{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Búsqueda de Trabajo Secuencial Óptima\n", "\n", "Mauricio M. Tejada\n", "\n", "ILADES - Universidad Alberto Hurtado\n", "\n", "Septiembre, 2017\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modelo con Búsqueda en el Trabajo (On th Job Search)\n", "\n", "Buscamos resolver la siguiente ecuación de Bellman:\n", "$$\n", "R=b+(\\alpha_0 - \\alpha_1)\\int_{R}^{\\overline{w}}\\frac{(1-F(w))}{r+\\lambda+\\alpha_1(1-F(w))}dw\n", "$$\n", "Como antes, suponemos que $\\log w \\sim N(\\mu,\\sigma)$ y que $\\overline{w}=\\infty$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Cargamos modulos necesarios\n", "%matplotlib inline\n", "import scipy.stats as stats\n", "import numpy as np\n", "from scipy import integrate\n", "import matplotlib.pyplot as plt " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Definición de Parámetros\n", "b = 1.0\n", "α0 = 0.30\n", "α1 = 0.02\n", "r = 0.1\n", "λ = 0.01\n", "μ = 0.8\n", "σ = 0.5\n", "F = stats.lognorm(s = σ, loc = 0, scale = np.exp(μ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Escribimos una función que, dados los parámetros, resuelve el salario de reserva iterando la ecuación de Bellman anterior:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def SolveModelOJS(parametrization, R0=1, tol=0.00001, step=0.5):\n", " b, α0, α1, r, λ, F = parametrization\n", " diff = 10\n", " \n", " integrando = lambda x: (1 - F.cdf(x))/(r + λ + α1*(1-F.cdf(x)))\n", " \n", " while diff > tol:\n", " R1 = b + (α0 - α1)*integrate.quad(integrando, R0, np.inf)[0]\n", " diff = np.abs(R1-R0)\n", " R0 = R0 + step*(R1-R0)\n", " \n", " h = α0*(1-F.cdf(R1))\n", " \n", " return R1, h" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Probemos ahora la función con la parametrización inicial:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "El salario de reserva es: 2.372716502901918\n", "La duración promedio del desempleo es: 7.42313801263\n" ] } ], "source": [ "parm = [b, α0, α1, r, λ, F] # Lista con la parametrización inicial\n", "\n", "Req, hueq = SolveModelOJS(parm)\n", "print(\"El salario de reserva es: \", Req) \n", "print(\"La duración promedio del desempleo es: \", 1/hueq) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Efecto de un cambio de ingresos (desutilidad) de los desempleados\n", "\n", "Ahora resolvamos el modelo para $b \\in [0,2]$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "b_values = np.linspace(0,2,10)\n", "R_values_b = np.zeros(len(b_values))\n", "h_values_b = np.zeros(len(b_values))\n", "\n", "for i in range(len(b_values)):\n", " parmi = [b_values[i], α0, α1, r, λ, F]\n", " R_values_b[i], h_values_b[i] = SolveModelOJS(parmi)[0:2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Graficamos el efecto sobre el salarios de reserva:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(b_values, R_values_b, 'r-', linewidth=2)\n", "plt.xlabel(r'$b$')\n", "plt.ylabel(r'$R$')\n", "plt.title('Efecto de '+r'$b$'+' sobre el Salario de Reserva')\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Graficamos el efecto sobre la probabilidad de salir del desempleo:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(b_values, h_values_b, 'r-', linewidth=2)\n", "plt.xlabel(r'$b$')\n", "plt.ylabel(r'$h$')\n", "plt.title('Efecto de '+r'$b$'+' sobre la Probabilidad de salir del Desempleo')\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Efecto de un cambio de la tasa a la cuál llegan las ofertas laborales en el estado de desempleo\n", "\n", "Ahora resolvamos el modelo para $\\alpha_0 \\in [0,1]$:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "α0_values = np.linspace(0,1,20)\n", "R_values_α0 = np.zeros(len(α0_values))\n", "h_values_α0 = np.zeros(len(α0_values))\n", "\n", "for i in range(len(α0_values)):\n", " parmi = [b, α0_values[i], α1, r, λ, F]\n", " R_values_α0[i], h_values_α0[i] = SolveModelOJS(parmi)[0:2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Graficamos el efecto sobre el salarios de reserva:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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yhL7RGsMdvv3tcG7oq6+Gfv3irkhEpFkpHBrj6afhxRdhn33gZz+LuxoRkWan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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(α0_values, R_values_α0, 'r-', linewidth=2)\n", "plt.xlabel(r'$\\alpha_0$')\n", "plt.ylabel(r'$R$')\n", "plt.title('Efecto de '+r'$\\alpha_{0}$'+' sobre el Salario de Reserva')\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Graficamos el efecto sobre la probabilidad de salir del desempleo:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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NcVcjIrJNFCBR2bgRrrkm3P71r2G33eKtR0RkGylAonL77TB/fhiq/fLL465G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\nkhEFiIiIZOT/A7uMJJil27luAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(α0_values, h_values_α0, 'r-', linewidth=2)\n", "plt.xlabel(r'$\\alpha_0$')\n", "plt.ylabel(r'$h$')\n", "plt.title('Efecto de '+r'$\\alpha_0$'+' sobre la Probabilidad de salir del Desempleo')\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Efecto de un cambio de la tasa a la cuál llegan las ofertas laborales en el estado de desempleo\n", "\n", "Ahora resolvamos el modelo para $\\alpha_1 \\in [0,\\alpha_0]$:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "α1_values = np.linspace(0,α0,20)\n", "R_values_α1 = np.zeros(len(α1_values))\n", "h_values_α1 = np.zeros(len(α1_values))\n", "\n", "for i in range(len(α1_values)):\n", " parmi = [b, α0, α1_values[i], r, λ, F]\n", " R_values_α1[i], h_values_α1[i] = SolveModelOJS(parmi)[0:2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Graficamos el efecto sobre el salarios de reserva:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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Vg0jGU3IQqZuxwP5m9hFhAre3zOyOiGMSqTM1SIukgJltQ1hH+mDg\nfne/MeKQRGpEyUFERMrRbSURESlHyUFERMpRchARkXKUHEREpBwlBxERKUfJQUREylFyEBGRcpQc\nRESkHCUHEREp5/8DjONA1C+M+OUAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(α1_values, R_values_α1, 'r-', linewidth=2)\n", "plt.xlabel(r'$\\alpha_1$')\n", "plt.ylabel(r'$R$')\n", "plt.title('Efecto de '+r'$\\alpha_{1}$'+' sobre el Salario de Reserva')\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Graficamos el efecto sobre la probabilidad de salir del desempleo:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(α1_values, h_values_α1, 'r-', linewidth=2)\n", "plt.xlabel(r'$\\alpha_1$')\n", "plt.ylabel(r'$h$')\n", "plt.title('Efecto de '+r'$\\alpha_1$'+' sobre la Probabilidad de salir del Desempleo')\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Distribución de Salarios Aceptados\n", "\n", "La distribución de salarios aceptados se deriva de la distribución de salarios $F(w)$. En particular, dicha distribución es $F(w)$ truncada a la izquierda al salario de reserva $R$. La función de densidad es:\n", "$$f_{A}(w) = f(w|w \\geq R )= \\frac{f(w)}{1-F(R)}$$\n", "La función acumulada en tanto es:\n", "$$F_{A}(w) = \\int^{w}_{R} f(w|w \\geq R ) = \\frac{F(w)-F(R)}{1-F(R)}$$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Función para obtener números aleatorios de una distribución truncada a la izquierda\n", "\n", "def randTruncDist(Distribution, TruncPoint, Ndraws):\n", " \"\"\" Random numbers from a truncated distribuion\n", " \n", " Distribution: Distribution Object (stats.scipy)\n", " TruncPoint: Truncation point (left truncation)\n", " Ndraws: Number of draws\n", " \n", " \"\"\"\n", " cdfTruncPoint = Distribution.cdf(TruncPoint)\n", " drawsU = cdfTruncPoint + (1 - cdfTruncPoint)*np.random.rand(Ndraws)\n", " return Distribution.ppf(drawsU)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparemos ahora las distribuciones de salarios aceptados y ofrecidos generando 10000 números aleatorios de ambas distribuciones." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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sU8zsKmA18H0Ad19qZlOIAsUeYJi7701z/SIikoa0goC7FwIFKSadXUL6McCY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\nfwBNF3s96uUEAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Ndraws = 10000\n", "obswages = randTruncDist(F,Req,Ndraws)\n", "wages = F.rvs(Ndraws)\n", "\n", "# Histograma\n", "plt.hist(obswages, bins=100, label='Salarios Aceptados')\n", "plt.hist(wages, bins=100, label='Salarios Ofrecidos')\n", "plt.title('Histograma: Salarios Aceptados vs. Salarios Ofrecidos')\n", "plt.legend()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.5.3" } }, "nbformat": 4, "nbformat_minor": 2 }