{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Optimal Growth I: The Stochastic Optimal Growth Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Optimal Growth I: The Stochastic Optimal Growth Model](#Optimal-Growth-I:-The-Stochastic-Optimal-Growth-Model) \n", " - [Overview](#Overview) \n", " - [The Model](#The-Model) \n", " - [Computation](#Computation) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "In this lecture we’re going to study a simple optimal growth model with one agent.\n", "\n", "The model is a version of the standard one sector infinite horizon growth model studied in\n", "\n", "- [[SLP89]](../zreferences.html#stokeylucas1989), chapter 2 \n", "- [[LS18]](../zreferences.html#ljungqvist2012), section 3.1 \n", "- [EDTC](http://johnstachurski.net/edtc.html), chapter 1 \n", "- [[Sun96]](../zreferences.html#sundaram1996), chapter 12 \n", "\n", "\n", "The technique we use to solve the model is dynamic programming.\n", "\n", "Our treatment of dynamic programming follows on from earlier\n", "treatments in our lectures on [shortest paths](short_path.html) and\n", "[job search](mccall_model.html).\n", "\n", "We’ll discuss some of the technical details of dynamic programming as we\n", "go along." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Model\n", "\n", "\n", "\n", "Consider an agent who owns an amount $y_t \\in \\mathbb R_+ := [0, \\infty)$ of a consumption good at time $t$.\n", "\n", "This output can either be consumed or invested.\n", "\n", "When the good is invested it is transformed one-for-one into capital.\n", "\n", "The resulting capital stock, denoted here by $k_{t+1}$, will then be used for production.\n", "\n", "Production is stochastic, in that it also depends on a shock $\\xi_{t+1}$ realized at the end of the current period.\n", "\n", "Next period output is\n", "\n", "$$\n", "y_{t+1} := f(k_{t+1}) \\xi_{t+1}\n", "$$\n", "\n", "where $f \\colon \\mathbb{R}_+ \\to \\mathbb{R}_+$ is called the production function.\n", "\n", "The resource constraint is\n", "\n", "\n", "\n", "$$\n", "k_{t+1} + c_t \\leq y_t \\tag{1}\n", "$$\n", "\n", "and all variables are required to be nonnegative." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Assumptions and Comments\n", "\n", "In what follows,\n", "\n", "- The sequence $\\{\\xi_t\\}$ is assumed to be IID. \n", "- The common distribution of each $\\xi_t$ will be denoted $\\phi$. \n", "- The production function $f$ is assumed to be increasing and continuous. \n", "- Depreciation of capital is not made explicit but can be incorporated into the production function. \n", "\n", "\n", "While many other treatments of the stochastic growth model use $k_t$ as the state variable, we will use $y_t$.\n", "\n", "This will allow us to treat a stochastic model while maintaining only one state variable.\n", "\n", "We consider alternative states and timing specifications in some of our other lectures." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Optimization\n", "\n", "Taking $y_0$ as given, the agent wishes to maximize\n", "\n", "\n", "\n", "$$\n", "\\mathbb E \\left[ \\sum_{t = 0}^{\\infty} \\beta^t u(c_t) \\right] \\tag{2}\n", "$$\n", "\n", "subject to\n", "\n", "\n", "\n", "$$\n", "y_{t+1} = f(y_t - c_t) \\xi_{t+1}\n", "\\quad \\text{and} \\quad\n", "0 \\leq c_t \\leq y_t\n", "\\quad \\text{for all } t \\tag{3}\n", "$$\n", "\n", "where\n", "\n", "- $u$ is a bounded, continuous and strictly increasing utility function and \n", "- $\\beta \\in (0, 1)$ is a discount factor \n", "\n", "\n", "In [(3)](#equation-og-conse) we are assuming that the resource constraint [(1)](#equation-outcsdp0) holds with equality — which is reasonable because $u$ is strictly increasing and no output will be wasted at the optimum.\n", "\n", "In summary, the agent’s aim is to select a path $c_0, c_1, c_2, \\ldots$ for consumption that is\n", "\n", "1. nonnegative, \n", "1. feasible in the sense of [(1)](#equation-outcsdp0), \n", "1. optimal, in the sense that it maximizes [(2)](#equation-texs0-og2) relative to all other feasible consumption sequences, and \n", "1. *adapted*, in the sense that the action $c_t$ depends only on\n", " observable outcomes, not future outcomes such as $\\xi_{t+1}$ \n", "\n", "\n", "In the present context\n", "\n", "- $y_t$ is called the *state* variable — it summarizes the “state of the world” at the start of each period. \n", "- $c_t$ is called the *control* variable — a value chosen by the agent each period after observing the state. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Policy Function Approach\n", "\n", "\n", "\n", "One way to think about solving this problem is to look for the best **policy function**.\n", "\n", "A policy function is a map from past and present observables into current action.\n", "\n", "We’ll be particularly interested in **Markov policies**, which are maps from the current state $y_t$ into a current action $c_t$.\n", "\n", "For dynamic programming problems such as this one (in fact for any [Markov decision process](https://en.wikipedia.org/wiki/Markov_decision_process)), the optimal policy is always a Markov policy.\n", "\n", "In other words, the current state $y_t$ provides a sufficient statistic\n", "for the history in terms of making an optimal decision today.\n", "\n", "This is quite intuitive but if you wish you can find proofs in texts such as [[SLP89]](../zreferences.html#stokeylucas1989) (section 4.1).\n", "\n", "Hereafter we focus on finding the best Markov policy.\n", "\n", "In our context, a Markov policy is a function $\\sigma \\colon\n", "\\mathbb R_+ \\to \\mathbb R_+$, with the understanding that states are mapped to actions via\n", "\n", "$$\n", "c_t = \\sigma(y_t) \\quad \\text{for all } t\n", "$$\n", "\n", "In what follows, we will call $\\sigma$ a *feasible consumption policy* if it satisfies\n", "\n", "\n", "\n", "$$\n", "0 \\leq \\sigma(y) \\leq y\n", "\\quad \\text{for all} \\quad\n", "y \\in \\mathbb R_+ \\tag{4}\n", "$$\n", "\n", "In other words, a feasible consumption policy is a Markov policy that respects the resource constraint.\n", "\n", "The set of all feasible consumption policies will be denoted by $\\Sigma$.\n", "\n", "Each $\\sigma \\in \\Sigma$ determines a [continuous state Markov process](../tools_and_techniques/stationary_densities.html) $\\{y_t\\}$ for output via\n", "\n", "\n", "\n", "$$\n", "y_{t+1} = f(y_t - \\sigma(y_t)) \\xi_{t+1},\n", "\\quad y_0 \\text{ given} \\tag{5}\n", "$$\n", "\n", "This is the time path for output when we choose and stick with the policy $\\sigma$.\n", "\n", "We insert this process into the objective function to get\n", "\n", "\n", "\n", "$$\n", "\\mathbb E\n", "\\left[ \\,\n", "\\sum_{t = 0}^{\\infty} \\beta^t u(c_t) \\,\n", "\\right] =\n", "\\mathbb E\n", "\\left[ \\,\n", "\\sum_{t = 0}^{\\infty} \\beta^t u(\\sigma(y_t)) \\,\n", "\\right] \\tag{6}\n", "$$\n", "\n", "This is the total expected present value of following policy $\\sigma$ forever,\n", "given initial income $y_0$.\n", "\n", "The aim is to select a policy that makes this number as large as possible.\n", "\n", "The next section covers these ideas more formally." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Optimality\n", "\n", "The **policy value function** $v_{\\sigma}$ associated with a given policy $\\sigma$ is the mapping defined by\n", "\n", "\n", "\n", "$$\n", "v_{\\sigma}(y) = \\mathbb E \\left[ \\sum_{t = 0}^{\\infty} \\beta^t u(\\sigma(y_t)) \\right] \\tag{7}\n", "$$\n", "\n", "when $\\{y_t\\}$ is given by [(5)](#equation-firstp0-og2) with $y_0 = y$.\n", "\n", "In other words, it is the lifetime value of following policy $\\sigma$\n", "starting at initial condition $y$.\n", "\n", "The **value function** is then defined as\n", "\n", "\n", "\n", "$$\n", "v^*(y) := \\sup_{\\sigma \\in \\Sigma} \\; v_{\\sigma}(y) \\tag{8}\n", "$$\n", "\n", "The value function gives the maximal value that can be obtained from state $y$, after considering all feasible policies.\n", "\n", "A policy $\\sigma \\in \\Sigma$ is called **optimal** if it attains the supremum in [(8)](#equation-vfcsdp0) for all $y \\in \\mathbb R_+$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Bellman Equation\n", "\n", "With our assumptions on utility and production function, the value function as defined in [(8)](#equation-vfcsdp0) also satisfies a **Bellman equation**.\n", "\n", "For this problem, the Bellman equation takes the form\n", "\n", "\n", "\n", "$$\n", "w(y) = \\max_{0 \\leq c \\leq y}\n", " \\left\\{\n", " u(c) + \\beta \\int w(f(y - c) z) \\phi(dz)\n", " \\right\\}\n", "\\qquad (y \\in \\mathbb R_+) \\tag{9}\n", "$$\n", "\n", "This is a *functional equation in* $w$.\n", "\n", "The term $\\int w(f(y - c) z) \\phi(dz)$ can be understood as the expected next period value when\n", "\n", "- $w$ is used to measure value \n", "- the state is $y$ \n", "- consumption is set to $c$ \n", "\n", "\n", "As shown in [EDTC](http://johnstachurski.net/edtc.html), theorem 10.1.11 and a range of other texts.\n", "\n", "> *The value function* $v^*$ *satisfies the Bellman equation*\n", "\n", "\n", "In other words, [(9)](#equation-fpb30) holds when $w=v^*$.\n", "\n", "The intuition is that maximal value from a given state can be obtained by optimally trading off\n", "\n", "- current reward from a given action, vs \n", "- expected discounted future value of the state resulting from that action \n", "\n", "\n", "The Bellman equation is important because it gives us more information about the value function.\n", "\n", "It also suggests a way of computing the value function, which we discuss below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Greedy policies\n", "\n", "The primary importance of the value function is that we can use it to compute optimal policies.\n", "\n", "The details are as follows.\n", "\n", "Given a continuous function $w$ on $\\mathbb R_+$, we say that $\\sigma \\in \\Sigma$ is $w$-**greedy** if $\\sigma(y)$ is a solution to\n", "\n", "\n", "\n", "$$\n", "\\max_{0 \\leq c \\leq y}\n", " \\left\\{\n", " u(c) + \\beta \\int w(f(y - c) z) \\phi(dz)\n", " \\right\\} \\tag{10}\n", "$$\n", "\n", "for every $y \\in \\mathbb R_+$.\n", "\n", "In other words, $\\sigma \\in \\Sigma$ is $w$-greedy if it optimally\n", "trades off current and future rewards when $w$ is taken to be the value\n", "function.\n", "\n", "In our setting, we have the following key result\n", "\n", "> *A feasible consumption policy is optimal if and only if it is* $v^*$-*greedy*\n", "\n", "\n", "The intuition is similar to the intuition for the Bellman equation, which was\n", "provided after [(9)](#equation-fpb30).\n", "\n", "See, for example, theorem 10.1.11 of [EDTC](http://johnstachurski.net/edtc.html).\n", "\n", "Hence, once we have a good approximation to $v^*$, we can compute the (approximately) optimal policy by computing the corresponding greedy policy.\n", "\n", "The advantage is that we are now solving a much lower dimensional optimization\n", "problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Bellman Operator\n", "\n", "How, then, should we compute the value function?\n", "\n", "One way is to use the so-called **Bellman operator**.\n", "\n", "(An operator is a map that sends functions into functions)\n", "\n", "The Bellman operator is denoted by $T$ and defined by\n", "\n", "\n", "\n", "$$\n", "Tw(y) := \\max_{0 \\leq c \\leq y}\n", "\\left\\{\n", " u(c) + \\beta \\int w(f(y - c) z) \\phi(dz)\n", "\\right\\}\n", "\\qquad (y \\in \\mathbb R_+) \\tag{11}\n", "$$\n", "\n", "In other words, $T$ sends the function $w$ into the new function\n", "$Tw$ defined [(11)](#equation-fcbell20-optgrowth).\n", "\n", "By construction, the set of solutions to the Bellman equation [(9)](#equation-fpb30) *exactly coincides with* the set of fixed points of $T$.\n", "\n", "For example, if $Tw = w$, then, for any $y \\geq 0$,\n", "\n", "$$\n", "w(y)\n", "= Tw(y)\n", "= \\max_{0 \\leq c \\leq y}\n", "\\left\\{\n", " u(c) + \\beta \\int v^*(f(y - c) z) \\phi(dz)\n", "\\right\\}\n", "$$\n", "\n", "which says precisely that $w$ is a solution to the Bellman equation.\n", "\n", "It follows that $v^*$ is a fixed point of $T$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Review of Theoretical Results\n", "\n", "\n", "\n", "One can also show that $T$ is a contraction mapping on the set of continuous bounded functions on $\\mathbb R_+$ under the supremum distance\n", "\n", "$$\n", "\\rho(g, h) = \\sup_{y \\geq 0} |g(y) - h(y)|\n", "$$\n", "\n", "See [EDTC](http://johnstachurski.net/edtc.html), lemma 10.1.18.\n", "\n", "Hence it has exactly one fixed point in this set, which we know is equal to the value function.\n", "\n", "It follows that\n", "\n", "- The value function $v^*$ is bounded and continuous. \n", "- Starting from any bounded and continuous $w$, the sequence $w, Tw, T^2 w, \\ldots$ generated by iteratively applying $T$ converges uniformly to $v^*$. \n", "\n", "\n", "This iterative method is called **value function iteration**.\n", "\n", "We also know that a feasible policy is optimal if and only if it is $v^*$-greedy.\n", "\n", "It’s not too hard to show that a $v^*$-greedy policy exists (see [EDTC](http://johnstachurski.net/edtc.html), theorem 10.1.11 if you get stuck).\n", "\n", "Hence at least one optimal policy exists.\n", "\n", "Our problem now is how to compute it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unbounded Utility\n", "\n", "\n", "\n", "The results stated above assume that the utility function is bounded.\n", "\n", "In practice economists often work with unbounded utility functions — and so will we.\n", "\n", "In the unbounded setting, various optimality theories exist.\n", "\n", "Unfortunately, they tend to be case specific, as opposed to valid for a large range of applications.\n", "\n", "Nevertheless, their main conclusions are usually in line with those stated for\n", "the bounded case just above (as long as we drop the word “bounded”).\n", "\n", "Consult, for example, section 12.2 of [EDTC](http://johnstachurski.net/edtc.html), [[Kam12]](../zreferences.html#kamihigashi2012) or [[MdRV10]](../zreferences.html#mv2010)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computation\n", "\n", "\n", "\n", "Let’s now look at computing the value function and the optimal policy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fitted Value Iteration\n", "\n", "\n", "\n", "The first step is to compute the value function by value function iteration.\n", "\n", "In theory, the algorithm is as follows\n", "\n", "1. Begin with a function $w$ — an initial condition. \n", "1. Solving [(11)](#equation-fcbell20-optgrowth), obtain the function $T w$. \n", "1. Unless some stopping condition is satisfied, set $w = Tw$ and go to step 2. \n", "\n", "\n", "This generates the sequence $w, Tw, T^2 w, \\ldots$.\n", "\n", "However, there is a problem we must confront before we implement this procedure: The iterates can neither be calculated exactly nor stored on a computer.\n", "\n", "To see the issue, consider [(11)](#equation-fcbell20-optgrowth).\n", "\n", "Even if $w$ is a known function, unless $Tw$ can be shown to have\n", "some special structure, the only way to store it is to record the\n", "value $Tw(y)$ for every $y \\in \\mathbb R_+$.\n", "\n", "Clearly this is impossible.\n", "\n", "What we will do instead is use **fitted value function iteration**.\n", "\n", "The procedure is to record the value of the function $Tw$ at only finitely many “grid” points $y_1 < y_2 < \\cdots < y_I$ and reconstruct it from this information when required.\n", "\n", "More precisely, the algorithm will be\n", "\n", "\n", "\n", "1. Begin with an array of values $\\{ w_1, \\ldots, w_I \\}$ representing the values of some initial function $w$ on the grid points $\\{ y_1, \\ldots, y_I \\}$. \n", "1. Build a function $\\hat w$ on the state space $\\mathbb R_+$ by interpolation or approximation, based on these data points. \n", "1. Obtain and record the value $T \\hat w(y_i)$ on each grid point $y_i$ by repeatedly solving [(11)](#equation-fcbell20-optgrowth). \n", "1. Unless some stopping condition is satisfied, set $\\{ w_1, \\ldots, w_I \\} = \\{ T \\hat w(y_1), \\ldots, T \\hat w(y_I) \\}$ and go to step 2. \n", "\n", "\n", "How should we go about step 2?\n", "\n", "This is a problem of function approximation, and there are many ways to approach it.\n", "\n", "What’s important here is that the function approximation scheme must not only produce a good approximation to $Tw$, but also combine well with the broader iteration algorithm described above.\n", "\n", "One good choice from both respects is continuous piecewise linear interpolation (see this paper for further discussion).\n", "\n", "The next figure illustrates piecewise linear interpolation of an arbitrary function on grid points $0, 0.2, 0.4, 0.6, 0.8, 1$." ] }, { "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 Plots, QuantEcon, Interpolations, NLsolve, Optim, Random\n", "gr(fmt = :png);" ] }, { "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": [ "f(x) = 2 .* cos.(6x) .+ sin.(14x) .+ 2.5\n", "c_grid = 0:.2:1\n", "f_grid = range(0, 1, length = 150)\n", "\n", "Af = LinearInterpolation(c_grid, f(c_grid))\n", "\n", "plt = plot(xlim = (0,1), ylim = (0,6))\n", "plot!(plt, f, f_grid, color = :blue, lw = 2, alpha = 0.8, label = \"true function\")\n", "plot!(plt, f_grid, Af.(f_grid), color = :green, lw = 2, alpha = 0.8,\n", " label = \"linear approximation\")\n", "plot!(plt, f, c_grid, seriestype = :sticks, linestyle = :dash, linewidth = 2, alpha = 0.5,\n", " label = \"\")\n", "plot!(plt, legend = :top)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another advantage of piecewise linear interpolation is that it preserves useful shape properties such as monotonicity and concavity / convexity." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Bellman Operator\n", "\n", "Here’s a function that implements the Bellman operator using linear interpolation" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "T (generic function with 1 method)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Optim\n", "\n", "function T(w, grid, β, u, f, shocks; compute_policy = false)\n", " w_func = LinearInterpolation(grid, w)\n", " # objective for each grid point\n", " objectives = (c -> u(c) + β * mean(w_func.(f(y - c) .* shocks)) for y in grid)\n", " results = maximize.(objectives, 1e-10, grid) # solver result for each grid point\n", "\n", " Tw = Optim.maximum.(results)\n", " if compute_policy\n", " σ = Optim.maximizer.(results)\n", " return Tw, σ\n", " end\n", "\n", " return Tw\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the expectation in [(11)](#equation-fcbell20-optgrowth) is computed via Monte Carlo, using the approximation\n", "\n", "$$\n", "\\int w(f(y - c) z) \\phi(dz) \\approx \\frac{1}{n} \\sum_{i=1}^n w(f(y - c) \\xi_i)\n", "$$\n", "\n", "where $\\{\\xi_i\\}_{i=1}^n$ are IID draws from $\\phi$.\n", "\n", "Monte Carlo is not always the most efficient way to compute integrals numerically but it does have some theoretical advantages in the present setting.\n", "\n", "(For example, it preserves the contraction mapping property of the Bellman operator — see, e.g., [[PalS13]](../zreferences.html#pal2013))\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### An Example\n", "\n", "Let’s test out our operator when\n", "\n", "- $f(k) = k^{\\alpha}$ \n", "- $u(c) = \\ln c$ \n", "- $\\phi$ is the distribution of $\\exp(\\mu + \\sigma \\zeta)$ when $\\zeta$ is standard normal \n", "\n", "\n", "As is well-known (see [[LS18]](../zreferences.html#ljungqvist2012), section 3.1.2), for this particular problem an exact analytical solution is available, with\n", "\n", "\n", "\n", "$$\n", "v^*(y) =\n", "\\frac{\\ln (1 - \\alpha \\beta) }{ 1 - \\beta}\n", "+\n", "\\frac{(\\mu + \\alpha \\ln (\\alpha \\beta))}{1 - \\alpha}\n", " \\left[\n", " \\frac{1}{1- \\beta} - \\frac{1}{1 - \\alpha \\beta}\n", " \\right]\n", " +\n", " \\frac{1}{1 - \\alpha \\beta} \\ln y \\tag{12}\n", "$$\n", "\n", "The optimal consumption policy is\n", "\n", "$$\n", "\\sigma^*(y) = (1 - \\alpha \\beta ) y\n", "$$\n", "\n", "Let’s code this up now so we can test against it below" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "v_star (generic function with 1 method)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "α = 0.4\n", "β = 0.96\n", "μ = 0\n", "s = 0.1\n", "\n", "c1 = log(1 - α * β) / (1 - β)\n", "c2 = (μ + α * log(α * β)) / (1 - α)\n", "c3 = 1 / (1 - β)\n", "c4 = 1 / (1 - α * β)\n", "\n", "# Utility\n", "u(c) = log(c)\n", "\n", "∂u∂c(c) = 1 / c\n", "\n", "# Deterministic part of production function\n", "f(k) = k^α\n", "\n", "f′(k) = α * k^(α - 1)\n", "\n", "# True optimal policy\n", "c_star(y) = (1 - α * β) * y\n", "\n", "# True value function\n", "v_star(y) = c1 + c2 * (c3 - c4) + c4 * log(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A First Test\n", "\n", "To test our code, we want to see if we can replicate the analytical solution numerically, using fitted value function iteration.\n", "\n", "We need a grid and some shock draws for Monte Carlo integration." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": true }, "outputs": [], "source": [ "using Random\n", "Random.seed!(42) # For reproducible results.\n", "\n", "grid_max = 4 # Largest grid point\n", "grid_size = 200 # Number of grid points\n", "shock_size = 250 # Number of shock draws in Monte Carlo integral\n", "\n", "grid_y = range(1e-5, grid_max, length = grid_size)\n", "shocks = exp.(μ .+ s * randn(shock_size))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let’s do some tests.\n", "\n", "As one preliminary test, let’s see what happens when we apply our Bellman operator to the exact solution $v^*$.\n", "\n", "In theory, the resulting function should again be $v^*$.\n", "\n", "In practice we expect some small numerical error." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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WY8nJKsyyDjVKtfjyAQwO+C4CxEQIB8P2ltbGRkdzs9/RSYf56BqeAqEYdZrfmKPNyMrMzx1r1RXoKVytAWAQQhAC9JoQCgTbmtuamhzNTX6Hg44I0YntPCXxaDIj5hxjdnZWbvbkNFWmmsIKngCDHIIQoEeEcDBsb25paHI2NvpcDm9YiI524SUyly6DpOWasrOz87Jnm2VmJaIPIJEgCAG+k8BGwvbm9vqGjuYmf2eHN/xNy4+TyFz6TJKWm5abk5+bNdckM2ABa4CEhSAEOI/Ac5yjrb2h3l7f6Oto84aF6Dk/XiJzadMFW74lL7cgJ3OeWabDqi4ASQFBCBCd5+dwNTW21tXTrc3eQCQ62lOgKLcmk7Xmm3JyCvOz55rlaPkBJB8EIaQuPugPtDY01da7mxpo2hed5ydQFKOyBCwFxpzcvILcWValGeEHkNQQhJBaBJ5jO1rb6mrbGxp8jk5vWBAEQqLz/Gx5upy87IKCyenaLI3YhQLAQEEQQkrgfV5vU31TbZ23pdHjC0cvZsRJZC5DjjSzIKOgYHSOpUhPYVVPgBSEIISkJfAc29HSWltnr6ujnQ468s12rzotZC005+UPKci5ziLDwp4AKQ6/AZBshKCfbqppPFfraf5P4y8iU7rMuaqcwpyiwsmZ+ky12FUCwKCBIIQkwbk7OmprW2rO0Xa7Nxw98Ue86rSgbYg1v7C4MHuEWaLABfwA4CIIQkhkPBdqa2o6d85RV+PxMtGLuXMSmdOUq8gekl00ZFKWPkuD834A8H0QhJB4hEjI11zbWF3jaqhz+8LRCe9Buc6TWWjKH1I0JH+BVa7GRxsAega/FpAwhKDfU3+usbra09zkDnLRpT49Gms4fUh6YVFpQcZQowTDPgGgtxCEMNjxftpZW91UddbT1ho9+SdQlFOfK80amjOsaEqOMQMjXwAgBghCGKR4n7ezpqq56qzbbqfDAiGEl8gc5jxV7tDC4UPnZKix2hkAxAWCEAYX3ufprDnbVHnWY2+PzvzjJHKHpVBXMLSouOg6qwIn/wAgvvCjAoMC72ecNVUNlZWe9m/yj5UonNYhhsJhw4YVLrLJMfMBAPoJghDEJIQC7tqz9Wcq3S0t3ohACOEkcmdaoWFI8fDhhYutcjnyDwD6GYIQRCCwEV9jTe3pM67Gek+QF6KT/yyF2sLikSOG3ID8A4ABhCCEgSSE2xprT53urKl2+SO8QHhK4jIVKAtGDB8xdGG6UikVu0AASD0IQhgInMfRcuZ0S1Wl001HeCJQlFubKckdWTSqeF62RouPIQCIB79A0I+EcNB1rrL25ElXuz162Vuf0uTPHpE/YuRVhWaLUuz6AAAQhNA/hGBLQ+2pk50159wBTohe/CFzuG3E6BnDsvJ1WP0FAAYRBCHEE+/ztp851XDyhNPDRHgiUBKnqUBVOGrM6KFjrHIpEhAABh8EIcQDz/uaamqOV3Q2NNARgRDiV5kCOaMLR4+8Js+gk4tdHgDAd0MQQkx4n7fl1Mmm0ycdboYTCC+RddqGphWPnTYit0CPBiAAJAAEIfSNEGprqPusurOuLtoEZFQWNn9s8fjRC7NUWAUGABIIghB6RwgHOypP1h0/Zu908UTKUVKnbXjayLFXj8zJxiVwASABIQihp1h3Z93xo61nzrgCLCGElhkihSUjxo9ZlKNBExAAEheCEC5L8DfWnj36dUdDo58lAqGcxgLdiPFXDEkfm6kXuzYAgFghCOE7CWzEWXWy5ujRDoeb5QkrVTizR+aPv2JZkUUvp2iaFrtAAIA4QBDCJQhBf3PF0fqKY04mJAjErzCEhpSMKRmzJEOJuYAAkGQQhHAennbVHDnSdOaUN8gRQty6TOWIK6eMLxpiwHrYAJCcEITwjbCj/exXh9vO1fgigkAoZ9rQtDFXLhqVlaZCGxAAkhmCEEiovbny8JftDQ0BlvASmSNzZH7JlfOGmjQyRCAAJD8EYUoLNNdXlh1qb2oNcYSVKNz544snlN6Qr0UCAkDqQBCmKH9zXeWXh9qa2yI8CcvUdFHJuCuvWJqlkiACASDFIAhTjr+l/szBL9pb2iM8Cck1TFHphElXjLcpKEQgAKSkWIOQ47jGxkaZTJaTk0Php3RwC9mbT3/xeVtja5gnIbnGP3zilRPHj7XiH0MAkNJi+hH8+9//vnr1aq1WG4lELBbLP/7xD5PJNHLkyK4d3G73q6+++pOf/CR6d8aMGcePH5fL5YSQsWPH7t+/P5Znh54LO9orDx5oqWsIcdGO0AmTppSMteLySAAAsQVhXl7ewYMHhw4dyvP8qlWrHnzwwQ8++MDpdEb/WlVVNXbs2KVLl3Z/yF/+8pfFixfH8qTQK6zXVXXoQNPZc0FWiMiU3qIJE6aUoiMUAKBLTEE4ffr06A2JRHLNNdc888wz3f+6cePGxYsXZ2Zmdt/IsixN03o91qjsd3zQX1v2ZX3FcSYicBKZK2/8+KmTrsxWIwEBALqLz/khQRC2bNmyaNGiri0sy27btu1Pf/rTBXv+13/9F0VRBoPhxRdfXLZs2cXHKSsrO68+may0tDQuRaYQjm05Xl5dXu72hQWKcmSOKZ469cZ8PVZHAwC4GCUIQq8e4PF4oqst63Q6k8kU3bhu3bp33333iy++0Gg00S1vv/32z372s/r6eqn0P0tznTt3rqioiKKo7du333XXXcePHx8+fHjXXxmGSUtLGzt2bPen02q1H3zwwSUr8fl8Wq22V8UnP0Fg6s9VH/7S4fEJhDhMBbbSKTOGGPtjhVCGYXQ6XdwPCz3h9/tVKpVEgstfiQMffhEFAgGFQtE9Wb6fRqO57Del1y3CjRs3bty4kRByxx13/PrXvyaEPPvss9u3b//000+7UpAQ8sYbb6xYseKCWocOHRq9ccstt7z44ov79+/vHoSEELlcXl5e3vNi8FnsLuRoP7V/X2tTK8sTWpehnTDr1vF5+n4bECMIAt5/sVAUpVarEYRiwYdfRFKptFdB2BO9DsKHHnrooYce6rr78ssvb9q0ad++fenp6V0b29radu3a9eKLL37XQXie7+zsxJnCeOGD/uqDn9efPB3ghKBcFxkz9ZqpY7JwvXgAgB6I6Rzh1q1bH3roobVr177//vuEEKVSuWLFCkLIW2+9NW3atGHDhkV3O3DgwM9+9rOdO3e+9tprV111lVQqfeONN8Lh8HXXXRf7C0h1gtBx6tipQwc9TIijpK78kskzp4y1KcQuCwAgYcQUhCqVatWqVe3t7e3t7YQQjUYTDUKKoqK9plFms3n69OlarZZhmBdeeEEQhPHjxx88eNBoNMZYfYoLdbRW7P24ra2TF4jTXJg3Zdbi4RYZessAAHqj14Nl+g/DMJmZmQzD9Hz/lO2mF8KhmkOfnzt+IsgJfqVRMu6q+ROHmpQD2heKaTAi8vl8OEcoInz4RdTbwTI9geW1Eo+n7mzFvr1Oj5+npK6CCTNnTRluwf9HAIA+wg9oIuEDzKlPP2k8WxPhiVufnTl97g3FVvSFAgDEAkGYIATBUXXqxOf7PUwoIlX6R09fMGNcugYZCAAQKwRhAuADzMmPdzfW1rM8cZmHFM+eOzVfj8VCAQDiAkE42DnPnq7Yv8/DhMJSVfiKWUumjRrgQTEAAMkNQTh4CeHg6b176qqqWZ64zIWj586blIsl5QAA4gxBOEj5WhqO7t7tcNOsRBEcN2vJzLEmzJIHAOgHCMLBh+frDx84U34kxAoefdaQq6+bMcSEM4IAAP0EQTi4cD7v0Q93tjS38xTlHjptwdxJGRgaCgDQnxCEg4ir7uzRPXtoXyigNGimXnfH+BzMEQQA6G8IwsGB588d/Ozs10fDnOC2Dps4/9rRNpXYNQEApAQEofg4P3Ns187mhlaOktIjZ944pxTjYgAABgyCUGT+tuavPtzp9vqDcp12xsI7xmdLMC4GAGAAIQjF1H664vjefYEI5zHmjpt/fUk2pgkCAAw0BKFIeL76871VxypYnrjyShcsmJmhiedVRQAAoIcQhCIQwqHj/97ZUNvASWT+K+bedtVoFUIQAEAkCMKBxtKesvfe7uhwhRRa7cwblozLwjlBAAARIQgHlN/eWvb+ex7az2jShl23dHI+LnINACAyBOHAcdfXlH/4gS/EeiwF0xYtGmbBJAkAAPEhCAdI2+mKY5/sDbG8O3vMgkXXpmvQIQoAMCggCAdC49dlJw58EeEET9HUHyyYqpeLXRAAAHwLQdjPBKHmy89Pl5WzgsQ35upb54xXYoAoAMBggiDsT4JQ9dneqqPHWSINT5h/6/QRWEQbAGCwQRD2G4E/s2/P2eOnWImMmrzwlilFOCsIADAIIQj7iXD6k93VJ06zErl0+uLFE/KRggAAgxOCsD8IZz7ZXX3idESqUF1148IrcsWuBwAAvhOCMN4E4fTePdUnTrESuWrmYqQgAMAgh8EbcVZ9YH91xUmWkitm3riwJE/scgAA4DIQhPFUV3ao8sjXHCWVT1u4qBQpCACQABCEcdN0/OtThw6xhOInXb/oyiFilwMAAD2CIIyPjnNVFZ/ujwhUqGTe0qnDKAwSBQBIEAjCOKDbmo/s2hXhBWb49JuuGi1BCgIAJA4EYayCbueX774binDe/JKb50+SIQUBABIKgjAmXMD/5Tvv+AMhOn34DQtn4ULzAAAJB0HYdwLPffXhTo/b49OlX71ovkmJNxMAIPHgt7vvTu39uL2xOajQj1+0JMeASysBACQkBGEfNVUcqz15ipPIs665cUymVuxyAACgjxCEfUG3t57cv58jFF96zVXFNrHLAQCAvkMQ9hrrZ8refy/Ecr6CK5fMGCl2OQAAEBMEYS8JfPm/P2QYP2POu/66aZgsAQCQ6BCEvXP28KH2xuawXDNxwQIzZksAACQ+BGEvuJsbqg+XCZTEOOP64nQMkAEASAYIwp7ig4HoOmqBYVOuvQJXlgAASBIIwp76+uOPGdrHmHIWzpuMM4MAAEkDQdgjradPtp6rjkiV466Zb5AjBwEAkgeC8PLCjLdi/6e8QOSls8flGsUuBwAA4glBeDmCcGT37mAwzGQMv27qaLGrAQCAOEMQXkbjqRMdDY1hmXrqvLlKTJcAAEg6CMLvw/qZ0wc+FwhRXzm7KE0tdjkAABB/CMLvU/7xJ8FAiLEOuXYSllIDAEhOCMLv1FFb01Fbw0qVE665Bp2iAADJCkH4HTi24tN9vECkY6aNzNSJXQ0AAPQXBOGlVZWVMR5vQJN29fQrxK4FAAD6EYLwEoIed82RcoGismdcY1Ri+jwAQDJDEF7C0f2fhSOsP2vkjFHZYtcCAAD9C0F4IXdrs6P2HCeRT5w9Q4LWIABAskMQnk8QKj7dzwmEDJ84PB1jZAAAkh+C8DwtVWfc7e0hhW7q9FKxawEAgIGAIPwPgedOHzwoEKIZNyXLoBC7HAAAGAgIwv+orTjh83gD2rRZk7G4NgBAqkAQfovnasrLCCG2kml6BRaSAQBIFQjCb9QcP+6nmYDWNvWKIrFrAQCAgYMgJIQQgWNryssJIemlUzVyvCcAACkEP/qEEFJ97LifYfx62zQ0BwEAUgyCkBCer//6CCEks3SaSoYp9AAAqQVBSBoqK/0ME9SYp4wbInYtAAAw0BCEpPrIEUKIacxENZqDAACpJ9WD0F5X6+vsCCt0EyfgGvQAAKko1YPwzFflAiHK4hKLCnMHAQBSUUoHId3Z6W1pYqWKKyeOFbsWAAAQR0oH4emvj/ECIQWjs40qsWsBAABxyGJ58NmzZ48dO0bTdHFx8YwZM6IbI5HIrl27Ojs7586dm5+ff8FDDh48eOrUqZKSkiuvvDKWp44dHw47qysJIcXj0RwEAEhdMbUIb7zxxh07dhw4cOCuu+5asmQJz/Mcx82bN+/3v//9gQMHSktL9+/f333/tWvX3nHHHeXl5UuXLn3hhRdiqzxW1SdPh8NhvzlndL5V3EoAAEBEMbUIT58+Hb3hcmeQS4UAAB32SURBVLkyMzNPnDhRV1fX0tJSUVGhVCrHjRv3+OOP7927N7qP3W5/8cUXT548WVRUdM8998yePfvee+/V6US7+G3jiQpCSOboK3AZegCAVBafc4R+v18ikZjN5vfff/+GG25QKpWEkJtvvvnTTz+laTq6z0cffTRmzJiioiJCSElJic1mu6C9OJBcrS1+Z2dYrikZM1SsGgAAYDCIqUVICPnlL39ZVlZWWVm5efPmvLy85ubmuXPnRv+UlZUlkUhaWlpGjBhBCGlubs7Nze16YE5OTnNz8wVH4zjuxRdf7L5FqVTec889l3zqSCQSiUT6VvbJr47ygiAtGK2V8ZEI37eDpLhY3n+IUSQSkclkEklKD3YTET78IopEIhRF8XxPf7dlMhlFXabfr3dB2NHREe3q1Ol0CxcuJITcfvvtV1999Ycffrh27dprr72W5/muLydFURRFsSwbvctxXPdqJBIJx3EXP0VNTU33uyqV6pK7RQ/4XX/6fnw47K2vFihq2NgRfTsCkBjef4hd9M0XBEHsQlIUPvwi6u2bL5VK4xyETqdz165dhBCbzRYNwgkTJhBCFi5cOHny5H/+859ZWVl2uz26c2dnJ8uy2dnZ0bvZ2dldfyKEtLe3Z2VlXVzxK6+80sNiWJZVqfoy7eHcuRqW40Om7LEFNpwf7LNIJNK39x9ix3GcSqVCi1As+PCLSBAEhUIhlcZzCZTefZFGjBixadOmTZs2PfPMM923RyIRl8tlNBrnzJmza9eu6D9UP/roo5KSErPZ7Pf7vV7v7Nmzjxw54nA4CCH19fW1tbVdMy4GWOPpM4SQtGEjkYIAAND3c4SHDh164oknpkyZIpVKd+7caTAYbrjhBoqinnrqqeXLl5eWlj7//POvvfYaIeSpp546fvz4e++9d8sttyxatOi2227bvHnzvffea7WKMG8h5GN8rU28RDZ6TPHAPzsAAAw2VJ9PMwQCgQ8//LCiokIQhDFjxixdulQulxNCXC7X5s2bHQ7H9ddfP336dEJIeXm50+mcN28ex3F//etfT548WVpaesstt1zQb8swTGZmJsMwPSyAYZg+zL44cfirmoOfhzKG3XL7Db19LHRH07Rerxe7ihTl8/nUajW6RsWCD7+IAoFA3LtG+x6EcTcwQbhn2za/o9Mye/HMEkyciAl+C0SEIBQXPvwi6o8gTK0vEu1wBBydEZlq3KhCsWsBAIBBIbWCsPrMWYEQae4woxIXXQIAAEJSLQg7a6sJIVlFw8QuBAAABosUCsKg1xtydrJS5cjiPLFrAQCAwSKFgvDsmWpeICSjAP2iAADQJYWCsKP2HCHEVoTBogAA8B+pEoRsKBiwt3CUdETxELFrAQCAQSRVgvBc5TmOFzhrXrpeIXYtAAAwiKRKELbWnCOEWAqKxC4EAAAGl5QIQoHnAq2NAkUNHYEgBACA86REELY3t0bCkbDWkp/W6yXZAAAguaVEEDbWNRJCVJn5l7s6IwAApJyUCEJ3UwMhJKMgX+xCAABg0En+IOTC4bCjXaCooUNyxK4FAAAGneQPwqb6Jo7jI6bsNC0mTgAAwIWSPwhb6hsJIbpsrC8KAACXkPxB6G1pIIRkFeIEIQAAXEKSB2HI7w97nKxUMTQvU+xaAABgMEryIKyvqRd4gaTl6JRJ/koBAKBvkjwe7C1thBBDdrbYhQAAwCCV5EHoa28lhKRnZ4ldCAAADFLJHIQCy0Y8nQIlycvJELsWAAAYpJI5CNva7DzHR7QWs0Yudi0AADBIJXMQtja3EkJUNvSLAgDAd0rmIPS0tRFCjBnoFwUAgO+UzEEYtLcSQrJy0CIEAIDvlLRBGPL5WD/DSpV5WWaxawEAgMEraYOwsbFFIISyZCilSfsaAQAgdkkbEp0tbYQQTTpWVgMAgO+TtEHobW8jhKRlIggBAOD7JGsQCqy7gxCSjan0AADwvZIzCBmPlw2HWaUuy6wVuxYAABjUkjMI29sdhBCJwUKJXQkAAAxyyRmEToeTEKIyp4ldCAAADHbJGYS0w0EI0achCAEA4DKSMwjDLgchxJJmEbsQAAAY7JIyCAWOdgkUlZmJFiEAAFxGEgYh4/ZykQgr15o0SrFrAQCAwS4Jg7Dd3kkIkZrSKIwZBQCAy0nCIHTaHYQQlQn9ogAAcHlJGIS000kI0WOkDAAA9EASBmHI00kISUu3il0IAAAkgKQLQoHnvG6BojJtaBECAMDlJVsQ0m4vz7KsUm/UKMSuBQAAEkCyBWG73UEIkRotGDIKAAA9kWxB6Ox0EELUWGUUAAB6JtmCkHF7CCE6o1HsQgAAIDEkWxCGGS8hRG9CEAIAQI8kWxDyPpoQYjLpxS4EAAASQ3IFoSDwAYYQYjYZxC4FAAASQ1IFYdAf4FmWU2j0KpnYtQAAQGJIqiB0uDyEEKLWil0IAAAkjKQKQq+HIYTIdOgXBQCAnkqqIGS8HkKIEkEIAAA9llRBGKBpQohKjyGjAADQU0kVhEGaJoTo9GgRAgBATyVVELI+mhCiN+rELgQAABJGUgVhdDY9JhECAEDPJU8QcpGIEA7yEplZrxa7FgAASBjJE4Qul0cgRNDopRJcgQkAAHoqeYLQ7aEJIRI1ThACAEAvJE8Q0l6aECLX47oTAADQC8kThD4vTQhR6zCJEAAAeiF5gjA6iVCD2fQAANAbyROEkegleY0IQgAA6IXkCcJvLslrxjlCAADohWQJQkHgg4xASSxYVgYAAHojSYKQoX0CL/AKjUqeJK8IAAAGRpLEBs34CSGUCmvKAABA7yRJEPqDIUKIRKEUuxAAAEgwSRKEoWCQECJRqMQuBAAAEowslge3trb+9a9/ra6ulkqlV1111bJlyyQSyeHDhz/88MPm5uYhQ4asWrXKZrN17b9t27bm5ubo7fT09JUrV8ZUezdBf5AQIlchCAEAoHdiahGeO3euqalp4sSJxcXFa9asWbt2LSHkjjvuCAaDU6dOPXbs2IQJExwOR9f+r732WllZmcvlcrlcXq831tq7ibYIZUp0jQIAQO/E1CKcOXPmzJkzo7ezs7MfffTRp59++vTp0zKZjBCycuXK4uLi3bt333777V0PWbFixeLFi2N50kuKBEOEEDkGywAAQC/FFIRdQqHQ7t27J02aRAiJpiAhhOM4r9drsVi677ljx47Dhw+PGTPmlltukUqlcXl2QkgkHCSEKDBYBgAAeinWIOzo6BgxYgRN06NGjfrkk0+6/2ndunVDhw699tpru7ZMnjzZYDDIZLKnnnrq9ddf37NnzwVZyLLssmXLum9Rq9Wvv/76JZ/a7/dLJN907YZ8DM/zRCrx+/0xviLooUAgEMd/ykCv+P1+QRC6Pv8wwHr74T979mxbW1v/1ZMirFbrqFGjAoEAy7I9f/9VKtVlvym9DsK///3vBw8eJITMnz9/4cKFNpvN6XQ2Nzc/9thjy5Yt27dvX3S3V1999W9/+9v+/fu7V/DSSy9Fbzz44IPDhg3797//vWjRou4Hl0gkFwShQqFQfccQGJZl//MnNkJJKINB9107Q9xFIhG822LhOK4nX2/oJ7398L/00kuHDh3KyMjov5KSnsPhGDp06L/+9S9BEBQKRc+DsCdfk14HYW5u7rhx4wgh3f+n5uTkPPHEE3l5eR6Px2g0btq06dlnn927d29ubu4lD6LX64uLixsbGy+uuPsJxe8nkUi6XiEfDlKE0mq1+GkYMN3ffxhgkm+JXUiK6u2bT1HUI488Esdx8ino7bfffuuttyTdxPHgvQ7CGTNmzJgxI3rb5XKZzebo7f3791utVoPBsGXLlscee+zjjz8uKiqK/qmjo+Pw4cPXXnstz/NqtZoQUlVV9fXXX69fvz5Or4KQUIgQotLgHCEAAPROTOcIf/vb3+7Zs2fYsGEdHR2VlZVvvPEGy7J33313VlbWnXfeGd3ngQceyMzMvP32248dO3bllVdOmjRJKpUeOHBg9erVU6dOjcdLIIQQIRIihGjV6KkDAIDeiSkIX3rppRMnTtTV1ZnN5pKSEp1OJwhCVVVV930sFotcLi8vLy8qKjpx4sSJEycIIRs3bszJyYmp8G54niNsRKCkGqU8XscEAIAUEVMQUhQ1bty46CnDri1dPaLdFRcXE0JycnLimH9dgv6QQAivUEqouB8bAACSXDKcbGcCQUIIJUe/KAAA9FoyBGHAHyCEUJhNDwAAvZccQRgkhEhx6QkAAOi9ZAjCYDBICJFicjcAAPReMgRh6JsVtxGEAACxYhhmz549A/NcNTU1FRUVA/Nc3yMZgjASChJCZOgaBQDogcbGRv2lRDPp6aefPnbsWJ8P/tJLL5WXl/dwZ41Gs2zZMtHXiI7P1SfEFQkECSEKDYIQAODycnNz7XY7IYSm6YyMjMrKyry8PEKISqXyer0bN26srq7u88F37tyZm5t75ZVX9mTnzMzM6dOnb9u27Z577unzM8YuGVqEbPQaTLgqLwBAD1AUpVar1Wp1dOlwpVIZvUtR1D/+8Y8ZM2bo9fp169Zt3Lix6yH33nvve++9d/GhamtrFyxYkJ+fX1BQsHr16ldfffXw4cNr1qyZOHHihg0bzpw5c9111+Xl5Q0fPvyRRx5hWfbkyZM/+MEP1q9fX1hYuGbNGkLIsmXL3nrrrYF66ZeWDC1CLhwihOBKCACQKHiBOEPCwDyXVEKZFT3ded++fZMnTyaETJw48dFHH121ahUhpL29fdu2bb///e8v3n/t2rXTp0//4IMPIpHIsWPHxo0b9/e//33lypVLlixRqVTt7e3PPffc2LFjnU7nbbfdtmnTptLS0vfff3/UqFEVFRUcxxFCpkyZUlZW5vf7NRpN3F5zLyVDEPLBICFEjYVGASBBeCPkxQp+YJ7LrKQeHt/Tzr+6urp58+YRQhYuXHjvvfceOXJkwoQJW7ZsueGGG9LS0i7eX6FQnDx58uTJk+PGjYsmqFwu12q10esxFBYWNjU1/etf/3I6nbm5uZ999llpaalKpXriiSe6LuFutVqlUmlzc/Pw4cPj84J7LymCMBwkhKjU6BoFgMRgUpDfTxqM17WWSqU8zxNCZDLZ8uXLN2/ePGHChK1btz7zzDOX3H/9+vW//e1vo1eWXbt27b333tv9r+++++7q1auXL19uMplCoRDDMISQjIyMrhSM4nle3GuKJcM5QiEcIoToNGqxCwEASGyFhYXNzc3R2ytXrvzzn//8xRdf2O32+fPnX3J/m832yiuv1NfXb9myZfXq1Xa7vStKCSEbN2588sknn3766UceeWTkyJHRjRR13qrQdrudoqjs7Ox+e02XlwRBKJBwSCCURt3jXnAAALiUOXPmfPnll9HbY8eOLSgo+PGPf3zXXXdd0Ibr8sYbbxw9etTj8XAcp1KptFptUVHRhx9+WFZW1tzcbLPZPv74487Ozj179mzatOmSRzh06NCUKVOil6oVS8IHYTAQFIjAy5RyacK/FgCAgSSXy2+88cbuo1RuuummL7/80u12R+8++uij48aN+/GPf/xdR/B6vQ8++ODMmTNfeumlnTt3arXadevWWSyW9evX79+//3e/+10oFJozZ86bb7758ssvz5w502KxXH/99d2PsH379pUrV/bTC+whShAGaOTSZTEMk5mZGe1E7uH+Op3O4XAd2LaZ0xh/8N8iv5WphqZpvV4vdhUpyufzqdVqcU+rpLLefvhXrlw5a9Ys0X/ue+jJJ5+USqWPPvroADxXY2Pjdddd9/XXXysvN//t7bfffuutt95+++1AIKBQKKTSeJ5hTfjBMsFAiBAiwbIyAADx8Itf/OL48eMXby8vL79gon1xcXFpaWksz0VR1LvvvnvZFOxvCR+E/mCIECIR+30EAEgOarV6ypQpF29vb2+vqqrqviU6RyIWubm5MR4hLhI+CIMBXIMJAKDfLVy4cOHChWJX0S8S/hxDKBqESgQhAAD0RcIHYTgQJITIsL4aAAD0ScIHYSQcJITI0SIEAOhnfr//V7/6ldhVxF/iB2EwSAhRqjBYBgCgfwUCgWeffVbsKuIv4YOQjYQJISoEIQBAz0QikR/96EfRSxISQhiGuf322y85h/vAgQOLFy+eOHHiwoULP/nkk7Vr1wqCcOutt9566611dXU7d+686aabJk2adPPNN0fXo9myZctbb7318MMPT548+ciRIwP6qmKQ8KNGBV4ghEgl1GX3BAAYTAZqMROBkPOX95TL5X6//y9/+cuDDz5ICNm+fbvdbtfpdBc8juO4G2+8ccuWLZMmTWpoaBAE4f777//jH/8YXYA7Ozv7+PHjjzzySE5OzsGDB5csWXLy5Mnjx49v2rTphRdeuPvuuzMyMgboBcYs8YNQIIQQxCAAJBDeT3vef3Ngnkui0RtvuHBRmxUrVjz22GPRINy8efMlV71hWTYQCHAcZ7FY0tPTCSEOh4MQUlRUFN3hxhtvbGlpqa6uNpvN2dnZ0Ubh/Pnz77777n59RXGX8EEY/VeVgCgEgMQh0ejNtz4gYgGLFi36yU9+cuzYMaPReOTIkffff//ifZRK5ZYtW9atW7dixYrrr7/+6aefvqDVuG7duv/7v/+76qqrLBYLTdMdHR2kW0wmkCQIQkIubPcDAMD3kclkP/zhDzdv3mw0GpctW3Zxv2jUsmXLli1b1tDQ8Pjjj99///1bt24lhAiCQFFUIBB45pln2tvbo+vLfPTRR9GVq+O7CujASPjBMtQ3faNIQgCAXlixYsWf//znLVu23HXXXZfcwe12f/TRRyzL5ufnFxcXE0KMRqNGo9m/f7/L5SKESKXSyspKQRC2bNlSUVExoNXHVRK0CAVCCIWuUQCA3rjiiitmzpzJMMzs2bMvuQPLsuvXr7/77rspihozZsyGDRskEsnGjRt/85vf0DT9l7/85U9/+tNtt93GcdwNN9xw3333paWl5ebmKhSJd2nYhA9CQeAJIQTXowEA6KUdO3Z8z1+tVuvu3bsv2Hj77bfffvvt0dvFxcU/+tGP+qu4AZTwQUgJVPQ/YhcCAJDAvvrqK5Zlu28ZO3bsd507TDIJH4ToGgUAiN22bdt8Pl/3LWvWrEEQJoboOCUKg2UAAGLw8ssvi12CaJLg1BpahAAA0HeJH4TRk4PIQQAA6JMkCEJ0jQIAQN8lfhBiiTUAAIhB4gdhdGGZxH8dAAAgiiQIEJ4QQiXDCwEAABEk/PQJgqVGAWBwmzBhwi9+8Yt169aJXUgCCwQCM2fO7KeDJ3wQCkhCABjc7rvvvqVLl4pdRcLTaDT9dOSED0LkIAAMclKpNC8vT+wq4Dsl/qk1gSeEUBgtAwAAfZLw+YG2IAAAxCLhg5DwWGINAAD6LvGDkCLk23XWAAAAeivxgzC6xJoELUIAAOiLJAhCQrDWKAAA9FXiB+E3l2ECAADoi8QPwm+6RhP/hQAAgBgSPj+ifaLR69QDAAD0VsIHocDzBC1CAADoqyTID4oQQlFoEQIAQF8kQRBGB8skwQsBAAARJHx+UDxPCCGYRwgAAH2S8EEoUIQQgp5RAADom4QPwm8m1KNFCAAAfZLwQUhhnVEAAIhBwgdhdEI9wfUIAQCgT5ImP9AuBACAvkj4IIyuKSNBixAAAPok8fMjutYorj4BAAB9kvhBSOEK9QAA0HcJH4TfzCDEREIAAOiThA/Cb5ZYwzlCAADok8TPD5wjBACAGCR8EFKCQL5daA0AAKC3Ej4Io9AiBACAvkn4IIzOI0QMAgBA3yR8EGKwDAAAxCLh8yN6jhBXnwAAgL6JKQhfffXVq6++evTo0XPmzPnrX/9KCOF5fl43GzZs6L5/bW3tzTffPHr06OXLl7e2tsZUOCG/+c1vjh8//u09zCMcUFVVVb/61a/EriJ1PffccwcPHhS7ihTV0tLywAMPiF1F6tqwYcOePXvie0xZLA/OyMh44oknsrOzjx49evfdd2dkZMyePXvPnj1vv/22VqslhOTl5XXtLAjC0qVLFyxYsH79+ueff/6HP/zhvn37Ynn2srKyhQsXftM1irOEA8vtduOHWERHjx4dP3682FWkKIZhPvvsM7GrSF0nTpwwGo3xPWZMQXjzzTdHbwwbNuzNN98sLy+fPXs2IeTqq6++uNADBw40Nzc/9dRTMpns+eeft1qtp06dGj16dCwFEEEgAhEoCqNGAQCgb2IKQkJIa2trS0vL6dOnKyoqXnzxxejG2267jaKoWbNmPfjgg2q1OrrxxIkTJSUlMpmMEKLRaEaPHl1RURFjEFLRy/IKBDkIAAB9E2sQ7ty5c8OGDbW1tStXriwqKqIo6rnnnps6darL5frd73538ODBd999N7qn3W43mUxdDzSbzXa7vfuh5HK52WyOJmUXiqIyMjIu+dQ0TS+/4475M+fyEvl9Lw2l2FCMrwV6juM4n8+Xm5srdiEpyufzHTp06Oc//7nYhaQinudpmsaHXyx+v/+DDz747W9/28P9d+3aNWbMmO/fp9dBOHny5OiN9957LyMjY9WqVatWrWIYZt68eevXr3/00Ucffvjh6A4TJkzIy8trbW3NysoihJhMJp/P13UcmqbNZnP3IyuVyi+++KKlpaX7RolEkpmZ2dsiAQAACCE9SZBeB+HmzZujN9LS0ro26nS6efPmdRvD+c0OEomEYZjo3SFDhlRWVkZvcxx37ty5IUOGXHDwvLy87uNrAAAA+luvp0+M+pZMJtu7d290YZf6+vrt27dPmzaturq6qamJEBKJRB577LHCwsKioqJdu3a99dZb1113nc/ne/vttwkhW7duNRqN06ZNi/vrAQAA6JWY5hGuWbNGq9VmZGSMHz9+0aJFP/vZzyorK8ePH5+WlmY0Gr/44ot//vOfUqm0rKxs165dCoVi69at9913X25u7uOPP75161aJJOGn8wMAQKKjok26PguHw4FA4ILJEm63W61WK5XKi/fned7j8ZhMplgmPEQikaeeemrXrl02m+3Xv/5112lLGAAOh2PHjh1fffVVMBjcsmWL2OWknO3bt+/YsaOuri4nJ2f16tVXX3212BWlkObm5scff7yyslIQhGnTpq1Zs6b7GSIYGDzPP/DAAzqd7plnnonXMWMdNapQKBQKxQUbu48OvYBEIrlgjEwfPPnkk7t27Xr11VfLysoWLFhw9uxZfBwHTGVl5ccff5yWlvavf/1L7FpS0TvvvHP99dePGjXq8OHD119//RdffFFaWip2UakiHA5PmjTpxz/+McdxTz/99PLly3ft2iV2USlnw4YNH3zwgcViieMxY20RDjyWZbOzs//xj3/MmjWLEDJ//vyFCxc++OCDYteVWsrKyubOnUvTtNiFpLQFCxbMnTv3l7/8pdiFpKJDhw7Nnz/f6/WKXUhqqaurW7x48f33379x48avvvoqXodNvLN0LS0tHR0dU6ZMid6dMmXKsWPHxC0JYOCFw+EzZ84MGzZM7EJSTk1NTUVFxf/+7//ecsstYteSWgRBuPfee1944YXoEp5xFGvX6MCz2+3dT0Cazeby8nJxSwIYeL/85S/z8/OXLl0qdiEpZ968eT6fT6vVvvPOO2LXklr++Mc/ZmVlzZ8/f+vWrfE9cuIFocFgCIVCHMdJpVJCCMMw33NKEiApPfXUU7t37/70008x9HrgnTt3jhCyadOma6+9tra2tmsVSehXLS0tzz///KFDh/rj4In3LcrJyZFKpTU1NdG71dXVBQUF4pYEMJCef/75LVu27Nmzx2q1il1L6rrzzjvtdntDQ4PYhaSK6upqh8MxfPhwi8Xy05/+9OjRoxaLJRgMxuXgiReEWq12yZIlr7zyCiGkoaHh/fffX758udhFAQyQP/zhD6+88spHH30UXbkQBlJlZWV0dIwgCBs3brRYLBcvjwX9ZNasWc5vvfbaayUlJU6nU6VSxeXgiReEhJDnnnvuk08+GTp0aElJyUMPPTRu3DixK0ohDQ0NFEVNnjyZYRiKooYPHy52RanlySefrK+vLywspCiKoqj/+Z//EbuiFPL5558XFBQUFBTYbLZXXnllx44dF08eg0SUeNMnogRBaG5uNplMOp1O7FoAIFWEw+H29na9Xo+hCckkUYMQAAAgLhKyaxQAACBeEIQAAJDSEIQAAJDSEIQAAJDSEIQAAJDSEIQAAJDSEIQAAJDSEIQAAJDSEIQAAJDSEIQAAJDSEIQAAJDSEIQAAJDSEIQAAJDS/h8GqJgN1wjpxQAAAABJRU5ErkJggg==" }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w = T(v_star.(grid_y), grid_y, β, log, k -> k^α, shocks)\n", "\n", "plt = plot(ylim = (-35,-24))\n", "plot!(plt, grid_y, w, linewidth = 2, alpha = 0.6, label = \"T(v_star)\")\n", "plot!(plt, v_star, grid_y, linewidth = 2, alpha=0.6, label = \"v_star\")\n", "plot!(plt, legend = :bottomright)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The two functions are essentially indistinguishable, so we are off to a good start.\n", "\n", "Now let’s have a look at iterating with the Bellman operator, starting off\n", "from an arbitrary initial condition.\n", "\n", "The initial condition we’ll start with is $w(y) = 5 \\ln (y)$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w = 5 * log.(grid_y) # An initial condition -- fairly arbitrary\n", "n = 35\n", "\n", "plot(xlim = (extrema(grid_y)), ylim = (-50, 10))\n", "lb = \"initial condition\"\n", "plt = plot(grid_y, w, color = :black, linewidth = 2, alpha = 0.8, label = lb)\n", "for i in 1:n\n", " w = T(w, grid_y, β, log, k -> k^α, shocks)\n", " plot!(grid_y, w, color = RGBA(i/n, 0, 1 - i/n, 0.8), linewidth = 2, alpha = 0.6,\n", " label = \"\")\n", "end\n", "\n", "lb = \"true value function\"\n", "plot!(plt, v_star, grid_y, color = :black, linewidth = 2, alpha = 0.8, label = lb)\n", "plot!(plt, legend = :bottomright)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure shows\n", "\n", "1. the first 36 functions generated by the fitted value function iteration algorithm, with hotter colors given to higher iterates \n", "1. the true value function $v^*$ drawn in black \n", "\n", "\n", "The sequence of iterates converges towards $v^*$.\n", "\n", "We are clearly getting closer.\n", "\n", "We can write a function that computes the exact fixed point" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "solve_optgrowth (generic function with 1 method)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function solve_optgrowth(initial_w; tol = 1e-6, max_iter = 500)\n", " fixedpoint(w -> T(w, grid_y, β, u, f, shocks), initial_w).zero # gets returned\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check our result by plotting it against the true value" ] }, { "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": [ "initial_w = 5 * log.(grid_y)\n", "v_star_approx = solve_optgrowth(initial_w)\n", "\n", "plt = plot(ylim = (-35, -24))\n", "plot!(plt, grid_y, v_star_approx, linewidth = 2, alpha = 0.6,\n", " label = \"approximate value function\")\n", "plot!(plt, v_star, grid_y, linewidth = 2, alpha = 0.6, label = \"true value function\")\n", "plot!(plt, legend = :bottomright)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure shows that we are pretty much on the money." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Policy Function\n", "\n", "\n", "\n", "To compute an approximate optimal policy, we take the approximate value\n", "function we just calculated and then compute the corresponding greedy policy.\n", "\n", "The next figure compares the result to the exact solution, which, as mentioned\n", "above, is $\\sigma(y) = (1 - \\alpha \\beta) y$." ] }, { "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": [ "Tw, σ = T(v_star_approx, grid_y, β, log, k -> k^α, shocks;\n", " compute_policy = true)\n", "cstar = (1 - α * β) * grid_y\n", "\n", "plt = plot(grid_y, σ, lw=2, alpha=0.6, label = \"approximate policy function\")\n", "plot!(plt, grid_y, cstar, lw = 2, alpha = 0.6, label = \"true policy function\")\n", "plot!(plt, legend = :bottomright)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure shows that we’ve done a good job in this instance of approximating\n", "the true policy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Once an optimal consumption policy $\\sigma$ is given, income follows [(5)](#equation-firstp0-og2).\n", "\n", "The next figure shows a simulation of 100 elements of this sequence for three different discount factors (and hence three different policies).\n", "\n", "\n", "\n", " \n", "In each sequence, the initial condition is $y_0 = 0.1$.\n", "\n", "The discount factors are discount_factors = (0.8, 0.9, 0.98).\n", "\n", "We have also dialed down the shocks a bit." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hide-output": true }, "outputs": [], "source": [ "s = 0.05\n", "shocks = exp.(μ .+ s * randn(shock_size))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Otherwise, the parameters and primitives are the same as the log linear model discussed earlier in the lecture.\n", "\n", "Notice that more patient agents typically have higher wealth.\n", "\n", "Replicate the figure modulo randomness." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Here’s one solution (assuming as usual that you’ve executed everything above)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function simulate_og(σ, y0 = 0.1, ts_length=100)\n", " y = zeros(ts_length)\n", " ξ = randn(ts_length-1)\n", " y[1] = y0\n", " for t in 1:(ts_length-1)\n", " y[t+1] = (y[t] - σ(y[t]))^α * exp(μ + s * ξ[t])\n", " end\n", " return y\n", "end\n", "\n", "plt = plot()\n", "\n", "for β in (0.9, 0.94, 0.98)\n", " Tw = similar(grid_y)\n", " initial_w = 5 * log.(grid_y)\n", "\n", " v_star_approx = fixedpoint(w -> T(w, grid_y, β, u, f, shocks),\n", " initial_w).zero\n", " Tw, σ = T(v_star_approx, grid_y, β, log, k -> k^α, shocks,\n", " compute_policy = true)\n", " σ_func = LinearInterpolation(grid_y, σ)\n", " y = simulate_og(σ_func)\n", "\n", " plot!(plt, y, lw = 2, alpha = 0.6, label = label = \"beta = \$β\")\n", "end\n", "\n", "plot!(plt, legend = :bottomright)" ] } ], "metadata": { "date": 1591310616.5718153, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "optgrowth.rst", "filename_with_path": "dynamic_programming/optgrowth", "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": "Optimal Growth I: The Stochastic Optimal Growth Model" }, "nbformat": 4, "nbformat_minor": 2 }