{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Optimal Growth II: Time Iteration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Optimal Growth II: Time Iteration](#Optimal-Growth-II:-Time-Iteration) \n", " - [Overview](#Overview) \n", " - [The Euler Equation](#The-Euler-Equation) \n", " - [Comparison with Value Function Iteration](#Comparison-with-Value-Function-Iteration) \n", " - [Implementation](#Implementation) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "In this lecture we’ll continue our [earlier study](optgrowth.html) of the stochastic optimal growth model.\n", "\n", "In that lecture we solved the associated discounted dynamic programming problem using value function iteration.\n", "\n", "The beauty of this technique is its broad applicability.\n", "\n", "With numerical problems, however, we can often attain higher efficiency in specific applications by deriving methods that are carefully tailored to the application at hand.\n", "\n", "The stochastic optimal growth model has plenty of structure to exploit for this purpose, especially when we adopt some concavity and smoothness assumptions over primitives.\n", "\n", "We’ll use this structure to obtain an **Euler equation** based method that’s more efficient than value function iteration for this and some other closely related applications.\n", "\n", "In a [subsequent lecture](egm_policy_iter.html) we’ll see that the numerical implementation part of the Euler equation method can be further adjusted to obtain even more efficiency." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Euler Equation\n", "\n", "Let’s take the model set out in [the stochastic growth model lecture](optgrowth.html) and add the assumptions that\n", "\n", "1. $ u $ and $ f $ are continuously differentiable and strictly concave \n", "1. $ f(0) = 0 $ \n", "1. $ \\lim_{c \\to 0} u'(c) = \\infty $ and $ \\lim_{c \\to \\infty} u'(c) = 0 $ \n", "1. $ \\lim_{k \\to 0} f'(k) = \\infty $ and $ \\lim_{k \\to \\infty} f'(k) = 0 $ \n", "\n", "\n", "The last two conditions are usually called **Inada conditions**.\n", "\n", "Recall the Bellman equation\n", "\n", "\n", "\n", "$$\n", "v^*(y) = \\max_{0 \\leq c \\leq y}\n", " \\left\\{\n", " u(c) + \\beta \\int v^*(f(y - c) z) \\phi(dz)\n", " \\right\\}\n", "\\quad \\text{for all} \\quad\n", "y \\in \\mathbb R_+ \\tag{1}\n", "$$\n", "\n", "Let the optimal consumption policy be denoted by $ c^* $.\n", "\n", "We know that $ c^* $ is a $ v^* $ greedy policy, so that $ c^*(y) $ is the maximizer in [(1)](#equation-cpi-fpb30).\n", "\n", "The conditions above imply that\n", "\n", "- $ c^* $ is the unique optimal policy for the stochastic optimal growth model \n", "- the optimal policy is continuous, strictly increasing and also **interior**, in the sense that $ 0 < c^*(y) < y $ for all strictly positive $ y $, and \n", "- the value function is strictly concave and continuously differentiable, with \n", "\n", "\n", "\n", "\n", "$$\n", "(v^*)'(y) = u' (c^*(y) ) := (u' \\circ c^*)(y) \\tag{2}\n", "$$\n", "\n", "The last result is called the **envelope condition** due to its relationship with the [envelope theorem](https://en.wikipedia.org/wiki/Envelope_theorem).\n", "\n", "To see why [(2)](#equation-cpi-env) might be valid, write the Bellman equation in the equivalent\n", "form\n", "\n", "$$\n", "v^*(y) = \\max_{0 \\leq k \\leq y}\n", " \\left\\{\n", " u(y-k) + \\beta \\int v^*(f(k) z) \\phi(dz)\n", " \\right\\},\n", "$$\n", "\n", "differentiate naively with respect to $ y $, and then evaluate at the optimum.\n", "\n", "Section 12.1 of [EDTC](http://johnstachurski.net/edtc.html) contains full proofs of these results, and closely related discussions can be found in many other texts.\n", "\n", "Differentiability of the value function and iteriority of the optimal policy\n", "imply that optimal consumption satisfies the first order condition associated\n", "with [(1)](#equation-cpi-fpb30), which is\n", "\n", "\n", "\n", "$$\n", "u'(c^*(y)) = \\beta \\int (v^*)'(f(y - c^*(y)) z) f'(y - c^*(y)) z \\phi(dz) \\tag{3}\n", "$$\n", "\n", "Combining [(2)](#equation-cpi-env) and the first-order condition [(3)](#equation-cpi-foc) gives the famous **Euler equation**\n", "\n", "\n", "\n", "$$\n", "(u'\\circ c^*)(y)\n", "= \\beta \\int (u'\\circ c^*)(f(y - c^*(y)) z) f'(y - c^*(y)) z \\phi(dz) \\tag{4}\n", "$$\n", "\n", "We can think of the Euler equation as a functional equation\n", "\n", "\n", "\n", "$$\n", "(u'\\circ \\sigma)(y)\n", "= \\beta \\int (u'\\circ \\sigma)(f(y - \\sigma(y)) z) f'(y - \\sigma(y)) z \\phi(dz) \\tag{5}\n", "$$\n", "\n", "over interior consumption policies $ \\sigma $, one solution of which is the optimal policy $ c^* $.\n", "\n", "Our aim is to solve the functional equation [(5)](#equation-cpi-euler-func) and hence obtain $ c^* $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Coleman Operator\n", "\n", "Recall the Bellman operator\n", "\n", "\n", "\n", "$$\n", "Tw(y) := \\max_{0 \\leq c \\leq y}\n", "\\left\\{\n", " u(c) + \\beta \\int w(f(y - c) z) \\phi(dz)\n", "\\right\\} \\tag{6}\n", "$$\n", "\n", "Just as we introduced the Bellman operator to solve the Bellman equation, we\n", "will now introduce an operator over policies to help us solve the Euler\n", "equation.\n", "\n", "This operator $ K $ will act on the set of all $ \\sigma \\in \\Sigma $\n", "that are continuous, strictly increasing and interior (i.e., $ 0 < \\sigma(y) < y $ for all strictly positive $ y $).\n", "\n", "Henceforth we denote this set of policies by $ \\mathscr P $\n", "\n", "1. The operator $ K $ takes as its argument a $ \\sigma \\in \\mathscr P $ and \n", "1. returns a new function $ K\\sigma $, where $ K\\sigma(y) $ is the $ c \\in (0, y) $ that solves \n", "\n", "\n", "\n", "\n", "$$\n", "u'(c)\n", "= \\beta \\int (u' \\circ \\sigma) (f(y - c) z ) f'(y - c) z \\phi(dz) \\tag{7}\n", "$$\n", "\n", "We call this operator the **Coleman operator** to acknowledge the work of [[Col90]](../zreferences.html#coleman1990) (although many people have studied this and other closely related iterative techniques).\n", "\n", "In essence, $ K\\sigma $ is the consumption policy that the Euler equation tells\n", "you to choose today when your future consumption policy is $ \\sigma $.\n", "\n", "The important thing to note about $ K $ is that, by\n", "construction, its fixed points coincide with solutions to the functional\n", "equation [(5)](#equation-cpi-euler-func).\n", "\n", "In particular, the optimal policy $ c^* $ is a fixed point.\n", "\n", "Indeed, for fixed $ y $, the value $ Kc^*(y) $ is the $ c $ that\n", "solves\n", "\n", "$$\n", "u'(c)\n", "= \\beta \\int (u' \\circ c^*) (f(y - c) z ) f'(y - c) z \\phi(dz)\n", "$$\n", "\n", "In view of the Euler equation, this is exactly $ c^*(y) $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Is the Coleman Operator Well Defined?\n", "\n", "In particular, is there always a unique $ c \\in (0, y) $ that solves\n", "[(7)](#equation-cpi-coledef)?\n", "\n", "The answer is yes, under our assumptions.\n", "\n", "For any $ \\sigma \\in \\mathscr P $, the right side of [(7)](#equation-cpi-coledef)\n", "\n", "- is continuous and strictly increasing in $ c $ on $ (0, y) $ \n", "- diverges to $ +\\infty $ as $ c \\uparrow y $ \n", "\n", "\n", "The left side of [(7)](#equation-cpi-coledef)\n", "\n", "- is continuous and strictly decreasing in $ c $ on $ (0, y) $ \n", "- diverges to $ +\\infty $ as $ c \\downarrow 0 $ \n", "\n", "\n", "Sketching these curves and using the information above will convince you that they cross exactly once as $ c $ ranges over $ (0, y) $.\n", "\n", "With a bit more analysis, one can show in addition that $ K \\sigma \\in \\mathscr P $\n", "whenever $ \\sigma \\in \\mathscr P $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison with Value Function Iteration\n", "\n", "How does Euler equation time iteration compare with value function iteration?\n", "\n", "Both can be used to compute the optimal policy, but is one faster or more\n", "accurate?\n", "\n", "There are two parts to this story.\n", "\n", "First, on a theoretical level, the two methods are essentially isomorphic.\n", "\n", "In particular, they converge at the same rate.\n", "\n", "We’ll prove this in just a moment.\n", "\n", "The other side to the story is the speed of the numerical implementation.\n", "\n", "It turns out that, once we actually implement these two routines, time iteration is faster and more accurate than value function iteration.\n", "\n", "More on this below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Equivalent Dynamics\n", "\n", "Let’s talk about the theory first.\n", "\n", "To explain the connection between the two algorithms, it helps to understand\n", "the notion of equivalent dynamics.\n", "\n", "(This concept is very helpful in many other contexts as well).\n", "\n", "Suppose that we have a function $ g \\colon X \\to X $ where $ X $ is a given set.\n", "\n", "The pair $ (X, g) $ is sometimes called a **dynamical system** and we\n", "associate it with trajectories of the form\n", "\n", "$$\n", "x_{t+1} = g(x_t), \\qquad x_0 \\text{ given}\n", "$$\n", "\n", "Equivalently, $ x_t = g^t(x_0) $, where $ g $ is the $ t $-th\n", "composition of $ g $ with itself.\n", "\n", "Here’s the picture\n", "\n", "\n", "\n", " \n", "Now let another function $ h \\colon Y \\to Y $ where $ Y $ is another set.\n", "\n", "Suppose further that\n", "\n", "- there exists a bijection $ \\tau $ from $ X $ to $ Y $ \n", "- the two functions **commute** under $ \\tau $, which is to say that\n", " $ \\tau(g(x)) = h (\\tau(x)) $ for all $ x \\in X $ \n", "\n", "\n", "The last statement can be written more simply as\n", "\n", "$$\n", "\\tau \\circ g = h \\circ \\tau\n", "$$\n", "\n", "or, by applying $ \\tau^{-1} $ to both sides\n", "\n", "\n", "\n", "$$\n", "g = \\tau^{-1} \\circ h \\circ \\tau \\tag{8}\n", "$$\n", "\n", "Here’s a commutative diagram that illustrates\n", "\n", "\n", "\n", " \n", "Here’s a similar figure that traces out the action of the maps on a point\n", "$ x \\in X $\n", "\n", "\n", "\n", " \n", "Now, it’s easy to check from [(8)](#equation-cpi-ghcom) that $ g^2 = \\tau^{-1} \\circ h^2 \\circ \\tau $ holds.\n", "\n", "In fact, if you like proofs by induction, you won’t have trouble showing that\n", "\n", "$$\n", "g^n = \\tau^{-1} \\circ h^n \\circ \\tau\n", "$$\n", "\n", "is valid for all $ n $.\n", "\n", "What does this tell us?\n", "\n", "It tells us that the following are equivalent\n", "\n", "- iterate $ n $ times with $ g $, starting at $ x $ \n", "- shift $ x $ to $ Y $ using $ \\tau $, iterate $ n $ times with $ h $ starting at $ \\tau(x) $, and shift the result $ h^n(\\tau(x)) $ back to $ X $ using $ \\tau^{-1} $ \n", "\n", "\n", "We end up with exactly the same object." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Back to Economics\n", "\n", "Have you guessed where this is leading?\n", "\n", "What we’re going to show now is that the operators $ T $ and $ K $\n", "commute under a certain bijection.\n", "\n", "The implication is that they have exactly the same rate of convergence.\n", "\n", "To make life a little easier, we’ll assume in the following analysis (although not\n", "always in our applications) that $ u(0) = 0 $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### A Bijection\n", "\n", "Let $ \\mathscr V $ be all strictly concave, continuously differentiable functions $ v $ mapping $ \\mathbb R_+ $ to itself and satisfying $ v(0) = 0 $ and $ v'(y) > u'(y) $ for all positive $ y $.\n", "\n", "For $ v \\in \\mathscr V $ let\n", "\n", "$$\n", "M v := h \\circ v' \\qquad \\text{where } h := (u')^{-1}\n", "$$\n", "\n", "Although we omit details, $ \\sigma := M v $ is actually the unique\n", "$ v $-greedy policy.\n", "\n", "- See proposition 12.1.18 of [EDTC](http://johnstachurski.net/edtc.html) \n", "\n", "\n", "It turns out that $ M $ is a bijection from $ \\mathscr V $ to $ \\mathscr P $.\n", "\n", "A (solved) exercise below asks you to confirm this." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Commutative Operators\n", "\n", "It is an additional solved exercise (see below) to show that $ T $ and $ K $ commute under $ M $, in the sense that\n", "\n", "\n", "\n", "$$\n", "M \\circ T = K \\circ M \\tag{9}\n", "$$\n", "\n", "In view of the preceding discussion, this implies that\n", "\n", "$$\n", "T^n = M^{-1} \\circ K^n \\circ M\n", "$$\n", "\n", "Hence, $ T $ and $ K $ converge at exactly the same rate!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "We’ve just shown that the operators $ T $ and $ K $ have the same rate of convergence.\n", "\n", "However, it turns out that, once numerical approximation is taken into account, significant differences arises.\n", "\n", "In particular, the image of policy functions under $ K $ can be calculated faster and with greater accuracy than the image of value functions under $ T $.\n", "\n", "Our intuition for this result is that\n", "\n", "- the Coleman operator exploits more information because it uses first order and envelope conditions \n", "- policy functions generally have less curvature than value functions, and hence admit more accurate approximations based on grid point information " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Operator\n", "\n", "Here’s some code that implements the Coleman operator." ] }, { "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 BenchmarkTools, Interpolations, Parameters, Plots, QuantEcon, Roots\n", "using Optim, Random" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using BenchmarkTools, Interpolations, Parameters, Plots, QuantEcon, Roots\n", "\n", "gr(fmt = :png);" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "K (generic function with 1 method)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function K!(Kg, g, grid, β, ∂u∂c, f, f′, shocks)\n", "# This function requires the container of the output value as argument Kg\n", "\n", " # Construct linear interpolation object\n", " g_func = LinearInterpolation(grid, g, extrapolation_bc=Line())\n", "\n", " # solve for updated consumption value\n", " for (i, y) in enumerate(grid)\n", " function h(c)\n", " vals = ∂u∂c.(g_func.(f(y - c) * shocks)) .* f′(y - c) .* shocks\n", " return ∂u∂c(c) - β * mean(vals)\n", " end\n", " Kg[i] = find_zero(h, (1e-10, y - 1e-10))\n", " end\n", " return Kg\n", "end\n", "\n", "# The following function does NOT require the container of the output value as argument\n", "K(g, grid, β, ∂u∂c, f, f′, shocks) =\n", " K!(similar(g), g, grid, β, ∂u∂c, f, f′, shocks)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It has some similarities to the code for the Bellman operator in our [optimal growth lecture](optgrowth.html).\n", "\n", "For example, it evaluates integrals by Monte Carlo and approximates functions using linear interpolation.\n", "\n", "Here’s that Bellman operator code again, which needs to be executed because we’ll use it in some tests below" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "T (generic function with 2 methods)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Optim\n", "\n", "function T(w, grid, β, u, f, shocks, Tw = similar(w);\n", " compute_policy = false)\n", "\n", " # apply linear interpolation to w\n", " w_func = LinearInterpolation(grid, w, extrapolation_bc=Line())\n", "\n", " if compute_policy\n", " σ = similar(w)\n", " end\n", "\n", " # set Tw[i] = max_c { u(c) + β E w(f(y - c) z)}\n", " for (i, y) in enumerate(grid)\n", " objective(c) = u(c) + β * mean(w_func.(f(y - c) .* shocks))\n", " res = maximize(objective, 1e-10, y)\n", "\n", " if compute_policy\n", " σ[i] = Optim.maximizer(res)\n", " end\n", " Tw[i] = Optim.maximum(res)\n", " end\n", "\n", " if compute_policy\n", " return Tw, σ\n", " else\n", " return Tw\n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Testing on the Log / Cobb–Douglas case\n", "\n", "As we [did for value function iteration](optgrowth.html), let’s start by\n", "testing our method in the presence of a model that does have an analytical\n", "solution.\n", "\n", "Here’s an object containing data from the log-linear growth model we used in the [value function iteration lecture](optgrowth.html)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "##NamedTuple_kw#253 (generic function with 2 methods)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isoelastic(c, γ) = isone(γ) ? log(c) : (c^(1 - γ) - 1) / (1 - γ)\n", "Model = @with_kw (α = 0.65, # Productivity parameter\n", " β = 0.95, # Discount factor\n", " γ = 1.0, # Risk aversion\n", " μ = 0.0, # First parameter in lognorm(μ, σ)\n", " s = 0.1, # Second parameter in lognorm(μ, σ)\n", " grid = range(1e-6, 4, length = 200), # Grid\n", " grid_min = 1e-6, # Smallest grid point\n", " grid_max = 4.0, # Largest grid point\n", " grid_size = 200, # Number of grid points\n", " u = (c, γ = γ) -> isoelastic(c, γ), # utility function\n", " ∂u∂c = c -> c^(-γ), # u′\n", " f = k -> k^α, # production function\n", " f′ = k -> α * k^(α - 1), # f′\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we generate an instance" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [], "source": [ "m = Model();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also need some shock draws for Monte Carlo integration" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using Random\n", "Random.seed!(42) # for reproducible results.\n", "\n", "shock_size = 250 # number of shock draws in Monte Carlo integral\n", "shocks = collect(exp.(m.μ .+ m.s * randn(shock_size))); # generate shocks" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a preliminary test, let’s see if $ K c^* = c^* $, as implied by the\n", "theory" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "verify_true_policy (generic function with 1 method)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function verify_true_policy(m, shocks, c_star)\n", " # compute (Kc_star)\n", " @unpack grid, β, ∂u∂c, f, f′ = m\n", " c_star_new = K(c_star, grid, β, ∂u∂c, f, f′, shocks)\n", "\n", " # plot c_star and Kc_star\n", " plot(grid, c_star, label = \"optimal policy cc_star\")\n", " plot!(grid, c_star_new, label = \"Kc_star\")\n", " plot!(legend = :topleft)\n", "end" ] }, { "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": [ "c_star = (1 - m.α * m.β) * m.grid # true policy (c_star)\n", "verify_true_policy(m, shocks, c_star)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can’t really distinguish the two plots, so we are looking good, at least\n", "for this test.\n", "\n", "Next let’s try iterating from an arbitrary initial condition and see if we\n", "converge towards $ c^* $.\n", "\n", "The initial condition we’ll use is the one that eats the whole pie: $ c(y) = y $" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "check_convergence (generic function with 1 method)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function check_convergence(m, shocks, c_star, g_init; n_iter = 15)\n", " @unpack grid, β, ∂u∂c, f, f′ = m\n", " g = g_init;\n", " plot(m.grid, g, lw = 2, alpha = 0.6, label = \"intial condition c(y) = y\")\n", " for i in 1:n_iter\n", " new_g = K(g, grid, β, ∂u∂c, f, f′, shocks)\n", " g = new_g\n", " plot!(grid, g, lw = 2, alpha = 0.6, label = \"\")\n", " end\n", " plot!(grid, c_star, color = :black, lw = 2, alpha = 0.8,\n", " label = \"true policy function c_star\")\n", " plot!(legend = :topleft)\n", "end" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "check_convergence(m, shocks, c_star, m.grid, n_iter = 15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the policy has converged nicely, in only a few steps.\n", "\n", "Now let’s compare the accuracy of iteration using the Coleman and Bellman operators.\n", "\n", "We’ll generate\n", "\n", "1. $ K^n c $ where $ c(y) = y $ \n", "1. $ (M \\circ T^n \\circ M^{-1}) c $ where $ c(y) = y $ \n", "\n", "\n", "In each case we’ll compare the resulting policy to $ c^* $.\n", "\n", "The theory on equivalent dynamics says we will get the same policy function\n", "and hence the same errors.\n", "\n", "But in fact we expect the first method to be more accurate for reasons\n", "discussed above" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "compare_error (generic function with 1 method)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function iterate_updating(func, arg_init; sim_length = 20)\n", " arg = arg_init;\n", " for i in 1:sim_length\n", " new_arg = func(arg)\n", " arg = new_arg\n", " end\n", " return arg\n", "end\n", "\n", "function compare_error(m, shocks, g_init, w_init; sim_length = 20)\n", " @unpack grid, β, u, ∂u∂c, f, f′ = m\n", " g, w = g_init, w_init\n", "\n", " # two functions for simplification\n", " bellman_single_arg(w) = T(w, grid, β, u, f, shocks)\n", " coleman_single_arg(g) = K(g, grid, β, ∂u∂c, f, f′, shocks)\n", "\n", " g = iterate_updating(coleman_single_arg, grid, sim_length = 20)\n", " w = iterate_updating(bellman_single_arg, u.(grid), sim_length = 20)\n", " new_w, vf_g = T(w, grid, β, u, f, shocks, compute_policy = true)\n", "\n", " pf_error = c_star - g\n", " vf_error = c_star - vf_g\n", "\n", " plot(grid, zero(grid), color = :black, lw = 1)\n", " plot!(grid, pf_error, lw = 2, alpha = 0.6, label = \"policy iteration error\")\n", " plot!(grid, vf_error, lw = 2, alpha = 0.6, label = \"value iteration error\")\n", " plot!(legend = :bottomleft)\n", "end" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compare_error(m, shocks, m.grid, m.u.(m.grid), sim_length=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, time iteration is much more accurate for a given\n", "number of iterations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Show that [(9)](#equation-cpi-ed-tk) is valid. In particular,\n", "\n", "- Let $ v $ be strictly concave and continuously differentiable on $ (0, \\infty) $ \n", "- Fix $ y \\in (0, \\infty) $ and show that $ MTv(y) = KMv(y) $ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Show that $ M $ is a bijection from $ \\mathscr V $ to $ \\mathscr P $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "Consider the same model as above but with the CRRA utility function\n", "\n", "$$\n", "u(c) = \\frac{c^{1 - \\gamma} - 1}{1 - \\gamma}\n", "$$\n", "\n", "Iterate 20 times with Bellman iteration and Euler equation time iteration\n", "\n", "- start time iteration from $ c(y) = y $ \n", "- start value function iteration from $ v(y) = u(y) $ \n", "- set $ \\gamma = 1.5 $ \n", "\n", "\n", "Compare the resulting policies and check that they are close." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 4\n", "\n", "Do the same exercise, but now, rather than plotting results, benchmark both approaches with 20\n", "iterations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution to Exercise 1\n", "\n", "Let $ T, K, M, v $ and $ y $ be as stated in the exercise.\n", "\n", "Using the envelope theorem, one can show that $ (Tv)'(y) = u'(c(y)) $\n", "where $ c(y) $ solves\n", "\n", "\n", "\n", "$$\n", "u'(c(y))\n", "= \\beta \\int v' (f(y - c(y)) z ) f'(y - c(y)) z \\phi(dz) \\tag{10}\n", "$$\n", "\n", "Hence $ MTv(y) = (u')^{-1} (u'(c(y))) = c(y) $.\n", "\n", "On the other hand, $ KMv(y) $ is the $ c(y) $ that solves\n", "\n", "$$\n", "\\begin{aligned}\n", " u'(c(y))\n", " & = \\beta \\int (u' \\circ (Mv)) (f(y - c(y)) z ) f'(y - c(y)) z \\phi(dz)\n", " \\\\\n", " & = \\beta \\int (u' \\circ ((u')^{-1} \\circ v'))\n", " (f(y - c(y)) z ) f'(y - c(y)) z \\phi(dz)\n", " \\\\\n", " & = \\beta \\int v'(f(y - c(y)) z ) f'(y - c(y)) z \\phi(dz)\n", "\\end{aligned}\n", "$$\n", "\n", "We see that $ c(y) $ is the same in each case." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution to Exercise 2\n", "\n", "We need to show that $ M $ is a bijection from $ \\mathscr V $ to $ \\mathscr P $.\n", "\n", "To see this, first observe that, in view of our assumptions above, $ u' $ is a strictly decreasing continuous bijection from $ (0,\\infty) $ to itself.\n", "\n", "It [follows](https://math.stackexchange.com/questions/672174/continuity-of-an-inverse-function) that $ h $ has the same properties.\n", "\n", "Moreover, for fixed $ v \\in \\mathscr V $, the derivative $ v' $ is\n", "a continuous, strictly decreasing function.\n", "\n", "Hence, for fixed $ v \\in \\mathscr V $, the map $ M v = h \\circ v' $\n", "is strictly increasing and continuous, taking values in $ (0, \\infty) $.\n", "\n", "Moreover, interiority holds because $ v' $ strictly dominates $ u' $, implying that\n", "\n", "$$\n", "(M v)(y) = h(v'(y)) < h(u'(y)) = y\n", "$$\n", "\n", "In particular, $ \\sigma(y) := (Mv)(y) $ is an element of $ \\mathscr\n", "P $.\n", "\n", "To see that each $ \\sigma \\in \\mathscr P $ has a preimage $ v \\in \\mathscr V $ with $ Mv = \\sigma $, fix any $ \\sigma \\in \\mathscr P $.\n", "\n", "Let $ v(y) := \\int_0^y u'(\\sigma(x)) dx $ with $ v(0) = 0 $.\n", "\n", "With a small amount of effort you will be able to show that $ v \\in \\mathscr V $ and $ Mv = \\sigma $.\n", "\n", "It’s also true that $ M $ is one-to-one on $ \\mathscr V $.\n", "\n", "To see this, suppose that $ v $ and $ w $ are elements of $ \\mathscr V $\n", "satisfying $ Mv = Mw $.\n", "\n", "Then $ v(0) = w(0) = 0 $ and $ v' = w' $ on $ (0, \\infty) $.\n", "\n", "The fundamental theorem of calculus then implies that $ v = w $ on $ \\mathbb R_+ $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution to Exercise 3\n", "\n", "Here’s the code, which will execute if you’ve run all the code above" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "hide-output": false }, "outputs": [], "source": [ "# Model instance with risk aversion = 1.5\n", "# others are the same as the previous instance\n", "m_ex = Model(γ = 1.5);" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "exercise2 (generic function with 3 methods)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function exercise2(m, shocks, g_init = m.grid, w_init = m.u.(m.grid); sim_length = 20)\n", "\n", " @unpack grid, β, u, ∂u∂c, f, f′ = m\n", " # initial policy and value\n", " g, w = g_init, w_init\n", " # iteration\n", " bellman_single_arg(w) = T(w, grid, β, u, f, shocks)\n", " coleman_single_arg(g) = K(g, grid, β, ∂u∂c, f, f′, shocks)\n", "\n", " g = iterate_updating(coleman_single_arg, grid, sim_length = 20)\n", " w = iterate_updating(bellman_single_arg, u.(m.grid), sim_length = 20)\n", " new_w, vf_g = T(w, grid, β, u, f, shocks, compute_policy = true)\n", "\n", " plot(grid, g, lw = 2, alpha = 0.6, label = \"policy iteration\")\n", " plot!(grid, vf_g, lw = 2, alpha = 0.6, label = \"value iteration\")\n", " return plot!(legend = :topleft)\n", "end" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exercise2(m_ex, shocks, m.grid, m.u.(m.grid), sim_length=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The policies are indeed close." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution to Exercise 4\n", "\n", "Here’s the code.\n", "\n", "It assumes that you’ve just run the code from the previous exercise" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "coleman (generic function with 1 method)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function bellman(m, shocks)\n", " @unpack grid, β, u, ∂u∂c, f, f′ = m\n", " bellman_single_arg(w) = T(w, grid, β, u, f, shocks)\n", " iterate_updating(bellman_single_arg, u.(grid), sim_length = 20)\n", "end\n", "function coleman(m, shocks)\n", " @unpack grid, β, ∂u∂c, f, f′ = m\n", " coleman_single_arg(g) = K(g, grid, β, ∂u∂c, f, f′, shocks)\n", " iterate_updating(coleman_single_arg, grid, sim_length = 20)\n", "end" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "BenchmarkTools.Trial: \n", " memory estimate: 155.94 MiB\n", " allocs estimate: 90741\n", " --------------\n", " minimum time: 334.046 ms (4.33% GC)\n", " median time: 341.577 ms (4.48% GC)\n", " mean time: 343.476 ms (4.81% GC)\n", " maximum time: 356.231 ms (4.30% GC)\n", " --------------\n", " samples: 15\n", " evals/sample: 1" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@benchmark bellman(m_ex, shocks)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "BenchmarkTools.Trial: \n", " memory estimate: 155.94 MiB\n", " allocs estimate: 90741\n", " --------------\n", " minimum time: 333.519 ms (4.54% GC)\n", " median time: 345.037 ms (4.50% GC)\n", " mean time: 344.282 ms (4.86% GC)\n", " maximum time: 355.788 ms (4.36% GC)\n", " --------------\n", " samples: 15\n", " evals/sample: 1" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@benchmark bellman(m_ex, shocks)" ] } ], "metadata": { "date": 1591310614.3656635, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "coleman_policy_iter.rst", "filename_with_path": "dynamic_programming/coleman_policy_iter", "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 II: Time Iteration" }, "nbformat": 4, "nbformat_minor": 2 }