{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Optimal Savings III: Occasionally Binding Constraints" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Optimal Savings III: Occasionally Binding Constraints](#Optimal-Savings-III:-Occasionally-Binding-Constraints) \n", " - [Overview](#Overview) \n", " - [The Optimal Savings Problem](#The-Optimal-Savings-Problem) \n", " - [Computation](#Computation) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "Next we study an optimal savings problem for an infinitely lived consumer—the “common ancestor” described in [[LS18]](../zreferences.html#ljungqvist2012), section 1.3.\n", "\n", "This is an essential sub-problem for many representative macroeconomic models\n", "\n", "- [[Aiy94]](../zreferences.html#aiyagari1994) \n", "- [[Hug93]](../zreferences.html#huggett1993) \n", "- etc. \n", "\n", "\n", "It is related to the decision problem in the [stochastic optimal growth\n", "model](optgrowth.html) and yet differs in important ways.\n", "\n", "For example, the choice problem for the agent includes an additive income term that leads to an occasionally binding constraint.\n", "\n", "Our presentation of the model will be relatively brief.\n", "\n", "- For further details on economic intuition, implication and models, see [[LS18]](../zreferences.html#ljungqvist2012) \n", "- Proofs of all mathematical results stated below can be found in this paper \n", "\n", "\n", "To solve the model we will use Euler equation based time iteration, similar to [this lecture](coleman_policy_iter.html).\n", "\n", "This method turns out to be\n", "\n", "- Globally convergent under mild assumptions, even when utility is unbounded (both above and below). \n", "- More efficient numerically than value function iteration. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### References\n", "\n", "Other useful references include [[Dea91]](../zreferences.html#deaton1991), [[DH10]](../zreferences.html#denhaan2010), [[Kuh13]](../zreferences.html#kuhn2013), [[Rab02]](../zreferences.html#rabault2002), [[Rei09]](../zreferences.html#reiter2009) and [[SE77]](../zreferences.html#schechtmanescudero1977)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Optimal Savings Problem\n", "\n", "\n", "\n", "Let’s write down the model and then discuss how to solve it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Set Up\n", "\n", "Consider a household that chooses a state-contingent consumption plan $ \\{c_t\\}_{t \\geq 0} $ to maximize\n", "\n", "$$\n", "\\mathbb{E} \\, \\sum_{t=0}^{\\infty} \\beta^t u(c_t)\n", "$$\n", "\n", "subject to\n", "\n", "\n", "\n", "$$\n", "c_t + a_{t+1} \\leq Ra_t + z_t,\n", "\\qquad c_t \\geq 0,\n", "\\qquad a_t \\geq -b\n", "\\qquad t = 0, 1, \\ldots \\tag{1}\n", "$$\n", "\n", "Here\n", "\n", "- $ \\beta \\in (0,1) $ is the discount factor \n", "- $ a_t $ is asset holdings at time $ t $, with ad-hoc borrowing constraint $ a_t \\geq -b $ \n", "- $ c_t $ is consumption \n", "- $ z_t $ is non-capital income (wages, unemployment compensation, etc.) \n", "- $ R := 1 + r $, where $ r > 0 $ is the interest rate on savings \n", "\n", "\n", "Non-capital income $ \\{z_t\\} $ is assumed to be a Markov process taking values in $ Z\\subset (0,\\infty) $ with stochastic kernel $ \\Pi $.\n", "\n", "This means that $ \\Pi(z, B) $ is the probability that $ z_{t+1} \\in\n", "B $ given $ z_t = z $.\n", "\n", "The expectation of $ f(z_{t+1}) $ given $ z_t = z $ is written as\n", "\n", "$$\n", "\\int f( \\acute z) \\, \\Pi(z, d \\acute z)\n", "$$\n", "\n", "We further assume that\n", "\n", "1. $ r > 0 $ and $ \\beta R < 1 $ \n", "1. $ u $ is smooth, strictly increasing and strictly concave with $ \\lim_{c \\to 0} u'(c) = \\infty $ and $ \\lim_{c \\to \\infty} u'(c) = 0 $ \n", "\n", "\n", "The asset space is $ [-b, \\infty) $ and the state is the pair $ (a,z) \\in S := [-b,\\infty) \\times Z $.\n", "\n", "A *feasible consumption path* from $ (a,z) \\in S $ is a consumption\n", "sequence $ \\{c_t\\} $ such that $ \\{c_t\\} $ and its induced asset path $ \\{a_t\\} $ satisfy\n", "\n", "1. $ (a_0, z_0) = (a, z) $ \n", "1. the feasibility constraints in [(1)](#equation-eqst), and \n", "1. measurability of $ c_t $ w.r.t. the filtration generated by $ \\{z_1, \\ldots, z_t\\} $ \n", "\n", "\n", "The meaning of the third point is just that consumption at time $ t $ can only be\n", "a function of outcomes that have already been observed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Value Function and Euler Equation\n", "\n", "The *value function* $ V \\colon S \\to \\mathbb{R} $ is defined by\n", "\n", "\n", "\n", "$$\n", "V(a, z) := \\sup \\, \\mathbb{E}\n", "\\left\\{\n", "\\sum_{t=0}^{\\infty} \\beta^t u(c_t)\n", "\\right\\} \\tag{2}\n", "$$\n", "\n", "where the supremum is over all feasible consumption paths from $ (a,z) $.\n", "\n", "An *optimal consumption path* from $ (a,z) $ is a feasible consumption path from $ (a,z) $ that attains the supremum in [(2)](#equation-eqvf).\n", "\n", "To pin down such paths we can use a version of the Euler equation, which in the present setting is\n", "\n", "\n", "\n", "$$\n", "u' (c_t)\n", "\\geq \\beta R \\, \\mathbb{E}_t [ u'(c_{t+1}) ] \\tag{3}\n", "$$\n", "\n", "and\n", "\n", "\n", "\n", "$$\n", "u' (c_t) = \\beta R \\, \\mathbb{E}_t [ u'(c_{t+1}) ]\n", "\\quad \\text{whenever }\n", "c_t < Ra_t + z_t + b \\tag{4}\n", "$$\n", "\n", "In essence, this says that the natural “arbitrage” relation $ u' (c_t) = \\beta R \\, \\mathbb{E}_t [ u'(c_{t+1}) ] $ holds when the choice of current consumption is interior.\n", "\n", "Interiority means that $ c_t $ is strictly less than its upper bound $ Ra_t + z_t + b $.\n", "\n", "(The lower boundary case $ c_t = 0 $ never arises at the optimum because\n", "$ u'(0) = \\infty $)\n", "\n", "When $ c_t $ does hit the upper bound $ Ra_t + z_t + b $, the\n", "strict inequality $ u' (c_t) > \\beta R \\, \\mathbb{E}_t [ u'(c_{t+1}) ] $\n", "can occur because $ c_t $ cannot increase sufficiently to attain equality.\n", "\n", "With some thought and effort, one can show that [(3)](#equation-ee00) and [(4)](#equation-ee01) are\n", "equivalent to\n", "\n", "\n", "\n", "$$\n", "u' (c_t)\n", "= \\max \\left\\{\n", "\\beta R \\, \\mathbb{E}_t [ u'(c_{t+1}) ] \\,,\\; u'(Ra_t + z_t + b)\n", "\\right\\} \\tag{5}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Optimality Results\n", "\n", "Given our assumptions, it is known that\n", "\n", "1. For each $ (a,z) \\in S $, a unique optimal consumption path from $ (a,z) $ exists. \n", "1. This path is the unique feasible path from $ (a,z) $ satisfying the\n", " Euler equality [(5)](#equation-eqeul0) and the transversality condition \n", "\n", "\n", "\n", "\n", "$$\n", "\\lim_{t \\to \\infty} \\beta^t \\, \\mathbb{E} \\, [ u'(c_t) a_{t+1} ] = 0. \\tag{6}\n", "$$\n", "\n", "Moreover, there exists an *optimal consumption function* $ c^* \\colon S \\to [0, \\infty) $ such that the path from $ (a,z) $ generated by\n", "\n", "$$\n", "(a_0, z_0) = (a, z),\n", "\\quad\n", "z_{t+1} \\sim \\Pi(z_t, dy),\n", "\\quad\n", "c_t = c^*(a_t, z_t)\n", "\\quad \\text{and} \\quad\n", "a_{t+1} = R a_t + z_t - c_t\n", "$$\n", "\n", "satisfies both [(5)](#equation-eqeul0) and [(6)](#equation-eqtv), and hence is the unique optimal\n", "path from $ (a,z) $.\n", "\n", "In summary, to solve the optimization problem, we need to compute $ c^* $.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computation\n", "\n", "\n", "\n", "There are two standard ways to solve for $ c^* $\n", "\n", "1. Time iteration (TI) using the Euler equality \n", "1. Value function iteration (VFI) \n", "\n", "\n", "Let’s look at these in turn." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Time Iteration\n", "\n", "We can rewrite [(5)](#equation-eqeul0) to make it a statement about functions rather than\n", "random variables.\n", "\n", "In particular, consider the functional equation\n", "\n", "\n", "\n", "$$\n", "u' \\circ c \\, (a, z)\n", "= \\max \\left\\{\n", "\\gamma \\int u' \\circ c \\, \\{R a + z - c(a, z), \\, \\acute z\\}\n", "\\, \\Pi(z,d \\acute z)\n", "\\, , \\;\n", " u'(Ra + z + b)\n", " \\right\\} \\tag{7}\n", "$$\n", "\n", "where $ \\gamma := \\beta R $ and $ u' \\circ c(s) := u'(c(s)) $.\n", "\n", "Equation [(7)](#equation-eqeul1) is a functional equation in $ c $.\n", "\n", "In order to identify a solution, let $ \\mathscr{C} $ be the set of candidate consumption functions $ c \\colon S \\to \\mathbb R $ such that\n", "\n", "- each $ c \\in \\mathscr{C} $ is continuous and (weakly) increasing \n", "- $ \\min Z \\leq c(a,z) \\leq Ra + z + b $ for all $ (a,z) \\in S $ \n", "\n", "\n", "In addition, let $ K \\colon \\mathscr{C} \\to \\mathscr{C} $ be defined as follows:\n", "\n", "For given $ c\\in \\mathscr{C} $, the value $ Kc(a,z) $ is the unique $ t \\in J(a,z) $ that solves\n", "\n", "\n", "\n", "$$\n", "u'(t)\n", "= \\max \\left\\{\n", "\\gamma \\int u' \\circ c \\, \\{R a + z - t, \\, \\acute z\\}\n", "\\, \\Pi(z,d \\acute z)\n", "\\, , \\;\n", " u'(Ra + z + b)\n", " \\right\\} \\tag{8}\n", "$$\n", "\n", "where\n", "\n", "\n", "\n", "$$\n", "J(a,z) := \\{t \\in \\mathbb{R} \\,:\\, \\min Z \\leq t \\leq Ra+ z + b\\} \\tag{9}\n", "$$\n", "\n", "We refer to $ K $ as Coleman’s policy function operator [[Col90]](../zreferences.html#coleman1990).\n", "\n", "It is known that\n", "\n", "- $ K $ is a contraction mapping on $ \\mathscr{C} $ under the metric \n", "\n", "\n", "$$\n", "\\rho(c, d) := \\| \\, u' \\circ c - u' \\circ d \\, \\|\n", " := \\sup_{s \\in S} | \\, u'(c(s)) - u'(d(s)) \\, |\n", " \\qquad \\quad (c, d \\in \\mathscr{C})\n", "$$\n", "\n", "- The metric $ \\rho $ is complete on $ \\mathscr{C} $ \n", "- Convergence in $ \\rho $ implies uniform convergence on compacts \n", "\n", "\n", "In consequence, $ K $ has a unique fixed point $ c^* \\in \\mathscr{C} $\n", "and $ K^n c \\to c^* $ as $ n \\to \\infty $ for any $ c \\in \\mathscr{C} $.\n", "\n", "By the definition of $ K $, the fixed points of $ K $ in $ \\mathscr{C} $ coincide with\n", "the solutions to [(7)](#equation-eqeul1) in $ \\mathscr{C} $.\n", "\n", "In particular, it can be shown that the path $ \\{c_t\\} $\n", "generated from $ (a_0,z_0) \\in S $ using policy function $ c^* $ is\n", "the unique optimal path from $ (a_0,z_0) \\in S $.\n", "\n", "**TL;DR** The unique optimal policy can be computed by picking any\n", "$ c \\in \\mathscr{C} $ and iterating with the operator $ K $ defined in [(8)](#equation-eqsifc)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Value Function Iteration\n", "\n", "The Bellman operator for this problem is given by\n", "\n", "\n", "\n", "$$\n", "Tv(a, z)\n", "= \\max_{0 \\leq c \\leq Ra + z + b}\n", "\\left\\{\n", " u(c) + \\beta \\int v(Ra + z - c, \\acute z) \\Pi(z, d \\acute z)\n", "\\right\\} \\tag{10}\n", "$$\n", "\n", "We have to be careful with VFI (i.e., iterating with\n", "$ T $) in this setting because $ u $ is not assumed to be bounded\n", "\n", "- In fact typically unbounded both above and below — e.g. $ u(c) = \\log c $. \n", "- In which case, the standard DP theory does not apply. \n", "- $ T^n v $ is not guaranteed to converge to the value function for arbitrary continous bounded $ v $. \n", "\n", "\n", "Nonetheless, we can always try the popular strategy “iterate and hope”.\n", "\n", "We can then check the outcome by comparing with that produced by TI.\n", "\n", "The latter is known to converge, as described above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation\n", "\n", "\n", "\n", "Here’s the code for a named-tuple constructor called `ConsumerProblem` that stores primitives, as well as\n", "\n", "- a `T` function, which implements the Bellman operator $ T $ specified above \n", "- a `K` function, which implements the Coleman operator $ K $ specified above \n", "- an `initialize`, which generates suitable initial conditions for iteration " ] }, { "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": false }, "outputs": [], "source": [ "using LinearAlgebra, Statistics\n", "using BenchmarkTools, Optim, Parameters, Plots, QuantEcon, Random\n", "using Optim: converged, maximum, maximizer, minimizer, iterations\n", "gr(fmt = :png);" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "initialize (generic function with 1 method)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# utility and marginal utility functions\n", "u(x) = log(x)\n", "du(x) = 1 / x\n", "\n", "# model\n", "function ConsumerProblem(;r = 0.01,\n", " β = 0.96,\n", " Π = [0.6 0.4; 0.05 0.95],\n", " z_vals = [0.5, 1.0],\n", " b = 0.0,\n", " grid_max = 16,\n", " grid_size = 50)\n", " R = 1 + r\n", " asset_grid = range(-b, grid_max, length = grid_size)\n", "\n", " return (r = r, R = R, β = β, b = b, Π = Π, z_vals = z_vals, asset_grid = asset_grid)\n", "end\n", "\n", "function T!(cp, V, out; ret_policy = false)\n", "\n", " # unpack input, set up arrays\n", " @unpack R, Π, β, b, asset_grid, z_vals = cp\n", " z_idx = 1:length(z_vals)\n", "\n", " # value function when the shock index is z_i\n", " vf = interp(asset_grid, V)\n", "\n", " opt_lb = 1e-8\n", "\n", " # solve for RHS of Bellman equation\n", " for (i_z, z) in enumerate(z_vals)\n", " for (i_a, a) in enumerate(asset_grid)\n", "\n", " function obj(c)\n", " EV = dot(vf.(R * a + z - c, z_idx), Π[i_z, :]) # compute expectation\n", " return u(c) + β * EV\n", " end\n", " res = maximize(obj, opt_lb, R .* a .+ z .+ b)\n", " converged(res) || error(\"Didn't converge\") # important to check\n", "\n", " if ret_policy\n", " out[i_a, i_z] = maximizer(res)\n", " else\n", " out[i_a, i_z] = maximum(res)\n", " end\n", "\n", " end\n", " end\n", " out\n", "end\n", "\n", "T(cp, V; ret_policy = false) =\n", " T!(cp, V, similar(V); ret_policy = ret_policy)\n", "\n", "get_greedy!(cp, V, out) =\n", " update_bellman!(cp, V, out, ret_policy = true)\n", "\n", "get_greedy(cp, V) =\n", " update_bellman(cp, V, ret_policy = true)\n", "\n", "function K!(cp, c, out)\n", " # simplify names, set up arrays\n", " @unpack R, Π, β, b, asset_grid, z_vals = cp\n", " z_idx = 1:length(z_vals)\n", " gam = R * β\n", "\n", " # policy function when the shock index is z_i\n", " cf = interp(asset_grid, c)\n", "\n", " # compute lower_bound for optimization\n", " opt_lb = 1e-8\n", "\n", " for (i_z, z) in enumerate(z_vals)\n", " for (i_a, a) in enumerate(asset_grid)\n", " function h(t)\n", " cps = cf.(R * a + z - t, z_idx) # c' for each z'\n", " expectation = dot(du.(cps), Π[i_z, :])\n", " return abs(du(t) - max(gam * expectation, du(R * a + z + b)))\n", " end\n", " opt_ub = R*a + z + b # addresses issue #8 on github\n", " res = optimize(h, min(opt_lb, opt_ub - 1e-2), opt_ub,\n", " method = Optim.Brent())\n", " out[i_a, i_z] = minimizer(res)\n", " end\n", " end\n", " return out\n", "end\n", "\n", "K(cp, c) = K!(cp, c, similar(c))\n", "\n", "function initialize(cp)\n", " # simplify names, set up arrays\n", " @unpack R, β, b, asset_grid, z_vals = cp\n", " shape = length(asset_grid), length(z_vals)\n", " V, c = zeros(shape...), zeros(shape...)\n", "\n", " # populate V and c\n", " for (i_z, z) in enumerate(z_vals)\n", " for (i_a, a) in enumerate(asset_grid)\n", " c_max = R * a + z + b\n", " c[i_a, i_z] = c_max\n", " V[i_a, i_z] = u(c_max) / (1 - β)\n", " end\n", " end\n", "\n", " return V, c\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Both `T` and `K` use linear interpolation along the asset grid to approximate the value and consumption functions.\n", "\n", "The following exercises walk you through several applications where policy functions are computed.\n", "\n", "In exercise 1 you will see that while VFI and TI produce similar results, the latter is much faster.\n", "\n", "Intuition behind this fact was provided in [a previous lecture on time iteration](coleman_policy_iter.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "The first exercise is to replicate the following figure, which compares TI and VFI as solution methods\n", "\n", "\n", "\n", " \n", "The figure shows consumption policies computed by iteration of $ K $ and $ T $ respectively\n", "\n", "- In the case of iteration with $ T $, the final value function is used to compute the observed policy. \n", "\n", "\n", "Consumption is shown as a function of assets with income $ z $ held fixed\n", "at its smallest value.\n", "\n", "The following details are needed to replicate the figure\n", "\n", "- The parameters are the default parameters in the definition of `consumerProblem`. \n", "- The initial conditions are the default ones from `initialize(cp)`. \n", "- Both operators are iterated 80 times. \n", "\n", "\n", "When you run your code you will observe that iteration with $ K $ is\n", "faster than iteration with $ T $.\n", "\n", "In the Julia console, a comparison of the operators can be made as follows" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "([-17.328679513998615 0.0; -4.664387247760648 7.125637140580436; … ; 69.82541010621486 70.57937835479346; 70.32526591846735 71.06452735149534], [0.5 1.0; 0.8297959183673469 1.329795918367347; … ; 16.33020408163265 16.83020408163265; 16.66 17.16])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cp = ConsumerProblem()\n", "v, c, = initialize(cp)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 492.517 μs (4676 allocations: 428.20 KiB)\n" ] } ], "source": [ "@btime T(cp, v);" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 695.109 μs (7925 allocations: 742.17 KiB)\n" ] } ], "source": [ "@btime K(cp, c);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Next let’s consider how the interest rate affects consumption.\n", "\n", "Reproduce the following figure, which shows (approximately) optimal consumption policies for different interest rates\n", "\n", "\n", "\n", " \n", "- Other than r, all parameters are at their default values \n", "- r steps through range(0, 0.04, length = 4) \n", "- Consumption is plotted against assets for income shock fixed at the smallest value \n", "\n", "\n", "The figure shows that higher interest rates boost savings and hence suppress consumption.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "Now let’s consider the long run asset levels held by households.\n", "\n", "We’ll take r = 0.03 and otherwise use default parameters.\n", "\n", "The following figure is a 45 degree diagram showing the law of motion for assets when consumption is optimal" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# solve for optimal consumption\n", "m = ConsumerProblem(r = 0.03, grid_max = 4)\n", "v_init, c_init = initialize(m)\n", "\n", "c = compute_fixed_point(c -> K(m, c),\n", " c_init,\n", " max_iter = 150,\n", " verbose = false)\n", "a = m.asset_grid\n", "R, z_vals = m.R, m.z_vals\n", "\n", "# generate savings plot\n", "plot(a, R * a .+ z_vals[1] - c[:, 1], label = \"Low income\")\n", "plot!(xlabel = \"Current assets\", ylabel = \"Next period assets\")\n", "plot!(a, R * a .+ z_vals[2] - c[:, 2], label = \"High income\")\n", "plot!(xlabel = \"Current assets\", ylabel = \"Next period assets\")\n", "plot!(a, a, linestyle = :dash, color = \"black\", label = \"\")\n", "plot!(xlabel = \"Current assets\", ylabel = \"Next period assets\")\n", "plot!(legend = :topleft)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The blue line and orange line represent the function\n", "\n", "$$\n", "a' = h(a, z) := R a + z - c^*(a, z)\n", "$$\n", "\n", "when income $ z $ takes its high and low values respectively.\n", "\n", "The dashed line is the 45 degree line.\n", "\n", "We can see from the figure that the dynamics will be stable — assets do not\n", "diverge.\n", "\n", "In fact there is a unique stationary distribution of assets that we can calculate by simulation\n", "\n", "- Can be proved via theorem 2 of [[HP92]](../zreferences.html#hopenhaynprescott1992). \n", "- Represents the long run dispersion of assets across households when households have idiosyncratic shocks. \n", "\n", "\n", "Ergodicity is valid here, so stationary probabilities can be calculated by averaging over a single long time series.\n", "\n", "- Hence to approximate the stationary distribution we can simulate a long time series for assets and histogram, as in the following figure \n", "\n", "\n", "\n", "\n", " \n", "Your task is to replicate the figure\n", "\n", "- Parameters are as discussed above \n", "- The histogram in the figure used a single time series $ \\{a_t\\} $ of length 500,000 \n", "- Given the length of this time series, the initial condition $ (a_0, z_0) $ will not matter \n", "- You might find it helpful to use the `MarkovChain` type from `quantecon` \n", "\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 4\n", "\n", "Following on from exercises 2 and 3, let’s look at how savings and aggregate asset holdings vary with the interest rate\n", "\n", "- Note: [[LS18]](../zreferences.html#ljungqvist2012) section 18.6 can be consulted for more background on the topic treated in this exercise \n", "\n", "\n", "For a given parameterization of the model, the mean of the stationary distribution can be interpreted as aggregate capital in an economy with a unit mass of *ex-ante* identical households facing idiosyncratic shocks.\n", "\n", "Let’s look at how this measure of aggregate capital varies with the interest\n", "rate and borrowing constraint.\n", "\n", "The next figure plots aggregate capital against the interest rate for b in (1, 3)\n", "\n", "\n", "\n", " \n", "As is traditional, the price (interest rate) is on the vertical axis.\n", "\n", "The horizontal axis is aggregate capital computed as the mean of the stationary distribution.\n", "\n", "Exercise 4 is to replicate the figure, making use of code from previous exercises.\n", "\n", "Try to explain why the measure of aggregate capital is equal to $ -b $\n", "when $ r=0 $ for both cases shown here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Starting value function iteration\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Starting policy function iteration\n" ] }, { "data": { "image/png": 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" }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cp = ConsumerProblem()\n", "N = 80\n", "\n", "V, c = initialize(cp)\n", "println(\"Starting value function iteration\")\n", "for i in 1:N\n", " V = T(cp, V)\n", "end\n", "c1 = T(cp, V, ret_policy=true)\n", "\n", "V2, c2 = initialize(cp)\n", "println(\"Starting policy function iteration\")\n", "for i in 1:N\n", " c2 = K(cp, c2)\n", "end\n", "\n", "plot(cp.asset_grid, c1[:, 1], label = \"value function iteration\")\n", "plot!(cp.asset_grid, c2[:, 1], label = \"policy function iteration\")\n", "plot!(xlabel = \"asset level\", ylabel = \"Consumption (low income)\")\n", "plot!(legend = :topleft)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r_vals = range(0, 0.04, length = 4)\n", "traces = []\n", "legends = []\n", "\n", "for r_val in r_vals\n", " cp = ConsumerProblem(r = r_val)\n", " v_init, c_init = initialize(cp)\n", " c = compute_fixed_point(x -> K(cp, x),\n", " c_init,\n", " max_iter = 150,\n", " verbose = false)\n", " traces = push!(traces, c[:, 1])\n", " legends = push!(legends, \"r = $(round(r_val, digits = 3))\")\n", "end\n", "\n", "plot(traces, label = reshape(legends, 1, length(legends)))\n", "plot!(xlabel = \"asset level\", ylabel = \"Consumption (low income)\")\n", "plot!(legend = :topleft)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3" ] }, { "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": [ "function compute_asset_series(cp, T = 500_000; verbose = false)\n", " @unpack Π, z_vals, R = cp # simplify names\n", " z_idx = 1:length(z_vals)\n", " v_init, c_init = initialize(cp)\n", " c = compute_fixed_point(x -> K(cp, x), c_init,\n", " max_iter = 150, verbose = false)\n", "\n", " cf = interp(cp.asset_grid, c)\n", "\n", " a = zeros(T + 1)\n", " z_seq = simulate(MarkovChain(Π), T)\n", " for t in 1:T\n", " i_z = z_seq[t]\n", " a[t+1] = R * a[t] + z_vals[i_z] - cf(a[t], i_z)\n", " end\n", " return a\n", "end\n", "\n", "cp = ConsumerProblem(r = 0.03, grid_max = 4)\n", "Random.seed!(42) # for reproducibility\n", "a = compute_asset_series(cp)\n", "histogram(a, nbins = 20, leg = false, normed = true, xlabel = \"assets\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 4" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Finished iteration b = 1.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Finished iteration b = 3.0\n" ] }, { "data": { "image/png": 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" }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = 25\n", "r_vals = range(0, 0.04, length = M)\n", "\n", "xs = []\n", "ys = []\n", "legends = []\n", "for b in [1.0, 3.0]\n", " asset_mean = zeros(M)\n", " for (i, r_val) in enumerate(r_vals)\n", " cp = ConsumerProblem(r = r_val, b = b)\n", " the_mean = mean(compute_asset_series(cp, 250_000))\n", " asset_mean[i] = the_mean\n", " end\n", " xs = push!(xs, asset_mean)\n", " ys = push!(ys, r_vals)\n", " legends = push!(legends, \"b = $b\")\n", " println(\"Finished iteration b = $b\")\n", "end\n", "plot(xs, ys, label = reshape(legends, 1, length(legends)))\n", "plot!(xlabel = \"capital\", ylabel = \"interest rate\", yticks = ([0, 0.045]))\n", "plot!(legend = :bottomright)" ] } ], "metadata": { "date": 1591310615.2438734, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "ifp.rst", "filename_with_path": "dynamic_programming/ifp", "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 Savings III: Occasionally Binding Constraints" }, "nbformat": 4, "nbformat_minor": 2 }