{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Job Search IV: Modeling Career Choice\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Job Search IV: Modeling Career Choice](#Job-Search-IV:-Modeling-Career-Choice) \n", " - [Overview](#Overview) \n", " - [Model](#Model) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "Next we study a computational problem concerning career and job choices\n", "\n", "The model is originally due to Derek Neal [[Nea99]](https://lectures.quantecon.org/zreferences.html#neal1999)\n", "\n", "This exposition draws on the presentation in [[LS18]](https://lectures.quantecon.org/zreferences.html#ljungqvist2012), section 6.5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model features\n", "\n", "- Career and job within career both chosen to maximize expected discounted wage flow \n", "- Infinite horizon dynamic programming with two state variables " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[32m\u001b[1mActivated\u001b[0m /home/qebuild/repos/lecture-source-jl/_build/website/jupyter/Project.toml\u001b[39m\n", "\u001b[36m\u001b[1mInfo\u001b[0m quantecon-notebooks-julia 0.1.0 activated, 0.2.0 requested\u001b[39m\n" ] } ], "source": [ "using InstantiateFromURL\n", "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.2.0\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using LinearAlgebra, Statistics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model\n", "\n", "In what follows we distinguish between a career and a job, where\n", "\n", "- a *career* is understood to be a general field encompassing many possible jobs, and \n", "- a *job* is understood to be a position with a particular firm \n", "\n", "\n", "For workers, wages can be decomposed into the contribution of job and career\n", "\n", "- $ w_t = \\theta_t + \\epsilon_t $, where \n", " \n", " - $ \\theta_t $ is contribution of career at time $ t $ \n", " - $ \\epsilon_t $ is contribution of job at time $ t $ \n", " \n", "\n", "\n", "At the start of time $ t $, a worker has the following options\n", "\n", "- retain a current (career, job) pair $ (\\theta_t, \\epsilon_t) $\n", " — referred to hereafter as “stay put” \n", "- retain a current career $ \\theta_t $ but redraw a job $ \\epsilon_t $\n", " — referred to hereafter as “new job” \n", "- redraw both a career $ \\theta_t $ and a job $ \\epsilon_t $\n", " — referred to hereafter as “new life” \n", "\n", "\n", "Draws of $ \\theta $ and $ \\epsilon $ are independent of each other and\n", "past values, with\n", "\n", "- $ \\theta_t \\sim F $ \n", "- $ \\epsilon_t \\sim G $ \n", "\n", "\n", "Notice that the worker does not have the option to retain a job but redraw\n", "a career — starting a new career always requires starting a new job\n", "\n", "A young worker aims to maximize the expected sum of discounted wages\n", "\n", "\n", "\n", "$$\n", "\\mathbb{E} \\sum_{t=0}^{\\infty} \\beta^t w_t \\tag{1}\n", "$$\n", "\n", "subject to the choice restrictions specified above\n", "\n", "Let $ V(\\theta, \\epsilon) $ denote the value function, which is the\n", "maximum of [(1)](#equation-exw) over all feasible (career, job) policies, given the\n", "initial state $ (\\theta, \\epsilon) $\n", "\n", "The value function obeys\n", "\n", "$$\n", "V(\\theta, \\epsilon) = \\max\\{I, II, III\\},\n", "$$\n", "\n", "where\n", "\n", "\n", "\n", "$$\n", "\\begin{aligned}\n", "& I = \\theta + \\epsilon + \\beta V(\\theta, \\epsilon) \\\\\n", "& II = \\theta + \\int \\epsilon' G(d \\epsilon') + \\beta \\int V(\\theta, \\epsilon') G(d \\epsilon') \\nonumber \\\\\n", "& III = \\int \\theta' F(d \\theta') + \\int \\epsilon' G(d \\epsilon') + \\beta \\int \\int V(\\theta', \\epsilon') G(d \\epsilon') F(d \\theta') \\nonumber\n", "\\end{aligned} \\tag{2}\n", "$$\n", "\n", "Evidently $ I $, $ II $ and $ III $ correspond to “stay put”, “new job” and “new life”, respectively" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameterization\n", "\n", "As in [[LS18]](https://lectures.quantecon.org/zreferences.html#ljungqvist2012), section 6.5, we will focus on a discrete version of the model, parameterized as follows:\n", "\n", "- both $ \\theta $ and $ \\epsilon $ take values in the set `linspace(0, B, N)` — an even grid of $ N $ points between $ 0 $ and $ B $ inclusive \n", "- $ N = 50 $ \n", "- $ B = 5 $ \n", "- $ \\beta = 0.95 $ \n", "\n", "\n", "The distributions $ F $ and $ G $ are discrete distributions\n", "generating draws from the grid points `linspace(0, B, N)`\n", "\n", "A very useful family of discrete distributions is the Beta-binomial family,\n", "with probability mass function\n", "\n", "$$\n", "p(k \\,|\\, n, a, b)\n", "= {n \\choose k} \\frac{B(k + a, n - k + b)}{B(a, b)},\n", "\\qquad k = 0, \\ldots, n\n", "$$\n", "\n", "Interpretation:\n", "\n", "- draw $ q $ from a β distribution with shape parameters $ (a, b) $ \n", "- run $ n $ independent binary trials, each with success probability $ q $ \n", "- $ p(k \\,|\\, n, a, b) $ is the probability of $ k $ successes in these $ n $ trials \n", "\n", "\n", "Nice properties:\n", "\n", "- very flexible class of distributions, including uniform, symmetric unimodal, etc. \n", "- only three parameters \n", "\n", "\n", "Here’s a figure showing the effect of different shape parameters when $ n=50 $\n", "\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots, QuantEcon, Distributions\n", "gr(fmt=:png);\n", "\n", "n = 50\n", "a_vals = [0.5, 1, 100]\n", "b_vals = [0.5, 1, 100]\n", "\n", "plt = plot()\n", "for (a, b) in zip(a_vals, b_vals)\n", " ab_label = \"a = $a, b = $b\"\n", " dist = BetaBinomial(n, a, b)\n", " plot!(plt, 0:n, pdf.(dist, support(dist)), label = ab_label)\n", "end\n", "plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Implementation:\n", "\n", "The code for solving the DP problem described above is found below:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "get_greedy (generic function with 1 method)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function CareerWorkerProblem(;β = 0.95,\n", " B = 5.0,\n", " N = 50,\n", " F_a = 1.0,\n", " F_b = 1.0,\n", " G_a = 1.0,\n", " G_b = 1.0)\n", " θ = range(0, B, length = N)\n", " ϵ = copy(θ)\n", " dist_F = BetaBinomial(N-1, F_a, F_b)\n", " dist_G = BetaBinomial(N-1, G_a, G_b)\n", " F_probs = pdf.(dist_F, support(dist_F))\n", " G_probs = pdf.(dist_G, support(dist_G))\n", " F_mean = sum(θ .* F_probs)\n", " G_mean = sum(ϵ .* G_probs)\n", " return (β = β, N = N, B = B, θ = θ, ϵ = ϵ,\n", " F_probs = F_probs, G_probs = G_probs,\n", " F_mean = F_mean, G_mean = G_mean)\n", "end\n", "\n", "function update_bellman!(cp, v, out; ret_policy = false)\n", "\n", " # new life. This is a function of the distribution parameters and is\n", " # always constant. No need to recompute it in the loop\n", " v3 = (cp.G_mean + cp.F_mean .+ cp.β .*\n", " cp.F_probs' * v * cp.G_probs)[1] # do not need 1 element array\n", "\n", " for j in 1:cp.N\n", " for i in 1:cp.N\n", " # stay put\n", " v1 = cp.θ[i] + cp.ϵ[j] + cp.β * v[i, j]\n", "\n", " # new job\n", " v2 = (cp.θ[i] .+ cp.G_mean .+ cp.β .*\n", " v[i, :]' * cp.G_probs)[1] # do not need a single element array\n", "\n", " if ret_policy\n", " if v1 > max(v2, v3)\n", " action = 1\n", " elseif v2 > max(v1, v3)\n", " action = 2\n", " else\n", " action = 3\n", " end\n", " out[i, j] = action\n", " else\n", " out[i, j] = max(v1, v2, v3)\n", " end\n", " end\n", " end\n", "end\n", "\n", "\n", "function update_bellman(cp, v; ret_policy = false)\n", " out = similar(v)\n", " update_bellman!(cp, v, out, ret_policy = ret_policy)\n", " return out\n", "end\n", "\n", "function get_greedy!(cp, v, out)\n", " update_bellman!(cp, v, out, ret_policy = true)\n", "end\n", "\n", "function get_greedy(cp, v)\n", " update_bellman(cp, v, ret_policy = true)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code defines\n", "\n", "- a named tuple `CareerWorkerProblem` that \n", " \n", " - encapsulates all the details of a particular parameterization \n", " - implements the Bellman operator $ T $ \n", " \n", "\n", "\n", "In this model, $ T $ is defined by $ Tv(\\theta, \\epsilon) = \\max\\{I, II, III\\} $, where\n", "$ I $, $ II $ and $ III $ are as given in [(2)](#equation-eyes), replacing $ V $ with $ v $\n", "\n", "The default probability distributions in `CareerWorkerProblem` correspond to discrete uniform distributions (see [the Beta-binomial figure](#beta-binom))\n", "\n", "In fact all our default settings correspond to the version studied in [[LS18]](https://lectures.quantecon.org/zreferences.html#ljungqvist2012), section 6.5.\n", "\n", "Hence we can reproduce figures 6.5.1 and 6.5.2 shown there, which exhibit the\n", "value function and optimal policy respectively\n", "\n", "Here’s the value function" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ "GKS: invalid bitmap size\n" ] } ], "source": [ "wp = CareerWorkerProblem()\n", "v_init = fill(100.0, wp.N, wp.N)\n", "func(x) = update_bellman(wp, x)\n", "v = compute_fixed_point(func, v_init, max_iter = 500, verbose = false)\n", "\n", "plot(linetype = :surface, wp.θ, wp.ϵ, transpose(v), xlabel=\"theta\", ylabel=\"epsilon\",\n", " seriescolor=:plasma, gridalpha = 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimal policy can be represented as follows (see [Exercise 3](#career-ex3) for code)\n", "\n", "\n", "\n", "\n", "\n", " \n", "Interpretation:\n", "\n", "- If both job and career are poor or mediocre, the worker will experiment with new job and new career \n", "- If career is sufficiently good, the worker will hold it and experiment with new jobs until a sufficiently good one is found \n", "- If both job and career are good, the worker will stay put \n", "\n", "\n", "Notice that the worker will always hold on to a sufficiently good career, but not necessarily hold on to even the best paying job\n", "\n", "The reason is that high lifetime wages require both variables to be large, and\n", "the worker cannot change careers without changing jobs\n", "\n", "- Sometimes a good job must be sacrificed in order to change to a better career " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Using the default parameterization in the `CareerWorkerProblem`,\n", "generate and plot typical sample paths for $ \\theta $ and $ \\epsilon $\n", "when the worker follows the optimal policy\n", "\n", "In particular, modulo randomness, reproduce the following figure (where the horizontal axis represents time)\n", "\n", "\n", "\n", " \n", "Hint: To generate the draws from the distributions $ F $ and $ G $, use the type [DiscreteRV](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/discrete_rv.jl)\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Let’s now consider how long it takes for the worker to settle down to a\n", "permanent job, given a starting point of $ (\\theta, \\epsilon) = (0, 0) $\n", "\n", "In other words, we want to study the distribution of the random variable\n", "\n", "$$\n", "T^* := \\text{the first point in time from which the worker's job no longer changes}\n", "$$\n", "\n", "Evidently, the worker’s job becomes permanent if and only if $ (\\theta_t, \\epsilon_t) $ enters the\n", "“stay put” region of $ (\\theta, \\epsilon) $ space\n", "\n", "Letting $ S $ denote this region, $ T^* $ can be expressed as the\n", "first passage time to $ S $ under the optimal policy:\n", "\n", "$$\n", "T^* := \\inf\\{t \\geq 0 \\,|\\, (\\theta_t, \\epsilon_t) \\in S\\}\n", "$$\n", "\n", "Collect 25,000 draws of this random variable and compute the median (which should be about 7)\n", "\n", "Repeat the exercise with $ \\beta=0.99 $ and interpret the change\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "As best you can, reproduce [the figure showing the optimal policy](#career-opt-pol)\n", "\n", "Hint: The `get_greedy()` method returns a representation of the optimal\n", "policy where values 1, 2 and 3 correspond to “stay put”, “new job” and “new life” respectively. Use this and the plots functions (e.g., `contour, contour!`) to produce the different shadings.\n", "\n", "Now set `G_a = G_b = 100` and generate a new figure with these parameters. Interpret." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wp = CareerWorkerProblem()\n", "\n", "function solve_wp(wp)\n", " v_init = fill(100.0, wp.N, wp.N)\n", " func(x) = update_bellman(wp, x)\n", " v = compute_fixed_point(func, v_init, max_iter = 500, verbose = false)\n", " optimal_policy = get_greedy(wp, v)\n", " return v, optimal_policy\n", "end\n", "\n", "v, optimal_policy = solve_wp(wp)\n", "\n", "F = DiscreteRV(wp.F_probs)\n", "G = DiscreteRV(wp.G_probs)\n", "\n", "function gen_path(T = 20)\n", " i = j = 1\n", " θ_ind = Int[]\n", " ϵ_ind = Int[]\n", "\n", " for t=1:T\n", " # do nothing if stay put\n", " if optimal_policy[i, j] == 2 # new job\n", " j = rand(G)[1]\n", " elseif optimal_policy[i, j] == 3 # new life\n", " i, j = rand(F)[1], rand(G)[1]\n", " end\n", " push!(θ_ind, i)\n", " push!(ϵ_ind, j)\n", " end\n", " return wp.θ[θ_ind], wp.ϵ[ϵ_ind]\n", "end\n", "\n", "plot_array = Any[]\n", "for i in 1:2\n", " θ_path, ϵ_path = gen_path()\n", " plt = plot(ϵ_path, label=\"epsilon\")\n", " plot!(plt, θ_path, label=\"theta\")\n", " plot!(plt, legend=:bottomright)\n", " push!(plot_array, plt)\n", "end\n", "plot(plot_array..., layout = (2,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "The median for the original parameterization can be computed as follows" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.0" ] } ], "source": [ "function gen_first_passage_time(optimal_policy)\n", " t = 0\n", " i = j = 1\n", " while true\n", " if optimal_policy[i, j] == 1 # Stay put\n", " return t\n", " elseif optimal_policy[i, j] == 2 # New job\n", " j = rand(G)[1]\n", " else # New life\n", " i, j = rand(F)[1], rand(G)[1]\n", " end\n", " t += 1\n", " end\n", "end\n", "\n", "\n", "M = 25000\n", "samples = zeros(M)\n", "for i in 1:M\n", " samples[i] = gen_first_passage_time(optimal_policy)\n", "end\n", "print(median(samples))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compute the median with $ \\beta=0.99 $ instead of the default value $ \\beta=0.95 $, replace `wp=CareerWorkerProblem()` with `wp=CareerWorkerProblem(β=0.99)`\n", "\n", "The medians are subject to randomness, but should be about 7 and 14 respectively. Not surprisingly, more patient workers will wait longer to settle down to their final job" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "14.0" ] } ], "source": [ "wp2 = CareerWorkerProblem(β=0.99)\n", "\n", "v2, optimal_policy2 = solve_wp(wp2)\n", "\n", "samples2 = zeros(M)\n", "for i in 1:M\n", " samples2[i] = gen_first_passage_time(optimal_policy2)\n", "end\n", "print(median(samples2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "Here’s the code to reproduce the original figure" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wp = CareerWorkerProblem();\n", "v, optimal_policy = solve_wp(wp)\n", "\n", "lvls = [0.5, 1.5, 2.5, 3.5]\n", "x_grid = range(0, 5, length = 50)\n", "y_grid = range(0, 5, length = 50)\n", "\n", "contour(x_grid, y_grid, optimal_policy', fill=true, levels=lvls,color = :Blues,\n", " fillalpha=1, cbar = false)\n", "contour!(xlabel=\"theta\", ylabel=\"epsilon\")\n", "annotate!([(1.8,2.5, text(\"new life\", 14, :white, :center))])\n", "annotate!([(4.5,2.5, text(\"new job\", 14, :center))])\n", "annotate!([(4.0,4.5, text(\"stay put\", 14, :center))])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we need only swap out for the new parameters" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wp = CareerWorkerProblem(G_a=100.0, G_b=100.0); # use new params\n", "v, optimal_policy = solve_wp(wp)\n", "\n", "lvls = [0.5, 1.5, 2.5, 3.5]\n", "x_grid = range(0, 5, length = 50)\n", "y_grid = range(0, 5, length = 50)\n", "\n", "contour(x_grid, y_grid, optimal_policy', fill=true, levels=lvls,color = :Blues,\n", " fillalpha=1, cbar = false)\n", "contour!(xlabel=\"theta\", ylabel=\"epsilon\")\n", "annotate!([(1.8,2.5, text(\"new life\", 14, :white, :center))])\n", "annotate!([(4.5,2.5, text(\"new job\", 14, :center))])\n", "annotate!([(4.0,4.5, text(\"stay put\", 14, :center))])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You will see that the region for which the worker\n", "will stay put has grown because the distribution for $ \\epsilon $\n", "has become more concentrated around the mean, making high-paying jobs\n", "less realistic" ] } ], "metadata": { "filename": "career.rst", "kernelspec": { "display_name": "Julia 1.2", "language": "julia", "name": "julia-1.2" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.2.0" }, "title": "Job Search IV: Modeling Career Choice" }, "nbformat": 4, "nbformat_minor": 2 }