{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Rational Expectations Agricultural Market Model\n",
"\n",
"**Randall Romero Aguilar, PhD**\n",
"\n",
"This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n",
"\n",
"Original (Matlab) CompEcon file: **demintro02.m**\n",
"\n",
"Running this file requires the Python version of CompEcon. This can be installed with pip by running\n",
"\n",
" !pip install compecon --upgrade\n",
"\n",
"Last updated: 2022-Ago-19\n",
"
\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"from compecon import qnwlogn, discmoments\n",
"plt.style.use('seaborn-dark')\n",
"plt.style.use('seaborn-talk')\n",
"pd.set_option('display.precision', 4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Generate yield distribution"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"sigma2 = 0.2 ** 2\n",
"y, w = qnwlogn(25, -0.5 * sigma2, sigma2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compute rational expectations equilibrium using function iteration, iterating on acreage planted"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" it a |a-aold|\n",
"======================\n",
" 0 1.0198 2.0e-02\n",
" 1 1.0171 2.7e-03\n",
" 2 1.0175 3.7e-04\n",
" 3 1.0174 5.0e-05\n",
" 4 1.0174 6.8e-06\n",
" 5 1.0174 9.3e-07\n",
" 6 1.0174 1.3e-07\n",
" 7 1.0174 1.7e-08\n",
" 8 1.0174 2.3e-09\n"
]
}
],
"source": [
"def A(aa, pp):\n",
" \"\"\"\n",
" Parameters\n",
" aa: acreage\n",
" pp: target price\n",
" \"\"\"\n",
" return 0.5 + 0.5 * np.dot(w, np.maximum(1.5 - 0.5 * aa * y, pp))\n",
"\n",
"ptarg = 1.0 # target price\n",
"a = 1.0 # initial guess for acreage\n",
"\n",
"print(f\"{'it':^4s} {'a':^8s} {'|a-aold|':^8s}\", '='*22, sep='\\n')\n",
"for it in range(50):\n",
" aold = a\n",
" a = A(a, ptarg)\n",
" print(f'{it:4d} {a:8.4f} {abs(a-aold):8.1e}')\n",
" if abs(a - aold) < 1.e-8:\n",
" break"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Intermediate outputs"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Expect | \n",
" Std Dev | \n",
"
\n",
" \n",
" \n",
" \n",
" | Market Price | \n",
" 0.9913 | \n",
" 0.1028 | \n",
"
\n",
" \n",
" | Farm Price | \n",
" 1.0348 | \n",
" 0.0506 | \n",
"
\n",
" \n",
" | Farm Revenue | \n",
" 1.0447 | \n",
" 0.1773 | \n",
"
\n",
" \n",
" | Government Expenditures | \n",
" 0.0573 | \n",
" 0.1038 | \n",
"
\n",
" \n",
"
\n",
"