231211_Nishikawa_AiyagariModel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7543eb2b",
   "metadata": {},
   "source": [
    "# 1. Background"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "375fbd07",
   "metadata": {},
   "source": [
    "## やること\n",
    "\n",
    "Aiyagari ModelをDiscrete Dynamic Programming(以下、DDP)を用いて解く\n",
    "\n",
    "Aiyagari Model: 以下のような分析に用いられる\n",
    "- 収入リスクがあるときのprecautiary(予防的な)貯蓄や、借入制約の影響\n",
    "- リスクシェアリング、アセットプライシング\n",
    "- 富の分布の形状"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "575ec0c6",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "- Aiyagari Model\n",
    "    - [Intermediate Quantitative Economics with Python: 74. The Aiyagari Model](https://python.quantecon.org/aiyagari.html)\n",
    "    - [Aiyagari(1994)Uninsured Idiosyncratic Risk and Aggregate Saving](https://www.jstor.org/stable/2118417)\n",
    "- DDP\n",
    "    - [DiscreteDP: Getting Started with a Simple Example](https://notes.quantecon.org/submission/5bd7a72df966080015bafbd1)\n",
    "    - [Advanced Quantitative Economics with Python: 4. Discrete State Dynamic Programming](https://python-advanced.quantecon.org/discrete_dp.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91c24222",
   "metadata": {},
   "source": [
    "# 2.  Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5abb20c",
   "metadata": {},
   "source": [
    "## 前提\n",
    "- エージェントは異質的\n",
    "- 借入・貸付に関して、外生的な手段1つのみ\n",
    "- 借入制約あり"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d263e48",
   "metadata": {},
   "source": [
    "## Households' Problem\n",
    "\n",
    "消費者は無限期間を生きるとし、個人個人に特有の(idiosyncratic)収入ショック( $ z_t $ )に直面すると仮定する。\n",
    "\n",
    "家計は、以下の最大化問題を解く。\n",
    "\n",
    "\\begin{align}\n",
    "\\max \\; & \\mathbb E[ \\sum_{t=0}^{\\infty} \\beta^t u(c_t)] \\\\\n",
    "\\text{s.t.} \\\\\n",
    "a_{t+1} + c_t &\\leq w z_t + (1 + r) a_t, \\\\\n",
    "c_t &\\geq 0,  \\\\\n",
    "a_t &\\geq -B,\n",
    "\\end{align}\n",
    "\n",
    "where\n",
    "\n",
    "- $ c_t $ : 今期の消費\n",
    "- $ a_t $ : 資産\n",
    "- $ z_t $ : 労働収入に関する外生的・確率的なリスク（e.g., 失業など）\n",
    "- $ w $ : 賃金率\n",
    "- $ r $ : 実質利子率\n",
    "- $ B $ : エージェントが借りられる最大値\n",
    "\n",
    "その他、以下を仮定。\n",
    "- $ \\{z_t\\} $ は、stochastic matrix $ P $のもとで、a finite state Markov chainに従うとする。\n",
    "- 賃金率・利子率は一定。\n",
    "\n",
    "※家計は余暇を効用に考慮していないため、労働供給を非弾力的に供給する。\n",
    "\n",
    "Recursive formulationは以下\n",
    "\n",
    "\\begin{align}\n",
    "v(a, z) = \\max_{a' \\geq -B} \\left\\{ u(wz+(1+r)a-a') +\\beta \\cdot \\mathbb E[v(a', z')] \\right\\},\n",
    "\\end{align}\n",
    "\n",
    "where\n",
    "- State variables: $ (z, a) $,\n",
    "- Control variables: $ a' $"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce2bd5ce",
   "metadata": {},
   "source": [
    "## Firms' Problem\n",
    "\n",
    "\n",
    "企業は競争的に行動し、CRS生産関数を仮定。結果的に企業の数は関係なくなるため、代表的企業を考慮する。\n",
    "\n",
    "企業のアウトプットは以下。\n",
    "\n",
    "\\begin{align}\n",
    "Y_t = A K_t^{\\alpha} N^{1 - \\alpha},\n",
    "\\end{align}\n",
    "\n",
    "where\n",
    "- $ A > 0 $,   $ \\alpha \\in (0, 1) $  \n",
    "- $ K_t $ : 総資本\n",
    "- $ N $ : 総労働供給（※Household Problemでの仮定により、一定）\n",
    "\n",
    "また、企業は以下の最大化問題を解く。\n",
    "\n",
    "\\begin{align}\n",
    "max_{K, N} \\left\\{ A K_t^{\\alpha} N^{1 - \\alpha} - (r + \\delta) K - w N \\right\\},\n",
    "\\end{align}\n",
    "where\n",
    "- $ \\delta $ : 資本消耗率\n",
    "\n",
    "KとNに関するFOCより、以下が得られる。\n",
    "\n",
    "\\begin{align}\n",
    "    \\begin{cases}\n",
    "        r &= A \\alpha  \\left( \\frac{N}{K} \\right)^{1 - \\alpha} - \\delta,  \\\\\n",
    "        w(r) &= A  (1 - \\alpha)  (\\frac{A \\alpha }{ r + \\delta})^{\\frac{\\alpha}{1 - \\alpha} }.\n",
    "    \\end{cases}\n",
    "\\end{align}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50248ecb",
   "metadata": {},
   "source": [
    "## 均衡: SREE(Stationary Rational Expectations Equilibrium)\n",
    "\n",
    "以下を満たすprices, savings and production policiesの集合を考える\n",
    "\n",
    "- 価格を所与として、家計は上記の最大化問題を解く\n",
    "- 価格を所与として、企業は上記の最大化問題を解く\n",
    "- 資本に関して、総需要と総供給が一致\n",
    "- 総量は一定"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fabc0440",
   "metadata": {},
   "source": [
    "# 3. Computation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce62cb95",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "-  [QuantEcon.py](https://quantecon.org/quantecon-py/).の[DiscreteDP](https://github.com/QuantEcon/QuantEcon.py/blob/master/quantecon/markov/ddp.py) class を用いる\n",
    "- Households Problemのパラメータをもとに利得行列R、確率遷移行列Qを生成する必要がある\n",
    "    - `R`(n × m): `R[s, a]`は、状態`s`において、アクション`a`により得られる利得を表す\n",
    "    - `Q`(n × m × n): `Q[s, a, s']`は、今期の状態が`s`で今期のアクションが`a`のときに、次期に状態`s'`に遷移する確率を表す\n",
    "- 状態: $ s_t := (a_t, z_t) $\n",
    "    - $ a_t $: 資産\n",
    "    - $ z_t $: ショック\n",
    "- アクション: $ a_{t+1} $\n",
    "    - 次期の資産\n",
    "- 効用関数:\n",
    "    - $ u(c) = log(c) $ と仮定する"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab368ac0",
   "metadata": {},
   "source": [
    "## Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "91d910f3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: quantecon in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (0.7.1)\r\n",
      "Requirement already satisfied: sympy in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from quantecon) (1.11.1)\r\n",
      "Requirement already satisfied: numpy>=1.17.0 in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from quantecon) (1.23.5)\r\n",
      "Requirement already satisfied: requests in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from quantecon) (2.28.2)\r\n",
      "Requirement already satisfied: scipy>=1.5.0 in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from quantecon) (1.10.1)\r\n",
      "Requirement already satisfied: numba>=0.49.0 in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from quantecon) (0.56.4)\r\n",
      "Requirement already satisfied: llvmlite<0.40,>=0.39.0dev0 in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from numba>=0.49.0->quantecon) (0.39.1)\r\n",
      "Requirement already satisfied: setuptools in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from numba>=0.49.0->quantecon) (66.0.0)\r\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from requests->quantecon) (2022.12.7)\r\n",
      "Requirement already satisfied: idna<4,>=2.5 in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from requests->quantecon) (3.4)\r\n",
      "Requirement already satisfied: urllib3<1.27,>=1.21.1 in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from requests->quantecon) (1.26.15)\r\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from requests->quantecon) (3.1.0)\r\n",
      "Requirement already satisfied: mpmath>=0.19 in /Users/maonshkw/opt/anaconda3/envs/oyamazemi/lib/python3.10/site-packages (from sympy->quantecon) (1.3.0)\r\n"
     ]
    }
   ],
   "source": [
    "!pip install quantecon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f5525f38",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (11, 5)  #set default figure size\n",
    "import numpy as np\n",
    "from quantecon.markov import DiscreteDP\n",
    "from numba import jit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1af998b",
   "metadata": {},
   "source": [
    "## Setting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "df0c676a",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Household:\n",
    "    \"\"\"\n",
    "    This class takes the parameters that define a household asset accumulation\n",
    "    problem and computes the corresponding reward and transition matrices R\n",
    "    and Q required to generate an instance of DiscreteDP, and thereby solve\n",
    "    for the optimal policy.\n",
    "\n",
    "    Comments on indexing: We need to enumerate the state space S as a sequence\n",
    "    S = {0, ..., n}.  To this end, (a_i, z_i) index pairs are mapped to s_i\n",
    "    indices according to the rule\n",
    "\n",
    "        s_i = a_i * z_size + z_i\n",
    "\n",
    "    To invert this map, use\n",
    "\n",
    "        a_i = s_i // z_size  (integer division)\n",
    "        z_i = s_i % z_size\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "\n",
    "    def __init__(self,\n",
    "                r=0.01,                      # Interest rate\n",
    "                w=1.0,                       # Wages\n",
    "                β=0.96,                      # Discount factor\n",
    "                a_min=1e-10,\n",
    "                Π=[[0.9, 0.1], [0.1, 0.9]],  # Markov chain\n",
    "                z_vals=[0.1, 1.0],           # Exogenous states\n",
    "                a_max=18,\n",
    "                a_size=200):\n",
    "\n",
    "        # Store values, set up grids over a and z\n",
    "        self.r, self.w, self.β = r, w, β\n",
    "        self.a_min, self.a_max, self.a_size = a_min, a_max, a_size\n",
    "\n",
    "        self.Π = np.asarray(Π)\n",
    "        self.z_vals = np.asarray(z_vals)\n",
    "        self.z_size = len(z_vals)\n",
    "\n",
    "        self.a_vals = np.linspace(a_min, a_max, a_size)\n",
    "        self.n = a_size * self.z_size\n",
    "\n",
    "        # Build the array Q\n",
    "        self.Q = np.zeros((self.n, a_size, self.n))\n",
    "        self.build_Q()\n",
    "\n",
    "        # Build the array R\n",
    "        self.R = np.empty((self.n, a_size))\n",
    "        self.build_R()\n",
    "\n",
    "    def set_prices(self, r, w):\n",
    "        \"\"\"\n",
    "        Use this method to reset prices. Calling the method will trigger a\n",
    "        re-build of R.\n",
    "        \"\"\"\n",
    "        self.r, self.w = r, w\n",
    "        self.build_R()\n",
    "\n",
    "    def build_Q(self):\n",
    "        populate_Q(self.Q, self.a_size, self.z_size, self.Π)\n",
    "\n",
    "    def build_R(self):\n",
    "        self.R.fill(-np.inf)\n",
    "        populate_R(self.R,\n",
    "                self.a_size,\n",
    "                self.z_size,\n",
    "                self.a_vals,\n",
    "                self.z_vals,\n",
    "                self.r,\n",
    "                self.w)\n",
    "\n",
    "\n",
    "# Do the hard work using JIT-ed functions\n",
    "\n",
    "@jit(nopython=True)\n",
    "def populate_R(R, a_size, z_size, a_vals, z_vals, r, w):\n",
    "    n = a_size * z_size\n",
    "    for s_i in range(n):\n",
    "        a_i = s_i // z_size\n",
    "        z_i = s_i % z_size\n",
    "        a = a_vals[a_i]\n",
    "        z = z_vals[z_i]\n",
    "        for new_a_i in range(a_size):\n",
    "            a_new = a_vals[new_a_i]\n",
    "            c = w * z + (1 + r) * a - a_new\n",
    "            if c > 0:\n",
    "                R[s_i, new_a_i] = np.log(c)  # Utility\n",
    "\n",
    "@jit(nopython=True)\n",
    "def populate_Q(Q, a_size, z_size, Π):\n",
    "    n = a_size * z_size\n",
    "    for s_i in range(n):\n",
    "        z_i = s_i % z_size\n",
    "        for a_i in range(a_size):\n",
    "            for next_z_i in range(z_size):\n",
    "                Q[s_i, a_i, a_i*z_size + next_z_i] = Π[z_i, next_z_i]\n",
    "\n",
    "\n",
    "@jit(nopython=True)\n",
    "def asset_marginal(s_probs, a_size, z_size):\n",
    "    a_probs = np.zeros(a_size)\n",
    "    for a_i in range(a_size):\n",
    "        for z_i in range(z_size):\n",
    "            a_probs[a_i] += s_probs[a_i*z_size + z_i]\n",
    "    return a_probs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2e62376",
   "metadata": {},
   "source": [
    "## 価格を固定したときの、資産蓄積政策の推移を求める"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5c7b1ef1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x900 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example prices\n",
    "r = 0.03\n",
    "w = 0.956\n",
    "\n",
    "# Create an instance of Household\n",
    "am = Household(a_max=20, r=r, w=w)\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 = am_ddp.solve(method='policy_iteration')\n",
    "\n",
    "# Simplify names\n",
    "z_size, a_size = am.z_size, am.a_size\n",
    "z_vals, a_vals = am.z_vals, am.a_vals\n",
    "n = a_size * z_size\n",
    "\n",
    "# Get all optimal actions across the set of a indices with z fixed in each row\n",
    "a_star = np.empty((z_size, a_size))\n",
    "for s_i in range(n):\n",
    "    a_i = s_i // z_size\n",
    "    z_i = s_i % z_size\n",
    "    a_star[z_i, a_i] = a_vals[results.sigma[s_i]]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9, 9))\n",
    "ax.plot(a_vals, a_vals, 'k--')  # 45 degrees\n",
    "for i in range(z_size):\n",
    "    lb = f'$z = {z_vals[i]:.2}$'\n",
    "    ax.plot(a_vals, a_star[i, :], lw=2, alpha=0.6, label=lb)\n",
    "    ax.set_xlabel('current assets')\n",
    "    ax.set_ylabel('next period assets')\n",
    "ax.legend(loc='upper left')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2093ed0c",
   "metadata": {},
   "source": [
    "## 均衡を求める"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4f5dfcd0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = 1.0\n",
    "N = 1.0\n",
    "α = 0.33\n",
    "β = 0.96\n",
    "δ = 0.05\n",
    "\n",
    "\n",
    "def r_to_w(r):\n",
    "    \"\"\"\n",
    "    Equilibrium wages associated with a given interest rate r.\n",
    "    \"\"\"\n",
    "    return A * (1 - α) * (A * α / (r + δ))**(α / (1 - α))\n",
    "\n",
    "def rd(K):\n",
    "    \"\"\"\n",
    "    Inverse demand curve for capital.  The interest rate associated with a\n",
    "    given demand for capital K.\n",
    "    \"\"\"\n",
    "    return A * α * (N / K)**(1 - α) - δ\n",
    "\n",
    "\n",
    "def prices_to_capital_stock(am, r):\n",
    "    \"\"\"\n",
    "    Map prices to the induced level of capital stock.\n",
    "\n",
    "    Parameters:\n",
    "    ----------\n",
    "\n",
    "    am : Household\n",
    "        An instance of an aiyagari_household.Household\n",
    "    r : float\n",
    "        The interest rate\n",
    "    \"\"\"\n",
    "    w = r_to_w(r)\n",
    "    am.set_prices(r, w)\n",
    "    aiyagari_ddp = DiscreteDP(am.R, am.Q, β)\n",
    "    # Compute the optimal policy\n",
    "    results = aiyagari_ddp.solve(method='policy_iteration')\n",
    "    # Compute the stationary distribution\n",
    "    stationary_probs = results.mc.stationary_distributions[0]\n",
    "    # Extract the marginal distribution for assets\n",
    "    asset_probs = asset_marginal(stationary_probs, am.a_size, am.z_size)\n",
    "    # Return K\n",
    "    return np.sum(asset_probs * am.a_vals)\n",
    "\n",
    "\n",
    "# Create an instance of Household\n",
    "am = Household(a_max=20)\n",
    "\n",
    "# Use the instance to build a discrete dynamic program\n",
    "am_ddp = DiscreteDP(am.R, am.Q, am.β)\n",
    "\n",
    "# Create a grid of r values at which to compute demand and supply of capital\n",
    "num_points = 20\n",
    "r_vals = np.linspace(0.005, 0.04, num_points)\n",
    "\n",
    "# Compute supply of capital\n",
    "k_vals = np.empty(num_points)\n",
    "for i, r in enumerate(r_vals):\n",
    "    k_vals[i] = prices_to_capital_stock(am, r)\n",
    "\n",
    "# Plot against demand for capital by firms\n",
    "fig, ax = plt.subplots(figsize=(11, 8))\n",
    "ax.plot(k_vals, r_vals, lw=2, alpha=0.6, label='supply of capital')\n",
    "ax.plot(k_vals, rd(k_vals), lw=2, alpha=0.6, label='demand for capital')\n",
    "ax.grid()\n",
    "ax.set_xlabel('capital')\n",
    "ax.set_ylabel('interest rate')\n",
    "ax.legend(loc='upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "02069b5f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}