{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Job Search I: The McCall Search Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Job Search I: The McCall Search Model](#Job-Search-I:-The-McCall-Search-Model) \n", " - [Overview](#Overview) \n", " - [The McCall Model](#The-McCall-Model) \n", " - [Computing the Optimal Policy: Take 1](#Computing-the-Optimal-Policy:-Take-1) \n", " - [Computing the Optimal Policy: Take 2](#Computing-the-Optimal-Policy:-Take-2) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> “Questioning a McCall worker is like having a conversation with an out-of-work friend:\n", "> ‘Maybe you are setting your sights too high’, or ‘Why did you quit your old job before you\n", "> had a new one lined up?’ This is real social science: an attempt to model, to understand,\n", "> human behavior by visualizing the situation people find themselves in, the options they face\n", "> and the pros and cons as they themselves see them.” – Robert E. Lucas, Jr." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "The McCall search model [[McC70]](../zreferences.html#mccall1970) helped transform economists’ way of thinking about labor markets.\n", "\n", "To clarify vague notions such as “involuntary” unemployment, McCall modeled the decision problem of unemployed agents directly, in terms of factors such as\n", "\n", "- current and likely future wages \n", "- impatience \n", "- unemployment compensation \n", "\n", "\n", "To solve the decision problem he used dynamic programming.\n", "\n", "Here we set up McCall’s model and adopt the same solution method.\n", "\n", "As we’ll see, McCall’s model is not only interesting in its own right but also an excellent vehicle for learning dynamic programming." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The McCall Model\n", "\n", "\n", "\n", "An unemployed worker receives in each period a job offer at wage $ W_t $.\n", "\n", "At time $ t $, our worker has two choices:\n", "\n", "1. Accept the offer and work permanently at constant wage $ W_t $. \n", "1. Reject the offer, receive unemployment compensation $ c $, and reconsider next period. \n", "\n", "\n", "The wage sequence $ \\{W_t\\} $ is assumed to be iid with probability mass function $ p_1, \\ldots, p_n $.\n", "\n", "Here $ p_i $ is the probability of observing wage offer $ W_t = w_i $ in the set $ w_1, \\ldots, w_n $.\n", "\n", "The worker is infinitely lived and aims to maximize the expected discounted sum of earnings.\n", "\n", "$$\n", "\\mathbb{E} \\sum_{t=0}^{\\infty} \\beta^t Y_t\n", "$$\n", "\n", "The constant $ \\beta $ lies in $ (0, 1) $ and is called a **discount factor**.\n", "\n", "The smaller is $ \\beta $, the more the worker discounts future utility relative to current utility.\n", "\n", "The variable $ Y_t $ is income, equal to\n", "\n", "- his wage $ W_t $ when employed \n", "- unemployment compensation $ c $ when unemployed " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A Trade Off\n", "\n", "The worker faces a trade-off:\n", "\n", "- Waiting too long for a good offer is costly, since the future is discounted. \n", "- Accepting too early is costly, since better offers might arrive in the future. \n", "\n", "\n", "To decide optimally in the face of this trade off, we use dynamic programming.\n", "\n", "Dynamic programming can be thought of as a two step procedure that\n", "\n", "1. first assigns values to “states” and \n", "1. then deduces optimal actions given those values \n", "\n", "\n", "We’ll go through these steps in turn." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Value Function\n", "\n", "In order to optimally trade off current and future rewards, we need to think about two things:\n", "\n", "1. the current payoffs we get from different choices \n", "1. the different states that those choices will lead to next period (in this case, either employment or unemployment) \n", "\n", "\n", "To weigh these two aspects of the decision problem, we need to assign *values* to states.\n", "\n", "To this end, let $ V(w) $ be the total lifetime *value* accruing to an unemployed worker who enters the current period unemployed but with wage offer $ w $ in hand.\n", "\n", "More precisely, $ V(w) $ denotes the value of the objective function [(1)](mccall_model_with_separation.html#equation-objective) when an agent in this situation makes *optimal* decisions now and at all future points in time.\n", "\n", "Of course $ V(w) $ is not trivial to calculate because we don’t yet know what decisions are optimal and what aren’t!\n", "\n", "But think of $ V $ as a function that assigns to each possible wage $ w $ the maximal lifetime value that can be obtained with that offer in hand.\n", "\n", "A crucial observation is that this function $ V $ must satisfy the recursion\n", "\n", "\n", "\n", "$$\n", "V(w)\n", "= \\max \\left\\{\n", " \\frac{w}{1 - \\beta}, \\, c + \\beta \\sum_{i=1}^n V(w_i) p_i\n", " \\right\\} \\tag{1}\n", "$$\n", "\n", "for every possible $ w_i $ in $ w_1, \\ldots, w_n $.\n", "\n", "This important equation is a version of the **Bellman equation**, which is\n", "ubiquitous in economic dynamics and other fields involving planning over time.\n", "\n", "The intuition behind it is as follows:\n", "\n", "- the first term inside the max operation is the lifetime payoff from accepting current offer $ w $, since \n", "\n", "\n", "$$\n", "w + \\beta w + \\beta^2 w + \\cdots = \\frac{w}{1 - \\beta}\n", "$$\n", "\n", "- the second term inside the max operation is the **continuation value**, which is the lifetime payoff from rejecting the current offer and then behaving optimally in all subsequent periods \n", "\n", "\n", "If we optimize and pick the best of these two options, we obtain maximal lifetime value from today, given current offer $ w $.\n", "\n", "But this is precisely $ V(w) $, which is the l.h.s. of [(1)](#equation-odu-pv)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Optimal Policy\n", "\n", "Suppose for now that we are able to solve [(1)](#equation-odu-pv) for the unknown\n", "function $ V $.\n", "\n", "Once we have this function in hand we can behave optimally (i.e., make the\n", "right choice between accept and reject).\n", "\n", "All we have to do is select the maximal choice on the r.h.s. of [(1)](#equation-odu-pv).\n", "\n", "The optimal action is best thought of as a **policy**, which is, in general, a map from\n", "states to actions.\n", "\n", "In our case, the state is the current wage offer $ w $.\n", "\n", "Given *any* $ w $, we can read off the corresponding best choice (accept or\n", "reject) by picking the max on the r.h.s. of [(1)](#equation-odu-pv).\n", "\n", "Thus, we have a map from $ \\mathbb{R} $ to $ \\{0, 1\\} $, with 1 meaning accept and zero meaning reject.\n", "\n", "We can write the policy as follows\n", "\n", "$$\n", "\\sigma(w) := \\mathbf{1}\n", " \\left\\{\n", " \\frac{w}{1 - \\beta} \\geq c + \\beta \\sum_{i=1}^n V(w_i) p_i\n", " \\right\\}\n", "$$\n", "\n", "Here $ \\mathbf{1}\\{ P \\} = 1 $ if statement $ P $ is true and equals zero otherwise.\n", "\n", "We can also write this as\n", "\n", "$$\n", "\\sigma(w) := \\mathbf{1} \\{ w \\geq \\bar w \\}\n", "$$\n", "\n", "where\n", "\n", "\n", "\n", "$$\n", "\\bar w := (1 - \\beta) \\left\\{ c + \\beta \\sum_{i=1}^n V(w_i) p_i \\right\\} \\tag{2}\n", "$$\n", "\n", "Here $ \\bar w $ is a constant depending on $ \\beta, c $ and the wage distribution, called the *reservation wage*.\n", "\n", "The agent should accept if and only if the current wage offer exceeds the reservation wage.\n", "\n", "Clearly, we can compute this reservation wage if we can compute the value function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computing the Optimal Policy: Take 1\n", "\n", "To put the above ideas into action, we need to compute the value function at\n", "points $ w_1, \\ldots, w_n $.\n", "\n", "In doing so, we can identify these values with the vector $ v = (v_i) $ where $ v_i := V(w_i) $.\n", "\n", "In view of [(1)](#equation-odu-pv), this vector satisfies the nonlinear system of equations\n", "\n", "\n", "\n", "$$\n", "v_i\n", "= \\max \\left\\{\n", " \\frac{w_i}{1 - \\beta}, \\, c + \\beta \\sum_{i=1}^n v_i p_i\n", " \\right\\}\n", "\\quad\n", "\\text{for } i = 1, \\ldots, n \\tag{3}\n", "$$\n", "\n", "It turns out that there is exactly one vector $ v := (v_i)_{i=1}^n $ in\n", "$ \\mathbb R^n $ that satisfies this equation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Algorithm\n", "\n", "To compute this vector, we proceed as follows:\n", "\n", "Step 1: pick an arbitrary initial guess $ v \\in \\mathbb R^n $.\n", "\n", "Step 2: compute a new vector $ v' \\in \\mathbb R^n $ via\n", "\n", "\n", "\n", "$$\n", "v'_i\n", "= \\max \\left\\{\n", " \\frac{w_i}{1 - \\beta}, \\, c + \\beta \\sum_{i=1}^n v_i p_i\n", " \\right\\}\n", "\\quad\n", "\\text{for } i = 1, \\ldots, n \\tag{4}\n", "$$\n", "\n", "Step 3: calculate a measure of the deviation between $ v $ and $ v' $, such as $ \\max_i |v_i - v_i'| $.\n", "\n", "Step 4: if the deviation is larger than some fixed tolerance, set $ v = v' $ and go to step 2, else continue.\n", "\n", "Step 5: return $ v $.\n", "\n", "This algorithm returns an arbitrarily good approximation to the true solution\n", "to [(3)](#equation-odu-pv2), which represents the value function.\n", "\n", "(Arbitrarily good means here that the approximation converges to the true\n", "solution as the tolerance goes to zero)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Fixed Point Theory\n", "\n", "What’s the math behind these ideas?\n", "\n", "First, one defines a mapping $ T $ from $ \\mathbb R^n $ to\n", "itself via\n", "\n", "\n", "\n", "$$\n", "Tv_i\n", "= \\max \\left\\{\n", " \\frac{w_i}{1 - \\beta}, \\, c + \\beta \\sum_{i=1}^n v_i p_i\n", " \\right\\}\n", "\\quad\n", "\\text{for } i = 1, \\ldots, n \\tag{5}\n", "$$\n", "\n", "(A new vector $ Tv $ is obtained from given vector $ v $ by evaluating\n", "the r.h.s. at each $ i $)\n", "\n", "One can show that the conditions of the Banach contraction mapping theorem are\n", "satisfied by $ T $ as a self-mapping on $ \\mathbb{R}^n $.\n", "\n", "One implication is that $ T $ has a unique fixed point in $ \\mathbb R^n $.\n", "\n", "Moreover, it’s immediate from the definition of $ T $ that this fixed\n", "point is precisely the value function.\n", "\n", "The iterative algorithm presented above corresponds to iterating with\n", "$ T $ from some initial guess $ v $.\n", "\n", "The Banach contraction mapping theorem tells us that this iterative process\n", "generates a sequence that converges to the fixed point." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation" ] }, { "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, NLsolve, Roots, Random, Plots, Parameters" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [], "source": [ "gr(fmt = :png);;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here’s the distribution of wage offers we’ll work with" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "support(dist) = 0:50\n" ] }, { "data": { "image/png": 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" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 50\n", "dist = BetaBinomial(n, 200, 100) # probability distribution\n", "@show support(dist)\n", "w = range(10.0, 60.0, length = n+1) # linearly space wages\n", "\n", "using StatsPlots\n", "plt = plot(w, pdf.(dist, support(dist)), xlabel = \"wages\", ylabel = \"probabilities\", legend = false)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can explore taking expectations over this distribution" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(E_w, E_w_2) = (43.333333333335695, 12.919896640724573)\n", "E * w = 43.3333333333357\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "dot(pdf.(dist, support(dist)), w) = 43.3333333333357\n" ] } ], "source": [ "E = expectation(dist) # expectation operator\n", "\n", "# exploring the properties of the operator\n", "wage(i) = w[i+1] # +1 to map from support of 0\n", "E_w = E(wage)\n", "E_w_2 = E(i -> wage(i)^2) - E_w^2 # variance\n", "@show E_w, E_w_2\n", "\n", "# use operator with left-multiply\n", "@show E * w # the `w` are values assigned for the discrete states\n", "@show dot(pdf.(dist, support(dist)), w); # identical calculation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To implement our algorithm, let’s have a look at the sequence of approximate value functions that\n", "this fixed point algorithm generates.\n", "\n", "Default parameter values are embedded in the function.\n", "\n", "Our initial guess $ v $ is the value of accepting at every given wage" ] }, { "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": [ "# parameters and constant objects\n", "\n", "c = 25\n", "β = 0.99\n", "num_plots = 6\n", "\n", "# Operator\n", "T(v) = max.(w/(1 - β), c + β * E*v) # (5) broadcasts over the w, fixes the v\n", "# alternatively, T(v) = [max(wval/(1 - β), c + β * E*v) for wval in w]\n", "\n", "# fill in matrix of vs\n", "vs = zeros(n + 1, 6) # data to fill\n", "vs[:, 1] .= w / (1-β) # initial guess of \"accept all\"\n", "\n", "# manually applying operator\n", "for col in 2:num_plots\n", " v_last = vs[:, col - 1]\n", " vs[:, col] .= T(v_last) # apply operator\n", "end\n", "plot(vs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One approach to solving the model is to directly implement this sort of iteration, and continues until measured deviation\n", "between successive iterates is below tol" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "compute_reservation_wage_direct (generic function with 1 method)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function compute_reservation_wage_direct(params; v_iv = collect(w ./(1-β)), max_iter = 500,\n", " tol = 1e-6)\n", " @unpack c, β, w = params\n", "\n", " # create a closure for the T operator\n", " T(v) = max.(w/(1 - β), c + β * E*v) # (5) fixing the parameter values\n", "\n", " v = copy(v_iv) # start at initial value. copy to prevent v_iv modification\n", " v_next = similar(v)\n", " i = 0\n", " error = Inf\n", " while i < max_iter && error > tol\n", " v_next .= T(v) # (4)\n", " error = norm(v_next - v)\n", " i += 1\n", " v .= v_next # copy contents into v. Also could have used v[:] = v_next\n", " end\n", " # now compute the reservation wage\n", " return (1 - β) * (c + β * E*v) # (2)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above, we use `v = copy(v_iv)` rather than just `v_iv = v`.\n", "\n", "To understand why, first recall that `v_iv` is a function argument – either defaulting to the given value, or passed into the function\n", "\n", "> - If we had gone `v = v_iv` instead, then it would have simply created a new name `v` which binds to whatever is located at `v_iv`. \n", "- Since we later use `v .= v_next` later in the algorithm, the values in it would be modified. \n", "- Hence, we would be modifying the `v_iv` vector we were passed in, which may not be what the caller of the function wanted. \n", "- The big issue this creates are “side-effects” where you can call a function and strange things can happen outside of the function that you didn’t expect. \n", "- If you intended for the modification to potentially occur, then the Julia style guide says that we should call the function `compute_reservation_wage_direct!` to make the possible side-effects clear. \n", "\n", "\n", "\n", "As usual, we are better off using a package, which may give a better algorithm and is likely to less error prone.\n", "\n", "In this case, we can use the `fixedpoint` algorithm discussed in [our Julia by Example lecture](../getting_started_julia/julia_by_example.html) to find the fixed point of the $ T $ operator." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "compute_reservation_wage (generic function with 1 method)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function compute_reservation_wage(params; v_iv = collect(w ./(1-β)), iterations = 500,\n", " ftol = 1e-6, m = 6)\n", " @unpack c, β, w = params\n", " T(v) = max.(w/(1 - β), c + β * E*v) # (5) fixing the parameter values\n", "\n", " v_star = fixedpoint(T, v_iv, iterations = iterations, ftol = ftol,\n", " m = 0).zero # (5)\n", " return (1 - β) * (c + β * E*v_star) # (3)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let’s compute the reservation wage at the default parameters" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "47.31649970147162" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mcm = @with_kw (c=25.0, β=0.99, w=w) # named tuples\n", "\n", "compute_reservation_wage(mcm()) # call with default parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparative Statics\n", "\n", "Now we know how to compute the reservation wage, let’s see how it varies with\n", "parameters.\n", "\n", "In particular, let’s look at what happens when we change $ \\beta $ and\n", "$ c $." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": false }, "outputs": [], "source": [ "grid_size = 25\n", "R = rand(grid_size, grid_size)\n", "\n", "c_vals = range(10.0, 30.0, length = grid_size)\n", "β_vals = range(0.9, 0.99, length = grid_size)\n", "\n", "for (i, c) in enumerate(c_vals)\n", " for (j, β) in enumerate(β_vals)\n", " R[i, j] = compute_reservation_wage(mcm(c=c, β=β)) # change from defaults\n", " end\n", "end" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "contour(c_vals, β_vals, R',\n", " title = \"Reservation Wage\",\n", " xlabel = \"c\",\n", " ylabel = \"beta\",\n", " fill = true)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, the reservation wage increases both with patience and with\n", "unemployment compensation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computing the Optimal Policy: Take 2\n", "\n", "The approach to dynamic programming just described is very standard and\n", "broadly applicable.\n", "\n", "For this particular problem, there’s also an easier way, which circumvents the\n", "need to compute the value function.\n", "\n", "Let $ \\psi $ denote the value of not accepting a job in this period but\n", "then behaving optimally in all subsequent periods.\n", "\n", "That is,\n", "\n", "\n", "\n", "$$\n", "\\psi\n", "= c + \\beta\n", " \\sum_{i=1}^n V(w_i) p_i \\tag{6}\n", "$$\n", "\n", "where $ V $ is the value function.\n", "\n", "By the Bellman equation, we then have\n", "\n", "$$\n", "V(w_i)\n", "= \\max \\left\\{ \\frac{w_i}{1 - \\beta}, \\, \\psi \\right\\}\n", "$$\n", "\n", "Substituting this last equation into [(6)](#equation-j1) gives\n", "\n", "\n", "\n", "$$\n", "\\psi\n", "= c + \\beta\n", " \\sum_{i=1}^n\n", " \\max \\left\\{\n", " \\frac{w_i}{1 - \\beta}, \\psi\n", " \\right\\} p_i \\tag{7}\n", "$$\n", "\n", "Which we could also write as $ \\psi = T_{\\psi}(\\psi) $ for the appropriate operator.\n", "\n", "This is a nonlinear equation that we can solve for $ \\psi $.\n", "\n", "One solution method for this kind of nonlinear equation is iterative.\n", "\n", "That is,\n", "\n", "Step 1: pick an initial guess $ \\psi $.\n", "\n", "Step 2: compute the update $ \\psi' $ via\n", "\n", "\n", "\n", "$$\n", "\\psi'\n", "= c + \\beta\n", " \\sum_{i=1}^n\n", " \\max \\left\\{\n", " \\frac{w_i}{1 - \\beta}, \\psi\n", " \\right\\} p_i \\tag{8}\n", "$$\n", "\n", "Step 3: calculate the deviation $ |\\psi - \\psi'| $.\n", "\n", "Step 4: if the deviation is larger than some fixed tolerance, set $ \\psi = \\psi' $ and go to step 2, else continue.\n", "\n", "Step 5: return $ \\psi $.\n", "\n", "Once again, one can use the Banach contraction mapping theorem to show that this process always converges.\n", "\n", "The big difference here, however, is that we’re iterating on a single number, rather than an $ n $-vector.\n", "\n", "Here’s an implementation:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "47.31649976654629" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function compute_reservation_wage_ψ(c, β; ψ_iv = E * w ./ (1 - β), max_iter = 500,\n", " tol = 1e-5)\n", " T_ψ(ψ) = [c + β * E*max.((w ./ (1 - β)), ψ[1])] # (7)\n", " # using vectors since fixedpoint doesn't support scalar\n", " ψ_star = fixedpoint(T_ψ, [ψ_iv]).zero[1]\n", " return (1 - β) * ψ_star # (2)\n", "end\n", "compute_reservation_wage_ψ(c, β)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can use this code to solve the exercise below.\n", "\n", "Another option is to solve for the root of the $ T_{\\psi}(\\psi) - \\psi $ equation" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "47.316499766546194" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function compute_reservation_wage_ψ2(c, β; ψ_iv = E * w ./ (1 - β), max_iter = 500,\n", " tol = 1e-5)\n", " root_ψ(ψ) = c + β * E*max.((w ./ (1 - β)), ψ) - ψ # (7)\n", " ψ_star = find_zero(root_ψ, ψ_iv)\n", " return (1 - β) * ψ_star # (2)\n", "end\n", "compute_reservation_wage_ψ2(c, β)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Compute the average duration of unemployment when $ \\beta=0.99 $ and\n", "$ c $ takes the following values\n", "\n", "> `c_vals = range(10, 40, length = 25)`\n", "\n", "\n", "That is, start the agent off as unemployed, computed their reservation wage\n", "given the parameters, and then simulate to see how long it takes to accept.\n", "\n", "Repeat a large number of times and take the average.\n", "\n", "Plot mean unemployment duration as a function of $ c $ in `c_vals`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Here’s one solution" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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QUVHRuXPn0tPTZTJZbm6uUqnMyMjQ7s3KylIoFEwNd+7cOXv2bHJyMqWUOX9tbW2dwyilBQUFZWVly5cvf++994qLi6Ojo7VvpKioqLS0lDnbrVu3YmJiqqqqtK+VnJxsb29fXl7O/KhUKtPT07V709LS1Go18zgnJ4d5Ym1t7d27d6Ojox88eFD/MKbrlHm5nJycrKysOu9drVbfuHHj+vXrtbW1zMdFKU1NTT179mxZWRnz9LKysoKCAt1nMa9YUlKi/Tw1Gk1ubi5TbVpaGvOxlJSUXLx4UVuYQqHQLUD3e3magwcPvv7665TS6upqlUrV8MHPi+Urs080cuTIGTNmaHtuG6ZWqzUajfaCO/BKZWWlnZ0d21WYoB49eqxcubJHjx5sF2Iivv76a6lUqn/z7uTJkz/++GO3bt2YWR9ACDl06ND27dsPHTqkVCqFQqGFhUUTnhyXRgEADKtr167PtYjMX3/9NWDAAN0lWsCgEIQAAIbFTDrU37p16wxUCTwRRo0CAACvIQgBAIDXEIQAAMBrCEIAAOA1BCEAAPAaghAAAHgN0ycAoC5ra+tVq1ZFRkayXQj8ByVErSGWPG65pKWl6a7T3bQQhABQF7OEB9tVNET3Bg58cLeMXsmjs9rxNwnbtGnTunVrA50cQQgAdfn4+Hz44YdsV9EQvq2u938PNbUF9MNwM7YLMU38/fsCAKC5kMqJh5jtIkwXghAAgOukcuphLWC7CpOFIAQA4Dq0CA0KQQgAwHV5CuohRovQUBCEAABchxahQSEIAQA4jRKSr6Bu6CM0GAQhAACnlSqJ2JxYYeqEwSAIAQA4TSpHB6FhIQgBADgNHYSGhiAEAOA0qQKTCA0LQQgAwGloERoaghAAgNOkcuqOPkJDQhACAHCaVE48rNkuwqQhCAEAOA2jRg0NQQgAwGlSBfoIDQtBCADAaWgRGhqCEACAu2RqQimxs2C7DpOGIAQA4C40B40AQQgAwF3oIDQCBCEAAHehRWgECEIAAO7CsjJGgCAEAOAuqRwLjRocghAAgLvQIjQCBCEAAHflKdBHaHAIQgAA7kKL0AgQhAAA3IVRo0aAIAQA4CiVhshqiKOI7TpMHYIQAICj8uTUzVqA9qChIQgBADgKHYTGgSAEAOAoqQKTCI0BQQgAwFFoERoHghAAgKOkcuqOIaOGhyAEAOAoqZx4WLNdBA8gCAEAOAqTCI0DQQgAwFG4GaFxIAgBADhKKqcIQiNAEAIAcJGGkuJq4mqFS6MGhyAEAOCigmoiERFz/JI2PHzGAABchJEyRoMgBADgIsymNxoEIQAAF0nlWF/NSBCEAABchBah0SAIAQC4SKpAH6GRIAgBALgoDy1CY0EQAgBwEUaNGg2CEACAi6QKrLhtJAhCAAAuyldQN4waNQoEIQAA55QqiZUZsTZnuw5+QBACAHCOVIFJhMaDIAQA4BxMIjQmBCEAAOdgyKgxIQgBADhHKifuGDJqLAhCAADOQYvQmBCEAACcI1Wgj9B4EIQAAJyDFqExIQgBADgHo0aNCUEIAMA5aBEak2GDMC0t7cMPPwwLC+vWrdu8efPKysoIITU1NV988UWnTp369Olz6tQpgxYAANDsVNWQWkpaWLBdB28YNgiTkpIkEsnq1as3b958+/btadOmEUJ++umn48eP792794MPPpgwYcLjx48NWgMAQPOC5qCRGXYlu5EjR44cOZJ5vHz58sGDBxNCNm7cuHHjxsDAwMDAwP3792/btm358uUGLQMAoBlBB6GRGa+PMC4urkOHDuXl5ZmZmd26dWM2hoaGJiYmGq0GAADuk8qx0KhRGWlt83v37n355ZdHjhwpLCwkhNjb2zPbHRwcCgoK6hxcUVExffp0a+v/WVZh27ZtPXr0qH9mtVqt0WjUarVhCgdOq6qqEgjw+4KPTPurTy81c7YQyGQKtgvhIqVSKRQKLSz07UEVi8VC4TOafMYIwpSUlEGDBq1ZsyY8PJwJwqqqKpFIRAiprKyUSCR1jre1tf3+++8HDBigu9HNzY15Sh1MED5xF5g8SqmtrS3bVQALTPurL9HU+tgLbG2t2C6EiywsLJ4rCPVh8CBMT09/7bXXlixZMmXKFEKIs7OznZ3do0ePwsLCCCHJycl+fn51niIUCl1cXHx8fAxdGwAAB+XJSQcHtovgE8P2EWZmZvbr12/GjBnjxo0rLS0tLS0lhEyaNGnNmjWU0pycnKioqEmTJhm0BgCA5gWjRo3MsEF44sSJsrKylStXtv5HVVXVsmXLpFKpm5tbUFDQ+++//8SePwAA3pIqiAduPWFEhr00OmvWrFmzZtXZaGtre+HChfLycpFIZGWFi+AAAP8DLUIjM9Ko0fq0A0cBAEBLpSEVKuKI8X9GhLVGAQA4JF9B3awFQjQIjQhBCADAIVhWxvgQhAAAHIIOQuNDEAIAcAhahMaHIAQA4BCpnLpjoVHjQhACAHCIVIEWobEhCAEAOEQqpwhCI0MQAgBwiFROMFjGyBCEAAAcIpVjfTVjQxACAHCFhpKiauqKwTLGhSAEAOCKwmriICIW+MVsXPi8AQC4QiqnHmgOGh2CEACAKzCbnhUIQgAArpAqsL4aCxCEAABcgRYhKxCEAABcgRW3WYEgBADgijwFJhGyAEEIAMAVaBGyAkEIAMAV6CNkBYIQAIAr8hTUDfMIjQ5BCADACWUqIhISsTnbdfAPghAAgBPQQcgWBCEAACegg5AtCEIAAE5Ai5At+gbh1q1bo6KimMc5OTk9e/YUiUQ9evRITU01WG0AADwiVRB3TCJkg15BSCldtGiRWq1mflywYMG9e/fmzZsnk8mmTZtmyPIAAPgCLUK26BWE5eXlxcXFwcHBhBCFQnHkyJHFixevWLEiMjLy8uXL+fn5Bi4SAMD0oY+QLXoFYXV1NSHE2tqaEHL58mW5XD506FBCSPv27Qkh2dnZhqwQAIAX0CJki15B6Orqam1tfe3aNULI3r17vb29O3ToQAhh2oJ2dnYGLREAgA+kciw0yg69glAoFE6bNm3mzJnh4eE7duyYPn26QCAghMTGxlpZWfn4+Bi4SAAA04cWIVv0XcNg9erVLVu2jIuL++abb+bNm8dsjI2Nffvtt62srAxWHgAAL8hriJoSe0u26+AlfYPQwsJi/vz5CQkJ2dnZhw8fZjZ2797dYIUBAPCIVE49sMooS/QNwosXL06bNu3x48f1d1FKm7QkAADewZBRFukbhNOmTbO0tDx06FBAQICFhYVBawIA4BupAh2ErNErCEtKSh4/fnz69OkBAwYYuiAAAB5Ci5BFeo0aFYlE5ubmmCYBAGAgGDLKIr2C0MbG5q233tq9e7ehqwEA4Kc8BSYRsqahS6Pp6el///0387hfv36fffZZZmbm4MGDXVxcdA8bP368AQsEAOABqZx6iHE7IHY0FITnz5+fPn267pajR48ePXq0zmEYNQoA8ILQR8iihoJw3Lhxr776qtFKAQDgLfQRsqihILSzs9MOkNm1a9fAgQPd3Nx0D8jPzz98+PDMmTMNWCAAgKlTa0iFmjiJ2K6Dr/S9JL1w4cL69+BNS0ubNWtWU5cEAMAv+QrqYiUQokHIkhfqm62qqrKxsWmqUgAA+AkdhOx6xoT6xMRE5u5LCoXi8OHDSUlJ2l1qtXrPnj0BAQGGLRAAwNShg5BdzwjC6Oho7b0mfvjhhzp7/f39/+///s8gdQEA8IZUQdwxiZA9zwjCd999NyIighDSvn37Xbt2vfzyy9pdIpFILEZjHgDgRUnlFJdGWfSMILSysmJuNxgdHe3u7h4fH5+dna1UKnWPwahRAIAXIZWTrs64NMoafe8+kZubO3DgwPz8/Pq7EIQAAC9CKsf6amzSNwjfeecdd3f3yMjIDh06iESY7QIA0GSwvhq79ArC4uLi7OzsXbt29enTx8D1AADwjlSB6RNs0utvELFYbGlpifvxAgA0OQ0lhQrqZo0+QtboFYTW1tYRERFbt241dDUAAHxTVE3sLYkFroyyR98+wtDQ0C+++KJv376DBg1ydHTU3YXBMgAAjSZVYDY9y/QNws8//zw/Pz8vL+/ChQt1diEIAQAaDeursU7fIHz48KFGozFoKQAAPIT11VinbxDa29sTQjIyMhISErKzsz08PIKCgtq2bWvI2gAATB8mEbJO3yBUqVSzZs3auXOnbrvw9ddf37lzZ4sWLQxTGwCA6ctT0LYt0CJkk74DlT7++ONdu3bNmTPn8uXLqampsbGxixcvPn369IwZMwxaHwCAaUMfIev0ahGq1eqtW7cuW7bss88+Y7b4+/t37969bdu206dPLywsdHFxMWSRAAAmC8vKsE6vT7+wsFAmk40YMaLO9pEjR2o0mvT09KavCwCAH9AiZJ1eQWhvb29mZvbgwYM62+/fv08IcXJyavq6AAD4IU9B3bGsDKv0CkIbG5sBAwZ88MEHJ0+e1G68du3atGnTgoOD/f39DVYeAIApK1cRCyER6ztsEQxC3wvTmzZtsrW1HTJkiIODQ4cOHZydnV955ZWKioqdO3catD4AABOGSYRcoO/fIb6+vgkJCXv27Lly5Up+fn7Xrl27d+8+ZcoUBwcHg9YHAGDCpApMImTfczTIzc3NAwMDxWKxXC5ntvzxxx8ES6wBADSWVE7d0SJkm75BeOHChbffflsqldbfhSAEAGgcDBnlAn2DcOLEiR4eHtu3b2/Tpo1BCwIA4A/0EXKBXkFYUFCQm5u7b9++Xr16GbogAAD+kMpJF0xAY5teo0YlEomdnV1NTY2hqwEA4BW0CLlAryC0sLBYuHDht99+qx0mAwAAL06qQB8h+57jxrwzZsxo27Ztz549JRKJ7q5ff/3VAIUBAJg+tAi5QN8gXLVq1bZt2ywsLK5du2ZpaWnQmgAA+EBRQ1Qa4oBfqGzTKwiVSuUXX3zx1ltvbdq0CXcfBABoElKsMsoNevURlpaWyuXyefPmIQUBAJoKJhFyhF5B6Orq6unpmZ2dbehqAAD4Ax2EHKFXEAqFwl9++eXzzz9PTEw0dEEAADwhlWOhUU7Qd7DMhg0b8vPzO3Xq5Onp6eHhobvr5s2bBigMAMDE5SnQIuSE57j7BG40AQDQhKRyEu7OdhGgfxBu2bLFoHUAAPCNVE49xPreFBYMB98BAAA7MGqUIxCEAADskCqoB+YRcgCCEACABTUaUqYkzlZs1wFGCMKVK1cOHTq0bdu2zO3sCSG7du1qrSM5OdnQNQAAcE2+grpYC4RoEHKAwYOQUjpp0iSxWFxRUcFsKS8vDwoKOvMPX19fQ9cAAMA1UgUmEXKFvqNGG23+/PmEkI0bN+putLW19ff3N/RLAwBwFpaV4Q52+ghPnjzp6ekZEhKyceNGSmn9A5RKpfx/aTQa49cJAGAgUjlxx5BRbjB4i7C+Pn36REdHe3l53bx5MyIiQiQSTZ8+XfeA8vLySZMmmZmZ6W6Miorq3bt3/bOp1WqNRqNSqQxbNHCSTCZjuwRghwl89eml5k5mpLKyhu1CmhmlUikUCi0sLPQ8XiwW10mT+lgIwqCgIObB0KFD58+fHxUVVScI7e3to6KiRo4cqc/ZmCAUiURNXyg0B3Z2dmyXAOxo7l99SW1tZyeBnR36CZ+PpaXlcwWhPliePiEQ4BI5APCRVIHZ9Fxh8CBMS0uLi4uTyWQZGRlxcXHl5eWRkZEPHjwoLi4+derUypUrx4wZY+gaAAC4BoNluMPgl0Y3bdp07tw5MzOzEydOnDhxYtWqVYmJiV9++WVpaWnLli2XLFkyY8YMQ9cAAMA1WF+NOwwehD/88EOdLeHh4d9++62hXxcAgLMoIYXV1A3rq3EDllgDADC2ompiZ0Es8QuYG/A9AAAYGzoIOQVBCABgbFI51lfjEAQhAICxoUXIKQhCAABjwyRCTkEQAgAYWx5ahFyCIAQAMDZMIuQUBCEAgLFJFdQDkwg5A0EIAGBsaBFyCoIQAMDY8iOit/gAAB02SURBVOTUHX2EnIEgBAAwqgo1MRMQGxZuggdPhiAEADAqTCLkGgQhAIBRoYOQa9A4B56qpaTX0Rq1hu06oFFqay3NzGrYrqKRylQk1AUtQg5BEAJPPSyn+QoS1d+M7UKgMeRypVhsyXYVjedixXYFoANBCDx1s5C+7CIIccYf5s1SZaXGzg7fHTQN9BECT8UX065IQQBAEAJvxRdRNAcBgCAIgZ80lCQU0y5OCEIAQBACLyVXUCcrgaOI7ToAgAMQhMBHcbguCgD/QBACH8UXYaQMAPwHghD4KL6IdkUHIQAQQhCEwEOUkFuYOwEA/0AQAu+kVtAWlgIs7QEADAQh8A6uiwKALgQh8A7WlAEAXQhC4J04DBkFAB0IQuCd28W4NAoA/4UgBH5Jr6SWQgFuiwoAWghC4Jf4YtrVme0iAIBLEITAL7jpBADUgSAEfonD3AkA+F8IQuAXrCkDAHUgCIFHsqsoJcTbBkEIAP+FIAQewd2XAKA+BCHwCBZXA4D6EITAI1hcDQDqQxACj2DIKADUhyAEvshXEGUt8bVDEALA/0AQAl/cLKIhzgLEIADUgSAEvsBNJwDgiRCEwBe30EEIAE+CIAS+wCRCAHgiBCHwQlE1qVBT/xYIQgCoC0EIvMBMnEAMAkB9CELgBVwXBYCnQRACL2BNGQB4GgQh8EI85k4AwFMgCMH0lSpJUTVti5EyAPAkCEIwfXFFtLOTQIgcBIAnQRCC6YsvxkgZAHgqBCGYPnQQAkADEIRg+uKLsbgaADwVghBMXIWa5FbR9vYIQgB4MgQhmLj4IhrsJDDHv3QAeAr8egATF4+bTgBAgxCEYOKwpgwANAxBCCYOq4wCQMMQhGDKZGqSKaMdHBCEAPBUCEIwZbeLaZBEYIF/5gDwdPgNAaYsDlPpAeBZEIRgyjCVHgCeCUEIpiweI2UA4FkQhGCyFDUkrZJ2lCAIAaAhCEIwWQklNMBBIDJjuw4A4DYEIZgszCAEAH0gCMFkYXE1ANAHghBMFhZXAwB9IAjBNClryaNy+hJGygDAsyAIwTTdKaFtWwiszdmuAwA4D0EIpgnXRQFATwhCME3xWFwNAPSDIATTFIchowCgHwQhmCC1hjwoo8EIQgDQA4IQTFBSKfWzE9hgpAwA6AFBCCYIU+kBQH8IQjBBGDIKAPpDEIIJwiqjAKA/BCGYmlpK7pbSzrg0CgD6QRCCqblXSr3EAjsLtusAgGYCQQimBtdFAeC5sBOElNK0tLSioiJWXh1MW3wx7YIgBAC9GTYIKyoqhgwZ4uLiIhAIUlJSmI05OTmdO3cePHhwQEDARx99ZNACgIfi0SIEgOdh2CA0MzObOnXqpUuXdDcuWbIkNDT00aNHDx48iIqKunjxokFrAF7RUHKnhHZ2RBACgL4Mu/aGjY3Nm2++WVNTo92i0Wj27t3LhJ+zs/P48eMjIyNfffVVg5YB/PGgnLpaCyQitusAgObD2ItQFRYWyuXyNm3aMD+2adPm2LFjdY6pra1NTU2Nj4/X3di2bVs7OzsjVQnNFq6LAsDzMnYQVlZWEkKsra2ZH8VicUVFRZ1j5HL52rVrd+zYobtxzZo1ISEh9U+oVqs1Go1arTZMvcBpVVVVAsH/xN51qXmQHZHJFGyVBMZR/6sHnlAqlUKh0MJC3wlSYrFYKHxGJ6Cxg9DNzY0QUlpa6u7uTggpKSlhHuiys7Nbs2bNyJEj9TkhE4QiEa6F8RGl1NbWVndLYkXNYn8zW1srtkoC46j/1QNPWFhYPFcQ6sPY0yfs7Oxat259/fp15sfY2NjOnTsbuQYwVZSQ28W0C9aUAYDnYfAW4eHDhxUKBSHkxIkT7u7uo0eP/uCDDz799FNnZ+cHDx6cOXNm9erVhq4BeCK5nEpEAme0BgHgeRg8CC9evFhVVTVz5sykpKSkpKQRI0Z88MEHGo1m8eLFjo6OJ0+e9Pb2NnQNwBO4+xIANILBg3DlypX1N86dO3fu3LmGfmngG9x9CQAaAWuNgunAKqMA0AgIQjARGCkDAI2DIAQT8biSis0FbtZs1wEAzQ2CEExEXBE6CAGgMRCEYCJuYcgoADQKghBMBEbKAEDjIAjBRNwqpl2d2S4CAJohBCGYgkwZFQqIpxgtQgB4bghCMAVxRbQbrosCQKMgCMEUYE0ZAGg0BCGYgnjMnQCAxkIQginAjekBoNEQhNDs5VTRGkpa2iAIAaAxEITQ7MUXozkIAI2HIIRmLw5rygDAC0AQQrMXX0QwUgYAGg1BCM0eLo0CwItAEELzVqAg8hrqZ4cgBIBGQhBC88Z0ECIGAaDREITQvOGmEwDwghCE0LxhcTUAeEEIQmje4jF3AgBeDIIQmrESlaBMRVu3QBACQOMhCKEZu10q7OIkECIHAeAFIAihGbtdIkAHIQC8IAQhNGMJpUJ0EALAC0IQQjN2Cy1CAHhh5mwX0ATW3BNQoYbtKsDYaikpVJJ29ghCAHghphCE5WpSK6BsVwEsWPJSrRlyEABejCkE4ZJgKhKZsV0FsKCysobtEgCg2UMfIQAA8BqCEAAAeA1BCAAAvNbsgzA5OTkxMZHtKoAFlZWVZ8+eZbsKYEd0dLRMJmO7CmBBYmJicnJy056z2QfhkSNHfv/9d7arABbk5OR8/PHHbFcB7Fi4cGFubi7bVQAL9uzZc/To0aY9Z7MPQgAAgBeBIAQAAF4TUMq5qej/+te/7t+/7+joqM/B2dnZarW6VatWhq4KuEahUNy9e7dbt25sFwIsuHnzZseOHa2trdkuBIwtLS3N0tLS29tbz+PXrVv3zIDgYhBWVFRcunSJ7SoAAKDZ6927d4sWLRo+hotBCAAAYDToIwQAAF5DEAIAAK81v0W309LSbty4kZGRMWrUqPbt2zMb4+Pjd+zYQQiZOnVq165dWS0QDCU9Pf3gwYMpKSn29vYTJ07s2LEjIaS6unrDhg0PHz4MCgqaNWuWpaUl22VC08vLy4uMjExJSTEzM+vVq9e4ceOEQiEh5Pz58/v37xeLxTNnzmzbti3bZYIBlZaWbt68uVevXj179iSEVFdXb9y48cGDBx07dpw9e/YL/sdvfi3C119/ffv27T/88IN2QZk7d+706dOnZcuWPj4+ffr0SUhIYLdCMJCFCxfev3+/U6dOGo0mNDQ0JiaGEDJx4sQTJ0706tVr//7977zzDts1gkGkpqZmZmZ26dKlTZs2n3766SeffEIIOXXq1NixY4OCgqysrMLCwjC/3rTNmzfv+++/1y4mNWXKlGPHjoWHhx84cGD69OkvenbaPAUFBUVFRTGPp02bNnfuXObx/PnzIyIi2KsLDEitVmsf/+tf/5o9e/bDhw+trKzKysoopfn5+SKRKCsri70CwRgOHDjQunVrSmm/fv1Wr17NbBw3btyXX37JZllgSNHR0UOGDBk7duzSpUsppcnJyVZWViUlJZTSwsJCkUiUkZHxIudvfi3C+mJiYvr27cs87tev39WrV9mtBwzE3Py/V/LLysokEklMTEzXrl3t7e0JIa6urgEBAbGxsewVCAanUqnOnDkTGhpKCImJienXrx+zHf/xTVhFRcWcOXPWr18vEPznNtzXrl0LDg6WSCSEEGdn544dO167du1FXsIUglAqlTo7OzOPXVxcpFIpu/WAoZ06dercuXNz5szJy8vTfvWEEFdXV3z7pqq4uNjR0dHGxuby5ctr164tLS2trq7W/Y+PS6Om6uOPP549e7a/v792S5P/xzeFIBSJRGq1mnmsUqmsrKzYrQcM6saNG5MnT/7jjz88PT11v3pCiFKpxLdvqpycnEpKSh4/fhwaGjpu3Djmi9b9j49VZkzShQsXbt++PWfOHN2NTf4fv/mNGq3Py8srOzubeZyVleXl5cVuPWA48fHxI0eO3LZt22uvvUb+96snhGRnZ+PbN23e3t5ff/21l5eXQqGQSCTZ2dk+Pj6EkKysLE9PT7arg6Z34MCBlJSUdu3aEULy8/PPnj2blpY2YsSIpv2PbwotwlGjRu3du5d5HBkZOWrUKHbrAQO5c+fO0KFD16xZM3z4cGbLwIED09LSmPHD169fLy0t7dOnD5slgmGUlZVpH1++fNnR0dHBwWHUqFHMLdhqamqioqJGjx7NXoFgKEuWLLlx48aZM2fOnDnTu3fvqVOnrlix4rXXXsvMzLx9+zYh5ObNmwUFBdre4kZqmjE9RjR79uyQkBBra2t/f/+QkJD4+PiioqLAwMBXX321T58+HTp0KCoqYrtGMIjevXvb29uH/OPDDz+klK5cudLd3X3ChAmurq6//vor2zWCQcydO7djx46jRo3q1auXo6PjgQMHKKUpKSleXl7Dhg0LCQkJDw9XKBRslwmGNW7cOGbUKKV0zZo1bm5uEyZMcHNz27BhwwueufmtNSqVShUKhfZHT09PKysrpVJ55coVQkivXr1EIhF71YEB5ebmVldXa38Ui8Xu7u6EkOTkZGZerW53OpgSjUaTlJSUnp7u6OgYHBxsZ2fHbJfJZFeuXLGxsXnllVfMzMzYLRIMLT8/39LSkhksSghJSUm5f/9+YGBg69atX/DMzS8IAQAAmpAp9BECAAA0GoIQAAB4DUEIAAC8hiAEAABeQxACAACvIQgB/istLW3Hjh2683OA+5RK5Y4dO1JSUtguBJorBCHAf125ciUiIkJ3HROuuXbt2q5du9iugk1VVVWbN29OTk7WbqmoqIiIiLh06RKLVUGzhiAEaE6ioqIWLlzIdhVsKisrmzVrlu5td2xsbJYvXx4SEsJiVdCsIQiBu4qLi1UqVf3tMpksLy+vtrb2ic8qLS2VyWS6W4qKip54sEqlys/Pr6mpaaCG0tLSgoKC56n6P6qqqkpKSuqc6olvp+GXKCoq0l1oX38KhSIvL6/+uyspKSksLHzas0pLS6uqquoU8LyfXlVV1RNfmlFZWVnnCyKE1NbW5ufny+XyOttramoKCgo0Gs3TCiaEiMXizz//PDg4WLtFLpfn5eU97XOrrq4uLS1t4ITAOy+4RBtAI2zdulUikVRUVNTZUllZuWrVKolEcuvWrc6dOxNCzM3Nhw0bxtyDnlIaExMTFhbG3J/Tycnp559/Zrbv27dPIpFcvHixe/fuhBCBQDBx4sTq6urjx4/7+fkRQmxsbFauXMkcHBwc/NFHH3322Wc2NjaEEGdn599++43ZtWPHDkJIbm4upfTMmTNBQUHMf5OWLVvu2LGDUvrw4UOJRLJz507dt7Nz506JRPLw4cPExESJRLJv375Ro0YJhUJCSHh4eH5+/p07d7p27UoIsbCweO+999RqNfPE/fv3t2/fnnkJPz+//fv3M9u/+uorPz+/mJiYDh06EEIsLS3Hjx9fVVU1e/ZsKysroVAokUgkEom/v/8TP97ExMQBAwYw9zE2MzPr27evXC6nlP71118BAQHMy7Vq1Wrv3r3M8bt375ZIJJcuXWJueCsUCqdMmaJUKo8ePerr60sIsbW1Xbt2LXNwYGDgggULFi1aJBaLCSGurq66n0ZCQkKfPn2Y925vb79kyZLa2lpKaXR0tEQiOXXq1ODBgwUCgUAgCAkJefToEaW0pKTkjTfe0N512cfH5+TJk5TSEydOhIaGMgunWVlZDRo06PHjx0lJScx9mG1sbJgPYffu3cXFxe7u7pGRkZTSzMzMYcOGMc+ytbX96KOPlEolpbS8vFwikWzYsOHdd99lVmH09fVlXggAQQgs2LBhAyGkvLy8zpaKiooVK1YQQgICAjZu3Hjz5s21a9daWFgsXLiQUhoXF8f8Qjx//nxiYuKyZcvMzMzWr19PKd25cyfzy3316tV///33Dz/8IBAIpkyZ0q5du3379t24cSMiIoIQEhcXRyn18/NzcnIKCwu7dOnS33//PW7cOIFAcPz4caoThHFxcZaWlj169Dh//vy1a9fGjRtHCNm3bx+lNDw8/JVXXtF9Oz169GC2MMvhu7u7L1q0KDY2dteuXba2tsOGDQsICNiwYcPff/+9dOlSQgiTu3v37hUIBDNmzIiNjY2Li3vnnXeEQuG5c+copYsWLRKJRO3bt9+2bdvNmze///57gUDw7bffJiUljR07ViKRMIvxX7hwof5nm5KS4uDg0Lp16z/++OPu3btnz559//33Kysrr1y5Ym5u3qdPn4sXL169enX48OECgeDIkSOU0q1btxJC/P39161b9/fffzNfwdSpU9u3bx8VFXX9+vVJkyYJBIKEhARKqZeXl5OTU8+ePa9cuXLjxo3Ro0cLBILTp09TSpOTk+3t7Xv27Hn69OmkpKSff/5ZJBJ9+eWXlNITJ04QQry9vb/66qvr16/v27fP2dl54MCBlNKIiAhPT8/Dhw+npKTcvHnzl19+OXPmDKX0t99+W7FixeXLl+/fvx8VFeXv7//SSy+Vl5dHRkYSQj7++GPmQ8jJyWHa01u3bq2qqmrbtq2Li8vevXtv37799ddfm5mZRUREUEqZfl93d/fJkydfunQpOjo6ODjYzc2tqqqqqf91Q/ODIAQWPDMId+/erd31xhtvtGnThlI6aNCggICA6upq7a7p06f7+vrSf4Lwp59+0u7q2bMnISQ2Npb5saqqSiwWL1myhFLq5+dnbW1dUFDA7KqpqfH39w8PD6c6QThu3LgWLVqUlJQwx9TW1nbo0KFDhw6UUubWP7dv32Z23blzhxDCtBeZIJw8ebK2jHfffZcQontbjE6dOo0aNaq2ttbHx2fEiBHa7RqNpnv37sOGDaOULlq0iBDy119/afcOHDgwNDSUUjp37lw3N7cGPtupU6daW1tnZmbW2T506FAnJyeZTMb8qFKp/Pz8QkJC6D9BuHr1au3BL7/8svbvBkppZWWlSCRatmwZpdTLy8vGxqa4uJjZpVarfX19+/XrRymdNGmSp6enbkN/0aJFdnZ2NTU1TBAuWLBAu+vbb78lhMhksqCgoJkzZzbwjhjnzp1jPnbmRnTMB87QBiHzRo4dO6bd9eGHHwqFwrS0NCYIe/Xqpd114cIFQggTusBzpnBjXjA9Q4YM0T4ODAw8dOiQSqU6f/78sGHDLl++rN3l5OSUkZFRUVHB/Dho0CDtrnbt2iUlJTFXSgkhYrHY29s7KyuL+bF3794uLi7MYzMzs9GjR//666+6Bdy+fXvQoEHade6FQuH48eOXLVtWWFg4duxYNze3rVu3rl27lhCyefNmBwcHpsn4xDIIIQMHDtTd8vjx4wcPHmRmZo4dOzY6Olq7y8fH5/r168xjc3PzAQMG6H4I2ptuNiw6OnrAgAEtW7ass/327dvDhw9nrgYTQiwsLMaOHbty5crKysonlp2WlsZcziWE2Nraenp6am+F2rdvX0dHR22dr7/+OjOQ9fTp00FBQdq3QAhp0aJFZWVleno686Pu19qxY0dCSFZWVpcuXfbs2WNrazthwoRu3brp3kTi4cOHhw4dysnJUSqVTPdhSkqKs7Pz09777du37ezshg4dqt3y5ptvrl279vLly6+//johZPDgwdpdzGVn7T8J4DMEIXCRNoEIIZaWliqVqqysTKVSnTp1ivlDXvfI/Pz8Jz5L90fteZjHzP2btDw8PGQyme6siczMTN3fp4QQ5gboxcXFLi4u06ZN27hx43fffScQCPbs2TN16lSmw+yJZdTZIhKJmGEmhJAtW7Zs375d91W0XWW2trYWFhZ1nkX0UFhY6O3tXWejWq2WSqUeHh513hGlVDtspE6Rz/XplZaWVlZWFhYWxsTETJgwQXevRCLRjs2p/8moVKo1a9aIxeLffvtt5cqVTk5OEydO/Prrr+3s7L7//vvPPvuse/funTp1kkgkTMdeeXl5A+89MzPT3d2d6ULWvkdCSHFx8RPfIyFEqVQ2cELgCQQhsID5da87qlDbLnkaOzs7oVD43nvv/fjjj/X3xsbGPlcBRUVFuj8WFhZaW1szozAYNjY2dY5hrr8xx7z77rs//vhjVFQUEyTvvPPOc706IaRFixaEkPXr10+dOvV5n9sw3b8MtMzNzUUiUf13ra3kudQ/j62trZ2dna2t7ZgxY+pEO+PkyZMNFLxp06b169fHxcUdPHjw559/lsvlmzZtWrZs2fvvv880uwkhiYmJ69ata7iw+t8a8x51v1mA+jB9Aljg5eVFCElNTdVuqdPOq8/a2jo0NPTIkSNN8if81atXdaP35MmTHTt21G1JhIWFnT17VneJmWPHjvn6+jKNKh8fn8GDB2/ZsmXLli3h4eHMVb7n8tJLL0kkkj/++ON5n2hra9vwwje9e/c+e/astg3EEAgE3bt3P3XqlHZGAaX02LFjHTp0cHBweN4aLl++rJ3nQCk9derUSy+9RAh59dVXT58+3XCj7WnMzc27d+/+3XffDRs2LDY2tqCgQC6X604NPH78OPPA1taWEKJ7i2at7t27l5aWxsTEaLccPXqUEBIWFtaIkoA/EITAgrCwsBYtWnzyySepqakZGRmLFy++cuXKM5/1zTffpKamjhkz5tatWwqFIisr6+DBgx9//HEjClCpVFOnTs3KyioqKlqwYEFCQsJHH32ke8CCBQsKCgqmTJmSnp6el5c3f/78Gzdu6L7W7Nmzr169GhMTM3PmzEYUYGlpuWzZsuPHj8+ePfvRo0cKhSItLW379u0///xzw0/s2LFjRUXFmjVrrl+/npCQUP+AxYsXKxSKESNG3LhxQy6XP378+KeffpLL5QsWLMjKypo+fXpmZmZubu7777+flJTUuE9PoVBMnTo1Ozu7sLBw7ty5d+/eZT69pUuXlpaWjhgxIjY2VqFQ5Obm/vXXX3PmzGn4bLNmzTpz5kxhYaFarY6JiYmNjQ0JCXF3d3d3d9+0adPjx49lMtmuXbtWr17NHG9vb+/t7b179+7z58/HxcXpNgEnT57s7u4+bdq069evl5eX79mz56effho+fHhgYGAj3ibwB4IQWODo6Lhly5YbN260adPGz8/v1q1bn3/++TOf1b9//8OHDz969Khr165isdjHxyciIqLh6fBP8+abb1pbW/v6+rq4uKxdu3bp0qUTJ07UPaBfv37bt28/f/58q1atPDw8Nm7cuHz5cmYIKGPIkCE+Pj6Ojo66w2Sey5w5czZu3Hjw4MH27duLxeLWrVt/8sknTMdVA8aNGzd79uzvvvsuLCysX79+9Q8IDg4+fvx4YWFh9+7dbWxs/P39N2/eTAgZPnz45s2bmXatl5fXzp07f/zxR2ZWyfOaNGmSUCj08fFxdXXduHHjN998w/QLdu3a9dSpU6WlpT169BCLxV5eXhMmTKg/d76OR48eDRkyxNXV1dLSslevXt27d1+1apVAINixY0daWpq/v7+dnd3ixYt1RzNt27atoqJi6NCh3bp1O3LkiHa7RCI5efKkpaVlWFiYg4PD5MmTBw8ezPMV6UAfAkop2zUATykUiocPH9rb27dq1eq5npiSklJSUuLo6Ojr66s7okRPrVq1GjRo0KZNm3JycnJyclq3bu3k5MTsopRqNBrtwEW1Wn3v3j2VShUYGKgdb8mQyWTe3t7Tp09fuXLl8xagq7a29uHDhzKZzN3d3dvbm5mK3iQePnxYXl7u6urKLCnAUKlU9+7dq62tDQwMtLa2bsRpvb29R48evW7duuzs7Nzc3DZt2mhHkGqlp6cXFBTY29v7+fk9M9oJIRUVFZmZmUql0tfXV3dQaHV19cOHD83NzQMCAnRHk9ZXW1srFAq1F7eTk5NLS0t9fHzqjOsBeCIEIfCONghf5CTffPPNV199lZycrBszfKANQrYLAWgyGDUK8HzWrVu3fv36R48effrpp3xLQQCThBYh8E5kZKS3t3d4eHjjnn79+vXExMSAgIBevXo1bWHNwp49e/z8/JiFewBMA4IQAAB4DaNGAQCA1xCEAADAawhCAADgNQQhAADwGoIQAAB4DUEIAAC89v+nj97ZqhZfwgAAAABJRU5ErkJggg==" }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function compute_stopping_time(w̄; seed=1234)\n", " Random.seed!(seed)\n", " stopping_time = 0\n", " t = 1\n", " # make sure the constraint is sometimes binding\n", " @assert length(w) - 1 ∈ support(dist) && w̄ <= w[end]\n", " while true\n", " # Generate a wage draw\n", " w_val = w[rand(dist)] # the wage dist set up earlier\n", " if w_val ≥ w̄\n", " stopping_time = t\n", " break\n", " else\n", " t += 1\n", " end\n", " end\n", " return stopping_time\n", "end\n", "\n", "compute_mean_stopping_time(w̄, num_reps=10000) = mean(i ->\n", " compute_stopping_time(w̄,\n", " seed = i), 1:num_reps)\n", "c_vals = range(10, 40, length = 25)\n", "stop_times = similar(c_vals)\n", "\n", "beta = 0.99\n", "for (i, c) in enumerate(c_vals)\n", " w̄ = compute_reservation_wage_ψ(c, beta)\n", " stop_times[i] = compute_mean_stopping_time(w̄)\n", "end\n", "\n", "plot(c_vals, stop_times, label = \"mean unemployment duration\",\n", " xlabel = \"unemployment compensation\", ylabel = \"months\")" ] } ], "metadata": { "date": 1591310615.931401, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "mccall_model.rst", "filename_with_path": "dynamic_programming/mccall_model", "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 I: The McCall Search Model" }, "nbformat": 4, "nbformat_minor": 2 }