{
"cells": [
{
"cell_type": "markdown",
"id": "d3a95813-a15a-4dce-9c8a-f8a314226c8c",
"metadata": {},
"source": [
"# 5. From Optimal Consumption to Aiyagari Model"
]
},
{
"cell_type": "markdown",
"id": "5761f245-c430-4dc8-b8f9-3dd9aa05585f",
"metadata": {},
"source": [
"DING Minjie, Spring 2025"
]
},
{
"cell_type": "markdown",
"id": "ed6c23dd-1a97-4d95-b625-ebfb09f71c7b",
"metadata": {},
"source": [
"_________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "3c3450bf-3988-4fae-81bf-b1b583927fcd",
"metadata": {},
"source": [
"In this tutorial, we will go over a basic optimal consumption problem, then extend it to Aiyagari model.\n",
"\n",
"1. A Basic Optimal Consumption Model using Endogenous Grid Method\n",
"2. Extend to Stationary Equilibrium: Solve Aiyagari Model"
]
},
{
"cell_type": "markdown",
"id": "0cdc64f9-746e-4c67-bd80-4429d74aaaea",
"metadata": {},
"source": [
"________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "c84cfaa8-abc9-4964-a0fc-8184c8a0ddfb",
"metadata": {},
"source": [
"# 1. A Basic Optimal Consumption Model using Endogenous Grid Method"
]
},
{
"cell_type": "markdown",
"id": "11629431-1285-4f68-b750-4687a17a8f4d",
"metadata": {},
"source": [
"___________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "90a8cdc5-b70d-479f-bd7d-154ff53e1936",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"ans = 'C:\\Users\\ading\\A_TA_Notes'
"
],
"text/plain": [
"ans = 'C:\\Users\\ading\\A_TA_Notes'"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cd\"C:\\Users\\ading\\A_TA_Notes\"\n",
"pwd"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "a22042a9-6ca4-431a-a4a7-93ad1d361900",
"metadata": {},
"outputs": [],
"source": [
"clear all; % Clears all variables from the workspace\n",
"close all; % Closes all open figure windows\n",
"clc; % Clears the Command Window"
]
},
{
"cell_type": "markdown",
"id": "91edb4ef-d3e9-4250-8028-ea0e4758dcfa",
"metadata": {},
"source": [
"## Parameters"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "0df1d7bf-5862-4275-9b00-a6db5816386b",
"metadata": {},
"outputs": [],
"source": [
"%% Code Cell 1: Basic Parameters\n",
"\n",
"% Households\n",
"gamma = 2; % risk aversion in consumption utility function \n",
"r = 0.04; % The rate at which savings grow\n",
"beta = 0.95; % How much future utility is worth today\n",
"\n",
"% Household income: discretize a normal distribution N(mu,sigma^2)\n",
"y_mu = 1; % mean of distribution\n",
"y_sd = 0.2; % standard deviation of income distribution\n",
"y_grid_size = 5; % number of grid\n",
"\n",
"width = fzero(@(x)discrete_normal(y_grid_size, y_mu, y_sd, x),2);\n",
"[temp, y_grid, y_distribution] = discrete_normal(y_grid_size, y_mu, y_sd, width);\n",
"y_cum_distribution = cumsum(y_distribution); % cumulative distribution\n",
"\n",
"% Asset gridss\n",
"a_grid_size = 500;\n",
"a_max = 50; \n",
"borrow_limit = 0;\n",
"a_grid_power = 0.5; %1 for linear, 0 for L-shaped\n",
"\n",
"a_grid = linspace(0,1,a_grid_size)';\n",
"a_grid = a_grid.^(1./a_grid_power);\n",
"a_grid = borrow_limit + (a_max - borrow_limit).*a_grid;\n",
"\n",
"% Iteration seeting\n",
"iteration_max = 1000; % maxium iteration\n",
"iteration_counter = 0; % iteration counting \n",
"\n",
"iteration_tolerance = 1.0e-6; % Tolerance for convergence \n",
"iteration_diff = 100; % initial difference \n",
"\n",
"% Simulation setting\n",
"simulation_n_size = 50000; % number of simulation individuals\n",
"simulation_t_size = 1000; % number of simulaton periods\n",
"\n",
"%mpc options\n",
"mpc_amount1 = 1.0e-10; %approximate thoeretical mpc\n",
"mpc_amount2 = 0.10; % one percent of average income: approx $500"
]
},
{
"cell_type": "markdown",
"id": "8a0c38f6-52b5-46ea-91e9-1100ec9c18e9",
"metadata": {},
"source": [
"Let's check grid for income."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "5ca0bcaf-0213-466c-a354-6e60073d7a5a",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"y_grid = 5×1 double\n",
" 0.6133\n",
" 0.8066\n",
" 1.0000\n",
" 1.1934\n",
" 1.3867\n",
""
],
"text/plain": [
"y_grid = 5×1 double\n",
" 0.6133\n",
" 0.8066\n",
" 1.0000\n",
" 1.1934\n",
" 1.3867\n"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
"y_distribution = 5×1 double\n",
" 0.0735\n",
" 0.2409\n",
" 0.3712\n",
" 0.2409\n",
" 0.0735\n",
""
],
"text/plain": [
"y_distribution = 5×1 double\n",
" 0.0735\n",
" 0.2409\n",
" 0.3712\n",
" 0.2409\n",
" 0.0735\n"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_grid\n",
"y_distribution"
]
},
{
"cell_type": "markdown",
"id": "c9360880-14ae-49eb-b219-b542a32a13bd",
"metadata": {},
"source": [
"As we do in last tutorial, we set local function to facilitate expression"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "856cfc98-9c37-4b31-a5cc-c809bce8a3e9",
"metadata": {},
"outputs": [],
"source": [
"%% Code Cell 2: Local function to facilitate expression\n",
"\n",
"% Utility function\n",
"if gamma == 1\n",
" u = @(c)log(c);\n",
"else \n",
" u = @(c)(c.^(1-gamma)-1)./(1-gamma);\n",
"end \n",
"\n",
"% Derivative of utility function to consumption\n",
"u1 = @(c) c.^(-gamma); \n",
"\n",
"% When we have u1, how to get consumption.\n",
"u1_inverse = @(u) u.^(-1./gamma);"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "af435f52-4a41-4e68-8772-4ff84ecc421f",
"metadata": {},
"outputs": [],
"source": [
"%% Code Cell 3: Initialize value functions and consumption function\n",
"\n",
"C_current = zeros(a_grid_size, y_grid_size); % current consumption\n",
"C_endo = zeros(a_grid_size, y_grid_size); % endogenous consumption from Euler equation\n",
"C_next = zeros(a_grid_size, y_grid_size); % next consumption from interpolation/budget constraint \n",
"A_endo = zeros(a_grid_size, y_grid_size); % endogenous asset from budget constraint\n",
"A_next = zeros(a_grid_size, y_grid_size); % next asset from interpolation/budget constraint\n",
"\n",
"[A_matrix Y_matrix]=ndgrid(a_grid, y_grid);\n",
"C_guess = r * A_matrix + Y_matrix; % initial guess of consupmtion\n",
"% Equivalent to: \n",
"% C_guess = zeros(a_grid_size,y_grid_size);\n",
"% for i_y = 1:y_grid_size\n",
"% C_guess(:,i_y) = r.*a_grid+y_grid(i_y);\n",
"% end"
]
},
{
"cell_type": "markdown",
"id": "5eca7de8-8648-43e1-ac8b-16cc924006ab",
"metadata": {},
"source": [
"You may wonder where is \"A_current\". A_current is fixed, which is exactly A_matrix."
]
},
{
"cell_type": "markdown",
"id": "ec5f9a96-def2-4341-a16b-a071fcf87db6",
"metadata": {},
"source": [
"## Iteration"
]
},
{
"cell_type": "markdown",
"id": "a1e53f99-1968-4c8f-81ba-11bce5e6eaff",
"metadata": {},
"source": [
"Then, we iterate using endogenous grid method."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "c1229619-8e12-4776-8a25-cc296cea0f17",
"metadata": {},
"outputs": [
{
"data": {
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"A_next = 500×5 double\n",
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration no. 1 max con fn diff is 50\n"
]
},
{
"data": {
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" 0 0 0.0860 0.2424 0.4218\n",
" 0 0 0.0870 0.2437 0.4232\n",
" 0 0 0.0883 0.2453 0.4250\n",
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" 0 0 0.0918 0.2498 0.4298\n",
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"..."
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"A_next = 500×5 double\n",
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" 0 0 0.0918 0.2498 0.4298\n",
" 0 0 0.0939 0.2525 0.4328\n",
" 0 0 0.0964 0.2556 0.4362\n",
"..."
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration no. 2 max con fn diff is 49.8381\n"
]
},
{
"data": {
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"A_next = 500×5 double\n",
" 0 0 0.0881 0.2397 0.4149\n",
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" 0 0 0.0887 0.2404 0.4157\n",
" 0 0 0.0895 0.2413 0.4166\n",
" 0 0 0.0906 0.2425 0.4180\n",
" 0 0 0.0920 0.2440 0.4197\n",
" 0 0 0.0938 0.2459 0.4218\n",
" 0 0 0.0958 0.2482 0.4243\n",
" 0 0 0.0982 0.2509 0.4273\n",
" 0 0 0.1009 0.2540 0.4306\n",
"..."
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"A_next = 500×5 double\n",
" 0 0 0.0881 0.2397 0.4149\n",
" 0 0 0.0882 0.2399 0.4151\n",
" 0 0 0.0887 0.2404 0.4157\n",
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" 0 0 0.0906 0.2425 0.4180\n",
" 0 0 0.0920 0.2440 0.4197\n",
" 0 0 0.0938 0.2459 0.4218\n",
" 0 0 0.0958 0.2482 0.4243\n",
" 0 0 0.0982 0.2509 0.4273\n",
" 0 0 0.1009 0.2540 0.4306\n",
"..."
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration no. 3 max con fn diff is 49.8381\n"
]
},
{
"data": {
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" 0 0 0.0898 0.2394 0.4109\n",
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" 0 0 0.0904 0.2401 0.4116\n",
" 0 0 0.0912 0.2410 0.4126\n",
" 0 0 0.0923 0.2422 0.4140\n",
" 0 0 0.0937 0.2438 0.4157\n",
" 0 0 0.0953 0.2457 0.4178\n",
" 0 0 0.0973 0.2481 0.4203\n",
" 0 0 0.0996 0.2508 0.4232\n",
" 0 0 0.1023 0.2539 0.4265\n",
"..."
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"A_next = 500×5 double\n",
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" 0 0 0.0973 0.2481 0.4203\n",
" 0 0 0.0996 0.2508 0.4232\n",
" 0 0 0.1023 0.2539 0.4265\n",
"..."
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration no. 4 max con fn diff is 0.022531\n"
]
},
{
"data": {
"text/html": [
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" 0 0 0.0906 0.2396 0.4093\n",
" 0 0 0.0917 0.2408 0.4106\n",
" 0 0 0.0931 0.2424 0.4124\n",
" 0 0 0.0948 0.2443 0.4145\n",
" 0 0 0.0967 0.2465 0.4169\n",
" 0 0 0.0990 0.2492 0.4198\n",
" 0 0 0.1016 0.2522 0.4230\n",
"..."
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" 0 0 0.0967 0.2465 0.4169\n",
" 0 0 0.0990 0.2492 0.4198\n",
" 0 0 0.1016 0.2522 0.4230\n",
"..."
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration no. 5 max con fn diff is 0.016748\n"
]
},
{
"data": {
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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{
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"output_type": "stream",
"text": [
"Iteration no. 6 max con fn diff is 0.015426\n"
]
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" 0 0 0.0890 0.2359 0.4027\n",
" 0 0 0.0901 0.2371 0.4040\n",
" 0 0 0.0914 0.2386 0.4057\n",
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" 0 0 0.0951 0.2427 0.4102\n",
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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"output_type": "stream",
"text": [
"Iteration no. 7 max con fn diff is 0.014611\n"
]
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" 0 0 0.0922 0.2387 0.4048\n",
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
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"output_type": "stream",
"text": [
"Iteration no. 8 max con fn diff is 0.013974\n"
]
},
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]
},
"execution_count": 7,
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"text": [
"Iteration no. 9 max con fn diff is 0.013423\n"
]
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"text": [
"Iteration no. 10 max con fn diff is 0.012917\n"
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"text": [
"Iteration no. 11 max con fn diff is 0.012437\n"
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"text": [
"Iteration no. 12 max con fn diff is 0.011977\n"
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"text": [
"Iteration no. 13 max con fn diff is 0.011535\n"
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"text": [
"Iteration no. 14 max con fn diff is 0.011113\n"
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"text": [
"Iteration no. 15 max con fn diff is 0.010703\n"
]
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"text": [
"Iteration no. 16 max con fn diff is 0.010312\n"
]
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"text": [
"Iteration no. 17 max con fn diff is 0.0099303\n"
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"text": [
"Iteration no. 18 max con fn diff is 0.0095659\n"
]
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"text": [
"Iteration no. 19 max con fn diff is 49.9988\n"
]
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"text": [
"Iteration no. 20 max con fn diff is 49.9988\n"
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"text": [
"Iteration no. 21 max con fn diff is 49.9958\n"
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"text": [
"Iteration no. 22 max con fn diff is 49.9958\n"
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"text": [
"Iteration no. 23 max con fn diff is 49.9865\n"
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" 0 0 0.0816 0.2224 0.3801\n",
" 0 0 0.0827 0.2236 0.3813\n",
" 0 0 0.0840 0.2250 0.3829\n",
" 0 0 0.0856 0.2267 0.3848\n",
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" 0 0 0.0897 0.2312 0.3897\n",
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"..."
]
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"execution_count": 7,
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"text": [
"Iteration no. 24 max con fn diff is 49.9865\n"
]
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"text": [
"Iteration no. 25 max con fn diff is 49.9774\n"
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"text": [
"Iteration no. 26 max con fn diff is 49.9774\n"
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"text": [
"Iteration no. 27 max con fn diff is 49.969\n"
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"text": [
"Iteration no. 28 max con fn diff is 49.969\n"
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"text": [
"Iteration no. 29 max con fn diff is 49.9612\n"
]
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"text": [
"Iteration no. 30 max con fn diff is 49.9612\n"
]
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"text": [
"Iteration no. 31 max con fn diff is 49.954\n"
]
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"text": [
"Iteration no. 32 max con fn diff is 49.954\n"
]
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"text": [
"Iteration no. 33 max con fn diff is 49.9474\n"
]
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"text": [
"Iteration no. 34 max con fn diff is 49.9474\n"
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"text": [
"Iteration no. 35 max con fn diff is 49.9412\n"
]
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"text": [
"Iteration no. 36 max con fn diff is 49.9412\n"
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"text": [
"Iteration no. 37 max con fn diff is 49.9356\n"
]
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"text": [
"Iteration no. 38 max con fn diff is 49.9356\n"
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"text": [
"Iteration no. 39 max con fn diff is 49.9304\n"
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"text": [
"Iteration no. 40 max con fn diff is 0.069343\n"
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"text": [
"Iteration no. 41 max con fn diff is 49.9998\n"
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"text": [
"Iteration no. 42 max con fn diff is 49.9235\n"
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"text": [
"Iteration no. 43 max con fn diff is 0.067045\n"
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"text": [
"Iteration no. 44 max con fn diff is 0.0032958\n"
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"text": [
"Iteration no. 45 max con fn diff is 0.0031623\n"
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"text": [
"Iteration no. 46 max con fn diff is 0.0030312\n"
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"text": [
"Iteration no. 47 max con fn diff is 0.0029078\n"
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"text": [
"Iteration no. 48 max con fn diff is 0.0027873\n"
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"text": [
"Iteration no. 49 max con fn diff is 0.0026695\n"
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"text": [
"Iteration no. 50 max con fn diff is 0.0025563\n"
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"text": [
"Iteration no. 51 max con fn diff is 0.0024478\n"
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"text": [
"Iteration no. 52 max con fn diff is 0.0023438\n"
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"text": [
"Iteration no. 53 max con fn diff is 0.0022441\n"
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"text": [
"Iteration no. 55 max con fn diff is 0.002057\n"
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"text": [
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"text": [
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"text": [
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"text": [
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"text": [
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"text": [
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"text": [
"Iteration no. 62 max con fn diff is 0.0015147\n"
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"text": [
"Iteration no. 63 max con fn diff is 0.0014498\n"
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"text": [
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"text": [
"Iteration no. 65 max con fn diff is 0.0013279\n"
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"text": [
"Iteration no. 66 max con fn diff is 0.0012709\n"
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"text": [
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"Iteration no. 68 max con fn diff is 0.0011639\n"
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"Iteration no. 78 max con fn diff is 0.00074919\n"
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"Iteration no. 80 max con fn diff is 0.00068591\n"
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"Iteration no. 81 max con fn diff is 0.00065629\n"
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"text": [
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"text": [
"Iteration no. 93 max con fn diff is 0.00038631\n"
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"text": [
"Iteration no. 94 max con fn diff is 0.00036962\n"
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"text": [
"Iteration no. 95 max con fn diff is 0.00035365\n"
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"text": [
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"text": [
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"Iteration no. 112 max con fn diff is 0.00016703\n"
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"text": [
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"text": [
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"..."
]
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"text": [
"Iteration no. 127 max con fn diff is 8.6333e-05\n"
]
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"text": [
"Iteration no. 129 max con fn diff is 7.9076e-05\n"
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"text": [
"Iteration no. 130 max con fn diff is 7.5681e-05\n"
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"text": [
"Iteration no. 131 max con fn diff is 7.2433e-05\n"
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"text": [
"Iteration no. 132 max con fn diff is 6.9325e-05\n"
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"text": [
"Iteration no. 133 max con fn diff is 6.6352e-05\n"
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"text": [
"Iteration no. 134 max con fn diff is 6.3506e-05\n"
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"text": [
"Iteration no. 135 max con fn diff is 6.0784e-05\n"
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"text": [
"Iteration no. 136 max con fn diff is 5.8179e-05\n"
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"text": [
"Iteration no. 137 max con fn diff is 5.5687e-05\n"
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"text": [
"Iteration no. 138 max con fn diff is 5.3302e-05\n"
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"text": [
"Iteration no. 139 max con fn diff is 5.102e-05\n"
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"text": [
"Iteration no. 140 max con fn diff is 4.8837e-05\n"
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"text": [
"Iteration no. 141 max con fn diff is 4.6747e-05\n"
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"text": [
"Iteration no. 142 max con fn diff is 4.4748e-05\n"
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"text": [
"Iteration no. 143 max con fn diff is 4.2835e-05\n"
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"text": [
"Iteration no. 144 max con fn diff is 4.1004e-05\n"
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"text": [
"Iteration no. 145 max con fn diff is 3.9253e-05\n"
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"text": [
"Iteration no. 146 max con fn diff is 3.7576e-05\n"
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"text": [
"Iteration no. 147 max con fn diff is 3.5972e-05\n"
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"text": [
"Iteration no. 148 max con fn diff is 3.4437e-05\n"
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"text": [
"Iteration no. 149 max con fn diff is 3.2968e-05\n"
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"text": [
"Iteration no. 150 max con fn diff is 3.1562e-05\n"
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"text": [
"Iteration no. 151 max con fn diff is 3.0217e-05\n"
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"text": [
"Iteration no. 152 max con fn diff is 2.8929e-05\n"
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"text": [
"Iteration no. 153 max con fn diff is 2.7697e-05\n"
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"text": [
"Iteration no. 154 max con fn diff is 2.6518e-05\n"
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"text": [
"Iteration no. 155 max con fn diff is 2.5389e-05\n"
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"text": [
"Iteration no. 156 max con fn diff is 2.4309e-05\n"
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"text": [
"Iteration no. 157 max con fn diff is 2.3275e-05\n"
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"text": [
"Iteration no. 158 max con fn diff is 2.2286e-05\n"
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"text": [
"Iteration no. 159 max con fn diff is 2.1339e-05\n"
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"text": [
"Iteration no. 160 max con fn diff is 2.0433e-05\n"
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"text": [
"Iteration no. 161 max con fn diff is 1.9565e-05\n"
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"text": [
"Iteration no. 162 max con fn diff is 1.8735e-05\n"
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"text": [
"Iteration no. 163 max con fn diff is 1.794e-05\n"
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"text": [
"Iteration no. 164 max con fn diff is 1.718e-05\n"
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"text": [
"Iteration no. 165 max con fn diff is 1.6451e-05\n"
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"text": [
"Iteration no. 166 max con fn diff is 1.5754e-05\n"
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"text": [
"Iteration no. 167 max con fn diff is 1.5087e-05\n"
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"text": [
"Iteration no. 168 max con fn diff is 1.4448e-05\n"
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"text": [
"Iteration no. 169 max con fn diff is 1.3836e-05\n"
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"text": [
"Iteration no. 170 max con fn diff is 1.325e-05\n"
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"..."
]
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"text": [
"Iteration no. 171 max con fn diff is 1.2689e-05\n"
]
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"text": [
"Iteration no. 172 max con fn diff is 1.2151e-05\n"
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"text": [
"Iteration no. 173 max con fn diff is 1.1636e-05\n"
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"text": [
"Iteration no. 174 max con fn diff is 1.1141e-05\n"
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"text": [
"Iteration no. 175 max con fn diff is 1.0667e-05\n"
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"text": [
"Iteration no. 176 max con fn diff is 1.0211e-05\n"
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"text": [
"Iteration no. 177 max con fn diff is 9.7734e-06\n"
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"text": [
"Iteration no. 178 max con fn diff is 9.3523e-06\n"
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"text": [
"Iteration no. 179 max con fn diff is 8.9467e-06\n"
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"text": [
"Iteration no. 180 max con fn diff is 8.5555e-06\n"
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"text": [
"Iteration no. 181 max con fn diff is 8.1778e-06\n"
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"text": [
"Iteration no. 182 max con fn diff is 7.8124e-06\n"
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"text": [
"Iteration no. 183 max con fn diff is 7.4585e-06\n"
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"text": [
"Iteration no. 184 max con fn diff is 7.115e-06\n"
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"text": [
"Iteration no. 185 max con fn diff is 6.7813e-06\n"
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"text": [
"Iteration no. 186 max con fn diff is 6.4565e-06\n"
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"text": [
"Iteration no. 187 max con fn diff is 6.14e-06\n"
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"text": [
"Iteration no. 188 max con fn diff is 5.8312e-06\n"
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"text": [
"Iteration no. 189 max con fn diff is 5.5298e-06\n"
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"text": [
"Iteration no. 190 max con fn diff is 5.2354e-06\n"
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"text": [
"Iteration no. 191 max con fn diff is 4.9479e-06\n"
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"text": [
"Iteration no. 192 max con fn diff is 4.6672e-06\n"
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"text": [
"Iteration no. 193 max con fn diff is 4.3933e-06\n"
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"text": [
"Iteration no. 194 max con fn diff is 4.1265e-06\n"
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"text": [
"Iteration no. 195 max con fn diff is 3.8669e-06\n"
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"text": [
"Iteration no. 196 max con fn diff is 3.6148e-06\n"
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"text": [
"Iteration no. 197 max con fn diff is 3.3707e-06\n"
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"text": [
"Iteration no. 198 max con fn diff is 3.1349e-06\n"
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"text": [
"Iteration no. 199 max con fn diff is 2.9078e-06\n"
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"text": [
"Iteration no. 200 max con fn diff is 2.6898e-06\n"
]
},
{
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
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"name": "stdout",
"output_type": "stream",
"text": [
"Iteration no. 201 max con fn diff is 2.4813e-06\n"
]
},
{
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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"name": "stdout",
"output_type": "stream",
"text": [
"Iteration no. 202 max con fn diff is 2.2825e-06\n"
]
},
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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"name": "stdout",
"output_type": "stream",
"text": [
"Iteration no. 203 max con fn diff is 2.0937e-06\n"
]
},
{
"data": {
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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"name": "stdout",
"output_type": "stream",
"text": [
"Iteration no. 204 max con fn diff is 1.9151e-06\n"
]
},
{
"data": {
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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"name": "stdout",
"output_type": "stream",
"text": [
"Iteration no. 205 max con fn diff is 1.7467e-06\n"
]
},
{
"data": {
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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"output_type": "stream",
"text": [
"Iteration no. 206 max con fn diff is 1.5887e-06\n"
]
},
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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"output_type": "stream",
"text": [
"Iteration no. 207 max con fn diff is 1.441e-06\n"
]
},
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"text": [
"Iteration no. 208 max con fn diff is 1.3035e-06\n"
]
},
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"..."
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
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"output_type": "stream",
"text": [
"Iteration no. 209 max con fn diff is 1.1759e-06\n"
]
},
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"data": {
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"..."
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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"output_type": "stream",
"text": [
"Iteration no. 210 max con fn diff is 1.058e-06\n"
]
},
{
"data": {
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"..."
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"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
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"output_type": "stream",
"text": [
"Iteration no. 211 max con fn diff is 9.4942e-07\n"
]
}
],
"source": [
"%% Code Cell 4: Iteration with Endogenous Grid Points \n",
"\n",
"C_current = C_guess;\n",
"\n",
"while iteration_counter <= iteration_max && iteration_diff > iteration_tolerance\n",
"\n",
" iteration_counter = iteration_counter + 1;\n",
" \n",
" emuc = u1(C_current)*y_distribution; \n",
" % expected marginal utility of consumption\n",
" muc1 = beta.*(1+r).*emuc; \n",
" % new marginal utility from Euler equation\n",
" C_endo = u1_inverse(muc1); \n",
" % endogenous consumption from marginal utility \n",
"\n",
" for i_y = 1:y_grid_size \n",
" % loop over different y\n",
" A_endo(:,i_y) = (C_endo + A_matrix(:,i_y) - Y_matrix(:,i_y))./(1+r); \n",
" % endogenous asset from budget constraint \n",
"\n",
" A_next(:,i_y) = interp1(A_endo(:,i_y), A_matrix(:,i_y), A_matrix(:,i_y));\n",
" % next asset from interpolation \n",
" end\n",
" \n",
" A_next = max(A_next, borrow_limit) \n",
" % borrowing constraint \n",
" C_next = (1 + r) .* A_matrix + Y_matrix - A_next; \n",
" % next consumption from budget constraint\n",
"\n",
" iteration_diff = max(max(abs(C_current - C_next)));\n",
" % update new difference\n",
" C_current = C_next; \n",
" % update current consumption\n",
"\n",
" % disp(['Iteration no. ' int2str(iteration_counter), ' max con fn diff is ' num2str(iteration_diff)]);\n",
"\n",
"end \n",
"\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "6339ba1a-e0b7-4f73-907d-882d26bc42c8",
"metadata": {},
"source": [
"For borrowing constraint binding case, people may have several other ways.\n"
]
},
{
"cell_type": "markdown",
"id": "52ff6052-34e0-4cfc-a721-3d803441bd20",
"metadata": {},
"source": [
"**Alternative 1: Loop over i_a and interpolate over single point**\n",
"terpolate"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "519e846a-30d5-4cc5-9e89-87fc298fd1b2",
"metadata": {},
"outputs": [],
"source": [
" % for ia = 1:na \n",
" % if a_grid(ia) < a_endo(1,iy) %borrowing constraint binds\n",
" % a_next(ia,iy) = borrow_limit; \n",
" % else %borrowing constraint does not bind;\n",
" % a_next(ia,iy) = lininterp1(ass1(:,iy),agrid,agrid(ia)); \n",
" % end \n",
" % end"
]
},
{
"cell_type": "markdown",
"id": "13a58a52-df91-46e2-8a78-2502c8e5c59d",
"metadata": {},
"source": [
"This method needs a local function \"lininterp1\", which is for linear interpolation. "
]
},
{
"cell_type": "markdown",
"id": "93b4ea5e-29dd-4c15-939f-a5c3dff48117",
"metadata": {},
"source": [
"**Alternative 2: Use logical operations to find index where borrowing constraint binds**"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b9f7bf5d-f5c3-4cda-8147-3a208bd2a1e2",
"metadata": {},
"outputs": [],
"source": [
" % bind_index = (A_matrix + Y_matrix - c_next) < 0; %find index where borrowing constraint binds\n",
" % c_next(bind_index) = A_matrix(bind_index) + Y_matrix(bind_index);"
]
},
{
"cell_type": "markdown",
"id": "e2fa2dff-9a56-4536-a579-b3d5b5310d61",
"metadata": {},
"source": [
"The above code just illustrates the idea, we need to modify when use it. "
]
},
{
"cell_type": "markdown",
"id": "36f7668b-0f71-4c2d-9129-c8118c8c6265",
"metadata": {},
"source": [
"## Simulation"
]
},
{
"cell_type": "markdown",
"id": "06392eb7-7949-48bd-a9bd-66a7d6c26a39",
"metadata": {},
"source": [
"Simulate for 1000 periods."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a2363242-e82c-4d9e-b866-95d632cb57ee",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Simulating, time period 100\n",
" Simulating, time period 200\n",
" Simulating, time period 300\n",
" Simulating, time period 400\n",
" Simulating, time period 500\n",
" Simulating, time period 600\n",
" Simulating, time period 700\n",
" Simulating, time period 800\n",
" Simulating, time period 900\n",
" Simulating, time period 1000\n"
]
}
],
"source": [
"%% Code Cell 5: Simulation\n",
"\n",
"%% DRAW RANDOM NUMBERS\n",
"rng(100);\n",
"Y_random = rand(simulation_n_size, simulation_t_size); \n",
"% generate a random matrix, \n",
"% row is n individual, \n",
"% column is t period\n",
"\n",
"Y_simulation_index = zeros(simulation_n_size,simulation_t_size);\n",
"A_simulation = zeros(simulation_n_size,simulation_t_size);\n",
" \n",
"%create interpolating function\n",
"%for i_y = 1:y_grid_size\n",
"% savinterp{i_y} = griddedInterpolant(a_grid,sav(:,i_y),'linear');\n",
"%end\n",
" \n",
"%loop over time periods\n",
"for i_t = 1:simulation_t_size\n",
" if mod(i_t,100) ==0\n",
" disp([' Simulating, time period ' int2str(i_t)]);\n",
" end\n",
" \n",
" %income realization: note we vectorize simulations at once because\n",
" %of matlab, in other languages we would loop over individuals\n",
" Y_simulation_index(Y_random(:,i_t)<= y_cum_distribution(1),i_t) = 1;\n",
" % for those random small than first pdf, give index 1\n",
"\n",
" for i_y = 2:y_grid_size\n",
" Y_simulation_index(Y_random(:,i_t) > y_cum_distribution(i_y - 1) & Y_random(:,i_t) <= y_cum_distribution(i_y),i_t) = i_y;\n",
" end\n",
" % for those random between pdf interval, give index\n",
" \n",
" % asset choice\n",
" if i_t < simulation_t_size\n",
" for i_y = 1 : y_grid_size\n",
" A_simulation(Y_simulation_index(:,i_t)==i_y, i_t + 1) = ...\n",
" interp1(a_grid, A_next(:,i_y), A_simulation(Y_simulation_index(:,i_t)==i_y,i_t));\n",
" end\n",
" end\n",
"\n",
"end\n",
" \n",
"%assign actual income values;\n",
"Y_simulation = y_grid(Y_simulation_index);"
]
},
{
"cell_type": "markdown",
"id": "95aae1c0-7af1-42d3-8754-5aa697a1ac96",
"metadata": {},
"source": [
"People sometimes use **griddedInterpolant**, since it enables object to interpolate, which is very flexible.\n",
"\n",
"In order to not learn something new nor complicated, I still use **interp1** here. \n",
"\n",
"I prefer to learn as less as possible, learning too much makes me tired."
]
},
{
"cell_type": "markdown",
"id": "1c40b01b-2a53-4a6c-8c3a-961757d17168",
"metadata": {},
"source": [
"## Graph"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "19c6ca2d-bcf0-41f2-9279-0026280c4b00",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean assets (relative to mean income) : 0.55045\n",
"Fraction borrowing constrained: 2.96%\n",
"10th Percentile: 0.11735\n",
"50th Percentile: 0.49915\n",
"90th Percentile: 1.0425\n",
"99th Percentile: 1.5788\n"
]
}
],
"source": [
"%% Code Cell 6: Make Plots\n",
"\n",
"figure(1);\n",
" \n",
"% consumption policy function\n",
"subplot(3,2,1);\n",
"plot(a_grid,C_next(:,1),'b-',a_grid,C_next(:,y_grid_size),'r-','LineWidth',1);\n",
"grid;\n",
"xlim([0 a_max]);\n",
"title('Consumption Policy Function');\n",
"legend('Lowest income state','Highest income state');\n",
"\n",
"% savings policy function\n",
"subplot(3,2,2);\n",
"plot(a_grid,A_next(:,1)-a_grid,'b-',a_grid,A_next(:,y_grid_size)-a_grid,'r-','LineWidth',1);\n",
"hold on;\n",
"plot(a_grid,zeros(a_grid_size,1),'k','LineWidth',0.5);\n",
"hold off;\n",
"grid;\n",
"xlim([0 a_max]);\n",
"title('Savings Policy Function (a''-a)');\n",
" \n",
"% consumption policy function: zoomed in\n",
"subplot(3,2,3);\n",
"plot(a_grid,C_next(:,1),'b-o',a_grid,C_next(:,y_grid_size),'r-o','LineWidth',2);\n",
"grid;\n",
"xlim([0 1]);\n",
"title('Consumption: Zoomed'); \n",
" \n",
"%income distribution\n",
"subplot(3,2,4);\n",
"hist(Y_simulation(:,simulation_t_size),y_grid);\n",
"h = findobj(gca,'Type','patch');\n",
"set(h,'FaceColor',[0 0.5 0.5],'EdgeColor','blue','LineStyle','-');\n",
"ylabel('')\n",
"title('Income distribution');\n",
" \n",
"%asset distribution\n",
"subplot(3,2,5);\n",
"hist(A_simulation(:,simulation_t_size),100);\n",
"h = findobj(gca,'Type','patch');\n",
"set(h,'FaceColor',[.7 .7 .7],'EdgeColor','black','LineStyle','-');\n",
"ylabel('')\n",
"title('Asset distribution');\n",
"\n",
"%convergence check\n",
"subplot(3,2,6);\n",
"plot([1:simulation_t_size]',mean(A_simulation,1),'k-','LineWidth',1.5);\n",
"ylabel('Time Period');\n",
"title('Mean Asset Convergence');\n",
" \n",
" \n",
"% asset distribution statistics\n",
"aysim = A_simulation(:,simulation_t_size) ./ mean(Y_simulation(:,simulation_t_size));\n",
"disp(['Mean assets (relative to mean income) : ' num2str(mean(aysim))]);\n",
"disp(['Fraction borrowing constrained: ' num2str(sum(aysim==borrow_limit)./simulation_n_size * 100) '%']);\n",
"disp(['10th Percentile: ' num2str(quantile(aysim,.1))]);\n",
"disp(['50th Percentile: ' num2str(quantile(aysim,.5))]);\n",
"disp(['90th Percentile: ' num2str(quantile(aysim,.9))]);\n",
"disp(['99th Percentile: ' num2str(quantile(aysim,.99))]);"
]
},
{
"cell_type": "markdown",
"id": "d0444c87-de6c-4aa0-92f1-002744bafa65",
"metadata": {},
"source": [
"## Compute MPC"
]
},
{
"cell_type": "markdown",
"id": "8d6aa2c5-983c-49d0-86b8-7d1d2e8edcdc",
"metadata": {},
"source": [
"When MPC is very small, an increase in asset almost has no effect on consumption. So, we have:"
]
},
{
"cell_type": "markdown",
"id": "74d7bb3c-7825-46a2-8540-6c2235e328d7",
"metadata": {},
"source": [
"$$\n",
"u'(1+MPC) = \\beta (1+r) u'(1+r)\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"id": "4b7b4a29-5f82-4569-8f44-73a03cc797bb",
"metadata": {},
"source": [
"$$\n",
"(1+MPC)^{-\\gamma} = \\beta(1+r) (1+r)^{-\\gamma}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "2fe24848-443b-4547-b481-0eef1e4e862c",
"metadata": {},
"source": [
"Rearrange and get:"
]
},
{
"cell_type": "markdown",
"id": "bb6742d8-b4f1-44ce-af65-f81598c3ba38",
"metadata": {},
"source": [
"$$\n",
"MPC = (1+r)[\\beta (1+r)]^{-\\frac{1}{\\gamma}} - 1\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "5ebe4cd0-3d76-4c5c-a942-cce8f652955e",
"metadata": {},
"source": [
"In the following code, griddedInterpolant is used instead of interp1, for its object. \n",
"\n",
"If we use interp1, the code is too long."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "a3ded612-7af1-4181-98ff-c345b0fd2e4f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean MPC amount 1: 0.19102\n",
"Mean MPC amount 2: 0.17411\n"
]
}
],
"source": [
"%% Code Cell 7: Compute MPCs\n",
"\n",
" \n",
"%theoretical mpc lower bound\n",
"mpc_limit = (1+r)*((beta*(1+r))^-(1./gamma))-1;\n",
" \n",
"for i_y = 1:y_grid_size\n",
" %create interpolating function\n",
" C_interp{i_y} = griddedInterpolant(a_grid,C_current(:,i_y),'linear');\n",
" \n",
" mpc1(:,i_y) = ( C_interp{i_y}(a_grid+mpc_amount1) - C_current(:,i_y) ) ./ mpc_amount1;\n",
" mpc2(:,i_y) = ( C_interp{i_y}(a_grid+mpc_amount2) - C_current(:,i_y) ) ./ mpc_amount2;\n",
" \n",
"end\n",
"\n",
" \n",
"figure(2);\n",
" \n",
"% mpc functions\n",
"subplot(1,2,1);\n",
"plot(a_grid,mpc1(:,1),'b-',a_grid,mpc2(:,1),'b--',...\n",
" a_grid,mpc1(:,y_grid_size),'r-',a_grid,mpc2(:,y_grid_size),'r--','LineWidth',1);\n",
"hold on;\n",
"plot(a_grid,mpc_limit.*ones(size(a_grid)),'k:','LineWidth',2); \n",
"hold off;\n",
"grid on;\n",
"xlim([0 10]);\n",
"title('MPC Function');\n",
"legend('Lowest income state: amount 1','Lowest income state: amount 1',...\n",
" 'Highest income state: amount 2','Lowest income state: amount 2',...\n",
" ['Theoretical MPC limit = ', num2str(mpc_limit)],'Location','NorthEast');\n",
" \n",
"% mpc distribution\n",
"mpc1_simulation = zeros(simulation_n_size,1);\n",
"mpc2_simulation = zeros(simulation_n_size,1);\n",
"for i_y = 1:y_grid_size\n",
" mpc1_simulation(Y_simulation_index(:,simulation_t_size)==i_y) = ...\n",
" ( C_interp{i_y}(A_simulation(Y_simulation_index(:,simulation_t_size)==i_y,simulation_t_size) + mpc_amount1) ...\n",
" - C_interp{i_y}(A_simulation(Y_simulation_index(:,simulation_t_size)==i_y,simulation_t_size)) ) ./ mpc_amount1;\n",
" mpc2_simulation(Y_simulation_index(:,simulation_t_size)==i_y) = ...\n",
" ( C_interp{i_y}(A_simulation(Y_simulation_index(:,simulation_t_size)==i_y,simulation_t_size) + mpc_amount2) ...\n",
" - C_interp{i_y}(A_simulation(Y_simulation_index(:,simulation_t_size)==i_y,simulation_t_size)) ) ./ mpc_amount2;\n",
"end\n",
" \n",
"subplot(1,2,2);\n",
"histogram(mpc1_simulation,[0:0.02:1.5]);\n",
"grid on;\n",
"h = findobj(gca,'Type','patch');\n",
"set(h,'FaceColor',[.7 .7 .7],'EdgeColor','black','LineStyle','-');\n",
"ylabel('')\n",
"title('MPC distribution');\n",
" \n",
"% mpc distribution statistics\n",
"disp(['Mean MPC amount 1: ' num2str(mean(mpc1_simulation))]);\n",
"disp(['Mean MPC amount 2: ' num2str(mean(mpc2_simulation))]);\n",
" "
]
},
{
"cell_type": "markdown",
"id": "c79effc8-1bdc-414f-854f-92a34d76f907",
"metadata": {},
"source": [
"______________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "14c8c90a-6497-4563-8aa5-fea13727fffc",
"metadata": {},
"source": [
"# 2. Extend to Stationary Equilibrium: Solve Aiyagari Model"
]
},
{
"cell_type": "markdown",
"id": "a218df49-7085-4122-a3bd-bbca447862fa",
"metadata": {},
"source": [
"_____________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "e5fe65f9-1f6a-46dc-a9e7-ead700091047",
"metadata": {},
"source": [
"In the basic model, interest rate and income is exogenous. In stationary equilibiurm of Aiyagari model, these two variables are endogenous."
]
},
{
"cell_type": "markdown",
"id": "d1f646ec-6a0f-46fd-9c7d-5ed20355e21e",
"metadata": {},
"source": [
"The process to solve Aiyagari Model is as follows."
]
},
{
"cell_type": "markdown",
"id": "ae22cd1f-804a-43dd-a02f-9127ee8d0d88",
"metadata": {},
"source": [
"\n",
"
![](\"./Figures/Aiyagari_1.jpg\")
\n",
"
\n",
"
![](\"./Figures/Aiyagari_2.jpg\")
\n",
"
ans = 'C:\\Users\\ading\\A_TA_Notes'
"
],
"text/plain": [
"ans = 'C:\\Users\\ading\\A_TA_Notes'"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cd\"C:\\Users\\ading\\A_TA_Notes\"\n",
"pwd"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "eafa5929-1931-4bfe-a776-959e71acd65d",
"metadata": {},
"outputs": [],
"source": [
"clear all; % Clears all variables from the workspace\n",
"close all; % Closes all open figure windows\n",
"clc; % Clears the Command Window"
]
},
{
"cell_type": "markdown",
"id": "a27f19be-77cf-40d5-b724-7e012edb76b5",
"metadata": {},
"source": [
"In parameters part, compared to basic model, changes are:\n",
"\n",
" No longer give exogenous interst rate r. Introduce production parameters to calculate r.\n",
"\n",
" Give one more set iteration parameters for capital K loop. And give initial guess of r and capital K."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "d76a1a88-fbc7-40a8-a711-c74d461956b8",
"metadata": {},
"outputs": [],
"source": [
"%% Code Cell 8: Parameters for Aiyagari\n",
"\n",
"% Households\n",
"gamma = 2; % risk aversion in consumption utility function \n",
"beta = 0.95; % How much future utility is worth today\n",
"\n",
"% Production\n",
"deprec = 0.10;\n",
"capshare = 0.4;\n",
"\n",
"% Household income: discretize a normal distribution N(mu,sigma^2)\n",
"y_mu = 1; % mean of distribution\n",
"y_sd = 0.2; % standard deviation of income distribution\n",
"y_grid_size = 5; % number of grid\n",
"\n",
"width = fzero(@(x)discrete_normal(y_grid_size, y_mu, y_sd, x),2);\n",
"[temp, y_grid, y_distribution] = discrete_normal(y_grid_size, y_mu, y_sd, width);\n",
"y_cum_distribution = cumsum(y_distribution); % cumulative distribution\n",
"\n",
"% Asset gridss\n",
"a_grid_size = 50;\n",
"a_max = 50; \n",
"borrow_limit = 0;\n",
"a_grid_power = 0.5; %1 for linear, 0 for L-shaped\n",
"\n",
"a_grid = linspace(0,1,a_grid_size)';\n",
"a_grid = a_grid.^(1./a_grid_power);\n",
"a_grid = borrow_limit + (a_max - borrow_limit).*a_grid;\n",
"\n",
"% Iteration setting\n",
"iteration_max = 1000; % maxium iteration\n",
"iteration_tolerance = 1.0e-6; % Tolerance for convergence \n",
"\n",
"\n",
"% Simulation setting\n",
"simulation_n_size = 50000; % number of simulation individuals\n",
"simulation_t_size = 1000; % number of simulaton periods\n",
"\n",
"% Iteration setting for capital\n",
"iteration_max_KL = 70;\n",
"iteration_tolerance_KL = 1.0e-5;\n",
"step_KL = 0.005;\n",
"\n",
"\n",
"\n",
"r_guess = 1./beta-1 - 0.001; % a bit lower than inverse of discount rate\n",
"KLratio_guess = ((r_guess + deprec)/capshare)^(1/(capshare - 1));"
]
},
{
"cell_type": "markdown",
"id": "34cf4ccc-8ae3-4a64-9846-b1ac2eace01b",
"metadata": {},
"source": [
"Run \"Code Cell 2: Local function to facilitate expression\". "
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "8e399863-872c-4aa7-9d09-56917dd41bdc",
"metadata": {},
"outputs": [],
"source": [
"%% Code Cell 2: Local function to facilitate expression\n",
"\n",
"% Utility function\n",
"if gamma == 1\n",
" u = @(c)log(c);\n",
"else \n",
" u = @(c)(c.^(1-gamma)-1)./(1-gamma);\n",
"end \n",
"\n",
"% Derivative of utility function to consumption\n",
"u1 = @(c) c.^(-gamma); \n",
"\n",
"% When we have u1, how to get consumption.\n",
"u1_inverse = @(u) u.^(-1./gamma);"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "5056d199-958a-44ed-b38b-b157071caf5f",
"metadata": {},
"outputs": [],
"source": [
"%% Code Cell 3: Initialize value functions and consumption function\n",
"\n",
"C_current = zeros(a_grid_size, y_grid_size); % current consumption\n",
"C_endo = zeros(a_grid_size, y_grid_size); % endogenous consumption from Euler equation\n",
"C_next = zeros(a_grid_size, y_grid_size); % next consumption from interpolation/budget constraint \n",
"A_endo = zeros(a_grid_size, y_grid_size); % endogenous asset from budget constraint\n",
"A_next = zeros(a_grid_size, y_grid_size); % next asset from interpolation/budget constraint\n",
"\n",
"[A_matrix Y_matrix]=ndgrid(a_grid, y_grid);"
]
},
{
"cell_type": "markdown",
"id": "2bdb83e1-8fed-491c-8334-036287081c61",
"metadata": {},
"source": [
"We need to simulate individuals first, so that we can get aggregate capital."
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "234ee9eb-8edd-4dc4-a4dc-0accac8dab4b",
"metadata": {},
"outputs": [],
"source": [
"%% Code Cell 9: Simulate labor efficiency realizations\n",
"\n",
"% Draw random numbers\n",
"rng(100);\n",
"Y_random = rand(simulation_n_size, simulation_t_size);\n",
"\n",
"% Simulate\n",
"Y_simulation_index = zeros(simulation_n_size, simulation_t_size);\n",
" \n",
"for i_t = 1 : simulation_t_size\n",
" %income realization: note we vectorize simulations at once because\n",
" %of matlab, in other languages we would loop over individuals\n",
" Y_simulation_index( Y_random(:,i_t) <= y_cum_distribution(1), i_t ) = 1;\n",
" for i_y = 2:y_grid_size\n",
" Y_simulation_index( Y_random(:,i_t) > y_cum_distribution(i_y-1) & Y_random(:,i_t) <= y_cum_distribution(i_y), i_t) = i_y;\n",
" end\n",
"end\n",
" \n",
"Y_simulation = y_grid(Y_simulation_index);\n",
"\n",
"% initial simulation for asset\n",
"A_simulation = zeros(simulation_n_size,simulation_t_size);"
]
},
{
"cell_type": "markdown",
"id": "83e71c9e-ca5f-4db9-9448-994fb36e06b4",
"metadata": {},
"source": [
"## Iteration"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "b19f4183-f3e8-45a3-86e0-aebb17099de9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Equm iter 1, r = 0.051632, KL ratio: 3.5309 KL diff: -29.8917%\n",
"Equm iter 2, r = 0.051768, KL ratio: 4.0401 KL diff: -19.6614%\n",
"Equm iter 3, r = 0.051857, KL ratio: 4.5026 KL diff: -10.3761%\n",
"Equm iter 4, r = 0.051905, KL ratio: 4.871 KL diff: -2.9935%\n",
"Equm iter 5, r = 0.051918, KL ratio: 5.1041 KL diff: 1.6649%\n",
"Equm iter 6, r = 0.051911, KL ratio: 5.2025 KL diff: 3.6154%\n",
"Equm iter 7, r = 0.051894, KL ratio: 5.2034 KL diff: 3.6154%\n",
"Equm iter 8, r = 0.051878, KL ratio: 5.1555 KL diff: 2.6434%\n",
"Equm iter 9, r = 0.051866, KL ratio: 5.0972 KL diff: 1.4694%\n",
"Equm iter 10, r = 0.051859, KL ratio: 5.0498 KL diff: 0.51677%\n",
"Equm iter 11, r = 0.051857, KL ratio: 5.0201 KL diff: -0.077136%\n",
"Equm iter 12, r = 0.051857, KL ratio: 5.0067 KL diff: -0.34339%\n",
"Equm iter 13, r = 0.051859, KL ratio: 5.0046 KL diff: -0.38225%\n",
"Equm iter 14, r = 0.05186, KL ratio: 5.0086 KL diff: -0.30064%\n",
"Equm iter 15, r = 0.051862, KL ratio: 5.0145 KL diff: -0.18152%\n",
"Equm iter 16, r = 0.051862, KL ratio: 5.0198 KL diff: -0.075194%\n",
"Equm iter 17, r = 0.051863, KL ratio: 5.0234 KL diff: -0.0030061%\n",
"Equm iter 18, r = 0.051863, KL ratio: 5.0253 KL diff: 0.033456%\n",
"Equm iter 19, r = 0.051863, KL ratio: 5.0257 KL diff: 0.042767%\n",
"Equm iter 20, r = 0.051862, KL ratio: 5.0254 KL diff: 0.036261%\n",
"Equm iter 21, r = 0.051862, KL ratio: 5.0248 KL diff: 0.023653%\n",
"Equm iter 22, r = 0.051862, KL ratio: 5.0242 KL diff: 0.011321%\n",
"Equm iter 23, r = 0.051862, KL ratio: 5.0237 KL diff: 0.0023308%\n",
"Equm iter 24, r = 0.051862, KL ratio: 5.0235 KL diff: -0.0026813%\n",
"Equm iter 25, r = 0.051862, KL ratio: 5.0234 KL diff: -0.0044368%\n",
"Equm iter 26, r = 0.051862, KL ratio: 5.0234 KL diff: -0.0041377%\n",
"Equm iter 27, r = 0.051862, KL ratio: 5.0235 KL diff: -0.002909%\n",
"Equm iter 28, r = 0.051862, KL ratio: 5.0235 KL diff: -0.001545%\n",
"Equm iter 29, r = 0.051862, KL ratio: 5.0236 KL diff: -0.00047084%\n"
]
}
],
"source": [
"%% Iterate over Kl ratio\n",
"\n",
"KLratio = KLratio_guess;\n",
"\n",
"iteration_counter_KL = 0;\n",
"iteration_diff_KL = 100; \n",
"while iteration_counter_KL <= iteration_max_KL && abs(iteration_diff_KL)>iteration_tolerance_KL\n",
" iteration_counter_KL = iteration_counter_KL + 1;\n",
"\n",
" r = capshare.*KLratio^(capshare-1) - deprec;\n",
" R = 1+r;\n",
" wage= (1-capshare).* KLratio^capshare;\n",
" % rescale efficiency units of labor so that output = 1.\n",
" % yscale = Y/L\n",
" yscale = (KLratio^-capshare)./(y_grid'*y_distribution);\n",
"\n",
" C_guess = r.*A_matrix + wage.* yscale.*Y_matrix;\n",
" C_current = C_guess;\n",
"\n",
"\n",
" % solve for policy functions with EGP\n",
" % this part is almost same as that in basic model,\n",
" % except that \"wage.* yscale.*\" before \"Y_matrix\".\n",
"\n",
" iteration_counter = 0; % iteration counting \n",
" iteration_diff = 100; % initial difference \n",
" while iteration_counter <= iteration_max && iteration_diff > iteration_tolerance\n",
"\n",
" iteration_counter = iteration_counter + 1;\n",
" \n",
" emuc = u1(C_current)*y_distribution; % expected marginal utility of consumption\n",
" muc1 = beta.*(1+r).*emuc; % new marginal utility from Euler equation\n",
" C_endo = u1_inverse(muc1); % endogenous consumption from marginal utility \n",
"\n",
" for i_y = 1:y_grid_size \n",
" % loop over different y\n",
" A_endo(:,i_y) = (C_endo + A_matrix(:,i_y) - wage.* yscale.* Y_matrix(:,i_y))./(1+r); \n",
" % endogenous asset from budget constraint \n",
"\n",
" A_next(:,i_y) = interp1(A_endo(:,i_y), A_matrix(:,i_y), A_matrix(:,i_y));\n",
" % next asset from interpolation \n",
" end\n",
" \n",
" A_next = max(A_next, borrow_limit); % borrowing constraint \n",
" C_next = (1 + r) .* A_matrix + wage.* yscale.* Y_matrix - A_next; % next consumption from budget constraint\n",
"\n",
" iteration_diff = max(max(abs(C_current - C_next)));% update new difference\n",
" C_current = C_next; % update current consumption\n",
"\n",
" % disp(['Iteration no. ' int2str(iteration_counter), ' max con fn diff is ' num2str(iteration_diff)]);\n",
" end \n",
"\n",
"\n",
" %simulate: start at assets from last interation\n",
" A_simulation(:,1) = A_simulation(:,simulation_t_size);\n",
" \n",
" %create interpolating function\n",
" for i_y = 1:y_grid_size\n",
" savinterp{i_y} = griddedInterpolant(a_grid,A_next(:,i_y),'linear');\n",
" end\n",
" \n",
" %loop over time periods\n",
" for i_t = 1:simulation_t_size \n",
" % asset choice\n",
" if i_t