{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Job Search II: Search and Separation\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Job Search II: Search and Separation](#Job-Search-II:-Search-and-Separation) \n", " - [Overview](#Overview) \n", " - [The Model](#The-Model) \n", " - [Solving the Model using Dynamic Programming](#Solving-the-Model-using-Dynamic-Programming) \n", " - [Implementation](#Implementation) \n", " - [The Reservation Wage](#The-Reservation-Wage) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "Previously [we looked](mccall_model.html) at the McCall job search model [[McC70]](../zreferences.html#mccall1970) as a way of understanding unemployment and worker decisions.\n", "\n", "One unrealistic feature of the model is that every job is permanent.\n", "\n", "In this lecture we extend the McCall model by introducing job separation.\n", "\n", "Once separation enters the picture, the agent comes to view\n", "\n", "- the loss of a job as a capital loss, and \n", "- a spell of unemployment as an *investment* in searching for an acceptable job " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": true }, "outputs": [], "source": [ "using InstantiateFromURL\n", "# optionally add arguments to force installation: instantiate = true, precompile = true\n", "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.8.0\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide-output": true }, "outputs": [], "source": [ "using LinearAlgebra, Statistics\n", "using Distributions, Expectations, Parameters, NLsolve, Plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Model\n", "\n", "The model concerns the life of an infinitely lived worker and\n", "\n", "- the opportunities he or she (let’s say he to save one character) has to work at different wages \n", "- exogenous events that destroy his current job \n", "- his decision making process while unemployed \n", "\n", "\n", "The worker can be in one of two states: employed or unemployed.\n", "\n", "He wants to maximize\n", "\n", "\n", "\n", "$$\n", "{\\mathbb E} \\sum_{t=0}^\\infty \\beta^t u(Y_t) \\tag{1}\n", "$$\n", "\n", "The only difference from the [baseline model](mccall_model.html) is that\n", "we’ve added some flexibility over preferences by introducing a utility function $ u $.\n", "\n", "It satisfies $ u'> 0 $ and $ u'' < 0 $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Timing and Decisions\n", "\n", "Here’s what happens at the start of a given period in our model with search and separation.\n", "\n", "If currently *employed*, the worker consumes his wage $ w $, receiving utility $ u(w) $.\n", "\n", "If currently *unemployed*, he\n", "\n", "- receives and consumes unemployment compensation $ c $ \n", "- receives an offer to start work *next period* at a wage $ w' $ drawn from a known distribution $ p_1, \\ldots, p_n $ \n", "\n", "\n", "He can either accept or reject the offer.\n", "\n", "If he accepts the offer, he enters next period employed with wage $ w' $.\n", "\n", "If he rejects the offer, he enters next period unemployed.\n", "\n", "When employed, the agent faces a constant probability $ \\alpha $ of becoming unemployed at the end of the period.\n", "\n", "(Note: we do not allow for job search while employed—this topic is taken\n", "up in a [later lecture](jv.html))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving the Model using Dynamic Programming\n", "\n", "Let\n", "\n", "- $ V(w) $ be the total lifetime value accruing to a worker who enters the current period *employed* with wage $ w $. \n", "- $ U $ be the total lifetime value accruing to a worker who is *unemployed* this period. \n", "\n", "\n", "Here *value* means the value of the objective function [(1)](#equation-objective) when the worker makes optimal decisions at all future points in time.\n", "\n", "Suppose for now that the worker can calculate the function $ V $ and the constant $ U $ and use them in his decision making.\n", "\n", "Then $ V $ and $ U $ should satisfy\n", "\n", "\n", "\n", "$$\n", "V(w) = u(w) + \\beta [(1-\\alpha)V(w) + \\alpha U ] \\tag{2}\n", "$$\n", "\n", "and\n", "\n", "\n", "\n", "$$\n", "U = u(c) + \\beta \\sum_i \\max \\left\\{ U, V(w_i) \\right\\} p_i \\tag{3}\n", "$$\n", "\n", "Let’s interpret these two equations in light of the fact that today’s tomorrow is tomorrow’s today.\n", "\n", "- The left hand sides of equations [(2)](#equation-bell1-mccall) and [(3)](#equation-bell2-mccall) are the values of a worker in a particular situation *today*. \n", "- The right hand sides of the equations are the discounted (by $ \\beta $) expected values of the possible situations that worker can be in *tomorrow*. \n", "- But *tomorrow* the worker can be in only one of the situations whose values *today* are on the left sides of our two equations. \n", "\n", "\n", "Equation [(3)](#equation-bell2-mccall) incorporates the fact that a currently unemployed worker will maximize his own welfare.\n", "\n", "In particular, if his next period wage offer is $ w' $, he will choose to remain unemployed unless $ U < V(w') $.\n", "\n", "Equations [(2)](#equation-bell1-mccall) and [(3)](#equation-bell2-mccall) are the Bellman equations\n", "for this model.\n", "\n", "Equations [(2)](#equation-bell1-mccall) and [(3)](#equation-bell2-mccall) provide enough information to solve out for both $ V $ and $ U $.\n", "\n", "Before discussing this, however, let’s make a small extension to the model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Stochastic Offers\n", "\n", "Let’s suppose now that unemployed workers don’t always receive job offers.\n", "\n", "Instead, let’s suppose that unemployed workers only receive an offer with probability $ \\gamma $.\n", "\n", "If our worker does receive an offer, the wage offer is drawn from $ p $ as before.\n", "\n", "He either accepts or rejects the offer.\n", "\n", "Otherwise the model is the same.\n", "\n", "With some thought, you will be able to convince yourself that $ V $ and $ U $ should now satisfy\n", "\n", "\n", "\n", "$$\n", "V(w) = u(w) + \\beta [(1-\\alpha)V(w) + \\alpha U ] \\tag{4}\n", "$$\n", "\n", "and\n", "\n", "\n", "\n", "$$\n", "U = u(c) +\n", " \\beta (1 - \\gamma) U +\n", " \\beta \\gamma \\sum_i \\max \\left\\{ U, V(w_i) \\right\\} p_i \\tag{5}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving the Bellman Equations\n", "\n", "We’ll use the same iterative approach to solving the Bellman equations that we\n", "adopted in the [first job search lecture](mccall_model.html).\n", "\n", "Here this amounts to\n", "\n", "1. make guesses for $ U $ and $ V $ \n", "1. plug these guesses into the right hand sides of [(4)](#equation-bell01-mccall) and [(5)](#equation-bell02-mccall) \n", "1. update the left hand sides from this rule and then repeat \n", "\n", "\n", "In other words, we are iterating using the rules\n", "\n", "\n", "\n", "$$\n", "V_{n+1} (w_i) = u(w_i) + \\beta [(1-\\alpha)V_n (w_i) + \\alpha U_n ] \\tag{6}\n", "$$\n", "\n", "and\n", "\n", "\n", "\n", "$$\n", "U_{n+1} = u(c) +\n", " \\beta (1 - \\gamma) U_n +\n", " \\beta \\gamma \\sum_i \\max \\{ U_n, V_n(w_i) \\} p_i \\tag{7}\n", "$$\n", "\n", "starting from some initial conditions $ U_0, V_0 $.\n", "\n", "Formally, we can define a “Bellman operator” T which maps:\n", "\n", "\n", "\n", "$$\n", "TV(\\cdot) = u(\\cdot) + \\beta (1-\\alpha)V(\\cdot) + \\alpha U \\tag{8}\n", "$$\n", "\n", "In which case we are searching for a fixed point\n", "\n", "\n", "\n", "$$\n", "TV^{*} = V^* \\tag{9}\n", "$$\n", "\n", "As before, the system always converges to the true solutions—in this case,\n", "the $ V $ and $ U $ that solve [(4)](#equation-bell01-mccall) and [(5)](#equation-bell02-mccall).\n", "\n", "A proof can be obtained via the Banach contraction mapping theorem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "Let’s implement this iterative process" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "solve_mccall_model (generic function with 1 method)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Distributions, LinearAlgebra, Expectations, Parameters, NLsolve, Plots\n", "\n", "function solve_mccall_model(mcm; U_iv = 1.0, V_iv = ones(length(mcm.w)), tol = 1e-5,\n", " iter = 2_000)\n", " # α, β, σ, c, γ, w = mcm.α, mcm.β, mcm.σ, mcm.c, mcm.γ, mcm.w\n", " @unpack α, β, σ, c, γ, w, dist, u = mcm\n", "\n", " # parameter validation\n", " @assert c > 0.0\n", " @assert minimum(w) > 0.0 # perhaps not strictly necessary, but useful here\n", "\n", " # necessary objects\n", " u_w = u.(w, σ)\n", " u_c = u(c, σ)\n", " E = expectation(dist) # expectation operator for wage distribution\n", "\n", " # Bellman operator T. Fixed point is x* s.t. T(x*) = x*\n", " function T(x)\n", " V = x[1:end-1]\n", " U = x[end]\n", " [u_w + β * ((1 - α) * V .+ α * U); u_c + β * (1 - γ) * U + β * γ * E * max.(U, V)]\n", " end\n", "\n", " # value function iteration\n", " x_iv = [V_iv; U_iv] # initial x val\n", " xstar = fixedpoint(T, x_iv, iterations = iter, xtol = tol, m = 0).zero\n", " V = xstar[1:end-1]\n", " U = xstar[end]\n", "\n", " # compute the reservation wage\n", " wbarindex = searchsortedfirst(V .- U, 0.0)\n", " if wbarindex >= length(w) # if this is true, you never want to accept\n", " w̄ = Inf\n", " else\n", " w̄ = w[wbarindex] # otherwise, return the number\n", " end\n", "\n", " # return a NamedTuple, so we can select values by name\n", " return (V = V, U = U, w̄ = w̄)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The approach is to iterate until successive iterates are closer together than some small tolerance level.\n", "\n", "We then return the current iterate as an approximate solution.\n", "\n", "Let’s plot the approximate solutions $ U $ and $ V $ to see what they look like.\n", "\n", "We’ll use the default parameterizations found in the code above." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "##NamedTuple_kw#254 (generic function with 2 methods)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# a default utility function\n", "u(c, σ) = (c^(1 - σ) - 1) / (1 - σ)\n", "\n", "# model constructor\n", "McCallModel = @with_kw (α = 0.2,\n", " β = 0.98, # discount rate\n", " γ = 0.7,\n", " c = 6.0, # unemployment compensation\n", " σ = 2.0,\n", " u = u, # utility function\n", " w = range(10, 20, length = 60), # wage values\n", " dist = BetaBinomial(59, 600, 400)) # distribution over wage values" ] }, { "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" } ], "source": [ "# plots setting\n", "gr(fmt=:png);\n", "\n", "mcm = McCallModel()\n", "@unpack V, U = solve_mccall_model(mcm)\n", "U_vec = fill(U, length(mcm.w))\n", "\n", "plot(mcm.w, [V U_vec], lw = 2, α = 0.7, label = [\"V\" \"U\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The value $ V $ is increasing because higher $ w $ generates a higher wage flow conditional on staying employed.\n", "\n", "At this point, it’s natural to ask how the model would respond if we perturbed the parameters.\n", "\n", "These calculations, called comparative statics, are performed in the next section." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Reservation Wage\n", "\n", "Once $ V $ and $ U $ are known, the agent can use them to make decisions in the face of a given wage offer.\n", "\n", "If $ V(w) > U $, then working at wage $ w $ is preferred to unemployment.\n", "\n", "If $ V(w) < U $, then remaining unemployed will generate greater lifetime value.\n", "\n", "Suppose in particular that $ V $ crosses $ U $ (as it does in the preceding figure).\n", "\n", "Then, since $ V $ is increasing, there is a unique smallest $ w $ in the set of possible wages such that $ V(w) \\geq U $.\n", "\n", "We denote this wage $ \\bar w $ and call it the reservation wage.\n", "\n", "Optimal behavior for the worker is characterized by $ \\bar w $\n", "\n", "- if the wage offer $ w $ in hand is greater than or equal to $ \\bar w $, then the worker accepts \n", "- if the wage offer $ w $ in hand is less than $ \\bar w $, then the worker rejects \n", "\n", "\n", "If $ V(w) < U $ for all $ w $, then the function returns np.inf.\n", "\n", "Let’s use it to look at how the reservation wage varies with parameters.\n", "\n", "In each instance below we’ll show you a figure and then ask you to reproduce it in the exercises." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Reservation Wage and Unemployment Compensation\n", "\n", "First, let’s look at how $ \\bar w $ varies with unemployment compensation.\n", "\n", "In the figure below, we use the default parameters in the McCallModel tuple, apart from\n", "c (which takes the values given on the horizontal axis)\n", "\n", "\n", "\n", " \n", "As expected, higher unemployment compensation causes the worker to hold out for higher wages.\n", "\n", "In effect, the cost of continuing job search is reduced." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Reservation Wage and Discounting\n", "\n", "Next let’s investigate how $ \\bar w $ varies with the discount rate.\n", "\n", "The next figure plots the reservation wage associated with different values of\n", "$ \\beta $\n", "\n", "\n", "\n", " \n", "Again, the results are intuitive: More patient workers will hold out for higher wages." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Reservation Wage and Job Destruction\n", "\n", "Finally, let’s look at how $ \\bar w $ varies with the job separation rate $ \\alpha $.\n", "\n", "Higher $ \\alpha $ translates to a greater chance that a worker will face termination in each period once employed.\n", "\n", "\n", "\n", " \n", "Once more, the results are in line with our intuition.\n", "\n", "If the separation rate is high, then the benefit of holding out for a higher wage falls.\n", "\n", "Hence the reservation wage is lower." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Reproduce all the reservation wage figures shown above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Plot the reservation wage against the job offer rate $ \\gamma $.\n", "\n", "Use" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "0.05:0.0375:0.95" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "γ_vals = range(0.05, 0.95, length = 25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Interpret your results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Using the solve_mccall_model function mentioned earlier in the lecture,\n", "we can create an array for reservation wages for different values of $ c $,\n", "$ \\beta $ and $ \\alpha $ and plot the results like so" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c_vals = range(2, 12, length = 25)\n", "\n", "models = [McCallModel(c = cval) for cval in c_vals]\n", "sols = solve_mccall_model.(models)\n", "w̄_vals = [sol.w̄ for sol in sols]\n", "\n", "plot(c_vals,\n", " w̄_vals,\n", " lw = 2,\n", " α = 0.7,\n", " xlabel = \"unemployment compensation\",\n", " ylabel = \"reservation wage\",\n", " label = \"w̄ as a function of c\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we could’ve done the above in one pass (which would be important if, for example, the parameter space was quite large)." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [], "source": [ "w̄_vals = [solve_mccall_model(McCallModel(c = cval)).w̄ for cval in c_vals];\n", "# doesn't allocate new arrays for models and solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Similar to above, we can plot $ \\bar w $ against $ \\gamma $ as follows" ] }, { "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": [ "γ_vals = range(0.05, 0.95, length = 25)\n", "\n", "models = [McCallModel(γ = γval) for γval in γ_vals]\n", "sols = solve_mccall_model.(models)\n", "w̄_vals = [sol.w̄ for sol in sols]\n", "\n", "plot(γ_vals, w̄_vals, lw = 2, α = 0.7, xlabel = \"job offer rate\",\n", " ylabel = \"reservation wage\", label = \"w̄ as a function of gamma\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, the reservation wage increases in $ \\gamma $.\n", "\n", "This is because higher $ \\gamma $ translates to a more favorable job\n", "search environment.\n", "\n", "Hence workers are less willing to accept lower offers." ] } ], "metadata": { "date": 1591310616.235898, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "mccall_model_with_separation.rst", "filename_with_path": "dynamic_programming/mccall_model_with_separation", "kernelspec": { "display_name": "Julia 1.4.2", "language": "julia", "name": "julia-1.4" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.4.2" }, "title": "Job Search II: Search and Separation" }, "nbformat": 4, "nbformat_minor": 2 }