{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Quickly Simulate an RBC Model\n", "\n", "Here I demonstrate how how relatively straightforward it is to appoximate, solve, and simulate a DSGE model using `linearsolve`. In the example that follows, I describe the procedure more carefully.\n", "\n", "\\begin{align}\n", "C_t^{-\\sigma} & = \\beta E_t \\left[C_{t+1}^{-\\sigma}(\\alpha A_{t+1} K_{t+1}^{\\alpha-1} + 1 - \\delta)\\right]\\\\\n", "C_t + K_{t+1} & = A_t K_t^{\\alpha} + (1-\\delta)K_t\\\\\n", "\\log A_{t+1} & = \\rho_a \\log A_{t} + \\epsilon_{t+1}\n", "\\end{align}\n", "\n", "In the block of code that immediately follows, I input the model, solve for the steady state, compute the linear approximation of the equilibirum conditions, and compute some impulse responses following a 1 percent shock to technology $A_t$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Import numpy, pandas, linearsolve, matplotlib.pyplot\n", "import numpy as np\n", "import pandas as pd\n", "import linearsolve as ls\n", "import matplotlib.pyplot as plt\n", "plt.style.use('classic')\n", "plt.rcParams['figure.facecolor'] = 'white'\n", "\n", "# Input model parameters\n", "parameters = pd.Series(dtype=float)\n", "parameters['alpha'] = .35\n", "parameters['beta'] = 0.99\n", "parameters['delta'] = 0.025\n", "parameters['rhoa'] = .9\n", "parameters['sigma'] = 1.5\n", "parameters['A'] = 1\n", "\n", "# Funtion that evaluates the equilibrium conditions\n", "def equations(variables_forward,variables_current,parameters):\n", " \n", " # Parameters \n", " p = parameters\n", " \n", " # Variables\n", " fwd = variables_forward\n", " cur = variables_current\n", " \n", " # Household Euler equation\n", " euler_eqn = p.beta*fwd.c**-p.sigma*(p.alpha*fwd.a*fwd.k**(p.alpha-1)+1-p.delta) - cur.c**-p.sigma\n", " \n", " # Goods market clearing\n", " market_clearing = cur.c + fwd.k - (1-p.delta)*cur.k - cur.a*cur.k**p.alpha\n", " \n", " # Exogenous technology\n", " technology_proc = p.rhoa*np.log(cur.a) - np.log(fwd.a)\n", " \n", " # Stack equilibrium conditions into a numpy array\n", " return np.array([\n", " euler_eqn,\n", " market_clearing,\n", " technology_proc\n", " ])\n", "\n", "# Initialize the model\n", "model = ls.model(equations = equations,\n", " n_states=2,\n", " n_exo_states = 1,\n", " variables=['a','k','c'],\n", " parameters = parameters)\n", "\n", "# Compute the steady state numerically\n", "guess = [1,1,1]\n", "model.compute_ss(guess)\n", "\n", "# Find the linear approximation around the non-stochastic steady state and solve\n", "model.approximate_and_solve()\n", "\n", "# Compute impulse responses and plot\n", "model.impulse(T=41,t0=5,shocks=[0.01])\n", "\n", "fig = plt.figure(figsize=(12,4))\n", "ax1 =fig.add_subplot(1,2,1)\n", "(model.irs['e_a'][['a','k','c']]*100).plot(lw='5',alpha=0.5,grid=True,ax=ax1).legend(loc='upper right',ncol=3)\n", "ax2 =fig.add_subplot(1,2,2)\n", "(model.irs['e_a'][['a','e_a']]*100).plot(lw='5',alpha=0.5,grid=True,ax=ax2).legend(loc='upper right',ncol=2);" ] } ], "metadata": { "anaconda-cloud": {}, "celltoolbar": "Raw Cell Format", "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": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 4 }