{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sudden Stop Model\n", "\n", "In this notebook we replicate the baseline model exposed in \n", "\n", "`From Sudden Stops to Fisherian Deflation, Quantitative Theory and Policy` by __Anton Korinek and Enrique G. Mendoza__\n", "\n", "The file `sudden_stop.yaml` which is printed below, describes the model, and must be included in the same directory as this notebook." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## importing necessary functions" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from matplotlib import pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from dolo import *\n", "from dolo.algos import time_iteration\n", "from dolo.algos import plot_decision_rule, simulate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## writing the model" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'/home/pablo/Mobilhome/econforge/dolo/examples/notebooks'" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pwd" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "\n", "
1\n", " 2\n", " 3\n", " 4\n", " 5\n", " 6\n", " 7\n", " 8\n", " 9\n", "10\n", "11\n", "12\n", "13\n", "14\n", "15\n", "16\n", "17\n", "18\n", "19\n", "20\n", "21\n", "22\n", "23\n", "24\n", "25\n", "26\n", "27\n", "28\n", "29\n", "30\n", "31\n", "32\n", "33\n", "34\n", "35\n", "36\n", "37\n", "38\n", "39\n", "40\n", "41\n", "42\n", "43\n", "44\n", "45\n", "46\n", "47\n", "48\n", "49\n", "50\n", "51\n", "52\n", "53\n", "54\n", "55\n", "56\n", "57\n", "58\n", "59\n", "60\n", "61\n", "62\n", "63\n", "64 | # This file adapts the model described in\n", "# "From Sudden Stops to Fisherian Deflation, Quantitative Theory and Policy"\n", "# by Anton Korinek and Enrique G. Mendoza\n", "\n", "name: Sudden Stop (General)\n", "\n", "symbols:\n", "\n", " exogenous: [y]\n", " states: [l]\n", " controls: [b, lam]\n", " values: [V, Vc]\n", " parameters: [beta, R, sigma, a, mu, kappa, delta_y, pi, lam_inf]\n", "\n", "\n", "definitions:\n", " c: 1 + y + l*R - b\n", "\n", "equations:\n", "\n", " transition:\n", " - l = b(-1)\n", "\n", " arbitrage:\n", " - lam = b/c\n", " - 1 - beta*(c(1)/c)^(-sigma)*R | lam_inf <= lam <= inf\n", "\n", " value:\n", " - V = c^(1.0-sigma)/(1.0-sigma) + beta*V(1)\n", " - Vc = c^(1.0-sigma)/(1.0-sigma)\n", "\n", "calibration:\n", "\n", " beta: 0.95\n", " R: 1.03\n", " sigma: 2.0\n", " a: 1/3\n", " mu: 0.8\n", " kappa: 1.3\n", " delta_y: 0.03\n", " pi: 0.05\n", " lam_inf: -0.2\n", " y: 1.0\n", " c: 1.0 + y\n", " b: 0.0\n", " l: 0.0\n", " lam: 0.0\n", "\n", " V: c^(1.0-sigma)/(1.0-sigma)/(1.0-beta)\n", " Vc: c^(1.0-sigma)/(1.0-sigma)\n", "\n", "\n", "exogenous: !MarkovChain\n", " values: [[ 1.0-delta_y ], # bad state\n", " [ 1.0 ]] # good state\n", " transitions: [[ 0.5, 1-0.5 ], # probabilities [p(L|L), p(H|L)]\n", " [ 0.5, 0.5 ]] # probabilities [p(L|H), p(H|H)]\n", "\n", "domain:\n", " l: [-1, 1]\n", "\n", "options:\n", " grid: !Cartesian\n", " orders: [10]\n", " |
Model | \n", "|
name | \n", "Sudden Stop (General) | \n", "
type | \n", "dtcc | \n", "
filename | \n", "../models/sudden_stop.yaml | \n", "
Type | Equation | Residual |
transition | $l_{t} = b_{t-1}$ | 0.000 |
arbitrage | $\\lambda_{t} = \\frac{b_{t}}{c_{t}}$ | 0.000 |
$1 - \\beta \\; \\left(\\frac{c_{t+1}}{c_{t}}\\right)^{- \\sigma} \\; R$ | 0.0215 | |
value | $V_{t} = \\frac{c_{t}^{1.0 - \\sigma}}{1.0 - \\sigma} + \\beta \\; V_{t+1}$ | |
$Vc_{t} = \\frac{c_{t}^{1.0 - \\sigma}}{1.0 - \\sigma}$ | ||
controls_lb | $- inf$ | |
$\\lambda_{inf}$ | ||
controls_ub | $inf$ | |
$inf$ | ||
definitions | $c_{t} = 1 + y_{t} + l_{t} \\; R - b_{t}$ |