +980,7 @@
},
{
"cell_type": "markdown",
- "id": "cbef4883",
+ "id": "98d5661c",
"metadata": {},
"source": [
"Set $f_{1,{s_t}}$ and $d_{s_t}$ as constant functions and\n",
@@ -993,7 +993,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9bd3668f",
+ "id": "de7fbb05",
"metadata": {},
"outputs": [],
"source": [
@@ -1002,7 +1002,7 @@
},
{
"cell_type": "markdown",
- "id": "e707f552",
+ "id": "063e4e9d",
"metadata": {},
"source": [
"## Example 2\n",
@@ -1072,7 +1072,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7670db4c",
+ "id": "4b03f49d",
"metadata": {},
"outputs": [],
"source": [
@@ -1123,7 +1123,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9da64b9d",
+ "id": "f664475a",
"metadata": {},
"outputs": [],
"source": [
@@ -1132,7 +1132,7 @@
},
{
"cell_type": "markdown",
- "id": "50af271a",
+ "id": "680c3e57",
"metadata": {},
"source": [
"Only $d_{s_t}$ depends on $s_t$."
@@ -1141,7 +1141,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d4b7c3ab",
+ "id": "3db405a5",
"metadata": {},
"outputs": [],
"source": [
@@ -1150,7 +1150,7 @@
},
{
"cell_type": "markdown",
- "id": "0047be53",
+ "id": "9dd1cff6",
"metadata": {},
"source": [
"Only $f_{1,{s_t}}$ depends on $s_t$."
@@ -1159,7 +1159,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2b7a605c",
+ "id": "e39824c5",
"metadata": {},
"outputs": [],
"source": [
@@ -1168,7 +1168,7 @@
},
{
"cell_type": "markdown",
- "id": "4775f6a6",
+ "id": "0b918d7c",
"metadata": {},
"source": [
"Only $f_{2,{s_t}}$ depends on $s_t$."
@@ -1177,7 +1177,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "de73b04f",
+ "id": "ce9948ea",
"metadata": {},
"outputs": [],
"source": [
@@ -1186,7 +1186,7 @@
},
{
"cell_type": "markdown",
- "id": "b7e8b178",
+ "id": "6471c144",
"metadata": {},
"source": [
"Only $\\alpha_0(s_t)$ depends on $s_t$."
@@ -1195,7 +1195,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "90e3e476",
+ "id": "d213f6be",
"metadata": {},
"outputs": [],
"source": [
@@ -1204,7 +1204,7 @@
},
{
"cell_type": "markdown",
- "id": "21aec75d",
+ "id": "7118bfd5",
"metadata": {},
"source": [
"Only $\\rho_{s_t}$ depends on $s_t$."
@@ -1213,7 +1213,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8f5fdfd5",
+ "id": "c2a27038",
"metadata": {},
"outputs": [],
"source": [
@@ -1222,7 +1222,7 @@
},
{
"cell_type": "markdown",
- "id": "b3af24fc",
+ "id": "ccf1d08e",
"metadata": {},
"source": [
"Only $\\sigma_{s_t}$ depends on $s_t$."
@@ -1231,7 +1231,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "66e3000c",
+ "id": "c82f838c",
"metadata": {},
"outputs": [],
"source": [
@@ -1240,7 +1240,7 @@
},
{
"cell_type": "markdown",
- "id": "77963a0f",
+ "id": "b033f87d",
"metadata": {},
"source": [
"## More examples\n",
diff --git a/_sources/matsuyama.ipynb b/_sources/matsuyama.ipynb
index 154e084c..9eb7fc0a 100644
--- a/_sources/matsuyama.ipynb
+++ b/_sources/matsuyama.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "c0ae2893",
+ "id": "5fa42e4b",
"metadata": {},
"source": [
"(matsuyama)=\n",
@@ -38,7 +38,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4f8557b0",
+ "id": "c9b3ecdd",
"metadata": {},
"outputs": [],
"source": [
@@ -50,7 +50,7 @@
},
{
"cell_type": "markdown",
- "id": "cc508d4e",
+ "id": "1ace5a13",
"metadata": {},
"source": [
"### Background\n",
@@ -347,7 +347,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d5328c61",
+ "id": "ba8efd0b",
"metadata": {},
"outputs": [],
"source": [
@@ -658,7 +658,7 @@
},
{
"cell_type": "markdown",
- "id": "607684ab",
+ "id": "8df5eab5",
"metadata": {},
"source": [
"### Time Series of Firm Measures\n",
@@ -675,7 +675,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "af61b9e8",
+ "id": "381ed754",
"metadata": {},
"outputs": [],
"source": [
@@ -713,7 +713,7 @@
},
{
"cell_type": "markdown",
- "id": "20477cb2",
+ "id": "47df5740",
"metadata": {},
"source": [
"In the first case, innovation in the two countries does not synchronize.\n",
@@ -772,7 +772,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e3c0bd86",
+ "id": "4717f6f8",
"metadata": {},
"outputs": [],
"source": [
@@ -826,7 +826,7 @@
},
{
"cell_type": "markdown",
- "id": "af907b7a",
+ "id": "4b9d3a02",
"metadata": {},
"source": [
"Additionally, instead of just seeing 4 plots at once, we might want to\n",
@@ -839,7 +839,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4ea11243",
+ "id": "f960b3b6",
"metadata": {},
"outputs": [],
"source": [
@@ -864,7 +864,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4cb1e5fb",
+ "id": "a9bdf43a",
"metadata": {},
"outputs": [],
"source": [
@@ -876,7 +876,7 @@
},
{
"cell_type": "markdown",
- "id": "47be0867",
+ "id": "71a321ce",
"metadata": {},
"source": [
"```{solution-end}\n",
diff --git a/_sources/muth_kalman.ipynb b/_sources/muth_kalman.ipynb
index f4deac9e..e907b1a1 100644
--- a/_sources/muth_kalman.ipynb
+++ b/_sources/muth_kalman.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "5159047a",
+ "id": "a4a96455",
"metadata": {},
"source": [
"(muth_kalman)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "245ab0a1",
+ "id": "0feacb83",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "71dea00f",
+ "id": "fa49cc05",
"metadata": {},
"source": [
"We'll also need the following imports:"
@@ -47,7 +47,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f64d39aa",
+ "id": "88e709c0",
"metadata": {},
"outputs": [],
"source": [
@@ -61,7 +61,7 @@
},
{
"cell_type": "markdown",
- "id": "4bcf3eb7",
+ "id": "482f55a5",
"metadata": {},
"source": [
"This lecture uses the Kalman filter to reformulate John F. Muth’s first\n",
@@ -183,7 +183,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "085b3a26",
+ "id": "3d86bbd6",
"metadata": {},
"outputs": [],
"source": [
@@ -214,7 +214,7 @@
},
{
"cell_type": "markdown",
- "id": "b6b6f688",
+ "id": "fc256c01",
"metadata": {},
"source": [
"## Some Useful State-Space Math\n",
@@ -271,7 +271,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "05d991ad",
+ "id": "2bf953b0",
"metadata": {},
"outputs": [],
"source": [
@@ -302,7 +302,7 @@
},
{
"cell_type": "markdown",
- "id": "d0d40624",
+ "id": "aaae7d9e",
"metadata": {},
"source": [
"Now that we have simulated our joint system, we have $x_t$,\n",
@@ -321,7 +321,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e600074a",
+ "id": "0b048867",
"metadata": {},
"outputs": [],
"source": [
@@ -336,7 +336,7 @@
},
{
"cell_type": "markdown",
- "id": "21b29964",
+ "id": "18c2a9b7",
"metadata": {},
"source": [
"Note how $x_t$ and $\\hat{x_t}$ differ.\n",
@@ -354,7 +354,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "685d7ded",
+ "id": "95d0a3e8",
"metadata": {},
"outputs": [],
"source": [
@@ -369,7 +369,7 @@
},
{
"cell_type": "markdown",
- "id": "db5c66c5",
+ "id": "3eb7d036",
"metadata": {},
"source": [
"We see above that $y$ seems to look like white noise around the\n",
@@ -384,7 +384,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9609258e",
+ "id": "d5810e71",
"metadata": {},
"outputs": [],
"source": [
@@ -398,7 +398,7 @@
},
{
"cell_type": "markdown",
- "id": "c74b4135",
+ "id": "903c766a",
"metadata": {},
"source": [
"## MA and AR Representations\n",
@@ -418,7 +418,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2ac0fe7c",
+ "id": "cb0928bc",
"metadata": {},
"outputs": [],
"source": [
@@ -442,7 +442,7 @@
},
{
"cell_type": "markdown",
- "id": "a4c7c242",
+ "id": "035dfef6",
"metadata": {},
"source": [
"The **moving average** coefficients in the top panel show tell-tale\n",
@@ -459,7 +459,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b15ce312",
+ "id": "81af6023",
"metadata": {},
"outputs": [],
"source": [
diff --git a/_sources/opt_tax_recur.ipynb b/_sources/opt_tax_recur.ipynb
index 14620713..d8cbd212 100644
--- a/_sources/opt_tax_recur.ipynb
+++ b/_sources/opt_tax_recur.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "a61ea34d",
+ "id": "789d2fd4",
"metadata": {},
"source": [
"(opt_tax_recur)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1a7e1db1",
+ "id": "e3275622",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "cdc0141b",
+ "id": "f94e6997",
"metadata": {},
"source": [
"## Overview\n",
@@ -75,7 +75,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6e0e0db2",
+ "id": "8f640e99",
"metadata": {},
"outputs": [],
"source": [
@@ -90,7 +90,7 @@
},
{
"cell_type": "markdown",
- "id": "b7f0253e",
+ "id": "48c98502",
"metadata": {},
"source": [
"## A Competitive Equilibrium with Distorting Taxes\n",
@@ -746,7 +746,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "afc575f5",
+ "id": "56a5d903",
"metadata": {
"load": "_static/lecture_specific/opt_tax_recur/sequential_allocation.py"
},
@@ -954,7 +954,7 @@
},
{
"cell_type": "markdown",
- "id": "bdab9285",
+ "id": "e6de7b6a",
"metadata": {},
"source": [
"## Recursive Formulation of the Ramsey Problem\n",
@@ -1259,7 +1259,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "32aeeaf2",
+ "id": "da58ac3d",
"metadata": {
"load": "_static/lecture_specific/opt_tax_recur/recursive_allocation.py"
},
@@ -1513,7 +1513,7 @@
},
{
"cell_type": "markdown",
- "id": "4c5376fa",
+ "id": "07394cac",
"metadata": {},
"source": [
"## Examples\n",
@@ -1572,7 +1572,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f1e6f2bf",
+ "id": "3b5c1729",
"metadata": {
"load": "_static/lecture_specific/opt_tax_recur/crra_utility.py"
},
@@ -1628,7 +1628,7 @@
},
{
"cell_type": "markdown",
- "id": "a872e276",
+ "id": "57990f89",
"metadata": {},
"source": [
"We set initial government debt $b_0 = 1$.\n",
@@ -1642,7 +1642,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8aa9287e",
+ "id": "b8d42481",
"metadata": {},
"outputs": [],
"source": [
@@ -1681,7 +1681,7 @@
},
{
"cell_type": "markdown",
- "id": "469b2fa4",
+ "id": "05a6999c",
"metadata": {},
"source": [
"**Tax smoothing**\n",
@@ -1726,7 +1726,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7ac8dd6f",
+ "id": "64e58417",
"metadata": {},
"outputs": [],
"source": [
@@ -1739,7 +1739,7 @@
},
{
"cell_type": "markdown",
- "id": "6c0dca37",
+ "id": "b8b400a4",
"metadata": {},
"source": [
"### Government Saving\n",
@@ -1798,7 +1798,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6b3627dc",
+ "id": "4122fb87",
"metadata": {},
"outputs": [],
"source": [
@@ -1830,7 +1830,7 @@
},
{
"cell_type": "markdown",
- "id": "ef80d8d5",
+ "id": "e9825777",
"metadata": {},
"source": [
"The figure indicates that if the government enters with positive debt, it sets\n",
@@ -1879,7 +1879,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bd4a5b24",
+ "id": "932aa50d",
"metadata": {},
"outputs": [],
"source": [
@@ -1907,7 +1907,7 @@
},
{
"cell_type": "markdown",
- "id": "92ca882c",
+ "id": "a48f6725",
"metadata": {},
"source": [
"The tax rates in the figure are equal for only two values of initial government debt.\n",
@@ -1946,7 +1946,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f1026bc1",
+ "id": "76740105",
"metadata": {
"load": "_static/lecture_specific/opt_tax_recur/log_utility.py"
},
@@ -1992,7 +1992,7 @@
},
{
"cell_type": "markdown",
- "id": "7b1b4456",
+ "id": "f541fd2a",
"metadata": {},
"source": [
"Also, suppose that $g_t$ follows a two-state IID process with equal\n",
@@ -2006,7 +2006,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eebabcd3",
+ "id": "17fcb971",
"metadata": {},
"outputs": [],
"source": [
@@ -2046,7 +2046,7 @@
},
{
"cell_type": "markdown",
- "id": "f1fbe536",
+ "id": "92baa0a9",
"metadata": {},
"source": [
"As should be expected, the recursive and sequential solutions produce almost\n",
diff --git a/_sources/orth_proj.ipynb b/_sources/orth_proj.ipynb
index 71651f1b..60cf7dc0 100644
--- a/_sources/orth_proj.ipynb
+++ b/_sources/orth_proj.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "e7099ecb",
+ "id": "e1531a25",
"metadata": {},
"source": [
"(orth_proj)=\n",
@@ -43,7 +43,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1709860a",
+ "id": "176f0161",
"metadata": {},
"outputs": [],
"source": [
@@ -53,7 +53,7 @@
},
{
"cell_type": "markdown",
- "id": "a18b113d",
+ "id": "8ed6a2c4",
"metadata": {},
"source": [
"### Further Reading\n",
@@ -780,7 +780,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "490582e8",
+ "id": "40219327",
"metadata": {},
"outputs": [],
"source": [
@@ -824,7 +824,7 @@
},
{
"cell_type": "markdown",
- "id": "8804807e",
+ "id": "37a6b9b6",
"metadata": {},
"source": [
"Here are the arrays we'll work with"
@@ -833,7 +833,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8dc2ae95",
+ "id": "48ecb6ad",
"metadata": {},
"outputs": [],
"source": [
@@ -848,7 +848,7 @@
},
{
"cell_type": "markdown",
- "id": "aac5caa8",
+ "id": "51d12551",
"metadata": {},
"source": [
"First, let's try projection of $y$ onto the column space of\n",
@@ -858,7 +858,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7f37e1ee",
+ "id": "34417ef8",
"metadata": {},
"outputs": [],
"source": [
@@ -868,7 +868,7 @@
},
{
"cell_type": "markdown",
- "id": "0c0a855c",
+ "id": "3dafcb58",
"metadata": {},
"source": [
"Now let's do the same using an orthonormal basis created from our\n",
@@ -878,7 +878,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "71ba92a5",
+ "id": "069c15d8",
"metadata": {},
"outputs": [],
"source": [
@@ -889,7 +889,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "743278ef",
+ "id": "492f2ea9",
"metadata": {},
"outputs": [],
"source": [
@@ -899,7 +899,7 @@
},
{
"cell_type": "markdown",
- "id": "1424842a",
+ "id": "b78d518c",
"metadata": {},
"source": [
"This is the same answer. So far so good. Finally, let's try the same\n",
@@ -909,7 +909,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "eafac243",
+ "id": "d7167517",
"metadata": {},
"outputs": [],
"source": [
@@ -920,7 +920,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7d8033a6",
+ "id": "5818cb6f",
"metadata": {},
"outputs": [],
"source": [
@@ -930,7 +930,7 @@
},
{
"cell_type": "markdown",
- "id": "4ba1f9a9",
+ "id": "3477cf0f",
"metadata": {},
"source": [
"Again, we obtain the same answer.\n",
diff --git a/_sources/permanent_income_dles.ipynb b/_sources/permanent_income_dles.ipynb
index ede1bfc9..7d3d32e6 100644
--- a/_sources/permanent_income_dles.ipynb
+++ b/_sources/permanent_income_dles.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "8a4b9984",
+ "id": "13f53bbf",
"metadata": {},
"source": [
"(permanent_income_dles)=\n",
@@ -28,7 +28,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "721ee0c9",
+ "id": "37103dd2",
"metadata": {
"tags": [
"hide-output"
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "b3c35105",
+ "id": "c8c932b5",
"metadata": {},
"source": [
"This lecture adds a third solution method for the\n",
@@ -62,7 +62,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0eaafc4c",
+ "id": "96267561",
"metadata": {},
"outputs": [],
"source": [
@@ -75,7 +75,7 @@
},
{
"cell_type": "markdown",
- "id": "1dcff982",
+ "id": "ce0b7049",
"metadata": {},
"source": [
"## The Permanent Income Model\n",
@@ -228,7 +228,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1ef1d58c",
+ "id": "18951211",
"metadata": {},
"outputs": [],
"source": [
@@ -266,7 +266,7 @@
},
{
"cell_type": "markdown",
- "id": "77d2d545",
+ "id": "1b87fa0f",
"metadata": {},
"source": [
"To check the solution of this model with that from the **LQ** problem,\n",
@@ -283,7 +283,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f7e4a67b",
+ "id": "f437d04f",
"metadata": {},
"outputs": [],
"source": [
@@ -292,7 +292,7 @@
},
{
"cell_type": "markdown",
- "id": "20651e46",
+ "id": "45e8493a",
"metadata": {},
"source": [
"The state vector in the DLE class is:\n",
@@ -322,7 +322,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fde2d1e3",
+ "id": "d204b8b7",
"metadata": {},
"outputs": [],
"source": [
diff --git a/_sources/rob_markov_perf.ipynb b/_sources/rob_markov_perf.ipynb
index 72b7bc4c..b492ec8f 100644
--- a/_sources/rob_markov_perf.ipynb
+++ b/_sources/rob_markov_perf.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "53fede6d",
+ "id": "108a730f",
"metadata": {},
"source": [
"(rob_markov_perf)=\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "21a691e9",
+ "id": "deb820c4",
"metadata": {
"tags": [
"hide-output"
@@ -35,7 +35,7 @@
},
{
"cell_type": "markdown",
- "id": "b7e268d6",
+ "id": "3a163c24",
"metadata": {},
"source": [
"## Overview\n",
@@ -62,7 +62,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bf10ffbb",
+ "id": "713354c9",
"metadata": {},
"outputs": [],
"source": [
@@ -74,7 +74,7 @@
},
{
"cell_type": "markdown",
- "id": "bf8e5d33",
+ "id": "3e70fa64",
"metadata": {},
"source": [
"### Basic Setup\n",
@@ -474,7 +474,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3a430aaf",
+ "id": "1d6bac7f",
"metadata": {
"load": "_static/lecture_specific/markov_perf/duopoly_mpe.py"
},
@@ -520,7 +520,7 @@
},
{
"cell_type": "markdown",
- "id": "a8686333",
+ "id": "ed6a86b0",
"metadata": {},
"source": [
"#### Markov Perfect Equilibrium with Robustness\n",
@@ -539,7 +539,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5de2866f",
+ "id": "892fb6a5",
"metadata": {},
"outputs": [],
"source": [
@@ -709,7 +709,7 @@
},
{
"cell_type": "markdown",
- "id": "a87c3133",
+ "id": "e235046f",
"metadata": {},
"source": [
"### Some Details\n",
@@ -783,7 +783,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "6a491c3d",
+ "id": "d7104648",
"metadata": {},
"outputs": [],
"source": [
@@ -814,7 +814,7 @@
},
{
"cell_type": "markdown",
- "id": "0b97029b",
+ "id": "bd0aba4a",
"metadata": {},
"source": [
"#### Consistency Check\n",
@@ -826,7 +826,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bbea8025",
+ "id": "7b663372",
"metadata": {},
"outputs": [],
"source": [
@@ -848,7 +848,7 @@
},
{
"cell_type": "markdown",
- "id": "b8935a64",
+ "id": "28c95478",
"metadata": {},
"source": [
"We can see that the results are consistent across the two functions.\n",
@@ -892,7 +892,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "12cd4ec4",
+ "id": "0eac3be0",
"metadata": {},
"outputs": [],
"source": [
@@ -961,7 +961,7 @@
},
{
"cell_type": "markdown",
- "id": "e395660e",
+ "id": "38ab00f5",
"metadata": {},
"source": [
"The following code prepares graphs that compare market-wide output $q_{1t} + q_{2t}$ and the price of the good\n",
@@ -975,7 +975,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ccdeb787",
+ "id": "9aed165c",
"metadata": {},
"outputs": [],
"source": [
@@ -997,7 +997,7 @@
},
{
"cell_type": "markdown",
- "id": "ea114f0c",
+ "id": "fdc85e5b",
"metadata": {},
"source": [
"Under the dynamics associated with the baseline model, the price path is higher with the Markov perfect equilibrium robust decision rules\n",
@@ -1013,7 +1013,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0e417313",
+ "id": "30e52630",
"metadata": {},
"outputs": [],
"source": [
@@ -1035,7 +1035,7 @@
},
{
"cell_type": "markdown",
- "id": "14f620b1",
+ "id": "10f60238",
"metadata": {},
"source": [
"Evidently, firm 1's output path is substantially lower when firms are robust firms while\n",
@@ -1081,7 +1081,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "95308878",
+ "id": "61e86e47",
"metadata": {},
"outputs": [],
"source": [
@@ -1095,7 +1095,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4fa7f6ab",
+ "id": "48ee9dfe",
"metadata": {},
"outputs": [],
"source": [
@@ -1124,7 +1124,7 @@
},
{
"cell_type": "markdown",
- "id": "6170e60c",
+ "id": "07658e1f",
"metadata": {},
"source": [
"We see from the above graph that under robustness concerns, player 1 and\n",
diff --git a/_sources/robustness.ipynb b/_sources/robustness.ipynb
index 9befc8a1..97e610c7 100644
--- a/_sources/robustness.ipynb
+++ b/_sources/robustness.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "2c7d7335",
+ "id": "532cb25e",
"metadata": {},
"source": [
"(rob)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "50f866e9",
+ "id": "ca3c43d3",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "4194c32e",
+ "id": "85ef8615",
"metadata": {},
"source": [
"## Overview\n",
@@ -88,7 +88,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "617268d9",
+ "id": "9950ec3f",
"metadata": {},
"outputs": [],
"source": [
@@ -101,7 +101,7 @@
},
{
"cell_type": "markdown",
- "id": "03df01b8",
+ "id": "fec81695",
"metadata": {},
"source": [
"(rb_vec)=\n",
@@ -961,7 +961,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fa2b1340",
+ "id": "c1bd11ab",
"metadata": {},
"outputs": [],
"source": [
@@ -1136,7 +1136,7 @@
},
{
"cell_type": "markdown",
- "id": "b253241a",
+ "id": "f769caff",
"metadata": {},
"source": [
"Here's another such figure, with $\\theta = 0.002$ instead of $0.02$\n",
diff --git a/_sources/rosen_schooling_model.ipynb b/_sources/rosen_schooling_model.ipynb
index d301bc58..b83d339e 100644
--- a/_sources/rosen_schooling_model.ipynb
+++ b/_sources/rosen_schooling_model.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "6a9193ef",
+ "id": "f55eb10e",
"metadata": {},
"source": [
"(rosen_schooling_model)=\n",
@@ -28,7 +28,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "cbe10232",
+ "id": "c7769fcb",
"metadata": {
"tags": [
"hide-output"
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "e91ac0c8",
+ "id": "16c949b8",
"metadata": {},
"source": [
"We'll also need the following imports:"
@@ -50,7 +50,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "acdf5e4f",
+ "id": "87b1ff22",
"metadata": {},
"outputs": [],
"source": [
@@ -62,7 +62,7 @@
},
{
"cell_type": "markdown",
- "id": "5c329ed6",
+ "id": "561b5a71",
"metadata": {},
"source": [
"## A One-Occupation Model\n",
@@ -182,7 +182,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "31218476",
+ "id": "0e6f3d63",
"metadata": {},
"outputs": [],
"source": [
@@ -193,7 +193,7 @@
},
{
"cell_type": "markdown",
- "id": "f7aabc0c",
+ "id": "66c490bf",
"metadata": {},
"source": [
"### Effects of Changes in Education Technology and Demand\n",
@@ -211,7 +211,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "57d61c7d",
+ "id": "db8488e2",
"metadata": {},
"outputs": [],
"source": [
@@ -264,7 +264,7 @@
},
{
"cell_type": "markdown",
- "id": "3346cbec",
+ "id": "149c6fc2",
"metadata": {},
"source": [
"We create three other instances by:\n",
@@ -277,7 +277,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b3f0ebaf",
+ "id": "dfc6e4f5",
"metadata": {},
"outputs": [],
"source": [
@@ -322,7 +322,7 @@
},
{
"cell_type": "markdown",
- "id": "24e5c0ec",
+ "id": "e7760128",
"metadata": {},
"source": [
"The first figure plots the impulse response of $n_t$ (on the left)\n",
@@ -350,7 +350,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a22513d1",
+ "id": "8ad38256",
"metadata": {},
"outputs": [],
"source": [
@@ -369,7 +369,7 @@
},
{
"cell_type": "markdown",
- "id": "d7d97c49",
+ "id": "39523037",
"metadata": {},
"source": [
"The next figure plots the impulse response of $n_t$ (on the left)\n",
@@ -380,7 +380,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "beaa91d1",
+ "id": "4d452d77",
"metadata": {},
"outputs": [],
"source": [
@@ -401,7 +401,7 @@
},
{
"cell_type": "markdown",
- "id": "21596ba1",
+ "id": "b6eb1816",
"metadata": {},
"source": [
"Both panels in the above figure show that raising $k$ lowers the effect of\n",
diff --git a/_sources/smoothing.ipynb b/_sources/smoothing.ipynb
index 2614ed04..45ab610a 100644
--- a/_sources/smoothing.ipynb
+++ b/_sources/smoothing.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "96fbaf24",
+ "id": "95121ea1",
"metadata": {},
"source": [
"(smoothing)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e8af3031",
+ "id": "66547f96",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "ac37cc4b",
+ "id": "dbf4fead",
"metadata": {},
"source": [
"## Overview\n",
@@ -88,7 +88,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "afd1edc4",
+ "id": "c07c641c",
"metadata": {},
"outputs": [],
"source": [
@@ -100,7 +100,7 @@
},
{
"cell_type": "markdown",
- "id": "dc8cc693",
+ "id": "031b413c",
"metadata": {},
"source": [
"### Relationship to Other Lectures\n",
@@ -293,7 +293,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ac89b7dc",
+ "id": "c09cef05",
"metadata": {},
"outputs": [],
"source": [
@@ -374,7 +374,7 @@
},
{
"cell_type": "markdown",
- "id": "57e4e2a7",
+ "id": "feea7c00",
"metadata": {},
"source": [
"### Interpretation of Graph\n",
@@ -658,7 +658,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c29fd950",
+ "id": "9b27c933",
"metadata": {},
"outputs": [],
"source": [
@@ -786,7 +786,7 @@
},
{
"cell_type": "markdown",
- "id": "734ca9e0",
+ "id": "ccbfe187",
"metadata": {},
"source": [
"Let's test by checking that $\\bar c$ and $b_2$ satisfy the budget constraint"
@@ -795,7 +795,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0a9add65",
+ "id": "3f20a19e",
"metadata": {},
"outputs": [],
"source": [
@@ -806,7 +806,7 @@
},
{
"cell_type": "markdown",
- "id": "61f08793",
+ "id": "f07aa5ea",
"metadata": {},
"source": [
"Below, we'll take the outcomes produced by this code -- in particular the implied\n",
@@ -965,7 +965,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7e839758",
+ "id": "4a20d780",
"metadata": {},
"outputs": [],
"source": [
@@ -1001,7 +1001,7 @@
},
{
"cell_type": "markdown",
- "id": "b9bd70ab",
+ "id": "6abe13a8",
"metadata": {},
"source": [
"In the graph on the left, for the same sample path of nonfinancial\n",
diff --git a/_sources/smoothing_tax.ipynb b/_sources/smoothing_tax.ipynb
index 42924bff..70a48b0b 100644
--- a/_sources/smoothing_tax.ipynb
+++ b/_sources/smoothing_tax.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "6f455a8d",
+ "id": "e06a60b4",
"metadata": {},
"source": [
"(smoothing_tax)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "817318ac",
+ "id": "06b0e22e",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "bea0fb39",
+ "id": "8e67c9c8",
"metadata": {},
"source": [
"## Overview\n",
@@ -102,7 +102,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5f75966e",
+ "id": "5a4f7f1d",
"metadata": {},
"outputs": [],
"source": [
@@ -113,7 +113,7 @@
},
{
"cell_type": "markdown",
- "id": "ef0b1402",
+ "id": "201ac5b4",
"metadata": {},
"source": [
"To exploit the isomorphism between consumption-smoothing and tax-smoothing models, we simply use code from {doc}`Consumption Smoothing with Complete and Incomplete Markets `\n",
@@ -129,7 +129,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b935a62d",
+ "id": "03912c7e",
"metadata": {},
"outputs": [],
"source": [
@@ -257,7 +257,7 @@
},
{
"cell_type": "markdown",
- "id": "98b5620c",
+ "id": "48d2ee91",
"metadata": {},
"source": [
"### Revisiting the consumption-smoothing model\n",
@@ -273,7 +273,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bac59870",
+ "id": "61a132b0",
"metadata": {},
"outputs": [],
"source": [
@@ -307,7 +307,7 @@
},
{
"cell_type": "markdown",
- "id": "235b4106",
+ "id": "33a5c277",
"metadata": {},
"source": [
"In the graph on the left, for the same sample path of nonfinancial\n",
@@ -327,7 +327,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "07088166",
+ "id": "69134072",
"metadata": {},
"outputs": [],
"source": [
@@ -354,7 +354,7 @@
},
{
"cell_type": "markdown",
- "id": "c7b1fca0",
+ "id": "f1aef870",
"metadata": {},
"source": [
"## Tax Smoothing with Complete Markets\n",
@@ -431,7 +431,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9c48eac8",
+ "id": "e41416c5",
"metadata": {},
"outputs": [],
"source": [
@@ -469,7 +469,7 @@
},
{
"cell_type": "markdown",
- "id": "44a2077e",
+ "id": "b40b0416",
"metadata": {},
"source": [
"### An Example of Tax Smoothing\n",
@@ -497,7 +497,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "81c60f32",
+ "id": "b89e546c",
"metadata": {},
"outputs": [],
"source": [
@@ -574,7 +574,7 @@
},
{
"cell_type": "markdown",
- "id": "63f65244",
+ "id": "d4061b32",
"metadata": {},
"source": [
"### Explanation\n",
@@ -630,7 +630,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "165d3f98",
+ "id": "1b959de4",
"metadata": {},
"outputs": [],
"source": [
@@ -747,7 +747,7 @@
},
{
"cell_type": "markdown",
- "id": "fc9a121c",
+ "id": "0cf6fa08",
"metadata": {},
"source": [
"### Parameters"
@@ -756,7 +756,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "76c7f411",
+ "id": "0feeaeb4",
"metadata": {},
"outputs": [],
"source": [
@@ -773,7 +773,7 @@
},
{
"cell_type": "markdown",
- "id": "380deb3d",
+ "id": "e1a5e02a",
"metadata": {},
"source": [
"### Example 1\n",
@@ -805,7 +805,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "14343e13",
+ "id": "fd674646",
"metadata": {},
"outputs": [],
"source": [
@@ -820,7 +820,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "287d5d6e",
+ "id": "19683457",
"metadata": {},
"outputs": [],
"source": [
@@ -831,7 +831,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c9b8fdd7",
+ "id": "7e222b11",
"metadata": {},
"outputs": [],
"source": [
@@ -843,7 +843,7 @@
},
{
"cell_type": "markdown",
- "id": "494621da",
+ "id": "3ff66283",
"metadata": {},
"source": [
"### Example 2\n",
@@ -869,7 +869,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e69c151e",
+ "id": "121ca452",
"metadata": {},
"outputs": [],
"source": [
@@ -884,7 +884,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "d0e842e1",
+ "id": "bc309788",
"metadata": {},
"outputs": [],
"source": [
@@ -894,7 +894,7 @@
},
{
"cell_type": "markdown",
- "id": "4843ddd5",
+ "id": "e4c2c974",
"metadata": {},
"source": [
"### Example 3\n",
@@ -923,7 +923,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "43699623",
+ "id": "e153d802",
"metadata": {},
"outputs": [],
"source": [
@@ -939,7 +939,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f3d3ac64",
+ "id": "21c5b76b",
"metadata": {},
"outputs": [],
"source": [
@@ -949,7 +949,7 @@
},
{
"cell_type": "markdown",
- "id": "88ba43ea",
+ "id": "aaeb3ade",
"metadata": {},
"source": [
"### Example 4\n",
@@ -976,7 +976,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1c50381e",
+ "id": "9a88f752",
"metadata": {},
"outputs": [],
"source": [
@@ -993,7 +993,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "840176be",
+ "id": "50a9389e",
"metadata": {},
"outputs": [],
"source": [
@@ -1003,7 +1003,7 @@
},
{
"cell_type": "markdown",
- "id": "f24ebc84",
+ "id": "4738ed31",
"metadata": {},
"source": [
"### Example 5\n",
@@ -1035,7 +1035,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "5bc97ae7",
+ "id": "7e879cb7",
"metadata": {},
"outputs": [],
"source": [
@@ -1054,7 +1054,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f294046d",
+ "id": "10bb1892",
"metadata": {},
"outputs": [],
"source": [
@@ -1064,7 +1064,7 @@
},
{
"cell_type": "markdown",
- "id": "83191beb",
+ "id": "bd1398b4",
"metadata": {},
"source": [
"### Continuous-State Gaussian Model\n",
diff --git a/_sources/stationary_densities.ipynb b/_sources/stationary_densities.ipynb
index 9f846721..7daace0a 100644
--- a/_sources/stationary_densities.ipynb
+++ b/_sources/stationary_densities.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "ccd2a982",
+ "id": "4d2fd32e",
"metadata": {},
"source": [
"(statd)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b927d496",
+ "id": "506113c6",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "7c5c28a9",
+ "id": "ee87d3f7",
"metadata": {},
"source": [
"## Overview\n",
@@ -84,7 +84,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ec0f75e2",
+ "id": "ef31b799",
"metadata": {},
"outputs": [],
"source": [
@@ -97,7 +97,7 @@
},
{
"cell_type": "markdown",
- "id": "a3a2e83f",
+ "id": "ee3bb151",
"metadata": {},
"source": [
"(statd_density_case)=\n",
@@ -487,7 +487,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "aa7d312d",
+ "id": "24e66de9",
"metadata": {},
"outputs": [],
"source": [
@@ -535,7 +535,7 @@
},
{
"cell_type": "markdown",
- "id": "a797df28",
+ "id": "41268de7",
"metadata": {},
"source": [
"The figure shows part of the density sequence $\\{\\psi_t\\}$, with each\n",
@@ -852,7 +852,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "152ad67e",
+ "id": "678c61b3",
"metadata": {},
"outputs": [],
"source": [
@@ -889,7 +889,7 @@
},
{
"cell_type": "markdown",
- "id": "e9f67b2b",
+ "id": "474fc5d1",
"metadata": {},
"source": [
"```{solution-end}\n",
@@ -927,7 +927,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "dd5d6c8f",
+ "id": "935e6a03",
"metadata": {},
"outputs": [],
"source": [
@@ -977,7 +977,7 @@
},
{
"cell_type": "markdown",
- "id": "145c5a01",
+ "id": "47af4aa9",
"metadata": {},
"source": [
"```{solution-end}\n",
@@ -1007,7 +1007,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8decaa42",
+ "id": "e1b05b84",
"metadata": {},
"outputs": [],
"source": [
@@ -1027,7 +1027,7 @@
},
{
"cell_type": "markdown",
- "id": "3cb45515",
+ "id": "c9684782",
"metadata": {},
"source": [
"Each data set is represented by a box, where the top and bottom of the box are the third and first quartiles of the data, and the red line in the center is the median.\n",
@@ -1075,7 +1075,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8038b7d7",
+ "id": "bd9280f3",
"metadata": {},
"outputs": [],
"source": [
@@ -1107,7 +1107,7 @@
},
{
"cell_type": "markdown",
- "id": "0ae43af1",
+ "id": "98910ffb",
"metadata": {},
"source": [
"```{solution-end}\n",
diff --git a/_sources/status.ipynb b/_sources/status.ipynb
index 3291938b..ebe02898 100644
--- a/_sources/status.ipynb
+++ b/_sources/status.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "0bca22cb",
+ "id": "49558d06",
"metadata": {},
"source": [
"# Execution Statistics\n",
diff --git a/_sources/tax_smoothing_1.ipynb b/_sources/tax_smoothing_1.ipynb
index ec155084..58f08839 100644
--- a/_sources/tax_smoothing_1.ipynb
+++ b/_sources/tax_smoothing_1.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "838a2d9e",
+ "id": "b750c3ea",
"metadata": {},
"source": [
"(tax_smoothing_1)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1ec7762e",
+ "id": "cefd7c1e",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "4b34cafe",
+ "id": "01eebbde",
"metadata": {},
"source": [
"## Reader's Guide\n",
@@ -49,7 +49,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "83f70f26",
+ "id": "e7d4c894",
"metadata": {},
"outputs": [],
"source": [
@@ -60,7 +60,7 @@
},
{
"cell_type": "markdown",
- "id": "d293e836",
+ "id": "7bb8a96a",
"metadata": {},
"source": [
"This lecture uses the method of **Markov jump linear quadratic dynamic programming** that is described in lecture\n",
@@ -304,7 +304,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7712e4f2",
+ "id": "d13d02c4",
"metadata": {},
"outputs": [],
"source": [
@@ -347,7 +347,7 @@
},
{
"cell_type": "markdown",
- "id": "79cd3ab1",
+ "id": "844f5a19",
"metadata": {},
"source": [
"We can now create an instance of `LQ`:"
@@ -356,7 +356,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f0db76ec",
+ "id": "69fbe2d4",
"metadata": {},
"outputs": [],
"source": [
@@ -367,7 +367,7 @@
},
{
"cell_type": "markdown",
- "id": "705acc0f",
+ "id": "4c0d5685",
"metadata": {},
"source": [
"We can see the isomorphism by noting that consumption is a martingale in\n",
@@ -407,7 +407,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "525204cb",
+ "id": "8c1a364e",
"metadata": {},
"outputs": [],
"source": [
@@ -416,7 +416,7 @@
},
{
"cell_type": "markdown",
- "id": "e563f0a7",
+ "id": "d8ad065c",
"metadata": {},
"source": [
"This explains the fanning out of the conditional empirical distribution of taxation across time, computing\n",
@@ -427,7 +427,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "29c2b0a5",
+ "id": "5b803b54",
"metadata": {},
"outputs": [],
"source": [
@@ -442,7 +442,7 @@
},
{
"cell_type": "markdown",
- "id": "a09850d1",
+ "id": "176eafb2",
"metadata": {},
"source": [
"We can see a similar, but a smoother pattern, if we plot government debt\n",
@@ -452,7 +452,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4ced9e3e",
+ "id": "d05c7153",
"metadata": {},
"outputs": [],
"source": [
@@ -467,7 +467,7 @@
},
{
"cell_type": "markdown",
- "id": "376cc817",
+ "id": "4a65a2ed",
"metadata": {},
"source": [
"## Python Class to Solve Markov Jump Linear Quadratic Control Problems\n",
@@ -532,7 +532,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2b407519",
+ "id": "f3e311cd",
"metadata": {},
"outputs": [],
"source": [
@@ -562,7 +562,7 @@
},
{
"cell_type": "markdown",
- "id": "5d838bde",
+ "id": "f886690f",
"metadata": {},
"source": [
"The decision rules are now dependent on the Markov state:"
@@ -571,7 +571,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c4f1be70",
+ "id": "964b434f",
"metadata": {},
"outputs": [],
"source": [
@@ -581,7 +581,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c88de900",
+ "id": "cb37840e",
"metadata": {},
"outputs": [],
"source": [
@@ -590,7 +590,7 @@
},
{
"cell_type": "markdown",
- "id": "ea3c5c3e",
+ "id": "33014a55",
"metadata": {},
"source": [
"Simulating a large number of such economies over time reveals\n",
@@ -603,7 +603,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "e4af4c51",
+ "id": "24304bd3",
"metadata": {},
"outputs": [],
"source": [
diff --git a/_sources/tax_smoothing_2.ipynb b/_sources/tax_smoothing_2.ipynb
index 70c3054d..c47edd5d 100644
--- a/_sources/tax_smoothing_2.ipynb
+++ b/_sources/tax_smoothing_2.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "c8e63083",
+ "id": "3c7f1c8f",
"metadata": {},
"source": [
"(tax_smoothing_2)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1f428f66",
+ "id": "1a332b7e",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "c821d196",
+ "id": "b8897794",
"metadata": {},
"source": [
"## An Application of Markov Jump Linear Quadratic Dynamic Programming\n",
@@ -84,7 +84,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "1ffc6a22",
+ "id": "6bbf3ed9",
"metadata": {},
"outputs": [],
"source": [
@@ -95,7 +95,7 @@
},
{
"cell_type": "markdown",
- "id": "439a7e27",
+ "id": "cdaa80b7",
"metadata": {},
"source": [
"## Two example specifications\n",
@@ -338,7 +338,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "31736683",
+ "id": "0cf601d3",
"metadata": {},
"outputs": [],
"source": [
@@ -397,7 +397,7 @@
},
{
"cell_type": "markdown",
- "id": "a15aa8a5",
+ "id": "f5b84a53",
"metadata": {},
"source": [
"With the above function, we can proceed to solve the model in two steps:\n",
@@ -458,7 +458,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f4434ac4",
+ "id": "e11c4cbc",
"metadata": {},
"outputs": [],
"source": [
@@ -510,7 +510,7 @@
},
{
"cell_type": "markdown",
- "id": "1404c25b",
+ "id": "518ebd96",
"metadata": {},
"source": [
"The above simulations show that when no penalty is imposed on different\n",
@@ -527,7 +527,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "401b9758",
+ "id": "24c7dd76",
"metadata": {},
"outputs": [],
"source": [
@@ -569,7 +569,7 @@
},
{
"cell_type": "markdown",
- "id": "c783a9c7",
+ "id": "99bf8aac",
"metadata": {},
"source": [
"## A Model with Restructuring\n",
@@ -752,7 +752,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fb019a69",
+ "id": "9871bca2",
"metadata": {},
"outputs": [],
"source": [
@@ -805,7 +805,7 @@
},
{
"cell_type": "markdown",
- "id": "6695f24e",
+ "id": "c4da65fb",
"metadata": {},
"source": [
"### Example with Restructuring\n",
@@ -836,7 +836,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4ecf7cc0",
+ "id": "3db06c90",
"metadata": {},
"outputs": [],
"source": [
@@ -879,7 +879,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "a843e1c6",
+ "id": "781f242f",
"metadata": {},
"outputs": [],
"source": [
@@ -905,7 +905,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "4bfcdd11",
+ "id": "b8a47a2e",
"metadata": {},
"outputs": [],
"source": [
diff --git a/_sources/tax_smoothing_3.ipynb b/_sources/tax_smoothing_3.ipynb
index e28ab2f6..6033d914 100644
--- a/_sources/tax_smoothing_3.ipynb
+++ b/_sources/tax_smoothing_3.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "724e0348",
+ "id": "4bd066a3",
"metadata": {},
"source": [
"(tax_smoothing_3)=\n",
@@ -25,7 +25,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "64ba472a",
+ "id": "95fc2d93",
"metadata": {
"tags": [
"hide-output"
@@ -38,7 +38,7 @@
},
{
"cell_type": "markdown",
- "id": "87ecf0ef",
+ "id": "f495fedc",
"metadata": {},
"source": [
"## Another Application of Markov Jump Linear Quadratic Dynamic Programming\n",
@@ -67,7 +67,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "8b9b5b46",
+ "id": "a18f2e86",
"metadata": {},
"outputs": [],
"source": [
@@ -78,7 +78,7 @@
},
{
"cell_type": "markdown",
- "id": "35d548b7",
+ "id": "43039ad0",
"metadata": {},
"source": [
"## Roll-Over Risk\n",
@@ -209,7 +209,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3a370559",
+ "id": "5a77a8c4",
"metadata": {},
"outputs": [],
"source": [
@@ -267,7 +267,7 @@
},
{
"cell_type": "markdown",
- "id": "6f3a8639",
+ "id": "c51e6f4a",
"metadata": {},
"source": [
"This model is simulated below, using the same process for $G_t$ as\n",
@@ -290,7 +290,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "26306cd4",
+ "id": "bc49c563",
"metadata": {},
"outputs": [],
"source": [
@@ -316,7 +316,7 @@
},
{
"cell_type": "markdown",
- "id": "4525070d",
+ "id": "a671b557",
"metadata": {},
"source": [
"We can adjust the model so that, rather than having debt fluctuate\n",
@@ -330,7 +330,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f955837b",
+ "id": "ab99716e",
"metadata": {},
"outputs": [],
"source": [
@@ -369,7 +369,7 @@
},
{
"cell_type": "markdown",
- "id": "26cd5433",
+ "id": "212dbc21",
"metadata": {},
"source": [
"With a lower interest rate, the government has an incentive to\n",
diff --git a/_sources/troubleshooting.ipynb b/_sources/troubleshooting.ipynb
index e0910cca..8f2fc284 100644
--- a/_sources/troubleshooting.ipynb
+++ b/_sources/troubleshooting.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "3f3a9204",
+ "id": "5873a4a4",
"metadata": {},
"source": [
"(troubleshooting)=\n",
diff --git a/_sources/un_insure.ipynb b/_sources/un_insure.ipynb
index 96a28408..45e29baa 100644
--- a/_sources/un_insure.ipynb
+++ b/_sources/un_insure.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "bf985118",
+ "id": "2d68cd92",
"metadata": {},
"source": [
"# Optimal Unemployment Insurance\n",
@@ -405,14 +405,14 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "69ca7278",
+ "id": "11c5a1ca",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
- "id": "6416248a",
+ "id": "18c6af48",
"metadata": {},
"source": [
"### Computational Details\n",
@@ -504,7 +504,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "67e14f95",
+ "id": "358ac6ac",
"metadata": {},
"outputs": [],
"source": [
@@ -515,7 +515,7 @@
},
{
"cell_type": "markdown",
- "id": "0d62876d",
+ "id": "98e61597",
"metadata": {},
"source": [
"We first create a class to set up a particular parametrization."
@@ -524,7 +524,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "52ae46a5",
+ "id": "c71e2e08",
"metadata": {},
"outputs": [],
"source": [
@@ -545,7 +545,7 @@
},
{
"cell_type": "markdown",
- "id": "1499ffa6",
+ "id": "571cf789",
"metadata": {},
"source": [
"### Parameter Values\n",
@@ -558,7 +558,7 @@
},
{
"cell_type": "markdown",
- "id": "07eb3dcf",
+ "id": "c86d71e4",
"metadata": {},
"source": [
"First, we create some helper functions."
@@ -567,7 +567,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9701f9b3",
+ "id": "4b478d58",
"metadata": {},
"outputs": [],
"source": [
@@ -591,7 +591,7 @@
},
{
"cell_type": "markdown",
- "id": "b9c5c9ec",
+ "id": "17ca0ce4",
"metadata": {},
"source": [
"Recall that under autarky the value for an unemployed worker\n",
@@ -625,7 +625,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "fb4b5ea0",
+ "id": "7cf161b8",
"metadata": {},
"outputs": [],
"source": [
@@ -642,7 +642,7 @@
},
{
"cell_type": "markdown",
- "id": "44d99e7e",
+ "id": "28b63e5b",
"metadata": {},
"source": [
"Since the calibration exercise is to match the hazard rate under autarky to the data, we must find an interest rate $r$ to match `p(a,r) = 0.1`.\n",
@@ -655,7 +655,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b6077e27",
+ "id": "febaf71c",
"metadata": {},
"outputs": [],
"source": [
@@ -671,7 +671,7 @@
},
{
"cell_type": "markdown",
- "id": "526b5466",
+ "id": "fb868cf3",
"metadata": {},
"source": [
"Now, let us create an instance of the model with our parametrization"
@@ -680,7 +680,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "68b8a2ad",
+ "id": "ca3ec4de",
"metadata": {},
"outputs": [],
"source": [
@@ -692,7 +692,7 @@
},
{
"cell_type": "markdown",
- "id": "deb12ec7",
+ "id": "ff90acf9",
"metadata": {},
"source": [
"We want to compute an $r$ that is consistent with the hazard rate 0.1 in autarky.\n",
@@ -703,7 +703,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "bab57580",
+ "id": "0db0efbd",
"metadata": {},
"outputs": [],
"source": [
@@ -718,7 +718,7 @@
},
{
"cell_type": "markdown",
- "id": "b4e4a8ec",
+ "id": "2f36c78d",
"metadata": {},
"source": [
"Now that we have calibrated our interest rate $r$, we can continue with solving the model with private information."
@@ -726,7 +726,7 @@
},
{
"cell_type": "markdown",
- "id": "5afb8bbd",
+ "id": "f9ed854b",
"metadata": {},
"source": [
"### Computation under Private Information"
@@ -734,7 +734,7 @@
},
{
"cell_type": "markdown",
- "id": "6ccb310b",
+ "id": "fa7729e2",
"metadata": {},
"source": [
"Our approach to solving the full model is a variant on Judd (1998) {cite}`Judd1998`, who uses a polynomial to approximate the value function and a numerical optimizer to perform the optimization at each iteration.\n",
@@ -744,7 +744,7 @@
},
{
"cell_type": "markdown",
- "id": "51e3934e",
+ "id": "13fadcef",
"metadata": {},
"source": [
"Our strategy involves finding a function $C(V)$ -- the expected cost of giving the worker value $V$ -- that satisfies the Bellman equation:\n",
@@ -761,7 +761,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2993ff21",
+ "id": "143c1034",
"metadata": {},
"outputs": [],
"source": [
@@ -789,7 +789,7 @@
},
{
"cell_type": "markdown",
- "id": "b8982cd5",
+ "id": "e36bc94e",
"metadata": {},
"source": [
"With these analytical solutions for optimal $c$ and $a$ in hand, we can reduce the minimization to {eq}`eq:hugo23` in the single variable\n",
@@ -812,7 +812,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "f5faa97a",
+ "id": "a01a1ddc",
"metadata": {},
"outputs": [],
"source": [
@@ -863,7 +863,7 @@
},
{
"cell_type": "markdown",
- "id": "2e735638",
+ "id": "c99de0b8",
"metadata": {},
"source": [
"The below code executes steps 4 and 5 in the Algorithm until convergence to a function $C^*(V)$."
@@ -872,7 +872,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0f537e1b",
+ "id": "21be3615",
"metadata": {},
"outputs": [],
"source": [
@@ -898,7 +898,7 @@
},
{
"cell_type": "markdown",
- "id": "23915298",
+ "id": "f1f2e3a0",
"metadata": {},
"source": [
"## Outcomes"
@@ -906,7 +906,7 @@
},
{
"cell_type": "markdown",
- "id": "a7c2efe7",
+ "id": "d57e3fb2",
"metadata": {},
"source": [
"Using the above functions, we create another instance of the parameters with the correctly calibrated interest rate, $r$."
@@ -915,7 +915,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3e6a0125",
+ "id": "9207818e",
"metadata": {},
"outputs": [],
"source": [
@@ -939,7 +939,7 @@
},
{
"cell_type": "markdown",
- "id": "059e45d5",
+ "id": "b2f9b1a7",
"metadata": {},
"source": [
"### Replacement Ratios and Continuation Values"
@@ -947,7 +947,7 @@
},
{
"cell_type": "markdown",
- "id": "728cb4a1",
+ "id": "f8f67aa2",
"metadata": {},
"source": [
"We want to graph the replacement ratio ($c/w$) and search effort $a$ as functions of the duration of unemployment.\n",
@@ -960,7 +960,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3b9ca7d6",
+ "id": "fcc2771d",
"metadata": {},
"outputs": [],
"source": [
@@ -978,7 +978,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "7ebf26a1",
+ "id": "22e55781",
"metadata": {},
"outputs": [],
"source": [
@@ -993,7 +993,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "ef97138a",
+ "id": "6949d7c7",
"metadata": {},
"outputs": [],
"source": [
@@ -1027,7 +1027,7 @@
},
{
"cell_type": "markdown",
- "id": "91c34b92",
+ "id": "a473b45d",
"metadata": {},
"source": [
"For an initial promised value $V^u = V_{\\rm aut}$, the planner chooses the autarky level of $0$ for the replacement ratio and instructs the worker to search at the autarky search intensity, regardless of the duration of unemployment\n",
diff --git a/_sources/zreferences.ipynb b/_sources/zreferences.ipynb
index 4b501156..9034ac00 100644
--- a/_sources/zreferences.ipynb
+++ b/_sources/zreferences.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "108e14a7",
+ "id": "4765db54",
"metadata": {},
"source": [
"(references)=\n",
diff --git a/additive_functionals.html b/additive_functionals.html
index 81a1c677..d6931aa8 100644
--- a/additive_functionals.html
+++ b/additive_functionals.html
@@ -274,13 +274,13 @@ 30. Additive and Multiplicative Function
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@@ -924,7 +924,7 @@ 30.3.1.1. Plotting
-
+
Notice the irregular but persistent growth in \(y_t\).
@@ -1068,7 +1068,7 @@ 30.4. Code
-
+
When we plot multiple realizations of a component in the 2nd, 3rd, and 4th panels, we also plot the population 95% probability coverage sets computed using the LinearStateSpace class.
@@ -1119,7 +1119,7 @@30.4.1. Associated Multiplicative Functi
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diff --git a/rosen_schooling_model.html b/rosen_schooling_model.html
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--- a/rosen_schooling_model.html
+++ b/rosen_schooling_model.html
@@ -264,7 +264,9 @@
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