{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# LQ Dynamic Programming Problems\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [LQ Dynamic Programming Problems](#LQ-Dynamic-Programming-Problems) \n", " - [Overview](#Overview) \n", " - [Introduction](#Introduction) \n", " - [Optimality – Finite Horizon](#Optimality-–-Finite-Horizon) \n", " - [Implementation](#Implementation) \n", " - [Extensions and Comments](#Extensions-and-Comments) \n", " - [Further Applications](#Further-Applications) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "Linear quadratic (LQ) control refers to a class of dynamic optimization problems that have found applications in almost every scientific field.\n", "\n", "This lecture provides an introduction to LQ control and its economic applications.\n", "\n", "As we will see, LQ systems have a simple structure that makes them an excellent workhorse for a wide variety of economic problems.\n", "\n", "Moreover, while the linear-quadratic structure is restrictive, it is in fact far more flexible than it may appear initially.\n", "\n", "These themes appear repeatedly below.\n", "\n", "Mathematically, LQ control problems are closely related to [the Kalman filter](../tools_and_techniques/kalman.html).\n", "\n", "- Recursive formulations of linear-quadratic control problems and Kalman filtering problems both involve matrix **Riccati equations**. \n", "- Classical formulations of linear control and linear filtering problems make use of similar matrix decompositions (see for example [this lecture](../time_series_models/lu_tricks.html) and [this lecture](../time_series_models/classical_filtering.html)). \n", "\n", "\n", "In reading what follows, it will be useful to have some familiarity with\n", "\n", "- matrix manipulations \n", "- vectors of random variables \n", "- dynamic programming and the Bellman equation (see for example [this lecture](short_path.html) and [this lecture](optgrowth.html)) \n", "\n", "\n", "For additional reading on LQ control, see, for example,\n", "\n", "- [[LS18]](../zreferences.html#ljungqvist2012), chapter 5 \n", "- [[HS08]](../zreferences.html#hansensargent2008), chapter 4 \n", "- [[HLL96]](../zreferences.html#hernandezlermalasserre1996), section 3.5 \n", "\n", "\n", "In order to focus on computation, we leave longer proofs to these sources (while trying to provide as much intuition as possible)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "The “linear” part of LQ is a linear law of motion for the state, while the “quadratic” part refers to preferences.\n", "\n", "Let’s begin with the former, move on to the latter, and then put them together into an optimization problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Law of Motion\n", "\n", "Let $ x_t $ be a vector describing the state of some economic system.\n", "\n", "Suppose that $ x_t $ follows a linear law of motion given by\n", "\n", "\n", "\n", "$$\n", "x_{t+1} = A x_t + B u_t + C w_{t+1},\n", "\\qquad t = 0, 1, 2, \\ldots \\tag{1}\n", "$$\n", "\n", "Here\n", "\n", "- $ u_t $ is a “control” vector, incorporating choices available to a decision maker confronting the current state $ x_t $. \n", "- $ \\{w_t\\} $ is an uncorrelated zero mean shock process satisfying $ \\mathbb E w_t w_t' = I $, where the right-hand side is the identity matrix. \n", "\n", "\n", "Regarding the dimensions\n", "\n", "- $ x_t $ is $ n \\times 1 $, $ A $ is $ n \\times n $ \n", "- $ u_t $ is $ k \\times 1 $, $ B $ is $ n \\times k $ \n", "- $ w_t $ is $ j \\times 1 $, $ C $ is $ n \\times j $ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example 1\n", "\n", "Consider a household budget constraint given by\n", "\n", "$$\n", "a_{t+1} + c_t = (1 + r) a_t + y_t\n", "$$\n", "\n", "Here $ a_t $ is assets, $ r $ is a fixed interest rate, $ c_t $ is\n", "current consumption, and $ y_t $ is current non-financial income.\n", "\n", "If we suppose that $ \\{ y_t \\} $ is serially uncorrelated and $ N(0,\n", "\\sigma^2) $, then, taking $ \\{ w_t \\} $ to be standard normal, we can write\n", "the system as\n", "\n", "$$\n", "a_{t+1} = (1 + r) a_t - c_t + \\sigma w_{t+1}\n", "$$\n", "\n", "This is clearly a special case of [(1)](#equation-lq-lom), with assets being the state and consumption being the control.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example 2\n", "\n", "One unrealistic feature of the previous model is that non-financial income has a zero mean and is often negative.\n", "\n", "This can easily be overcome by adding a sufficiently large mean.\n", "\n", "Hence in this example we take $ y_t = \\sigma w_{t+1} + \\mu $ for some positive real number $ \\mu $.\n", "\n", "Another alteration that’s useful to introduce (we’ll see why soon) is to\n", "change the control variable from consumption\n", "to the deviation of consumption from some “ideal” quantity $ \\bar c $.\n", "\n", "(Most parameterizations will be such that $ \\bar c $ is large relative to the amount of consumption that is attainable in each period, and hence the household wants to increase consumption)\n", "\n", "For this reason, we now take our control to be $ u_t := c_t - \\bar c $.\n", "\n", "In terms of these variables, the budget constraint $ a_{t+1} = (1 + r) a_t - c_t + y_t $ becomes\n", "\n", "\n", "\n", "$$\n", "a_{t+1} = (1 + r) a_t - u_t - \\bar c + \\sigma w_{t+1} + \\mu \\tag{2}\n", "$$\n", "\n", "How can we write this new system in the form of equation [(1)](#equation-lq-lom)?\n", "\n", "If, as in the previous example, we take $ a_t $ as the state, then we run into a problem:\n", "the law of motion contains some constant terms on the right-hand side.\n", "\n", "This means that we are dealing with an *affine* function, not a linear one\n", "(recall [this discussion](../tools_and_techniques/linear_algebra.html#la-linear-map)).\n", "\n", "Fortunately, we can easily circumvent this problem by adding an extra state variable.\n", "\n", "In particular, if we write\n", "\n", "\n", "\n", "$$\n", "\\left(\n", "\\begin{array}{c}\n", "a_{t+1} \\\\\n", "1\n", "\\end{array}\n", "\\right) =\n", "\\left(\n", "\\begin{array}{cc}\n", "1 + r & -\\bar c + \\mu \\\\\n", "0 & 1\n", "\\end{array}\n", "\\right)\n", "\\left(\n", "\\begin{array}{c}\n", "a_t \\\\\n", "1\n", "\\end{array}\n", "\\right) +\n", "\\left(\n", "\\begin{array}{c} -1 \\\\\n", "0\n", "\\end{array}\n", "\\right)\n", "u_t +\n", "\\left(\n", "\\begin{array}{c}\n", "\\sigma \\\\\n", "0\n", "\\end{array}\n", "\\right)\n", "w_{t+1} \\tag{3}\n", "$$\n", "\n", "then the first row is equivalent to [(2)](#equation-lq-lomwc).\n", "\n", "Moreover, the model is now linear, and can be written in the form of\n", "[(1)](#equation-lq-lom) by setting\n", "\n", "\n", "\n", "$$\n", "x_t :=\n", "\\left(\n", "\\begin{array}{c}\n", "a_t \\\\\n", "1\n", "\\end{array}\n", "\\right),\n", "\\quad\n", "A :=\n", "\\left(\n", "\\begin{array}{cc}\n", "1 + r & -\\bar c + \\mu \\\\\n", "0 & 1\n", "\\end{array}\n", "\\right),\n", "\\quad\n", "B :=\n", "\\left(\n", "\\begin{array}{c}\n", "-1 \\\\\n", "0\n", "\\end{array}\n", "\\right),\n", "\\quad\n", "C :=\n", "\\left(\n", "\\begin{array}{c}\n", "\\sigma \\\\\n", "0\n", "\\end{array}\n", "\\right) \\tag{4}\n", "$$\n", "\n", "In effect, we’ve bought ourselves linearity by adding another state." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Preferences\n", "\n", "In the LQ model, the aim is to minimize a flow of losses, where time-$ t $ loss is given by the quadratic expression\n", "\n", "\n", "\n", "$$\n", "x_t' R x_t + u_t' Q u_t \\tag{5}\n", "$$\n", "\n", "Here\n", "\n", "- $ R $ is assumed to be $ n \\times n $, symmetric and nonnegative definite \n", "- $ Q $ is assumed to be $ k \\times k $, symmetric and positive definite \n", "\n", "\n", ">**Note**\n", ">\n", ">In fact, for many economic problems, the definiteness conditions on $ R $ and $ Q $ can be relaxed. It is sufficient that certain submatrices of $ R $ and $ Q $ be nonnegative definite. See [[HS08]](../zreferences.html#hansensargent2008) for details" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example 1\n", "\n", "A very simple example that satisfies these assumptions is to take $ R $\n", "and $ Q $ to be identity matrices, so that current loss is\n", "\n", "$$\n", "x_t' I x_t + u_t' I u_t = \\| x_t \\|^2 + \\| u_t \\|^2\n", "$$\n", "\n", "Thus, for both the state and the control, loss is measured as squared distance from the origin.\n", "\n", "(In fact the general case [(5)](#equation-lq-pref-flow) can also be understood in this\n", "way, but with $ R $ and $ Q $ identifying other – non-Euclidean – notions of “distance” from the zero vector).\n", "\n", "Intuitively, we can often think of the state $ x_t $ as representing deviation from a target, such\n", "as\n", "\n", "- deviation of inflation from some target level \n", "- deviation of a firm’s capital stock from some desired quantity \n", "\n", "\n", "The aim is to put the state close to the target, while using controls parsimoniously." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example 2\n", "\n", "In the household problem [studied above](#lq-hhp), setting $ R=0 $\n", "and $ Q=1 $ yields preferences\n", "\n", "$$\n", "x_t' R x_t + u_t' Q u_t = u_t^2 = (c_t - \\bar c)^2\n", "$$\n", "\n", "Under this specification, the household’s current loss is the squared deviation of consumption from the ideal level $ \\bar c $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimality – Finite Horizon\n", "\n", "\n", "\n", "Let’s now be precise about the optimization problem we wish to consider, and look at how to solve it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Objective\n", "\n", "We will begin with the finite horizon case, with terminal time $ T \\in \\mathbb N $.\n", "\n", "In this case, the aim is to choose a sequence of controls $ \\{u_0, \\ldots, u_{T-1}\\} $ to minimize the objective\n", "\n", "\n", "\n", "$$\n", "\\mathbb E \\,\n", "\\left\\{\n", " \\sum_{t=0}^{T-1} \\beta^t (x_t' R x_t + u_t' Q u_t) + \\beta^T x_T' R_f x_T\n", "\\right\\} \\tag{6}\n", "$$\n", "\n", "subject to the law of motion [(1)](#equation-lq-lom) and initial state $ x_0 $.\n", "\n", "The new objects introduced here are $ \\beta $ and the matrix $ R_f $.\n", "\n", "The scalar $ \\beta $ is the discount factor, while $ x' R_f x $ gives terminal loss associated with state $ x $.\n", "\n", "Comments:\n", "\n", "- We assume $ R_f $ to be $ n \\times n $, symmetric and nonnegative definite \n", "- We allow $ \\beta = 1 $, and hence include the undiscounted case \n", "- $ x_0 $ may itself be random, in which case we require it to be independent of the shock sequence $ w_1, \\ldots, w_T $ \n", "\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Information\n", "\n", "There’s one constraint we’ve neglected to mention so far, which is that the\n", "decision maker who solves this LQ problem knows only the present and the past,\n", "not the future.\n", "\n", "To clarify this point, consider the sequence of controls $ \\{u_0, \\ldots, u_{T-1}\\} $.\n", "\n", "When choosing these controls, the decision maker is permitted to take into account the effects of the shocks\n", "$ \\{w_1, \\ldots, w_T\\} $ on the system.\n", "\n", "However, it is typically assumed — and will be assumed here — that the\n", "time-$ t $ control $ u_t $ can be made with knowledge of past and\n", "present shocks only.\n", "\n", "The fancy [measure-theoretic](https://en.wikipedia.org/wiki/Measure_%28mathematics%29) way of saying this is that $ u_t $ must be measurable with respect to the $ \\sigma $-algebra generated by $ x_0, w_1, w_2,\n", "\\ldots, w_t $.\n", "\n", "This is in fact equivalent to stating that $ u_t $ can be written in the form $ u_t = g_t(x_0, w_1, w_2, \\ldots, w_t) $ for some Borel measurable function $ g_t $.\n", "\n", "(Just about every function that’s useful for applications is Borel measurable,\n", "so, for the purposes of intuition, you can read that last phrase as “for some function $ g_t $”).\n", "\n", "Now note that $ x_t $ will ultimately depend on the realizations of $ x_0, w_1, w_2, \\ldots, w_t $.\n", "\n", "In fact it turns out that $ x_t $ summarizes all the information about these historical shocks that the decision maker needs to set controls optimally.\n", "\n", "More precisely, it can be shown that any optimal control $ u_t $ can always be written as a function of the current state alone.\n", "\n", "Hence in what follows we restrict attention to control policies (i.e., functions) of the form $ u_t = g_t(x_t) $.\n", "\n", "Actually, the preceding discussion applies to all standard dynamic programming problems.\n", "\n", "What’s special about the LQ case is that – as we shall soon see — the optimal $ u_t $ turns out to be a linear function of $ x_t $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution\n", "\n", "To solve the finite horizon LQ problem we can use a dynamic programming\n", "strategy based on backwards induction that is conceptually similar to the approach adopted in [this lecture](short_path.html).\n", "\n", "For reasons that will soon become clear, we first introduce the notation $ J_T(x) = x' R_f x $.\n", "\n", "Now consider the problem of the decision maker in the second to last period.\n", "\n", "In particular, let the time be $ T-1 $, and suppose that the\n", "state is $ x_{T-1} $.\n", "\n", "The decision maker must trade off current and (discounted) final losses, and hence\n", "solves\n", "\n", "$$\n", "\\min_u \\{\n", "x_{T-1}' R x_{T-1} + u' Q u + \\beta \\,\n", "\\mathbb E J_T(A x_{T-1} + B u + C w_T)\n", "\\}\n", "$$\n", "\n", "At this stage, it is convenient to define the function\n", "\n", "\n", "\n", "$$\n", "J_{T-1} (x) =\n", "\\min_u \\{\n", "x' R x + u' Q u + \\beta \\,\n", "\\mathbb E J_T(A x + B u + C w_T)\n", "\\} \\tag{7}\n", "$$\n", "\n", "The function $ J_{T-1} $ will be called the $ T-1 $ value function, and $ J_{T-1}(x) $ can be thought of as representing total “loss-to-go” from state $ x $ at time $ T-1 $ when the decision maker behaves optimally.\n", "\n", "Now let’s step back to $ T-2 $.\n", "\n", "For a decision maker at $ T-2 $, the value $ J_{T-1}(x) $ plays a role analogous to that played by the terminal loss $ J_T(x) = x' R_f x $ for the decision maker at $ T-1 $.\n", "\n", "That is, $ J_{T-1}(x) $ summarizes the future loss associated with moving to state $ x $.\n", "\n", "The decision maker chooses her control $ u $ to trade off current loss against future loss, where\n", "\n", "- the next period state is $ x_{T-1} = Ax_{T-2} + B u + C w_{T-1} $, and hence depends on the choice of current control \n", "- the “cost” of landing in state $ x_{T-1} $ is $ J_{T-1}(x_{T-1}) $ \n", "\n", "\n", "Her problem is therefore\n", "\n", "$$\n", "\\min_u\n", "\\{\n", "x_{T-2}' R x_{T-2} + u' Q u + \\beta \\,\n", "\\mathbb E J_{T-1}(Ax_{T-2} + B u + C w_{T-1})\n", "\\}\n", "$$\n", "\n", "Letting\n", "\n", "$$\n", "J_{T-2} (x)\n", "= \\min_u\n", "\\{\n", "x' R x + u' Q u + \\beta \\,\n", "\\mathbb E J_{T-1}(Ax + B u + C w_{T-1})\n", "\\}\n", "$$\n", "\n", "the pattern for backwards induction is now clear.\n", "\n", "In particular, we define a sequence of value functions $ \\{J_0, \\ldots, J_T\\} $ via\n", "\n", "$$\n", "J_{t-1} (x)\n", "= \\min_u\n", "\\{\n", "x' R x + u' Q u + \\beta \\,\n", "\\mathbb E J_{t}(Ax + B u + C w_t)\n", "\\}\n", "\\quad \\text{and} \\quad\n", "J_T(x) = x' R_f x\n", "$$\n", "\n", "The first equality is the Bellman equation from dynamic programming theory specialized to the finite horizon LQ problem.\n", "\n", "Now that we have $ \\{J_0, \\ldots, J_T\\} $, we can obtain the optimal controls.\n", "\n", "As a first step, let’s find out what the value functions look like.\n", "\n", "It turns out that every $ J_t $ has the form $ J_t(x) = x' P_t x + d_t $ where $ P_t $ is a $ n \\times n $ matrix and $ d_t $ is a constant.\n", "\n", "We can show this by induction, starting from $ P_T := R_f $ and $ d_T = 0 $.\n", "\n", "Using this notation, [(7)](#equation-lq-lsm) becomes\n", "\n", "\n", "\n", "$$\n", "J_{T-1} (x) =\n", "\\min_u \\{\n", "x' R x + u' Q u + \\beta \\,\n", "\\mathbb E (A x + B u + C w_T)' P_T (A x + B u + C w_T)\n", "\\} \\tag{8}\n", "$$\n", "\n", "To obtain the minimizer, we can take the derivative of the r.h.s. with respect to $ u $ and set it equal to zero.\n", "\n", "Applying the relevant rules of [matrix calculus](../tools_and_techniques/linear_algebra.html#la-mcalc), this gives\n", "\n", "\n", "\n", "$$\n", "u = - (Q + \\beta B' P_T B)^{-1} \\beta B' P_T A x \\tag{9}\n", "$$\n", "\n", "Plugging this back into [(8)](#equation-lq-fswb) and rearranging yields\n", "\n", "$$\n", "J_{T-1} (x) = x' P_{T-1} x + d_{T-1}\n", "$$\n", "\n", "where\n", "\n", "\n", "\n", "$$\n", "P_{T-1}\n", "= R - \\beta^2 A' P_T B (Q + \\beta B' P_T B)^{-1} B' P_T A +\n", "\\beta A' P_T A \\tag{10}\n", "$$\n", "\n", "and\n", "\n", "\n", "\n", "$$\n", "d_{T-1} := \\beta \\mathop{\\mathrm{trace}}(C' P_T C) \\tag{11}\n", "$$\n", "\n", "(The algebra is a good exercise — we’ll leave it up to you).\n", "\n", "If we continue working backwards in this manner, it soon becomes clear that $ J_t (x) = x' P_t x + d_t $ as claimed, where $ \\{P_t\\} $ and $ \\{d_t\\} $ satisfy the recursions\n", "\n", "\n", "\n", "$$\n", "P_{t-1}\n", "= R - \\beta^2 A' P_t B (Q + \\beta B' P_t B)^{-1} B' P_t A +\n", "\\beta A' P_t A\n", "\\quad \\text{with } \\quad\n", "P_T = R_f \\tag{12}\n", "$$\n", "\n", "and\n", "\n", "\n", "\n", "$$\n", "d_{t-1} = \\beta (d_t + \\mathop{\\mathrm{trace}}(C' P_t C))\n", "\\quad \\text{with } \\quad\n", "d_T = 0 \\tag{13}\n", "$$\n", "\n", "Recalling [(9)](#equation-lq-oc0), the minimizers from these backward steps are\n", "\n", "\n", "\n", "$$\n", "u_t = - F_t x_t\n", "\\quad \\text{where} \\quad\n", "F_t := (Q + \\beta B' P_{t+1} B)^{-1} \\beta B' P_{t+1} A \\tag{14}\n", "$$\n", "\n", "These are the linear optimal control policies we [discussed above](#lq-cp).\n", "\n", "In particular, the sequence of controls given by [(14)](#equation-lq-oc) and [(1)](#equation-lq-lom) solves our finite horizon LQ problem.\n", "\n", "Rephrasing this more precisely, the sequence $ u_0, \\ldots, u_{T-1} $ given by\n", "\n", "\n", "\n", "$$\n", "u_t = - F_t x_t\n", "\\quad \\text{with} \\quad\n", "x_{t+1} = (A - BF_t) x_t + C w_{t+1} \\tag{15}\n", "$$\n", "\n", "for $ t = 0, \\ldots, T-1 $ attains the minimum of [(6)](#equation-lq-object) subject to our constraints." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "We will use code from [lqcontrol.jl](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/lqcontrol.jl)\n", "in [QuantEcon.jl](http://quantecon.org/quantecon-jl)\n", "to solve finite and infinite horizon linear quadratic control problems.\n", "\n", "In the module, the various updating, simulation and fixed point methods act on a type called `LQ`, which includes\n", "\n", "- Instance data: \n", " \n", " - The required parameters $ Q, R, A, B $ and optional parameters C, β, T, R_f, N specifying a given LQ model \n", " \n", " - set $ T $ and $ R_f $ to `None` in the infinite horizon case \n", " - set `C = None` (or zero) in the deterministic case \n", " \n", " - the value function and policy data \n", " \n", " - $ d_t, P_t, F_t $ in the finite horizon case \n", " - $ d, P, F $ in the infinite horizon case \n", " \n", " \n", "- Methods: \n", " \n", " - `update_values` — shifts $ d_t, P_t, F_t $ to their $ t-1 $ values via [(12)](#equation-lq-pr), [(13)](#equation-lq-dd) and [(14)](#equation-lq-oc) \n", " - `stationary_values` — computes $ P, d, F $ in the infinite horizon case \n", " - `compute_sequence` —- simulates the dynamics of $ x_t, u_t, w_t $ given $ x_0 $ and assuming standard normal shocks \n", " \n", "\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### An Application\n", "\n", "Early Keynesian models assumed that households have a constant marginal\n", "propensity to consume from current income.\n", "\n", "Data contradicted the constancy of the marginal propensity to consume.\n", "\n", "In response, Milton Friedman, Franco Modigliani and others built models\n", "based on a consumer’s preference for an intertemporally smooth consumption stream.\n", "\n", "(See, for example, [[Fri56]](../zreferences.html#friedman1956) or [[MB54]](../zreferences.html#modiglianibrumberg1954)).\n", "\n", "One property of those models is that households purchase and sell financial assets to make consumption streams smoother than income streams.\n", "\n", "The household savings problem [outlined above](#lq-hhp) captures these ideas.\n", "\n", "The optimization problem for the household is to choose a consumption sequence in order to minimize\n", "\n", "\n", "\n", "$$\n", "\\mathbb E \\,\n", "\\left\\{\n", " \\sum_{t=0}^{T-1} \\beta^t (c_t - \\bar c)^2 + \\beta^T q a_T^2\n", "\\right\\} \\tag{16}\n", "$$\n", "\n", "subject to the sequence of budget constraints $ a_{t+1} = (1 + r) a_t - c_t + y_t, \\ t \\geq 0 $.\n", "\n", "Here $ q $ is a large positive constant, the role of which is to induce the consumer to target zero debt at the end of her life.\n", "\n", "(Without such a constraint, the optimal choice is to choose $ c_t = \\bar c $ in each period, letting assets adjust accordingly).\n", "\n", "As before we set $ y_t = \\sigma w_{t+1} + \\mu $ and $ u_t := c_t - \\bar c $, after which the constraint can be written as in [(2)](#equation-lq-lomwc).\n", "\n", "We saw how this constraint could be manipulated into the LQ formulation $ x_{t+1} =\n", "Ax_t + Bu_t + Cw_{t+1} $ by setting $ x_t = (a_t \\; 1)' $ and using the definitions in [(4)](#equation-lq-lowmc2).\n", "\n", "To match with this state and control, the objective function [(16)](#equation-lq-pio) can\n", "be written in the form of [(6)](#equation-lq-object) by choosing\n", "\n", "$$\n", "Q := 1,\n", "\\quad\n", "R :=\n", "\\left(\n", "\\begin{array}{cc}\n", "0 & 0 \\\\\n", "0 & 0\n", "\\end{array}\n", "\\right),\n", "\\quad \\text{and} \\quad\n", "R_f :=\n", "\\left(\n", "\\begin{array}{cc}\n", "q & 0 \\\\\n", "0 & 0\n", "\\end{array}\n", "\\right)\n", "$$\n", "\n", "Now that the problem is expressed in LQ form, we can proceed to the solution\n", "by applying [(12)](#equation-lq-pr) and [(14)](#equation-lq-oc).\n", "\n", "After generating shocks $ w_1, \\ldots, w_T $, the dynamics for assets and\n", "consumption can be simulated via [(15)](#equation-lq-xud).\n", "\n", "The following figure was computed using $ r = 0.05, \\beta = 1 / (1 + r), \\bar c = 2, \\mu = 1, \\sigma = 0.25, T = 45 $ and $ q = 10^6 $.\n", "\n", "The shocks $ \\{w_t\\} $ were taken to be iid and standard normal." ] }, { "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 Plots, Plots.PlotMeasures, QuantEcon\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": [ "# model parameters\n", "r = 0.05\n", "β = 1 / (1 + r)\n", "T = 45\n", "c̄ = 2.0\n", "σ = 0.25\n", "μ = 1.0\n", "q = 1e6\n", "\n", "# formulate as an LQ problem\n", "Q = 1.0\n", "R = zeros(2, 2)\n", "Rf = zeros(2, 2); Rf[1, 1] = q\n", "A = [1 + r -c̄ + μ; 0 1]\n", "B = [-1.0, 0]\n", "C = [σ, 0]\n", "\n", "# compute solutions and simulate\n", "lq = QuantEcon.LQ(Q, R, A, B, C; bet = β, capT = T, rf = Rf)\n", "x0 = [0.0, 1]\n", "xp, up, wp = compute_sequence(lq, x0)\n", "\n", "# convert back to assets, consumption and income\n", "assets = vec(xp[1, :]) # a_t\n", "c = vec(up .+ c̄) # c_t\n", "income = vec(σ * wp[1, 2:end] .+ μ) # y_t\n", "\n", "# plot results\n", "p = plot([assets, c, zeros(T + 1), income, cumsum(income .- μ)],\n", " lab = [\"assets\" \"consumption\" \"\" \"non-financial income\" \"cumulative unanticipated income\"],\n", " color = [:blue :green :black :orange :red],\n", " xaxis = \"Time\", layout = (2, 1),\n", " bottom_margin = 20mm, size = (600, 600))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The top panel shows the time path of consumption $ c_t $ and income $ y_t $ in the simulation.\n", "\n", "As anticipated by the discussion on consumption smoothing, the time path of\n", "consumption is much smoother than that for income.\n", "\n", "(But note that consumption becomes more irregular towards the end of life,\n", "when the zero final asset requirement impinges more on consumption choices).\n", "\n", "The second panel in the figure shows that the time path of assets $ a_t $ is\n", "closely correlated with cumulative unanticipated income, where the latter is defined as\n", "\n", "$$\n", "z_t := \\sum_{j=0}^t \\sigma w_t\n", "$$\n", "\n", "A key message is that unanticipated windfall gains are saved rather\n", "than consumed, while unanticipated negative shocks are met by reducing assets.\n", "\n", "(Again, this relationship breaks down towards the end of life due to the zero final asset requirement).\n", "\n", "These results are relatively robust to changes in parameters.\n", "\n", "For example, let’s increase $ \\beta $ from $ 1 / (1 + r) \\approx 0.952 $ to $ 0.96 $ while keeping other parameters fixed.\n", "\n", "This consumer is slightly more patient than the last one, and hence puts\n", "relatively more weight on later consumption values" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false, "html-class": "collapse" }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compute solutions and simulate\n", "lq = QuantEcon.LQ(Q, R, A, B, C; bet = 0.96, capT = T, rf = Rf)\n", "x0 = [0.0, 1]\n", "xp, up, wp = compute_sequence(lq, x0)\n", "\n", "# convert back to assets, consumption and income\n", "assets = vec(xp[1, :]) # a_t\n", "c = vec(up .+ c̄) # c_t\n", "income = vec(σ * wp[1, 2:end] .+ μ) # y_t\n", "\n", "# plot results\n", "p = plot([assets, c, zeros(T + 1), income, cumsum(income .- μ)],\n", " lab = [\"assets\" \"consumption\" \"\" \"non-financial income\" \"cumulative unanticipated income\"],\n", " color = [:blue :green :black :orange :red],\n", " xaxis = \"Time\", layout = (2, 1),\n", " bottom_margin = 20mm, size = (600, 600))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now have a slowly rising consumption stream and a hump-shaped build\n", "up of assets in the middle periods to fund rising consumption.\n", "\n", "However, the essential features are the same: consumption is smooth relative to income, and assets are strongly positively correlated with cumulative unanticipated income." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Extensions and Comments\n", "\n", "Let’s now consider a number of standard extensions to the LQ problem treated above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Time-Varying Parameters\n", "\n", "In some settings it can be desirable to allow $ A, B, C, R $ and $ Q $ to depend on $ t $.\n", "\n", "For the sake of simplicity, we’ve chosen not to treat this extension in our implementation given below.\n", "\n", "However, the loss of generality is not as large as you might first imagine.\n", "\n", "In fact, we can tackle many models with time-varying parameters by suitable choice of state variables.\n", "\n", "One illustration is given [below](#lq-nsi).\n", "\n", "For further examples and a more systematic treatment, see [[HS13]](../zreferences.html#hansensargent2013), section 2.4.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a Cross-Product Term\n", "\n", "In some LQ problems, preferences include a cross-product term $ u_t' N x_t $, so that the objective function becomes\n", "\n", "\n", "\n", "$$\n", "\\mathbb E \\,\n", "\\left\\{\n", " \\sum_{t=0}^{T-1} \\beta^t (x_t' R x_t + u_t' Q u_t + 2 u_t' N x_t) + \\beta^T x_T' R_f x_T\n", "\\right\\} \\tag{17}\n", "$$\n", "\n", "Our results extend to this case in a straightforward way.\n", "\n", "The sequence $ \\{P_t\\} $ from [(12)](#equation-lq-pr) becomes\n", "\n", "\n", "\n", "$$\n", "P_{t-1}\n", "= R - (\\beta B' P_t A + N)' (Q + \\beta B' P_t B)^{-1} (\\beta B' P_t A + N) +\n", "\\beta A' P_t A\n", "\\quad \\text{with } \\quad\n", "P_T = R_f \\tag{18}\n", "$$\n", "\n", "The policies in [(14)](#equation-lq-oc) are modified to\n", "\n", "\n", "\n", "$$\n", "u_t = - F_t x_t\n", "\\quad \\text{where} \\quad\n", "F_t := (Q + \\beta B' P_{t+1} B)^{-1} (\\beta B' P_{t+1} A + N) \\tag{19}\n", "$$\n", "\n", "The sequence $ \\{d_t\\} $ is unchanged from [(13)](#equation-lq-dd).\n", "\n", "We leave interested readers to confirm these results (the calculations are long but not overly difficult).\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Infinite Horizon\n", "\n", "\n", "\n", "Finally, we consider the infinite horizon case, with [cross-product term](#lq-cpt), unchanged dynamics and\n", "objective function given by\n", "\n", "\n", "\n", "$$\n", "\\mathbb E \\,\n", "\\left\\{\n", " \\sum_{t=0}^{\\infty} \\beta^t (x_t' R x_t + u_t' Q u_t + 2 u_t' N x_t)\n", "\\right\\} \\tag{20}\n", "$$\n", "\n", "In the infinite horizon case, optimal policies can depend on time\n", "only if time itself is a component of the state vector $ x_t $.\n", "\n", "In other words, there exists a fixed matrix $ F $ such that $ u_t = -\n", "F x_t $ for all $ t $.\n", "\n", "That decision rules are constant over time is intuitive — after all, the decision maker faces the\n", "same infinite horizon at every stage, with only the current state changing.\n", "\n", "Not surprisingly, $ P $ and $ d $ are also constant.\n", "\n", "The stationary matrix $ P $ is the solution to the\n", "[discrete time algebraic Riccati equation](https://en.wikipedia.org/wiki/Algebraic_Riccati_equation).\n", "\n", "\n", "\n", "\n", "\n", "$$\n", "P = R - (\\beta B' P A + N)' (Q + \\beta B' P B)^{-1} (\\beta B' P A + N) +\n", "\\beta A' P A \\tag{21}\n", "$$\n", "\n", "Equation [(21)](#equation-lq-pr-ih) is also called the *LQ Bellman equation*, and the map\n", "that sends a given $ P $ into the right-hand side of [(21)](#equation-lq-pr-ih) is\n", "called the *LQ Bellman operator*.\n", "\n", "The stationary optimal policy for this model is\n", "\n", "\n", "\n", "$$\n", "u = - F x\n", "\\quad \\text{where} \\quad\n", "F = (Q + \\beta B' P B)^{-1} (\\beta B' P A + N) \\tag{22}\n", "$$\n", "\n", "The sequence $ \\{d_t\\} $ from [(13)](#equation-lq-dd) is replaced by the constant value\n", "\n", "\n", "\n", "$$\n", "d\n", ":= \\mathop{\\mathrm{trace}}(C' P C) \\frac{\\beta}{1 - \\beta} \\tag{23}\n", "$$\n", "\n", "The state evolves according to the time-homogeneous process $ x_{t+1} = (A - BF) x_t + C w_{t+1} $.\n", "\n", "An example infinite horizon problem is treated [below](#lqc-mwac).\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Certainty Equivalence\n", "\n", "Linear quadratic control problems of the class discussed above have the property of *certainty equivalence*.\n", "\n", "By this we mean that the optimal policy $ F $ is not affected by the parameters in $ C $, which specify the shock process.\n", "\n", "This can be confirmed by inspecting [(22)](#equation-lq-oc-ih) or [(19)](#equation-lq-oc-cp).\n", "\n", "It follows that we can ignore uncertainty when solving for optimal behavior, and plug it back in when examining optimal state dynamics." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further Applications\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Application 1: Age-Dependent Income Process\n", "\n", "[Previously](#lq-mfpa) we studied a permanent income model that generated consumption smoothing.\n", "\n", "One unrealistic feature of that model is the assumption that the mean of the random income process does not depend on the consumer’s age.\n", "\n", "A more realistic income profile is one that rises in early working life, peaks towards the middle and maybe declines toward end of working life, and falls more during retirement.\n", "\n", "In this section, we will model this rise and fall as a symmetric inverted “U” using a polynomial in age.\n", "\n", "As before, the consumer seeks to minimize\n", "\n", "\n", "\n", "$$\n", "\\mathbb E \\,\n", "\\left\\{\n", " \\sum_{t=0}^{T-1} \\beta^t (c_t - \\bar c)^2 + \\beta^T q a_T^2\n", "\\right\\} \\tag{24}\n", "$$\n", "\n", "subject to $ a_{t+1} = (1 + r) a_t - c_t + y_t, \\ t \\geq 0 $.\n", "\n", "For income we now take $ y_t = p(t) + \\sigma w_{t+1} $ where $ p(t) := m_0 + m_1 t + m_2 t^2 $.\n", "\n", "(In [the next section](#lq-nsi2) we employ some tricks to implement a more sophisticated model).\n", "\n", "The coefficients $ m_0, m_1, m_2 $ are chosen such that $ p(0)=0, p(T/2) = \\mu, $ and $ p(T)=0 $.\n", "\n", "You can confirm that the specification $ m_0 = 0, m_1 = T \\mu / (T/2)^2, m_2 = - \\mu / (T/2)^2 $ satisfies these constraints.\n", "\n", "To put this into an LQ setting, consider the budget constraint, which becomes\n", "\n", "\n", "\n", "$$\n", "a_{t+1} = (1 + r) a_t - u_t - \\bar c + m_1 t + m_2 t^2 + \\sigma w_{t+1} \\tag{25}\n", "$$\n", "\n", "The fact that $ a_{t+1} $ is a linear function of\n", "$ (a_t, 1, t, t^2) $ suggests taking these four variables as the state\n", "vector $ x_t $.\n", "\n", "Once a good choice of state and control (recall $ u_t = c_t - \\bar c $)\n", "has been made, the remaining specifications fall into place relatively easily.\n", "\n", "Thus, for the dynamics we set\n", "\n", "\n", "\n", "$$\n", "x_t :=\n", "\\left(\n", "\\begin{array}{c}\n", "a_t \\\\\n", "1 \\\\\n", "t \\\\\n", "t^2\n", "\\end{array}\n", "\\right),\n", "\\quad\n", "A :=\n", "\\left(\n", "\\begin{array}{cccc}\n", "1 + r & -\\bar c & m_1 & m_2 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 1 & 1 & 0 \\\\\n", "0 & 1 & 2 & 1 \\\\\n", "\\end{array}\n", "\\right),\n", "\\quad\n", "B :=\n", "\\left(\n", "\\begin{array}{c}\n", "-1 \\\\\n", "0 \\\\\n", "0 \\\\\n", "0\n", "\\end{array}\n", "\\right),\n", "\\quad\n", "C :=\n", "\\left(\n", "\\begin{array}{c}\n", "\\sigma \\\\\n", "0 \\\\\n", "0 \\\\\n", "0\n", "\\end{array}\n", "\\right) \\tag{26}\n", "$$\n", "\n", "If you expand the expression $ x_{t+1} = A x_t + B u_t + C w_{t+1} $ using\n", "this specification, you will find that assets follow [(25)](#equation-lq-hib) as desired,\n", "and that the other state variables also update appropriately.\n", "\n", "To implement preference specification [(24)](#equation-lq-pip) we take\n", "\n", "\n", "\n", "$$\n", "Q := 1,\n", "\\quad\n", "R :=\n", "\\left(\n", "\\begin{array}{cccc}\n", "0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0\n", "\\end{array}\n", "\\right)\n", "\\quad \\text{and} \\quad\n", "R_f :=\n", "\\left(\n", "\\begin{array}{cccc}\n", "q & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0\n", "\\end{array}\n", "\\right) \\tag{27}\n", "$$\n", "\n", "The next figure shows a simulation of consumption and assets computed using\n", "the `compute_sequence` method of `lqcontrol.jl` with initial assets set to zero.\n", "\n", "\n", "\n", "\n", "\n", " \n", "Once again, smooth consumption is a dominant feature of the sample paths.\n", "\n", "The asset path exhibits dynamics consistent with standard life cycle theory.\n", "\n", "Exercise 1 gives the full set of parameters used here and asks you to replicate the figure.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Application 2: A Permanent Income Model with Retirement\n", "\n", "In the [previous application](#lq-nsi), we generated income dynamics with an inverted U shape using polynomials, and placed them in an LQ framework.\n", "\n", "It is arguably the case that this income process still contains unrealistic features.\n", "\n", "A more common earning profile is where\n", "\n", "1. income grows over working life, fluctuating around an increasing trend, with growth flattening off in later years \n", "1. retirement follows, with lower but relatively stable (non-financial) income \n", "\n", "\n", "Letting $ K $ be the retirement date, we can express these income dynamics\n", "by\n", "\n", "\n", "\n", "$$\n", "y_t =\n", "\\begin{cases}\n", "p(t) + \\sigma w_{t+1} & \\quad \\text{if } t \\leq K \\\\\n", "s & \\quad \\text{otherwise } \\\\\n", "\\end{cases} \\tag{28}\n", "$$\n", "\n", "Here\n", "\n", "- $ p(t) := m_1 t + m_2 t^2 $ with the coefficients $ m_1, m_2 $ chosen such that $ p(K) = \\mu $ and $ p(0) = p(2K)=0 $ \n", "- $ s $ is retirement income \n", "\n", "\n", "We suppose that preferences are unchanged and given by [(16)](#equation-lq-pio).\n", "\n", "The budget constraint is also unchanged and given by $ a_{t+1} = (1 + r) a_t - c_t + y_t $.\n", "\n", "Our aim is to solve this problem and simulate paths using the LQ techniques described in this lecture.\n", "\n", "In fact this is a nontrivial problem, as the kink in the dynamics [(28)](#equation-lq-cases) at $ K $ makes it very difficult to express the law of motion as a fixed-coefficient linear system.\n", "\n", "However, we can still use our LQ methods here by suitably linking two component LQ problems.\n", "\n", "These two LQ problems describe the consumer’s behavior during her working life (`lq_working`) and retirement (`lq_retired`).\n", "\n", "(This is possible because in the two separate periods of life, the respective income processes\n", "[polynomial trend and constant] each fit the LQ framework)\n", "\n", "The basic idea is that although the whole problem is not a single time-invariant LQ problem, it is\n", "still a dynamic programming problem, and hence we can use appropriate Bellman equations at\n", "every stage.\n", "\n", "Based on this logic, we can\n", "\n", "1. solve `lq_retired` by the usual backwards induction procedure, iterating back to the start of retirement \n", "1. take the start-of-retirement value function generated by this process, and use it as the terminal condition $ R_f $ to feed into the `lq_working` specification \n", "1. solve `lq_working` by backwards induction from this choice of $ R_f $, iterating back to the start of working life \n", "\n", "\n", "This process gives the entire life-time sequence of value functions and optimal policies.\n", "\n", "The next figure shows one simulation based on this procedure.\n", "\n", "\n", "\n", "\n", "\n", " \n", "The full set of parameters used in the simulation is discussed in [Exercise 2](#lqc-ex2), where you are asked to replicate the figure.\n", "\n", "Once again, the dominant feature observable in the simulation is consumption\n", "smoothing.\n", "\n", "The asset path fits well with standard life cycle theory, with dissaving early\n", "in life followed by later saving.\n", "\n", "Assets peak at retirement and subsequently decline.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Application 3: Monopoly with Adjustment Costs\n", "\n", "Consider a monopolist facing stochastic inverse demand function\n", "\n", "$$\n", "p_t = a_0 - a_1 q_t + d_t\n", "$$\n", "\n", "Here $ q_t $ is output, and the demand shock $ d_t $ follows\n", "\n", "$$\n", "d_{t+1} = \\rho d_t + \\sigma w_{t+1}\n", "$$\n", "\n", "where $ \\{w_t\\} $ is iid and standard normal.\n", "\n", "The monopolist maximizes the expected discounted sum of present and future profits\n", "\n", "\n", "\n", "$$\n", "\\mathbb E \\,\n", "\\left\\{\n", " \\sum_{t=0}^{\\infty} \\beta^t\n", " \\pi_t\n", "\\right\\}\n", "\\quad \\text{where} \\quad\n", "\\pi_t := p_t q_t - c q_t - \\gamma (q_{t+1} - q_t)^2 \\tag{29}\n", "$$\n", "\n", "Here\n", "\n", "- $ \\gamma (q_{t+1} - q_t)^2 $ represents adjustment costs \n", "- $ c $ is average cost of production \n", "\n", "\n", "This can be formulated as an LQ problem and then solved and simulated,\n", "but first let’s study the problem and try to get some intuition.\n", "\n", "One way to start thinking about the problem is to consider what would happen\n", "if $ \\gamma = 0 $.\n", "\n", "Without adjustment costs there is no intertemporal trade-off, so the\n", "monopolist will choose output to maximize current profit in each period.\n", "\n", "It’s not difficult to show that profit-maximizing output is\n", "\n", "$$\n", "\\bar q_t := \\frac{a_0 - c + d_t}{2 a_1}\n", "$$\n", "\n", "In light of this discussion, what we might expect for general $ \\gamma $ is that\n", "\n", "- if $ \\gamma $ is close to zero, then $ q_t $ will track the time path of $ \\bar q_t $ relatively closely \n", "- if $ \\gamma $ is larger, then $ q_t $ will be smoother than $ \\bar q_t $, as the monopolist seeks to avoid adjustment costs \n", "\n", "\n", "This intuition turns out to be correct.\n", "\n", "The following figures show simulations produced by solving the corresponding LQ problem.\n", "\n", "The only difference in parameters across the figures is the size of $ \\gamma $.\n", "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "To produce these figures we converted the monopolist problem into an LQ problem.\n", "\n", "The key to this conversion is to choose the right state — which can be a bit of an art.\n", "\n", "Here we take $ x_t = (\\bar q_t \\;\\, q_t \\;\\, 1)' $, while the control is chosen as $ u_t = q_{t+1} - q_t $.\n", "\n", "We also manipulated the profit function slightly.\n", "\n", "In [(29)](#equation-lq-object-mp), current profits are $ \\pi_t := p_t q_t - c q_t - \\gamma (q_{t+1} - q_t)^2 $.\n", "\n", "Let’s now replace $ \\pi_t $ in [(29)](#equation-lq-object-mp) with $ \\hat \\pi_t := \\pi_t - a_1 \\bar q_t^2 $.\n", "\n", "This makes no difference to the solution, since $ a_1 \\bar q_t^2 $ does not depend on the controls.\n", "\n", "(In fact we are just adding a constant term to [(29)](#equation-lq-object-mp), and optimizers are not affected by constant terms)\n", "\n", "The reason for making this substitution is that, as you will be able to\n", "verify, $ \\hat \\pi_t $ reduces to the simple quadratic\n", "\n", "$$\n", "\\hat \\pi_t = -a_1 (q_t - \\bar q_t)^2 - \\gamma u_t^2\n", "$$\n", "\n", "After negation to convert to a minimization problem, the objective becomes\n", "\n", "\n", "\n", "$$\n", "\\min\n", "\\mathbb E \\,\n", " \\sum_{t=0}^{\\infty} \\beta^t\n", "\\left\\{\n", " a_1 ( q_t - \\bar q_t)^2 + \\gamma u_t^2\n", "\\right\\} \\tag{30}\n", "$$\n", "\n", "It’s now relatively straightforward to find $ R $ and $ Q $ such that\n", "[(30)](#equation-lq-object-mp2) can be written as [(20)](#equation-lq-object-ih).\n", "\n", "Furthermore, the matrices $ A, B $ and $ C $ from [(1)](#equation-lq-lom)\n", "can be found by writing down the dynamics of each element of the state.\n", "\n", "[Exercise 3](#lqc-ex3) asks you to complete this process, and reproduce the preceding figures." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Replicate the figure with polynomial income [shown above](#solution-lqc-ex1-fig).\n", "\n", "The parameters are $ r = 0.05, \\beta = 1 / (1 + r), \\bar c = 1.5, \\mu = 2, \\sigma = 0.15, T = 50 $ and $ q = 10^4 $.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Replicate the figure on work and retirement [shown above](#solution-lqc-ex2-fig).\n", "\n", "The parameters are $ r = 0.05, \\beta = 1 / (1 + r), \\bar c = 4, \\mu = 4, \\sigma = 0.35, K = 40, T = 60, s = 1 $ and $ q = 10^4 $.\n", "\n", "To understand the overall procedure, carefully read the section containing that figure.\n", "\n", "Some hints are as follows:\n", "\n", "First, in order to make our approach work, we must ensure that both LQ problems have the same state variables and control.\n", "\n", "As with previous applications, the control can be set to $ u_t = c_t - \\bar c $.\n", "\n", "For `lq_working`, $ x_t, A, B, C $ can be chosen as in [(26)](#equation-lq-lowmc3).\n", "\n", "- Recall that $ m_1, m_2 $ are chosen so that $ p(K) = \\mu $ and $ p(2K)=0 $. \n", "\n", "\n", "For `lq_retired`, use the same definition of $ x_t $ and $ u_t $, but modify $ A, B, C $ to correspond to constant income $ y_t = s $.\n", "\n", "For `lq_retired`, set preferences as in [(27)](#equation-lq-4sp).\n", "\n", "For `lq_working`, preferences are the same, except that $ R_f $ should\n", "be replaced by the final value function that emerges from iterating `lq_retired`\n", "back to the start of retirement.\n", "\n", "With some careful footwork, the simulation can be generated by patching\n", "together the simulations from these two separate models.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "Reproduce the figures from the monopolist application [given above](#lqc-mwac).\n", "\n", "For parameters, use $ a_0 = 5, a_1 = 0.5, \\sigma = 0.15, \\rho = 0.9,\n", "\\beta = 0.95 $ and $ c = 2 $, while $ \\gamma $ varies between 1 and 50\n", "(see figures)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Here’s one solution.\n", "\n", "We use some fancy plot commands to get a certain style — feel free to\n", "use simpler ones.\n", "\n", "The model is an LQ permanent income / life-cycle model with hump-shaped\n", "income.\n", "\n", "$$\n", "y_t = m_1 t + m_2 t^2 + \\sigma w_{t+1}\n", "$$\n", "\n", "where $ \\{w_t\\} $ is iid $ N(0, 1) $ and the coefficients\n", "$ m_1 $ and $ m_2 $ are chosen so that\n", "$ p(t) = m_1 t + m_2 t^2 $ has an inverted U shape with\n", "\n", "- $ p(0) = 0, p(T/2) = \\mu $, and \n", "- $ p(T) = 0 $. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# model parameters\n", "r = 0.05\n", "β = 1 / (1 + r)\n", "T = 50\n", "c̄ = 1.5\n", "σ = 0.15\n", "μ = 2\n", "q = 1e4\n", "m1 = T * (μ / (T / 2)^2)\n", "m2 = -(μ / (T / 2)^2)\n", "\n", "# formulate as an LQ problem\n", "Q = 1.0\n", "R = zeros(4, 4)\n", "Rf = zeros(4, 4); Rf[1, 1] = q\n", "A = [1 + r -c̄ m1 m2;\n", " 0 1 0 0;\n", " 0 1 1 0;\n", " 0 1 2 1]\n", "B = [-1.0, 0.0, 0.0, 0.0]\n", "C = [σ, 0.0, 0.0, 0.0]\n", "\n", "# compute solutions and simulate\n", "lq = QuantEcon.LQ(Q, R, A, B, C; bet = β, capT = T, rf = Rf)\n", "x0 = [0.0, 1, 0, 0]\n", "xp, up, wp = compute_sequence(lq, x0)\n", "\n", "# convert results back to assets, consumption and income\n", "ap = vec(xp[1, 1:end]) # assets\n", "c = vec(up .+ c̄) # consumption\n", "time = 1:T\n", "income = σ * vec(wp[1, 2:end]) + m1 * time + m2 * time.^2 # income\n", "\n", "# plot results\n", "p1 = plot(Vector[income, ap, c, zeros(T + 1)],\n", " lab = [\"non-financial income\" \"assets\" \"consumption\" \"\"],\n", " color = [:orange :blue :green :black],\n", " xaxis = \"Time\", layout = (2,1),\n", " bottom_margin = 20mm, size = (600, 600))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "This is a permanent income / life-cycle model with polynomial growth in\n", "income over working life followed by a fixed retirement income. The\n", "model is solved by combining two LQ programming problems as described in\n", "the lecture." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# model parameters\n", "r = 0.05\n", "β = 1/(1 + r)\n", "T = 60\n", "K = 40\n", "c̄ = 4\n", "σ = 0.35\n", "μ = 4\n", "q = 1e4\n", "s = 1\n", "m1 = 2 * μ / K\n", "m2 = - μ / K^2\n", "\n", "# formulate LQ problem 1 (retirement)\n", "Q = 1.0\n", "R = zeros(4, 4)\n", "Rf = zeros(4, 4); Rf[1, 1] = q\n", "A = [1+r s-c̄ 0 0;\n", " 0 1 0 0;\n", " 0 1 1 0;\n", " 0 1 2 1]\n", "B = [-1.0, 0, 0, 0]\n", "C = zeros(4)\n", "\n", "# initialize LQ instance for retired agent\n", "lq_retired = QuantEcon.LQ(Q, R, A, B, C; bet = β, capT = T - K, rf = Rf)\n", "\n", "# since update_values!() changes its argument in place, we need another identical instance\n", "# just to get the correct value function\n", "lq_retired_proxy = QuantEcon.LQ(Q, R, A, B, C; bet = β, capT = T - K, rf = Rf)\n", "\n", "# iterate back to start of retirement, record final value function\n", "for i in 1:(T - K)\n", " update_values!(lq_retired_proxy)\n", "end\n", "Rf2 = lq_retired_proxy.P\n", "\n", "# formulate LQ problem 2 (working life)\n", "Q = 1.0\n", "R = zeros(4, 4)\n", "A = [1 + r -c̄ m1 m2;\n", " 0 1 0 0;\n", " 0 1 1 0;\n", " 0 1 2 1]\n", "B = [-1.0, 0, 0, 0]\n", "C = [σ, 0, 0, 0]\n", "\n", "# set up working life LQ instance with terminal Rf from lq_retired\n", "lq_working = QuantEcon.LQ(Q, R, A, B, C; bet = β, capT = K, rf = Rf2)\n", "\n", "# simulate working state / control paths\n", "x0 = [0.0, 1, 0, 0]\n", "xp_w, up_w, wp_w = compute_sequence(lq_working, x0)\n", "\n", "# simulate retirement paths (note the initial condition)\n", "xp_r, up_r, wp_r = compute_sequence(lq_retired, xp_w[:, end])\n", "\n", "# convert results back to assets, consumption and income\n", "xp = [xp_w xp_r[:, 2:end]]\n", "assets = vec(xp[1, :]) # assets\n", "\n", "up = [up_w up_r]\n", "c = vec(up .+ c̄) # consumption\n", "\n", "time = 1:K\n", "income_w = σ * vec(wp_w[1, 2:K+1]) + m1 .* time + m2 .* time.^2 # income\n", "income_r = ones(T - K) * s\n", "income = [income_w; income_r]\n", "\n", "# plot results\n", "p2 = plot([income, assets, c, zeros(T + 1)],\n", " lab = [\"non-financial income\" \"assets\" \"consumption\" \"\"],\n", " color = [:orange :blue :green :black],\n", " xaxis = \"Time\", layout = (2, 1),\n", " bottom_margin = 20mm, size = (600, 600))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "The first task is to find the matrices $ A, B, C, Q, R $ that define\n", "the LQ problem.\n", "\n", "Recall that $ x_t = (\\bar q_t \\;\\, q_t \\;\\, 1)' $, while\n", "$ u_t = q_{t+1} - q_t $.\n", "\n", "Letting $ m_0 := (a_0 - c) / 2a_1 $ and $ m_1 := 1 / 2 a_1 $, we\n", "can write $ \\bar q_t = m_0 + m_1 d_t $, and then, with some\n", "manipulation\n", "\n", "$$\n", "\\bar q_{t+1} = m_0 (1 - \\rho) + \\rho \\bar q_t + m_1 \\sigma w_{t+1}\n", "$$\n", "\n", "By our definition of $ u_t $, the dynamics of $ q_t $ are\n", "$ q_{t+1} = q_t + u_t $.\n", "\n", "Using these facts you should be able to build the correct\n", "$ A, B, C $ matrices (and then check them against those found in the\n", "solution code below).\n", "\n", "Suitable $ R, Q $ matrices can be found by inspecting the objective\n", "function, which we repeat here for convenience:\n", "\n", "$$\n", "\\min\n", "\\mathbb E \\,\n", "\\left\\{\n", " \\sum_{t=0}^{\\infty} \\beta^t\n", " a_1 ( q_t - \\bar q_t)^2 + \\gamma u_t^2\n", "\\right\\}\n", "$$\n", "\n", "Our solution code is" ] }, { "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": [ "# model parameters\n", "a0 = 5.0\n", "a1 = 0.5\n", "σ = 0.15\n", "ρ = 0.9\n", "γ = 1.0\n", "β = 0.95\n", "c = 2.0\n", "T = 120\n", "\n", "# useful constants\n", "m0 = (a0 - c) / (2 * a1)\n", "m1 = 1 / (2 * a1)\n", "\n", "# formulate LQ problem\n", "Q = γ\n", "R = [a1 -a1 0; -a1 a1 0; 0 0 0]\n", "A = [ρ 0 m0 * (1 - ρ); 0 1 0; 0 0 1]\n", "\n", "B = [0.0, 1, 0]\n", "C = [m1 * σ, 0, 0]\n", "\n", "lq = QuantEcon.LQ(Q, R, A, B, C; bet = β)\n", "\n", "# simulate state / control paths\n", "x0 = [m0, 2, 1]\n", "xp, up, wp = compute_sequence(lq, x0, 150)\n", "q̄ = vec(xp[1, :])\n", "q = vec(xp[2, :])\n", "\n", "# plot simulation results\n", "p3 = plot(eachindex(q), [q̄ q],\n", " lab = [\"q bar\" \"q\"],\n", " color = [:black :blue],\n", " xaxis = \"Time\", title = \"Dynamics with γ = $γ\",\n", " bottom_margin = 20mm, top_margin = 10mm,\n", " size = (700, 500))" ] } ], "metadata": { "date": 1591310615.7549725, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "lqcontrol.rst", "filename_with_path": "dynamic_programming/lqcontrol", "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": "LQ Dynamic Programming Problems" }, "nbformat": 4, "nbformat_minor": 2 }