{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "(smoothing)=\n", "```{raw} html\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
\n", "```\n", "\n", "# Consumption Smoothing with Complete and Incomplete Markets\n", "\n", "```{index} single: Consumption; Tax\n", "```\n", "\n", "```{contents} Contents\n", ":depth: 2\n", "```\n", "\n", "In addition to what's in Anaconda, this lecture uses the library:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "hide-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Requirement already up-to-date: quantecon in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (0.4.8)\r\n", "Requirement already satisfied, skipping upgrade: numpy in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from quantecon) (1.18.5)\r\n", "Requirement already satisfied, skipping upgrade: requests in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from quantecon) (2.24.0)\r\n", "Requirement already satisfied, skipping upgrade: scipy>=1.0.0 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from quantecon) (1.5.0)\r\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied, skipping upgrade: sympy in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from quantecon) (1.6.1)\r\n", "Requirement already satisfied, skipping upgrade: numba>=0.38 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from quantecon) (0.50.1)\r\n", "Requirement already satisfied, skipping upgrade: chardet<4,>=3.0.2 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from requests->quantecon) (3.0.4)\r\n", "Requirement already satisfied, skipping upgrade: idna<3,>=2.5 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from requests->quantecon) (2.10)\r\n", "Requirement already satisfied, skipping upgrade: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from requests->quantecon) (1.25.9)\r\n", "Requirement already satisfied, skipping upgrade: certifi>=2017.4.17 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from requests->quantecon) (2020.6.20)\r\n", "Requirement already satisfied, skipping upgrade: mpmath>=0.19 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from sympy->quantecon) (1.1.0)\r\n", "Requirement already satisfied, skipping upgrade: llvmlite<0.34,>=0.33.0.dev0 in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from numba>=0.38->quantecon) (0.33.0+1.g022ab0f)\r\n", "Requirement already satisfied, skipping upgrade: setuptools in /Users/matthewmckay/anaconda3/envs/quantecon/lib/python3.8/site-packages (from numba>=0.38->quantecon) (49.2.0.post20200714)\r\n" ] } ], "source": [ "!pip install --upgrade quantecon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "This lecture describes two types of consumption-smoothing models.\n", "\n", "{cite}`Hall1978`* one is in the **complete markets** tradition of Kenneth Arrow \n", "* the other is in the **incomplete markets** tradition of Hall \n", "\n", "*Complete markets* allow a consumer to buy or sell claims contingent on all possible states of the world.\n", "\n", "*Incomplete markets* allow a consumer to buy or sell only a limited set of securities, often only a single risk-free security.\n", "\n", "Hall {cite}`Hall1978` worked in an incomplete markets tradition by assuming\n", "that the only asset that can be traded is a risk-free one period bond.\n", "\n", "Hall assumed an exogenous stochastic process of nonfinancial income and\n", "an exogenous and time-invariant gross interest rate on one period risk-free debt that equals\n", "$\\beta^{-1}$, where $\\beta \\in (0,1)$ is also a consumer's\n", "intertemporal discount factor.\n", "\n", "This is equivalent to saying that it costs $\\beta^{-1}$ of time $t$ consumption to buy one unit of consumption at time $t+1$ for sure.\n", "\n", "So $\\beta^{-1}$ is the price of a one-period risk-free claim to consumption next period.\n", "\n", "We maintain Hall's assumption about the interest rate when we describe an\n", "incomplete markets version of our model.\n", "\n", "In addition, we extend Hall's assumption about the risk-free interest rate to its appropriate counterpart when we create another model in which there are markets\n", "in a complete array of one-period Arrow state-contingent securities.\n", "\n", "We'll consider two closely related but distinct alternative assumptions about the consumer's\n", "exogenous nonfinancial income process:\n", "\n", "* that it is generated by a finite $N$ state Markov chain (setting $N=2$ most of the time in this lecture)\n", "* that it is described by a linear state space model with a continuous\n", " state vector in ${\\mathbb R}^n$ driven by a Gaussian vector IID shock\n", " process\n", "\n", "We'll spend most of this lecture studying the finite-state Markov specification, but will begin by studying the linear state space specification because it\n", "is so closely linked to earlier lectures.\n", "\n", "Let's start with some imports:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import quantecon as qe\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import scipy.linalg as la" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Relationship to Other Lectures\n", "\n", "This lecture can be viewed as a followup to [Optimal Savings II: LQ Techniques](https://python-intro.quantecon.org/perm_income_cons.html)\n", "\n", "This lecture is also a prologomenon to a lecture on tax-smoothing {doc}`smoothing_tax `\n", "\n", "## Background\n", "\n", "Outcomes in consumption-smoothing models emerge from two\n", "sources:\n", "\n", "* a consumer who wants to maximize an\n", " intertemporal objective function that expresses its preference for\n", " paths of consumption that are *smooth* in the\n", " sense of varying as little as possible both across time and across realized Markov states\n", "* opportunities that allow the consumer to transform\n", " an erratic nonfinancial income\n", " process into a smoother consumption process by\n", " purchasing or selling one or more financial securities\n", "\n", "In the **complete markets version**, each period the consumer\n", "can buy or sell a complete set of one-period ahead state-contingent securities whose\n", "payoffs depend on next period's realization of the Markov state.\n", "\n", "* In the two-state Markov chain case, two such securities are traded each period.\n", "* In an $N$ state Markov state version, $N$ such securities are traded each period.\n", "* In a continuous state Markov state version, a continuum of such securities are traded each period.\n", "\n", "These state-contingent securities are commonly called Arrow securities, after Kenneth Arrow \n", "\n", "In the **incomplete markets version**, the consumer can buy and sell only one security each period, a risk-free one-period bond with gross\n", "one-period return $\\beta^{-1}$.\n", "\n", "## Linear State Space Version of Complete Markets Model\n", "\n", "We'll study a complete markets model adapted to a setting with a continuous Markov state like that in the [first lecture on the permanent income model](https://python-intro.quantecon.org/perm_income.html).\n", "\n", "In that model\n", "\n", "* a consumer can trade only a single risk-free one-period bond bearing gross one-period risk-free interest rate equal to $\\beta^{-1}$.\n", "* a consumer's exogenous nonfinancial income is governed by a linear state space model driven by Gaussian shocks, the kind of model studied in an earlier lecture about [linear state space models](https://python-intro.quantecon.org/linear_models.html).\n", "\n", "Let's write down a complete markets counterpart of that model.\n", "\n", "Suppose that nonfinancial income is governed by the state\n", "space system\n", "\n", "$$\n", "\\begin{aligned}\n", " x_{t+1} & = A x_t + C w_{t+1} \\cr\n", " y_t & = S_y x_t\n", "\\end{aligned}\n", "$$\n", "\n", "where $x_t$ is an $n \\times 1$ vector and $w_{t+1} \\sim {\\cal N}(0,I)$ is IID over time.\n", "\n", "We want a natural counterpart of the Hall assumption that the one-period risk-free\n", "gross interest rate is $\\beta^{-1}$.\n", "\n", "We make the good guess that prices\n", "of one-period ahead Arrow securities are described by the **pricing kernel**\n", "\n", "```{math}\n", ":label: cs_14\n", "\n", "q_{t+1}(x_{t+1} \\,|\\, x_t) = \\beta \\phi(x_{t+1} \\,|\\, A x_t, CC')\n", "```\n", "\n", "where $\\phi(\\cdot \\,|\\, \\mu, \\Sigma)$ is a multivariate Gaussian\n", "distribution with mean vector $\\mu$ and covariance matrix\n", "$\\Sigma$.\n", "\n", "With the pricing kernel $q_{t+1}(x_{t+1} \\,|\\, x_t)$ in hand, we can price claims to consumption at time $t+1$ consumption that pay off when\n", "$x_{t+1} \\in S$ at time $t+1$:\n", "\n", "$$\n", "\\int_S q_{t+1}(x_{t+1} \\,|\\, x_t) d x_{t+1}\n", "$$\n", "\n", "where $S$ is a subset of $\\mathbb R^n$.\n", "\n", "The price $\\int_S q_{t+1}(x_{t+1} \\,|\\, x_t) d x_{t+1}$ of such a claim depends on state $x_t$ because the prices of the $x_{t+1}$-contingent\n", "securities depend on $x_t$ through the pricing kernel $q(x_{t+1} \\,|\\, x_t)$.\n", "\n", "Let $b(x_{t+1})$ be a vector of state-contingent debt due at $t+1$\n", "as a function of the $t+1$ state $x_{t+1}$.\n", "\n", "Using the pricing kernel assumed in {eq}`cs_14`, the value at\n", "$t$ of $b(x_{t+1})$ is evidently\n", "\n", "$$\n", "\\beta \\int b(x_{t+1}) \\phi(x_{t+1} \\,|\\, A x_t, CC') d x_{t+1} = \\beta \\mathbb E_t b_{t+1}\n", "$$\n", "\n", "In our complete markets setting, the consumer faces a sequence of budget\n", "constraints\n", "\n", "$$\n", "c_t + b_t = y_t + \\beta \\mathbb E_t b_{t+1}, \\quad t \\geq 0\n", "$$\n", "\n", "Please note that\n", "\n", "$$\n", "E_t b_{t+1} = \\int \\phi_{t+1}(x_{t+1} | A x_t, C C') b_{t+1}(x_{t+1}) d x_{t+1}\n", "$$\n", "\n", "which verifies that $E_t b_{t+1}$ is the **value** of time $t+1$ state-contingent claims on time $t+1$ consumption issued by the consumer at time $t$\n", "\n", "We can solve the time $t$ budget constraint forward to obtain\n", "\n", "$$\n", "b_t = \\mathbb E_t \\sum_{j=0}^\\infty \\beta^j (y_{t+j} - c_{t+j} )\n", "$$\n", "\n", "The consumer cares about the expected value\n", "of\n", "\n", "$$\n", "\\sum_{t=0}^\\infty \\beta^t u(c_t), \\quad 0 < \\beta < 1\n", "$$\n", "\n", "In the incomplete markets version of the model, we assumed that\n", "$u(c_t) = - (c_t -\\gamma)^2$, so that the above utility functional\n", "became\n", "\n", "$$\n", "-\\sum_{t=0}^\\infty \\beta^t ( c_t - \\gamma)^2, \\quad 0 < \\beta < 1\n", "$$\n", "\n", "But in the complete markets version, it is tractable to assume a more general utility function that satisfies $u' > 0$ and $u'' < 0$.\n", "\n", "The first-order conditions for the consumer's problem with complete\n", "markets and our assumption about Arrow securities prices are\n", "\n", "$$\n", "u'(c_{t+1}) = u'(c_t) \\quad \\text{for all } t\\geq 0\n", "$$\n", "\n", "which implies $c_t = \\bar c$ for some $\\bar c$.\n", "\n", "So it follows that\n", "\n", "$$\n", "b_t = \\mathbb E_t \\sum_{j=0}^\\infty \\beta^j (y_{t+j} - \\bar c)\n", "$$\n", "\n", "or\n", "\n", "```{math}\n", ":label: cs_15\n", "\n", "b_t = S_y (I - \\beta A)^{-1} x_t - \\frac{1}{1-\\beta} \\bar c\n", "```\n", "\n", "where $\\bar c$ satisfies\n", "\n", "```{math}\n", ":label: cs_16\n", "\n", "\\bar b_0 = S_y (I - \\beta A)^{-1} x_0 - \\frac{1}{1 - \\beta } \\bar c\n", "```\n", "\n", "where $\\bar b_0$ is an initial level of the consumer's debt due at time $t=0$, specified\n", "as a parameter of the problem.\n", "\n", "Thus, in the complete markets version of the consumption-smoothing\n", "model, $c_t = \\bar c, \\forall t \\geq 0$ is determined by {eq}`cs_16`\n", "and the consumer's debt is the fixed function of\n", "the state $x_t$ described by {eq}`cs_15`.\n", "\n", "Please recall that in the LQ permanent income model studied in [permanent income model](https://python-intro.quantecon.org/perm_income.html), the state is\n", "$x_t, b_t$, where $b_t$ is a complicated function of past state vectors $x_{t-j}$.\n", "\n", "Notice that in contrast to that incomplete markets model, at time $t$ the state vector is $x_t$ alone in our complete markets model.\n", "\n", "Here's an example that shows how in this setting the availability of insurance against fluctuating nonfinancial income\n", "allows the consumer completely to smooth consumption across time and across states of the world" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { "image/png": "/Users/matthewmckay/repos-collab/phd-macro-theory-book/_build/jupyter_execute/smoothing_5_0.png" }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def complete_ss(β, b0, x0, A, C, S_y, T=12):\n", " \"\"\"\n", " Computes the path of consumption and debt for the previously described\n", " complete markets model where exogenous income follows a linear\n", " state space\n", " \"\"\"\n", " # Create a linear state space for simulation purposes\n", " # This adds \"b\" as a state to the linear state space system\n", " # so that setting the seed places shocks in same place for\n", " # both the complete and incomplete markets economy\n", " # Atilde = np.vstack([np.hstack([A, np.zeros((A.shape[0], 1))]),\n", " # np.zeros((1, A.shape[1] + 1))])\n", " # Ctilde = np.vstack([C, np.zeros((1, 1))])\n", " # S_ytilde = np.hstack([S_y, np.zeros((1, 1))])\n", "\n", " lss = qe.LinearStateSpace(A, C, S_y, mu_0=x0)\n", "\n", " # Add extra state to initial condition\n", " # x0 = np.hstack([x0, np.zeros(1)])\n", "\n", " # Compute the (I - β * A)^{-1}\n", " rm = la.inv(np.eye(A.shape[0]) - β * A)\n", "\n", " # Constant level of consumption\n", " cbar = (1 - β) * (S_y @ rm @ x0 - b0)\n", " c_hist = np.ones(T) * cbar\n", "\n", " # Debt\n", " x_hist, y_hist = lss.simulate(T)\n", " b_hist = np.squeeze(S_y @ rm @ x_hist - cbar / (1 - β))\n", "\n", "\n", " return c_hist, b_hist, np.squeeze(y_hist), x_hist\n", "\n", "\n", "# Define parameters\n", "N_simul = 80\n", "α, ρ1, ρ2 = 10.0, 0.9, 0.0\n", "σ = 1.0\n", "\n", "A = np.array([[1., 0., 0.],\n", " [α, ρ1, ρ2],\n", " [0., 1., 0.]])\n", "C = np.array([[0.], [σ], [0.]])\n", "S_y = np.array([[1, 1.0, 0.]])\n", "β, b0 = 0.95, -10.0\n", "x0 = np.array([1.0, α / (1 - ρ1), α / (1 - ρ1)])\n", "\n", "# Do simulation for complete markets\n", "s = np.random.randint(0, 10000)\n", "np.random.seed(s) # Seeds get set the same for both economies\n", "out = complete_ss(β, b0, x0, A, C, S_y, 80)\n", "c_hist_com, b_hist_com, y_hist_com, x_hist_com = out\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(15, 5))\n", "\n", "# Consumption plots\n", "ax[0].set_title('Consumption and income')\n", "ax[0].plot(np.arange(N_simul), c_hist_com, label='consumption')\n", "ax[0].plot(np.arange(N_simul), y_hist_com, label='income', alpha=.6, linestyle='--')\n", "ax[0].legend()\n", "ax[0].set_xlabel('Periods')\n", "ax[0].set_ylim([80, 120])\n", "\n", "# Debt plots\n", "ax[1].set_title('Debt and income')\n", "ax[1].plot(np.arange(N_simul), b_hist_com, label='debt')\n", "ax[1].plot(np.arange(N_simul), y_hist_com, label='Income', alpha=.6, linestyle='--')\n", "ax[1].legend()\n", "ax[1].axhline(0, color='k')\n", "ax[1].set_xlabel('Periods')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interpretation of Graph\n", "\n", "In the above graph, please note that:\n", "\n", "- nonfinancial income fluctuates in a stationary manner.\n", "- consumption is completely constant.\n", "- the consumer's debt fluctuates in a stationary manner; in fact, in\n", " this case, because nonfinancial income is a first-order\n", " autoregressive process, the consumer's debt is an exact affine function\n", " (meaning linear plus a constant) of the consumer's nonfinancial\n", " income.\n", "\n", "### Incomplete Markets Version\n", "\n", "The incomplete markets version of the model with nonfinancial income being governed by a linear state space system\n", "is described in [permanent income model](https://python-intro.quantecon.org/perm_income.html) and a followup\n", "lecture on the [permanent income model](https://python-intro.quantecon.org/perm_income_cons.html).\n", "\n", "In that incomplete markerts setting, consumption follows a random walk and the consumer's debt follows a process with a unit root.\n", "\n", "### Finite State Markov Income Process\n", "\n", "We now turn to a finite-state Markov version of the model in which the consumer's nonfinancial income is an exact function of a Markov state that\n", "takes one of $N$ values.\n", "\n", "We'll start with a setting in which in each version of our consumption-smoothing model, nonfinancial income is governed by a two-state Markov chain\n", "(it's easy to generalize this to an $N$ state Markov chain).\n", "\n", "In particular, the *state* $s_t \\in \\{1, 2\\}$ follows\n", "a Markov chain with transition probability matrix\n", "\n", "$$\n", "P_{ij} = \\mathbb P \\{s_{t+1} = j \\,|\\, s_t = i \\}\n", "$$\n", "\n", "where $\\mathbb P$ means conditional probability\n", "\n", "Nonfinancial income $\\{y_t\\}$ obeys\n", "\n", "$$\n", "y_t =\n", "\\begin{cases}\n", " \\bar y_1 & \\quad \\text{if } s_t = 1 \\\\\n", " \\bar y_2 & \\quad \\text{if } s_t = 2\n", "\\end{cases}\n", "$$\n", "\n", "A consumer wishes to maximize\n", "\n", "```{math}\n", ":label: cs_1\n", "\n", "\\mathbb E\n", "\\left[\n", " \\sum_{t=0}^\\infty \\beta^t u(c_t)\n", "\\right]\n", "\\quad\n", "\\text{where} \\quad\n", "u(c_t) = - (c_t -\\gamma)^2\n", "\\quad \\text{and} \\quad\n", " 0 < \\beta < 1\n", "```\n", "\n", "Here $\\gamma >0$ is a bliss level of consumption\n", "\n", "### Market Structure\n", "\n", "Our complete and incomplete markets models differ in how thoroughly the market structure allows a\n", "consumer to transfer resources across time and Markov states, there\n", "being more transfer opportunities in the complete markets setting than\n", "in the incomplete markets setting.\n", "\n", "Watch how these differences in opportunities affect\n", "\n", "- how smooth consumption is across time and Markov states\n", "- how the consumer chooses to make his levels of indebtedness behave\n", " over time and across Markov states\n", "\n", "## Model 1 (Complete Markets)\n", "\n", "At each date $t \\geq 0$, the consumer trades a full array of **one-period ahead\n", "Arrow securities**.\n", "\n", "We assume that prices of these securities are exogenous to the consumer.\n", "\n", "*Exogenous* means that they are unaffected by the consumer's decisions.\n", "\n", "In Markov state $s_t$ at time $t$, one unit of consumption\n", "in state $s_{t+1}$ at time $t+1$ costs $q(s_{t+1} \\,|\\, s_t)$ units of the time $t$ consumption good.\n", "\n", "The prices $q(s_{t+1} \\,|\\, s_t)$ are given and can be organized into a matrix $Q$ with $Q_{ij} = q(j | i)$\n", "\n", "At time $t=0$, the consumer starts with an inherited level of debt\n", "due at time $0$ of $b_0$ units of time $0$ consumption\n", "goods.\n", "\n", "The consumer's budget constraint at $t \\geq 0$ in Markov\n", "state $s_t$ is\n", "\n", "```{math}\n", ":label: cs_budget1\n", "\n", "c_t + b_t\n", "\\leq y(s_t) +\n", "\\sum_j q(j \\,|\\, s_t ) \\, b_{t+1}( j \\,|\\, s_t)\n", "```\n", "\n", "where $b_t$ is the consumer's one-period debt that falls due at time $t$ and $b_{t+1}(j\\,|\\, s_t)$ are the consumer's time\n", "$t$ sales of the time $t+1$ consumption good in Markov state $j$.\n", "\n", "These are\n", "\n", "* when multiplied by $q(j\\,|\\, s_t)$, a source of time $t$ **revenues** for the consumer\n", "* when $s_{t+1} = j$, a source of time $t+1$ **expenditures** for the consumer\n", "\n", "A natural analog of Hall's assumption that the one-period risk-free gross\n", "interest rate is $\\beta^{-1}$ is\n", "\n", "```{math}\n", ":label: cs_2\n", "\n", "q(j \\,|\\, i) = \\beta P_{ij}\n", "```\n", "\n", "To understand how this is a natural analogue, observe that in state $i$ it costs $\\sum_j q(j \\,|\\, i)$ to purchase one unit of consumption next period *for sure*, i.e., meaning no matter what state of the world occurs at $t+1$.\n", "\n", "Hence the **implied price** of a risk-free claim on one unit of consumption next\n", "period is\n", "\n", "$$\n", "\\sum_j q(j \\,|\\, i) = \\sum_j \\beta P_{ij} = \\beta\n", "$$\n", "\n", "This confirms the sense in which {eq}`cs_2` is a natural counterpart to Hall's assumption that the\n", "risk-free one-period gross interest rate is $R = \\beta^{-1}$.\n", "\n", "It is timely please to recall that the gross one-period risk-free interest rate is the reciprocal of the price at time $t$ of a risk-free claim on\n", "one unit of consumption tomorrow.\n", "\n", "First-order necessary conditions for maximizing the consumer's expected utility subject to the sequence of budget constraints {eq}`cs_budget1` are\n", "\n", "$$\n", "\\beta \\frac{u'(c_{t+1})}{u'(c_t) } \\mathbb P\\{s_{t+1}\\,|\\, s_t \\}\n", " = q(s_{t+1} \\,|\\, s_t)\n", "$$\n", "\n", "for all $s_t, s_{t+1}$\n", "\n", "or, under our assumption {eq}`cs_2` about the values taken by Arrow security prices,\n", "\n", "```{math}\n", ":label: cs_3\n", "\n", "c_{t+1} = c_t\n", "```\n", "\n", "Thus, our consumer sets $c_t = \\bar c$ for all $t \\geq 0$ for some value $\\bar c$ that it is our job now to determine along with\n", "values for $b_{t+1}(j | s_t = i)$ for $i=1,2$ and $j = 1,2$\n", "\n", "We'll use a *guess and verify* method to determine these objects\n", "\n", "**Guess:** We'll make the plausible guess that\n", "\n", "```{math}\n", ":label: eq_guess\n", "\n", "b_{t+1}(s_{t+1} = j \\,|\\, s_t = i) = b(j) ,\n", " \\quad i=1,2; \\;\\; j= 1,2\n", "```\n", "\n", "so that the amount borrowed today depends only on *tomorrow's* Markov state. (Why is this is a plausible guess?)\n", "\n", "To determine $\\bar c$, we shall deduce implications of the consumer's budget constraints in each Markov state today and our guess {eq}`eq_guess` about the consumer's debt level choices.\n", "\n", "For $t \\geq 1$, these imply\n", "\n", "```{math}\n", ":label: cs_4a\n", "\n", "\\begin{aligned}\n", " \\bar c + b(1) & = y(1) + q(1\\,|\\, 1) b(1) + q(2 \\,|\\, 1) b(2) \\cr\n", " \\bar c + b(2) & = y(2) + q(1\\,|\\, 2) b(1) + q(2 \\,|\\, 2) b(2)\n", "\\end{aligned}\n", "```\n", "\n", "or\n", "\n", "$$\n", "\\begin{bmatrix}\n", " b(1) \\cr b(2)\n", "\\end{bmatrix} +\n", "\\begin{bmatrix}\n", "\\bar c \\cr \\bar c\n", "\\end{bmatrix} =\n", "\\begin{bmatrix}\n", " y(1) \\cr y(2)\n", "\\end{bmatrix} +\n", "\\beta\n", "\\begin{bmatrix}\n", " P_{11} & P_{12} \\cr P_{21} & P_{22}\n", "\\end{bmatrix}\n", "\\begin{bmatrix}\n", " b(1) \\cr b(2)\n", "\\end{bmatrix}\n", "$$\n", "\n", "These are $2$ equations in the $3$ unknowns\n", "$\\bar c, b(1), b(2)$.\n", "\n", "To get a third equation, we assume that at time $t=0$, $b_0$\n", "is the debt due; and we assume that at time $t=0$, the Markov\n", "state $s_0 =1$\n", "\n", "(We could instead have assumed that at time $t=0$ the Markov state $s_0 = 2$, which would affect our answer as we shall see)\n", "\n", "Since we have assumed that $s_0 = 1$, the budget constraint at time $t=0$ is\n", "\n", "```{math}\n", ":label: cs_5\n", "\n", "\\bar c + b_0 = y(1) + q(1 \\,|\\, 1) b(1) + q(2\\,|\\,1) b(2)\n", "```\n", "\n", "where $b_0$ is the (exogenous) debt the consumer is assumed to bring into period $0$\n", "\n", "If we substitute {eq}`cs_5` into the first equation of {eq}`cs_4a` and rearrange, we\n", "discover that\n", "\n", "```{math}\n", ":label: cs_6\n", "\n", "b(1) = b_0\n", "```\n", "\n", "We can then use the second equation of {eq}`cs_4a` to deduce the restriction\n", "\n", "```{math}\n", ":label: cs_7\n", "\n", "y(1) - y(2) + [q(1\\,|\\, 1) - q(1\\,|\\, 2) - 1 ] b_0 +\n", "[q(2\\,|\\,1) + 1 - q(2 \\,|\\, 2) ] b(2) = 0 ,\n", "```\n", "\n", "an equation that we can solve for the unknown $b(2)$.\n", "\n", "Knowing $b(1)$ and $b(2)$, we can solve equation {eq}`cs_5` for the constant level of consumption $\\bar c$.\n", "\n", "### Key Outcomes\n", "\n", "The preceding calculations indicate that in the complete markets version\n", "of our model, we obtain the following striking results:\n", "\n", "* The consumer chooses to make consumption perfectly constant across\n", " time and across Markov states.\n", "* State-contingent debt purchases $b_{t+1}(s_{t+1} = j | s_t = i)$ depend only on $j$\n", "* If the initial Markov state is $s_0 =j$ and initial consumer debt is $b_0$, then debt in Markov state $j$ satisfied $b(j) = b_0$\n", "\n", "To summarize what we have achieved up to now, we have computed the constant level of\n", "consumption $\\bar c$ and indicated how that level depends on the underlying specifications of preferences, Arrow securities prices, the stochastic process of exogenous nonfinancial income, and the initial debt level $b_0$\n", "\n", "* The consumer's debt neither accumulates, nor decumulates, nor drifts --\n", " instead, the debt level each period is an exact function of the Markov\n", " state, so in the two-state Markov case, it switches between two\n", " values.\n", "* We have verified guess {eq}`eq_guess`.\n", "* When the state $s_t$ returns to the initial state $s_0$, debt returns to the initial debt level.\n", "* Debt levels in all other states depend on virtually all remaining parameters of the model.\n", "\n", "### Code\n", "\n", "Here's some code that, among other things, contains a function called consumption_complete().\n", "\n", "This function computes $\\{ b(i) \\}_{i=1}^{N}, \\bar c$ as outcomes given a set of parameters for the general case with $N$ Markov states\n", "under the assumption of complete markets" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "class ConsumptionProblem:\n", " \"\"\"\n", " The data for a consumption problem, including some default values.\n", " \"\"\"\n", "\n", " def __init__(self,\n", " β=.96,\n", " y=[2, 1.5],\n", " b0=3,\n", " P=[[.8, .2],\n", " [.4, .6]],\n", " init=0):\n", " \"\"\"\n", " Parameters\n", " ----------\n", "\n", " β : discount factor\n", " y : list containing the two income levels\n", " b0 : debt in period 0 (= initial state debt level)\n", " P : 2x2 transition matrix\n", " init : index of initial state s0\n", " \"\"\"\n", " self.β = β\n", " self.y = np.asarray(y)\n", " self.b0 = b0\n", " self.P = np.asarray(P)\n", " self.init = init\n", "\n", " def simulate(self, N_simul=80, random_state=1):\n", " \"\"\"\n", " Parameters\n", " ----------\n", "\n", " N_simul : number of periods for simulation\n", " random_state : random state for simulating Markov chain\n", " \"\"\"\n", " # For the simulation define a quantecon MC class\n", " mc = qe.MarkovChain(self.P)\n", " s_path = mc.simulate(N_simul, init=self.init, random_state=random_state)\n", "\n", " return s_path\n", "\n", "\n", "def consumption_complete(cp):\n", " \"\"\"\n", " Computes endogenous values for the complete market case.\n", "\n", " Parameters\n", " ----------\n", "\n", " cp : instance of ConsumptionProblem\n", "\n", " Returns\n", " -------\n", "\n", " c_bar : constant consumption\n", " b : optimal debt in each state\n", "\n", " associated with the price system\n", "\n", " Q = β * P\n", " \"\"\"\n", " β, P, y, b0, init = cp.β, cp.P, cp.y, cp.b0, cp.init # Unpack\n", "\n", " Q = β * P # assumed price system\n", "\n", " # construct matrices of augmented equation system\n", " n = P.shape[0] + 1\n", "\n", " y_aug = np.empty((n, 1))\n", " y_aug[0, 0] = y[init] - b0\n", " y_aug[1:, 0] = y\n", "\n", " Q_aug = np.zeros((n, n))\n", " Q_aug[0, 1:] = Q[init, :]\n", " Q_aug[1:, 1:] = Q\n", "\n", " A = np.zeros((n, n))\n", " A[:, 0] = 1\n", " A[1:, 1:] = np.eye(n-1)\n", "\n", " x = np.linalg.inv(A - Q_aug) @ y_aug\n", "\n", " c_bar = x[0, 0]\n", " b = x[1:, 0]\n", "\n", " return c_bar, b\n", "\n", "\n", "def consumption_incomplete(cp, s_path):\n", " \"\"\"\n", " Computes endogenous values for the incomplete market case.\n", "\n", " Parameters\n", " ----------\n", "\n", " cp : instance of ConsumptionProblem\n", " s_path : the path of states\n", " \"\"\"\n", " β, P, y, b0 = cp.β, cp.P, cp.y, cp.b0 # Unpack\n", "\n", " N_simul = len(s_path)\n", "\n", " # Useful variables\n", " n = len(y)\n", " y.shape = (n, 1)\n", " v = np.linalg.inv(np.eye(n) - β * P) @ y\n", "\n", " # Store consumption and debt path\n", " b_path, c_path = np.ones(N_simul+1), np.ones(N_simul)\n", " b_path[0] = b0\n", "\n", " # Optimal decisions from (12) and (13)\n", " db = ((1 - β) * v - y) / β\n", "\n", " for i, s in enumerate(s_path):\n", " c_path[i] = (1 - β) * (v - b_path[i] * np.ones((n, 1)))[s, 0]\n", " b_path[i + 1] = b_path[i] + db[s, 0]\n", "\n", " return c_path, b_path[:-1], y[s_path]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's test by checking that $\\bar c$ and $b_2$ satisfy the budget constraint" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cp = ConsumptionProblem()\n", "c_bar, b = consumption_complete(cp)\n", "np.isclose(c_bar + b[1] - cp.y[1] - (cp.β * cp.P)[1, :] @ b, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, we'll take the outcomes produced by this code -- in particular the implied\n", "consumption and debt paths -- and compare them with outcomes\n", "from an incomplete markets model in the spirit of Hall {cite}`Hall1978`\n", "\n", "## Model 2 (One-Period Risk-Free Debt Only)\n", "\n", "This is a version of the original models of Hall (1978)\n", "in which the consumer's ability to substitute intertemporally is\n", "constrained by his ability to buy or sell only one security, a risk-free\n", "one-period bond bearing a constant gross interest rate that equals\n", "$\\beta^{-1}$.\n", "\n", "Given an initial debt $b_0$ at time $0$, the\n", "consumer faces a sequence of budget constraints\n", "\n", "$$\n", "c_t + b_t = y_t + \\beta b_{t+1}, \\quad t \\geq 0\n", "$$\n", "\n", "where $\\beta$ is the price at time $t$ of a risk-free claim\n", "on one unit of time consumption at time $t+1$.\n", "\n", "First-order conditions for the consumer's problem are\n", "\n", "$$\n", "\\sum_{j} u'(c_{t+1,j}) P_{ij} = u'(c_{t, i})\n", "$$\n", "\n", "For our assumed quadratic utility function this implies\n", "\n", "```{math}\n", ":label: cs_8\n", "\n", "\\sum_j c_{t+1,j} P_{ij} = c_{t,i}\n", "```\n", "\n", "which for our finite-state Markov setting is Hall's (1978) conclusion that consumption follows a random walk.\n", "\n", "As we saw in our first lecture on the [permanent income model](https://python-intro.quantecon.org/perm_income.html), this leads to\n", "\n", "```{math}\n", ":label: cs_9\n", "\n", "b_t = \\mathbb E_t \\sum_{j=0}^\\infty \\beta^j y_{t+j} - (1 -\\beta)^{-1} c_t\n", "```\n", "\n", "and\n", "\n", "```{math}\n", ":label: cs_10\n", "\n", "c_t = (1-\\beta)\n", " \\left[\n", " \\mathbb E_t \\sum_{j=0}^\\infty \\beta^j y_{t+j} - b_t\n", " \\right]\n", "```\n", "\n", "Equation {eq}`cs_10` expresses $c_t$ as a net interest rate factor $1 - \\beta$ times the sum\n", "of the expected present value of nonfinancial income $\\mathbb E_t \\sum_{j=0}^\\infty \\beta^j y_{t+j}$ and financial wealth $-b_t$.\n", "\n", "Substituting {eq}`cs_10` into the one-period budget constraint and rearranging leads to\n", "\n", "```{math}\n", ":label: cs_11\n", "\n", "b_{t+1} - b_t\n", "= \\beta^{-1} \\left[ (1-\\beta)\n", "\\mathbb E_t \\sum_{j=0}^\\infty\\beta^j y_{t+j} - y_t \\right]\n", "```\n", "\n", "Now let's calculate the key term $\\mathbb E_t \\sum_{j=0}^\\infty\\beta^j y_{t+j}$ in our finite Markov chain setting.\n", "\n", "Define\n", "\n", "$$\n", "v_t := \\mathbb E_t \\sum_{j=0}^\\infty \\beta^j y_{t+j}\n", "$$\n", "\n", "which in the spirit of dynamic programming we can write as a *Bellman equation*\n", "\n", "$$\n", "v_t := y_t + \\beta \\mathbb E_t v_{t+1}\n", "$$\n", "\n", "In our two-state Markov chain setting, $v_t = v(1)$ when $s_t= 1$ and $v_t = v(2)$ when $s_t=2$.\n", "\n", "Therefore, we can write our Bellman equation as\n", "\n", "$$\n", "\\begin{aligned}\n", " v(1) & = y(1) + \\beta P_{11} v(1) + \\beta P_{12} v(2)\n", " \\\\\n", " v(2) & = y(2) + \\beta P_{21} v(1) + \\beta P_{22} v(2)\n", "\\end{aligned}\n", "$$\n", "\n", "or\n", "\n", "$$\n", "\\vec v = \\vec y + \\beta P \\vec v\n", "$$\n", "\n", "where $\\vec v = \\begin{bmatrix} v(1) \\cr v(2) \\end{bmatrix}$ and $\\vec y = \\begin{bmatrix} y(1) \\cr y(2) \\end{bmatrix}$.\n", "\n", "We can also write the last expression as\n", "\n", "$$\n", "\\vec v = (I - \\beta P)^{-1} \\vec y\n", "$$\n", "\n", "In our finite Markov chain setting, from expression {eq}`cs_10`, consumption at date $t$ when debt is $b_t$ and the Markov state today is $s_t = i$ is evidently\n", "\n", "```{math}\n", ":label: cs_12\n", "\n", "c(b_t, i) = (1 - \\beta) \\left( [(I - \\beta P)^{-1} \\vec y]_i - b_t \\right)\n", "```\n", "\n", "and the increment to debt is\n", "\n", "```{math}\n", ":label: cs_13\n", "\n", "b_{t+1} - b_t = \\beta^{-1} [ (1- \\beta) v(i) - y(i) ]\n", "```\n", "\n", "### Summary of Outcomes\n", "\n", "In contrast to outcomes in the complete markets model, in the incomplete\n", "markets model\n", "\n", "- consumption drifts over time as a random walk; the level of\n", " consumption at time $t$ depends on the level of debt that the\n", " consumer brings into the period as well as the expected discounted\n", " present value of nonfinancial income at $t$.\n", "- the consumer's debt drifts upward over time in response to low\n", " realizations of nonfinancial income and drifts downward over time in\n", " response to high realizations of nonfinancial income.\n", "- the drift over time in the consumer's debt and the dependence of\n", " current consumption on today's debt level account for the drift over\n", " time in consumption.\n", "\n", "### The Incomplete Markets Model\n", "\n", "The code above also contains a function called consumption_incomplete() that uses {eq}`cs_12` and {eq}`cs_13` to\n", "\n", "* simulate paths of $y_t, c_t, b_{t+1}$\n", "* plot these against values of $\\bar c, b(s_1), b(s_2)$ found in a corresponding complete markets economy\n", "\n", "Let's try this, using the same parameters in both complete and incomplete markets economies" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { "image/png": "/Users/matthewmckay/repos-collab/phd-macro-theory-book/_build/jupyter_execute/smoothing_11_0.png" }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cp = ConsumptionProblem()\n", "s_path = cp.simulate()\n", "N_simul = len(s_path)\n", "\n", "c_bar, debt_complete = consumption_complete(cp)\n", "\n", "c_path, debt_path, y_path = consumption_incomplete(cp, s_path)\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(15, 5))\n", "\n", "ax[0].set_title('Consumption paths')\n", "ax[0].plot(np.arange(N_simul), c_path, label='incomplete market')\n", "ax[0].plot(np.arange(N_simul), c_bar * np.ones(N_simul),\n", " label='complete market')\n", "ax[0].plot(np.arange(N_simul), y_path, label='income', alpha=.6, ls='--')\n", "ax[0].legend()\n", "ax[0].set_xlabel('Periods')\n", "\n", "ax[1].set_title('Debt paths')\n", "ax[1].plot(np.arange(N_simul), debt_path, label='incomplete market')\n", "ax[1].plot(np.arange(N_simul), debt_complete[s_path],\n", " label='complete market')\n", "ax[1].plot(np.arange(N_simul), y_path, label='income', alpha=.6, ls='--')\n", "ax[1].legend()\n", "ax[1].axhline(0, color='k', ls='--')\n", "ax[1].set_xlabel('Periods')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the graph on the left, for the same sample path of nonfinancial\n", "income $y_t$, notice that\n", "\n", "* consumption is constant when there are complete markets, but takes a random walk in the incomplete markets version of the model.\n", "* the consumer's debt oscillates between two values that are functions\n", " of the Markov state in the complete markets model, while the\n", " consumer's debt drifts in a \"unit root\" fashion in the incomplete\n", " markets economy.\n", "\n", "### A sequel\n", "\n", "In {doc}`tax smoothing with complete and incomplete markets `, we reinterpret the mathematics and Python code presented in this lecture in order\n", "to construct tax-smoothing models in the incomplete markets tradition of Barro {cite}`Barro1979` as well as in the complete markets tradition of Lucas and Stokey {cite}`LucasStokey1983`." ] } ], "metadata": { "jupytext": { "text_representation": { "extension": ".md", "format_name": "myst" } }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" }, "source_map": [ 10, 32, 37, 81, 87, 268, 342, 619, 740, 744, 748, 901, 930 ] }, "nbformat": 4, "nbformat_minor": 4 }