{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<a id='aiyagari'></a>\n",
    "<div id=\"qe-notebook-header\" style=\"text-align:right;\">\n",
    "        <a href=\"https://quantecon.org/\" title=\"quantecon.org\">\n",
    "                <img style=\"width:250px;display:inline;\" src=\"https://assets.quantecon.org/img/qe-menubar-logo.svg\" alt=\"QuantEcon\">\n",
    "        </a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Aiyagari Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contents\n",
    "\n",
    "- [The Aiyagari Model](#The-Aiyagari-Model)  \n",
    "  - [Overview](#Overview)  \n",
    "  - [The Economy](#The-Economy)  \n",
    "  - [Firms](#Firms)  \n",
    "  - [Code](#Code)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "In this lecture we describe the structure of a class of models that build on work by Truman Bewley [[Bew77]](../zreferences.html#bewley1977).\n",
    "\n",
    "We begin by discussing an example of a Bewley model due to <a href=/_static/pdfs/aiyagari_obit.pdf download>Rao Aiyagari</a>.\n",
    "\n",
    "The model features\n",
    "\n",
    "- Heterogeneous agents.  \n",
    "- A single exogenous vehicle for borrowing and lending.  \n",
    "- Limits on amounts individual agents may borrow.  \n",
    "\n",
    "\n",
    "The Aiyagari model has been used to investigate many topics, including\n",
    "\n",
    "- precautionary savings and the effect of liquidity constraints [[Aiy94]](../zreferences.html#aiyagari1994)  \n",
    "- risk sharing and asset pricing [[HL96]](../zreferences.html#heaton1996)  \n",
    "- the shape of the wealth distribution [[BBZ15]](../zreferences.html#benhabib2015)  \n",
    "- etc., etc., etc.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "\n",
    "The primary reference for this lecture is [[Aiy94]](../zreferences.html#aiyagari1994).\n",
    "\n",
    "A textbook treatment is available in chapter 18 of [[LS18]](../zreferences.html#ljungqvist2012).\n",
    "\n",
    "A continuous time version of the model by SeHyoun Ahn and Benjamin Moll can be found [here](http://nbviewer.jupyter.org/github/QuantEcon/QuantEcon.notebooks/blob/master/aiyagari_continuous_time.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Economy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Households\n",
    "\n",
    "Infinitely lived households / consumers face idiosyncratic income shocks.\n",
    "\n",
    "A unit interval of  *ex ante* identical households face a common borrowing constraint.\n",
    "\n",
    "The savings problem faced by a typical  household is\n",
    "\n",
    "$$\n",
    "\\max \\mathbb E \\sum_{t=0}^{\\infty} \\beta^t u(c_t)\n",
    "$$\n",
    "\n",
    "subject to\n",
    "\n",
    "$$\n",
    "a_{t+1} + c_t \\leq w z_t + (1 + r) a_t\n",
    "\\quad\n",
    "c_t \\geq 0,\n",
    "\\quad \\text{and} \\quad\n",
    "a_t \\geq -B\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "- $ c_t $ is current consumption  \n",
    "- $ a_t $ is assets  \n",
    "- $ z_t $ is an exogenous component of labor income capturing stochastic unemployment risk, etc.  \n",
    "- $ w $ is a wage rate  \n",
    "- $ r $ is a net interest rate  \n",
    "- $ B $ is the maximum amount that the agent is allowed to borrow  \n",
    "\n",
    "\n",
    "The exogenous process $ \\{z_t\\} $ follows a finite state Markov chain with given stochastic matrix $ P $.\n",
    "\n",
    "The wage and interest rate are fixed over time.\n",
    "\n",
    "In this simple version of the model, households supply labor  inelastically because they do not value leisure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Firms\n",
    "\n",
    "Firms produce output by hiring capital and labor.\n",
    "\n",
    "Firms act competitively and face constant returns to scale.\n",
    "\n",
    "Since returns to scale are constant the number of firms does not matter.\n",
    "\n",
    "Hence we can consider a single (but nonetheless competitive) representative firm.\n",
    "\n",
    "The firm’s output is\n",
    "\n",
    "$$\n",
    "Y_t = A K_t^{\\alpha} N^{1 - \\alpha}\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "- $ A $ and $ \\alpha $ are parameters with $ A > 0 $ and $ \\alpha \\in (0, 1) $  \n",
    "- $ K_t $ is aggregate capital  \n",
    "- $ N $ is total labor supply (which is constant in this simple version of the model)  \n",
    "\n",
    "\n",
    "The firm’s problem is\n",
    "\n",
    "$$\n",
    "max_{K, N} \\left\\{ A K_t^{\\alpha} N^{1 - \\alpha} - (r + \\delta) K - w N \\right\\}\n",
    "$$\n",
    "\n",
    "The parameter $ \\delta $ is the depreciation rate.\n",
    "\n",
    "From the first-order condition with respect to capital, the firm’s inverse demand for capital is\n",
    "\n",
    "\n",
    "<a id='equation-aiy-rgk'></a>\n",
    "$$\n",
    "r = A \\alpha  \\left( \\frac{N}{K} \\right)^{1 - \\alpha} - \\delta \\tag{1}\n",
    "$$\n",
    "\n",
    "Using this expression and the firm’s first-order condition for labor, we can pin down\n",
    "the equilibrium wage rate as a function of $ r $ as\n",
    "\n",
    "\n",
    "<a id='equation-aiy-wgr'></a>\n",
    "$$\n",
    "w(r) = A  (1 - \\alpha)  (A \\alpha / (r + \\delta))^{\\alpha / (1 - \\alpha)} \\tag{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equilibrium\n",
    "\n",
    "We construct  a *stationary rational expectations equilibrium* (SREE).\n",
    "\n",
    "In such an equilibrium\n",
    "\n",
    "- prices induce behavior that generates aggregate quantities consistent with the prices  \n",
    "- aggregate quantities and prices are constant over time  \n",
    "\n",
    "\n",
    "In more detail, an SREE lists a set of prices, savings and production policies such that\n",
    "\n",
    "- households want to choose the specified savings policies taking the prices as given  \n",
    "- firms maximize profits taking the same prices as given  \n",
    "- the resulting aggregate quantities are consistent with the prices; in particular, the demand for capital equals the supply  \n",
    "- aggregate quantities (defined as cross-sectional averages) are constant  \n",
    "\n",
    "\n",
    "In practice, once parameter values are set, we can check for an SREE by the following steps\n",
    "\n",
    "1. pick a proposed quantity $ K $ for aggregate capital  \n",
    "1. determine corresponding prices, with interest rate $ r $ determined by [(1)](#equation-aiy-rgk) and a wage rate $ w(r) $ as given in [(2)](#equation-aiy-wgr)  \n",
    "1. determine the common optimal savings policy of the households given these prices  \n",
    "1. compute aggregate capital as the mean of steady state capital given this savings policy  \n",
    "\n",
    "\n",
    "If this final quantity agrees with $ K $ then we have a SREE."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code\n",
    "\n",
    "Let’s look at how we might compute such an equilibrium in practice.\n",
    "\n",
    "To solve the household’s dynamic programming problem we’ll use the [DiscreteDP](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/markov/ddp.jl) type from [QuantEcon.jl](http://quantecon.org/quantecon-jl).\n",
    "\n",
    "Our first task is the least exciting one: write code that maps parameters for a household problem into the `R` and `Q` matrices needed to generate an instance of `DiscreteDP`.\n",
    "\n",
    "Below is a piece of boilerplate code that does just this.\n",
    "\n",
    "In reading the code, the following information will be helpful\n",
    "\n",
    "- `R` needs to be a matrix where `R[s, a]` is the reward at state `s` under action `a`.  \n",
    "- `Q` needs to be a three dimensional array where `Q[s, a, s']` is the probability of transitioning to state `s'` when the current state is `s` and the current action is `a`.  \n",
    "\n",
    "\n",
    "(For a detailed discussion of `DiscreteDP` see [this lecture](../dynamic_programming/discrete_dp.html))\n",
    "\n",
    "Here we take the state to be $ s_t := (a_t, z_t) $, where $ a_t $ is assets and $ z_t $ is the shock.\n",
    "\n",
    "The action is the choice of next period asset level $ a_{t+1} $.\n",
    "\n",
    "The object also includes a default set of parameters that we’ll adopt unless otherwise specified."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "hide-output": true
   },
   "outputs": [],
   "source": [
    "using InstantiateFromURL\n",
    "# optionally add arguments to force installation: instantiate = true, precompile = true\n",
    "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.8.0\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "using LinearAlgebra, Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "using Parameters, Plots, QuantEcon\n",
    "gr(fmt = :png);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "setup_R! (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Household = @with_kw (r = 0.01,\n",
    "                      w = 1.0,\n",
    "                      σ = 1.0,\n",
    "                      β = 0.96,\n",
    "                      z_chain = MarkovChain([0.9 0.1; 0.1 0.9], [0.1; 1.0]),\n",
    "                      a_min = 1e-10,\n",
    "                      a_max = 18.0,\n",
    "                      a_size = 200,\n",
    "                      a_vals = range(a_min, a_max, length = a_size),\n",
    "                      z_size = length(z_chain.state_values),\n",
    "                      n = a_size * z_size,\n",
    "                      s_vals = gridmake(a_vals, z_chain.state_values),\n",
    "                      s_i_vals = gridmake(1:a_size, 1:z_size),\n",
    "                      u = σ == 1 ? x -> log(x) : x -> (x^(1 - σ) - 1) / (1 - σ),\n",
    "                      R = setup_R!(fill(-Inf, n, a_size), a_vals, s_vals, r, w, u),\n",
    "                      # -Inf is the utility of dying (0 consumption)\n",
    "                      Q = setup_Q!(zeros(n, a_size, n), s_i_vals, z_chain))\n",
    "\n",
    "function setup_Q!(Q, s_i_vals, z_chain)\n",
    "    for next_s_i in 1:size(Q, 3)\n",
    "        for a_i in 1:size(Q, 2)\n",
    "            for s_i in 1:size(Q, 1)\n",
    "                z_i = s_i_vals[s_i, 2]\n",
    "                next_z_i = s_i_vals[next_s_i, 2]\n",
    "                next_a_i = s_i_vals[next_s_i, 1]\n",
    "                if next_a_i == a_i\n",
    "                    Q[s_i, a_i, next_s_i] = z_chain.p[z_i, next_z_i]\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    return Q\n",
    "end\n",
    "\n",
    "function setup_R!(R, a_vals, s_vals, r, w, u)\n",
    "    for new_a_i in 1:size(R, 2)\n",
    "        a_new = a_vals[new_a_i]\n",
    "        for s_i in 1:size(R, 1)\n",
    "            a = s_vals[s_i, 1]\n",
    "            z = s_vals[s_i, 2]\n",
    "            c = w * z + (1 + r) * a - a_new\n",
    "            if c > 0\n",
    "                R[s_i, new_a_i] = u(c)\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    return R\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a first example of what we can do, let’s compute and plot an optimal accumulation policy at fixed prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create an instance of Household\n",
    "am = Household(a_max = 20.0, r = 0.03, w = 0.956)\n",
    "\n",
    "# Use the instance to build a discrete dynamic program\n",
    "am_ddp = DiscreteDP(am.R, am.Q, am.β)\n",
    "\n",
    "# Solve using policy function iteration\n",
    "results = solve(am_ddp, PFI)\n",
    "\n",
    "# Simplify names\n",
    "@unpack z_size, a_size, n, a_vals = am\n",
    "z_vals = am.z_chain.state_values\n",
    "\n",
    "# Get all optimal actions across the set of\n",
    "# a indices with z fixed in each column\n",
    "a_star = reshape([a_vals[results.sigma[s_i]] for s_i in 1:n], a_size, z_size)\n",
    "\n",
    "labels = [\"z = $(z_vals[1])\", \"z = $(z_vals[2])\"]\n",
    "plot(a_vals, a_star, label = labels, lw = 2, alpha = 0.6)\n",
    "plot!(a_vals, a_vals, label = \"\", color = :black, linestyle = :dash)\n",
    "plot!(xlabel = \"current assets\", ylabel = \"next period assets\", grid = false)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows asset accumulation policies at different values of the exogenous state.\n",
    "\n",
    "Now we want to calculate the equilibrium.\n",
    "\n",
    "Let’s do this visually as a first pass.\n",
    "\n",
    "The following code draws aggregate supply and demand curves.\n",
    "\n",
    "The intersection gives equilibrium interest rates and capital"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Firms' parameters\n",
    "const A = 1\n",
    "const N = 1\n",
    "const α = 0.33\n",
    "const β = 0.96\n",
    "const δ = 0.05\n",
    "\n",
    "function r_to_w(r)\n",
    "    return A * (1 - α) * (A * α / (r + δ)) ^ (α / (1 - α))\n",
    "end\n",
    "\n",
    "function rd(K)\n",
    "    return A * α * (N / K) ^ (1 - α) - δ\n",
    "end\n",
    "\n",
    "function prices_to_capital_stock(am, r)\n",
    "\n",
    "    # Set up problem\n",
    "    w = r_to_w(r)\n",
    "    @unpack a_vals, s_vals, u = am\n",
    "    setup_R!(am.R, a_vals, s_vals, r, w, u)\n",
    "\n",
    "    aiyagari_ddp = DiscreteDP(am.R, am.Q, am.β)\n",
    "\n",
    "    # Compute the optimal policy\n",
    "    results = solve(aiyagari_ddp, PFI)\n",
    "\n",
    "    # Compute the stationary distribution\n",
    "    stationary_probs = stationary_distributions(results.mc)[:, 1][1]\n",
    "\n",
    "    # Return K\n",
    "    return dot(am.s_vals[:, 1], stationary_probs)\n",
    "end\n",
    "\n",
    "# Create an instance of Household\n",
    "am = Household(β = β, a_max = 20.0)\n",
    "\n",
    "# Create a grid of r values at which to compute demand and supply of capital\n",
    "r_vals = range(0.005, 0.04, length = 20)\n",
    "\n",
    "# Compute supply of capital\n",
    "k_vals = prices_to_capital_stock.(Ref(am), r_vals)\n",
    "\n",
    "# Plot against demand for capital by firms\n",
    "demand = rd.(k_vals)\n",
    "labels =  [\"demand for capital\" \"supply of capital\"]\n",
    "plot(k_vals, [demand r_vals], label = labels, lw = 2, alpha = 0.6)\n",
    "plot!(xlabel = \"capital\", ylabel = \"interest rate\", xlim = (2, 14), ylim = (0.0, 0.1))"
   ]
  }
 ],
 "metadata": {
  "date": 1591310624.6542974,
  "download_nb": 1,
  "download_nb_path": "https://julia.quantecon.org/",
  "filename": "aiyagari.rst",
  "filename_with_path": "multi_agent_models/aiyagari",
  "kernelspec": {
   "display_name": "Julia 1.4.2",
   "language": "julia",
   "name": "julia-1.4"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.4.2"
  },
  "title": "The Aiyagari Model"
 },
 "nbformat": 4,
 "nbformat_minor": 2
}