{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# How to pay for a war: part 2\n", "\n", "### An application of Markov jump linear quadratic dynamic programming\n", "\n", "#### By [Sebastian Graves](https://github.com/sebgraves) and [Thomas J. Sargent](http://www.tomsargent.com/)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook is a [sequel to an earlier notebook](https://github.com/QuantEcon/TaxSmoothing/blob/master/Tax_Smoothing_1.ipynb).\n", "\n", "We use Markov jump linear quadratic (LQ) dynamic programming problems to implement some suggestions by Barro (1999, 2003) for extending his classic 1979 model of tax smoothing.\n", "\n", "Barro's 1979 model is about a government that borrows and lends in order to help it minimize an intertemporal measure of distortions caused by taxes. Technically, Barro's 1979 model looks a lot like a consumption smoothing model. Our generalizations of his 1979 model will also look like a souped up consumption smoothing model.\n", "\n", "Tractability induced Barro in 1979 to assume that \n", "\n", " * the government trades only one-period risk-free debt, and \n", " \n", " * the one-period risk-free interest rate is constant. \n", " \n", " \n", "In our [earlier notebook](https://github.com/QuantEcon/TaxSmoothing/blob/master/Tax_Smoothing_1.ipynb) we relaxed the second of these assumptions but not the first. In particular, we used *Markov jump linear quadratic dynamic programming* to allow the exogenous interest rate to vary over time.\n", "\n", "In this notebook, we add a maturity composition decision to the government's problem by expanding the dimension of the state.\n", "\n", "\n", " \n", "We assume \n", "\n", " * that the government borrows or saves in the form of risk-free bonds of maturities $1, 2, \\ldots , H$\n", " \n", " * that interest rates on those bonds are time-varying and in particular governed by a jointly stationary stochastic process.\n", "\n", "\n", "###### Two example specifications\n", "\n", "We'll describe two possible specifications. \n", "\n", " * In one specification, each period the government issues zero coupon bonds of one- and two-period maturities and redeems them only when they mature. In this version, the maturity structure of government debt is partly inherited from the past at each date.\n", " \n", " * In the second specification, the government redesigns the maturity structure of the debt each period. \n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A model with two-period debt and no restructuring\n", "\n", "\n", "Let $T_t$ denote tax collections, $\\beta$ a discount factor, $b_{t,t+1}$ time $t+1$ goods that the government promises to pay at $t$, $b_{t,t+2}$ time\n", "$t+2$ goods that the government promises to pay at time $t$, $G_t$ government purchases, $p_{t,t+1}$ the number of time $t$ goods received per time $t+1$ goods promised, and $p_{t,t+2}$ the number of time $t$ goods received per time\n", "$t+2$ goods promised.\n", "\n", "Evidently, $p_{t, t+1}, p_{t,t+2}$ are inversely\n", "related to appropriate corresponding gross interest rates on government debt.\n", "\n", "In the spirit of Barro (1979), the stochastic process of government expenditures is exogenous. \n", "\n", "Given initial conditions $b_{-2,0}, b_{-1,0}, z_0, i_0$, where $i_0$ is the initial Markov state, the government chooses\n", "a contingency plan for $\\{b_{t, t+1}, b_{t,t+2}, T_t\\}_{t=0}^\\infty$ to maximize\n", "\n", "$$- E_0 \\sum_{t=0}^\\infty \\beta^t \\left[ T_t^2 + c_1( b_{t,t+1} - b_{t,t+2})^2 \\right]$$\n", "\n", "subject to the constraints\n", "\n", "\\begin{align*}\n", " T_t & = G_t + b_{t-2,t} + b_{t-1,t} - p_{t,t+2} b_{t,t+2} - p_{t,t+1} b_{t,t+1} \\cr\n", " G_t & = U_{g,t} z_t \\cr\n", " z_{t+1} & = A_{22,t} z_t + C_{2,t} w_{t+1} \\cr\n", " \\begin{bmatrix}\n", " p_{t,t+1} \\cr\n", " p_{t,t+2} \\cr\n", " U_{g,t} \\cr\n", " A_{22,t} \\cr\n", " C_{2,t}\n", " \\end{bmatrix} & \\sim \\textrm{functions of Markov state with transition matrix } \\Pi \\end{align*}\n", "\n", "Here $w_{t+1} \\sim {\\cal N}(0,I)$ and $\\Pi_{ij}$ is the probability that the Markov state\n", "moves from state $i$ to state $j$ in one period. The variables $T_t, b_{t, t+1}, b_{t,t+2}$ are *control* variables chosen at $t$, while the variables $b_{t-1,t}, b_{t-2,t}$ are endogenous state variables inherited from the past at time $t$ and $p_{t,t+1}, p_{t,t+2}$ are exogenous state variables at time $t$. \n", "\n", "The parameter $c_1$ imposes a penalty on the government's issuing different quantities of one and two-period debt. This penalty deters the government from taking large \"long-short\" positions in debt of different maturities. An example below will show this in action.\n", "\n", "As well as extending the model to allow for a maturity decision for government debt, we can also in principle allow the matrices $U_{g,t}, A_{22,t}, C_{2,t}$ to depend on the Markov state.\n", "\n", "### Mapping the two-period model into an LQ Markov jump problem\n", "\n", "First define\n", "\n", "$$\\hat b_t = b_{t-1,t} + b_{t-2,t} ,$$\n", "\n", "which is debt due at time $t$. Then define the endogenous part of the state:\n", "\n", "$$\\bar b_t = \\begin{bmatrix}\n", " \\hat b_t \\cr\n", " b_{t-1,t+1}\n", " \\end{bmatrix}\n", "$$\n", " \n", " and the complete state\n", "$$x_t = \\begin{bmatrix} \\bar b_t \\cr\n", " z_t\n", " \\end{bmatrix}$$\n", " \n", "and the control vector\n", "$$u_{t} = \\begin{bmatrix}\n", " b_{t,t+1} \\cr\n", " b_{t,t+2}\n", " \\end{bmatrix}$$\n", " \n", "The endogenous part of state vector follows the law of motion:\n", "\n", "$$\\begin{bmatrix}\n", " \\hat b_{t+1} \\cr\n", " b_{t,t+2}\n", " \\end{bmatrix}\n", " =\n", " \\begin{bmatrix}\n", " 0 & 1 \\cr\n", " 0 & 0\n", " \\end{bmatrix}\n", " \\begin{bmatrix}\n", " \\hat b_{t} \\cr\n", " b_{t-1,t+1}\n", " \\end{bmatrix}\n", "+\n", " \\begin{bmatrix}\n", " 1 & 0 \\cr\n", " 0 & 1 \\cr\n", " \\end{bmatrix}\n", " \\begin{bmatrix}\n", " b_{t,t+1} \\cr\n", " b_{t,t+2}\n", " \\end{bmatrix}\n", "$$\n", "\n", "or\n", "\n", "$$\\bar b_{t+1} = A_{11} \\bar b_t + B_1 u_t$$\n", "\n", "Define the following functions of the state\n", "\n", "$$G_t = S_{G,t} x_t, \\quad \\hat b_t = S_1 x_t$$\n", "\n", "and\n", "\n", "$$M_t = \\begin{bmatrix} - p_{t,t+1} & - p_{t,t+2} \\end{bmatrix}$$\n", "\n", "where $p_{t,t+1}$ is the discount on one period loans in the discrete Markov state at time $t$ and\n", "$p_{t,t+2}$ is the discount on two period loans in the discrete Markov state\n", "\n", "Define $$S_t = S_{G,t} + S_1 .$$\n", "\n", "Note that in discrete Markov state $i$\n", "\n", "$$T_t = M_t u_t + S_t x_t .$$\n", "\n", "It follows that\n", "\n", "$$T_t^2 = x_t' S_t' S_t x_t + u_t' M_t' M_t u_t + 2 u_t' M_t' S_t x_t$$\n", "\n", "or\n", "\n", "$$T_t^2 = x_t'R_t x_t + u_t' Q_t u_t + 2 u_t' W_t x_t$$\n", "\n", "where\n", "\n", "$$R_t = S_t'S_t, \\quad Q_t = M_t' M_t, \\quad W_t = M_t' S_t$$\n", "\n", "Because the payoff function also includes the penalty parameter on issuing debt of different maturities, we have:\n", "\n", "$$T_t^2 + c_1( b_{t,t+1} - b_{t,t+2})^2 = x_t'R_t x_t + u_t' Q_t u_t + 2 u_t' W_t x_t + c_1 u_t'Q^c u_t$$\n", "\n", "where $Q^c = \\begin{bmatrix} 1 & -1 \\\\ -1 & 1 \\end{bmatrix}$. Therefore, the overall Q matrix for the Markov jump LQ problem is:\n", "\n", "$$Q_t^c = Q_t + c_1Q^c$$\n", "\n", "The law of motion of the state in all discrete Markov states $i$ is\n", "\n", "$$x_{t+1} = A_t x_t + B u_t + C_t w_{t+1}$$\n", "\n", "where\n", "\n", "$$A_t = \\begin{bmatrix} A_{11} & 0 \\cr\n", " 0 & A_{22,t}\n", " \\end{bmatrix}, \\quad\n", " B = \\begin{bmatrix}\n", " B_1 \\cr\n", " 0\n", " \\end{bmatrix}, \\quad\n", " C_t = \\begin{bmatrix} 0 \\cr C_{2,t} \\end{bmatrix}\n", "$$\n", "\n", "Thus, in this problem all the matrices apart from $B$ may depend on the Markov state at time $t$.\n", "\n", "## Function to map two-period model into a Markov jump linear quadratic control problem\n", "As shown in the [previous notebook](https://github.com/QuantEcon/TaxSmoothing/blob/master/Tax_Smoothing_1.ipynb), the LQ_Markov class can solve Markov jump LQ problems when given the $A,B,C,R,Q,W$ matrices for each state of the world. The below function maps the primitive matrices and parameters from the above two-period model into the matrices that the LQ_Markov class requires:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import quantecon as qe\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "def LQ_markov_mapping(A22,C2,Ug,p1,p2,c1=0):\n", "\n", " \"\"\"\n", " Function which takes A22, C2, Ug, p_{t,t+1},p_{t,t+2} and penalty parameter c1, and returns the \n", " required matrices for the LQ_Markov model: A,B,C,R,Q,W.\n", " This version uses the condensed version of the endogenous state.\n", " \"\"\"\n", " \n", " # Make sure all matrices can be treated as 2D arrays #\n", " A22 = np.atleast_2d(A22)\n", " C2 = np.atleast_2d(C2)\n", " Ug = np.atleast_2d(Ug)\n", " p1 = np.atleast_2d(p1)\n", " p2 = np.atleast_2d(p2)\n", " \n", " # Find number of states (z) and shocks (w)\n", " nz, nw = C2.shape\n", " \n", " # Create A11, B1, S1, S2, Sg, S matrices\n", " A11 = np.zeros((2,2))\n", " A11[0,1]=1\n", " \n", " B1 = np.eye(2)\n", " \n", " S1 = np.hstack((np.eye(1),np.zeros((1,nz+1))))\n", " Sg = np.hstack((np.zeros((1,2)),Ug))\n", " S = S1 + Sg\n", " \n", " # Create M matrix\n", " M = np.hstack((-p1,-p2))\n", " \n", " # Create A,B,C matrices\n", " A_T = np.hstack((A11,np.zeros((2,nz))))\n", " A_B = np.hstack((np.zeros((nz,2)),A22))\n", " A = np.vstack((A_T,A_B))\n", " \n", " B = np.vstack((B1,np.zeros((nz,2))))\n", " \n", " C = np.vstack((np.zeros((2,nw)),C2))\n", "\n", " # Create Q^c matrix\n", " Qc = np.array([[1,-1],[-1,1]])\n", " \n", " # Create R,Q,W matrices\n", " \n", " R = S.T.dot(S)\n", " Q = M.T.dot(M) + c1*Qc\n", " W = M.T.dot(S)\n", " \n", " return A,B,C,R,Q,W" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the above function, we can proceed to solve the model in two steps:\n", "\n", "1. Use **LQ_markov_mapping** to map $U_{g,t}, A_{22,t}, C_{2,t}, p_{t,t+1}, p_{t,t+2}$ into the $A,B,C,R,Q,W$ matrices for each of the n states of the world.\n", "\n", "2. Use the **LQ_markov** class to solve the resulting n-state Markov jump LQ problem.\n", "\n", "### Example showing the importance of the penalty on different issuance across maturities\n", "\n", "To implement a simple example of the two-period model, we assume that $G_t$ follows an AR(1) process: \n", "\n", "$$G_{t+1} = \\bar G + \\rho G_t + \\sigma w_{t+1}$$\n", "\n", "To do this, we set $z_t = \\begin{bmatrix} 1 \\\\ G_t \\end{bmatrix}$, and consequently:\n", "\n", "$$A_{22} = \\begin{bmatrix} 1 & 0 \\\\ \\bar G & \\rho \\end{bmatrix} \\hspace{2mm} , \\hspace{2mm} C_2 = \\begin{bmatrix} 0 \\\\ \\sigma \\end{bmatrix} \\hspace{2mm} , \\hspace{2mm} U_g = \\begin{bmatrix} 0 & 1 \\end{bmatrix}$$\n", "\n", "Therefore, in this example, $A_{22}, C_2$ and $U_g$ are not time-varying.\n", "\n", "We will assume that there are two states of the world, one with a flatter yield curve, and one with a steeper yield curve. In state 1, prices are:\n", "\n", "$$p^1_{t,t+1} = \\beta \\hspace{2mm} , \\hspace{2mm} p^1_{t,t+2} = \\beta^2 - 0.02$$\n", "\n", "and in state 2, prices are:\n", "\n", "$$p^2_{t,t+1} = \\beta \\hspace{2mm} , \\hspace{2mm} p^2_{t,t+2} = \\beta^2 + 0.02$$\n", "\n", "We first solve the model with no penalty parameter on different issuance across maturities, i.e. $c_1 = 0$. We also need to specify a transition matrix for the state of the world, we use:\n", "\n", "$$\\Pi = \\begin{bmatrix} 0.9 & 0.1 \\\\ 0.1 & 0.9 \\end{bmatrix}$$\n", "\n", "Thus, each Markov state is persisent, and there is an equal chance of moving from one to the other.\n", "\n", "(You should download [the file lq_markov.py](https://github.com/QuantEcon/TaxSmoothing/blob/master/lq_markov.py) and put it in the same directory as this notebook before you execute the next line.)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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fhE4xZoNZar9hGIYRjVnuDcMwDMMwStAoAfXeeQe23RZGj4ZRo2DDDeOdl5X2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\nK6/U7AvPPacLEY0u7m++Wb0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ZLfd/+5tmOvrLX5L5vsjyvTYyqYp759wezrlbnXNvOOde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iY+w4QQQgghhBBCCCkKOveEEEIIIYQQQojnUNwTQgghhBBCCCGeQ3FPCCGE\nEEIIIYR4DsU9IYQQQgghhBDiORT3hBBCCCGEEEKI51DcE0IIIYQQQgghnkNxTwghhBBCCCGEeA7F\nPSGEEEIIIYQQ4jkU94QQQgghhBBCiOdQ3BNCCCGEEEIIIZ5DcU8IIYQQQgghhHgOxT0hhBBCCCGE\nEOI5/x/DLgBkzWvhOQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from lq_markov import LQ_Markov\n", "from collections import namedtuple\n", "\n", "# Create namedtuple to keep the R,Q,A,B,C,W matrices for each state of the world\n", "world = namedtuple('world', ['A', 'B', 'C', 'R', 'Q', 'W'])\n", "\n", "# Model parameters \n", "beta, Gbar, rho, sigma, c1 = 0.95, 5, 0.8, 1, 0\n", "p1, p2, p3, p4 = beta, beta**2 - 0.02, beta, beta**2 + 0.02\n", "\n", "# Basic model matrices\n", "A22 = np.array([[1,0],[Gbar, rho],])\n", "C_2 = np.array([[0], [sigma]])\n", "Ug = np.array([[0,1]])\n", "\n", "A1,B1,C1,R1,Q1,W1 = LQ_markov_mapping(A22,C_2,Ug,p1,p2,c1)\n", "A2,B2,C2,R2,Q2,W2 = LQ_markov_mapping(A22,C_2,Ug,p3,p4,c1)\n", "\n", "# Small penalties on debt required to implement no-ponzi scheme\n", "R1[0,0] = R1[0,0] + 1e-9\n", "R2[0,0] = R2[0,0] + 1e-9\n", "\n", "#Sets up the two states of the world\n", "v1 = world(A=A1,B=B1,C=C1,R=R1,Q=Q1,W=W1)\n", "v2 = world(A=A2,B=B2,C=C2,R=R2,Q=Q2,W=W2)\n", "\n", "Pi = np.array([[0.9,0.1],[0.1,0.9]])\n", "\n", "# Solve the model using the LQ_Markov class\n", "MJLQBarro = LQ_Markov(beta,Pi,v1,v2)\n", "\n", "# Simulate the model\n", "x0 = np.array([[100,50,1,10]])\n", "x,u,w,t = MJLQBarro.compute_sequence(x0,ts_length=300)\n", "\n", "#Plot of one and two-period debt issuance\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.plot(u[0,:])\n", "plt.title('One-period debt issuance')\n", "plt.xlabel('Time')\n", "plt.subplot(122)\n", "plt.plot(u[1,:])\n", "plt.title('Two-period debt issuance')\n", "plt.xlabel('Time')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above simulations show that when no penalty is imposed on different issuances across maturities, the government has an incentive to take large \"long-short\" positions in debt of different maturities. To prevent such an outcome, we now set $c_1 = 0.01$. This penalty is enough to ensure that the government issues positive quantities of both one and two-period debt:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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8AtxtZv0BzOx04CRgODAYmA/8x8w6ZNpwvWXMH38cxowpdy1ERKQcFJiLiIhI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\nHsp+2mlUZdkJq2MOmPnlQPaEeUUF/e4nXacQQtkZN2G+fn3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ev24dcO21VCzw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fzV0kICPSn42u1V/M1PKDtjFeavvgrsvTfw9NPOY8hqKHt1tb/PcFTshHmYUPbqaqB7d+dOK0k7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\nMAzArQBqAJwJABsE+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Put small penalty on different issuance across maturities\n", "c1 = 0.01\n", "\n", "A1,B1,C1,R1,Q1,W1 = LQ_markov_mapping(A22,C_2,Ug,p1,p2,c1)\n", "A2,B2,C2,R2,Q2,W2 = LQ_markov_mapping(A22,C_2,Ug,p3,p4,c1)\n", "\n", "# Small penalties on debt required to implement no-ponzi scheme\n", "R1[0,0] = R1[0,0] + 1e-9\n", "R2[0,0] = R2[0,0] + 1e-9\n", "\n", "#Sets up the two states of the world\n", "v1 = world(A=A1,B=B1,C=C1,R=R1,Q=Q1,W=W1)\n", "v2 = world(A=A2,B=B2,C=C2,R=R2,Q=Q2,W=W2)\n", "\n", "# Solve the model using the LQ_Markov class\n", "MJLQBarro2 = LQ_Markov(beta,Pi,v1,v2)\n", "\n", "# Simulate the model\n", "x,u,w,t = MJLQBarro2.compute_sequence(x0,ts_length=300)\n", "\n", "#Plot of one and two-period debt issuance\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.plot(u[0,:])\n", "plt.title('One-period debt issuance')\n", "plt.xlabel('Time')\n", "plt.subplot(122)\n", "plt.plot(u[1,:])\n", "plt.title('Two-period debt issuance')\n", "plt.xlabel('Time')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A model with restructuring\n", "\n", "This model alters two features of the previous model:\n", "\n", "1. The maxium horizon of government debt is now extended to a general *H* periods.\n", "\n", "2. The government is able to redesign the maturity structure of debt every period.\n", "\n", "We impose a cost on adjusting issuance of each maturity by amending the payoff function to become:\n", "\n", "$$T_t^2 + \\sum_{j=0}^{H-1} c_2 (b_{t+j}^{t-1} - b_{t+j+1}^t)^2$$\n", "\n", "The government's budget constraint is now:\n", "\n", "\$$\n", "T_t + \\sum_{j=1}^Hp_{t,t+j} b_{t+j}^t = b_t^{t-1} + \\sum_{j=1}^{H-1} p_{t,t+j} b_{t+j}^{t-1} + G_t\n", "\$$\n", "\n", "To map this into the Markov Jump LQ framework, we define state and control variables. \n", "\n", "Let:\n", "\n", "$$\\bar b_t = \\begin{bmatrix} b^{t-1}_t \\\\ b^{t-1}_{t+1} \\\\ \\vdots \\\\ b^{t-1}_{t+H-1} \\end{bmatrix} \\hspace{2mm} , \\hspace{2mm} u_t = \\begin{bmatrix} b^{t}_{t+1} \\\\ b^{t}_{t+2} \\\\ \\vdots \\\\ b^{t}_{t+H} \\end{bmatrix}$$\n", "\n", "Thus, $\\bar b_t$ is the endogenous state (debt issued last period) and $u_t$ is the control (debt issued today). As before, we will also have the exogenous state $z_t$, which determines government spending. Therefore, the full state is:\n", "\n", "$$x_t = \\begin{bmatrix} \\bar b_t \\\\ z_t \\end{bmatrix}$$\n", "\n", "We also define a vector $p_t$ that contains the time $t$ price of goods in period $t + j$:\n", "\n", "$$p_t = \\begin{bmatrix} p_{t,t+1} \\\\ p_{t,t+2} \\\\ \\vdots \\\\ p_{t,t+H} \\end{bmatrix}$$\n", "\n", "Finally, we define three useful matrices $S_s, S_x, \\tilde S_x$:\n", "\n", "$$\\begin{bmatrix} p_{t,t+1} \\\\ p_{t,t+2} \\\\ \\vdots \\\\ p_{t,t+H-1} \\end{bmatrix} = S_s p_t \\text{ where } S_s = \\begin{bmatrix} 1 & 0 & 0 & \\cdots & 0 \\\\ 0 & 1 & 0 & \\cdots & 0 \\\\ \\vdots & & \\ddots & & \\\\ 0 & 0 & \\cdots & 1 & 0 \\end{bmatrix}$$\n", "\n", "\n", "$$\\begin{bmatrix} b^{t-1}_{t+1} \\\\ b^{t-1}_{t+2} \\\\ \\vdots \\\\ b^{t-1}_{t+T-1} \\end{bmatrix} = S_x \\bar b_t \\text{ where } S_x = \\begin{bmatrix} 0 & 1 & 0 & \\cdots & 0 \\\\ 0 & 0 & 1 & \\cdots & 0 \\\\ \\vdots & & & \\ddots & \\\\ 0 & 0 & \\cdots & 0 & 1 \\end{bmatrix}$$\n", "\n", "$$b^{t-1}_t = \\tilde S_x \\bar b_t \\text{ where } \\tilde S_x = \\begin{bmatrix} 1 & 0 & 0 & \\cdots & 0 \\end{bmatrix}$$\n", "\n", "In terms of dimensions, the first two matrices defined above are $(H-1) \\times H$. The last is $1 \\times H$. \n", "\n", "We can now write the government's budget constraint in matrix notation. Rearranging the government budget constraint gives:\n", "\n", "$$T_t = b_t^{t-1} + \\sum_{j=1}^{H-1} p_{t+j}^t b_{t+j}^{t-1} + G_t - \\sum_{j=1}^H p_{t+j}^t b_{t+j}^t$$\n", "\n", "or\n", "\n", "\$$\n", "T_t = \\tilde S_x \\bar b_t + (S_s p_t) \\cdot (S_x \\bar b_t) + U_g z_t - p_t \\cdot u_t\n", "\$$\n", "\n", "If we want to write this in terms of the full state, we have:\n", "\n", "$$T_t = \\begin{bmatrix} (\\tilde S_x + p_t'S_s'S_x) & Ug \\end{bmatrix} x_t - p_t' u_t$$\n", "\n", "To simplify the notation, let $S_t = \\begin{bmatrix} (\\tilde S_x + p_t'S_s'S_x) & Ug \\end{bmatrix}$.\n", "\n", "Then $$T_t = S_t x_t - p_t' u_t$$\n", "\n", "Therefore\n", "\n", "$$T_t^2 = x_t' R_t x_t + u_t ' Q_t u_t + 2 u_t'W_t x_t$$\n", "\n", "where\n", "\n", "$$R_t = S_t'S_t , \\hspace{5mm} Q_t = p_t p_t' , \\hspace{5mm} W_t = -p_t S_t$$\n", "\n", "Because the payoff function also includes the penalty parameter for rescheduling, we have:\n", "\n", "$$T_t^2 + \\sum_{j=0}^{H-1} c_2 (b_{t+j}^{t-1} - b_{t+j+1}^t)^2 = T_t^2 + c_2(\\bar b_t - u_t)'(\\bar b_t - u_t)$$\n", "\n", "Because the complete state is $x_t$ and not $\\bar b_t$, we rewrite this as:\n", "\n", "$$T_t^2 + c_2(S_c x_t - u_t)'(S_c x_t - u_t)$$\n", "\n", "where $S_c = \\begin{bmatrix} I & 0 \\end{bmatrix}$\n", "\n", "Multiplying this out gives:\n", "\n", "$$T_t^2 + c_2 x_t' S_c' S_c x_t - 2c_2 u_t' S_c x_t + c_2 u_t'u_t$$\n", "\n", "Therefore, with the cost term, we must amend our $R,Q,W$ matrices as follows:\n", "\n", "$$R^c_t = R_t + c_2 S_c'S_c$$\n", "$$Q^c_t = Q_t + c_2 I$$\n", "$$W^c_t = W_t - c_2 S_c$$\n", "\n", "To finish mapping into the Markov jump LQ setup, we need to construct the law of motion for the full state. This is simpler than in the previous setup, as we now have $\\bar b_{t+1} = u_t$. \n", "\n", "Therefore:\n", "\n", "\$$\n", "x_{t+1} \\equiv \\begin{bmatrix} \\bar b_{t+1} \\\\ z_{t+1} \\end{bmatrix} = A_t x_t + B u_t + C_t w_{t+1}\n", "\$$\n", "\n", "where\n", "\n", "$$A_t = \\begin{bmatrix} 0 & 0 \\\\ 0 & A_{22,t} \\end{bmatrix} , \\hspace{5mm} B = \\begin{bmatrix} I \\\\ 0 \\end{bmatrix} , \\hspace{5mm} C = \\begin{bmatrix} 0 \\\\ C_{2,t} \\end{bmatrix}$$\n", "\n", "This completes the mapping into a Markov jump LQ problem.\n", "\n", "## Function to map model with restructuring into a Markov jump linear quadratic control problem\n", "\n", "As with the previous model, we can use a function to map the primitives of the model with restructuring into the matrices that the LQ_Markov class requires:\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def LQ_markov_mapping_restruct(A22,C2,Ug,T,p_t,c=0):\n", "\n", " \"\"\"\n", " Function which takes A22, C2, T, p_t,c and returns the required matrices for the LQ_Markov model: A,B,C,R,Q,W\n", " Note, p_t should be a T by 1 matrix.\n", " c is the rescheduling cost (a scalar)\n", " This version uses the condensed version of the endogenous state.\n", " \"\"\"\n", " \n", " # Make sure all matrices can be treated as 2D arrays == #\n", " A22 = np.atleast_2d(A22)\n", " C2 = np.atleast_2d(C2)\n", " Ug = np.atleast_2d(Ug)\n", " p_t = np.atleast_2d(p_t)\n", " \n", " # Find number of states (z) and shocks (w)\n", " nz, nw = C2.shape\n", " \n", " # Create Sx,tSx,Ss,S_t matrices (tSx stands for \\tilde S_x)\n", " Ss = np.hstack((np.eye(T-1),np.zeros((T-1,1))))\n", " Sx = np.hstack((np.zeros((T-1,1)),np.eye(T-1)))\n", " tSx = np.zeros((1,T))\n", " tSx[0,0] = 1\n", "\n", " S_t = np.hstack((tSx + p_t.T.dot(Ss.T).dot(Sx), Ug))\n", " \n", " # Create A,B,C matrices\n", " A_T = np.hstack((np.zeros((T,T)),np.zeros((T,nz))))\n", " A_B = np.hstack((np.zeros((nz,T)),A22))\n", " A = np.vstack((A_T,A_B))\n", " \n", " B = np.vstack((np.eye(T),np.zeros((nz,T))))\n", " \n", " C = np.vstack((np.zeros((T,nw)),C2))\n", "\n", " # Create cost matrix Sc\n", " Sc = np.hstack((np.eye(T),np.zeros((T,nz))))\n", " \n", " # Create R_t,Q_t,W_t matrices\n", " \n", " R_c = S_t.T.dot(S_t) + c*Sc.T.dot(Sc)\n", " Q_c = p_t.dot(p_t.T) + c*np.eye(T)\n", " W_c = -p_t.dot(S_t) - c*Sc\n", " \n", " return A,B,C,R_c,Q_c,W_c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example model with restructuring\n", "\n", "As an example for the model with restructuring, consider this model where $H = 3$.\n", "\n", "We will assume that there are two states of the world, one with a flatter yield curve, and one with a steeper yield curve. In state 1, prices are:\n", "\n", "$$p^1_{t,t+1} = 0.9695 \\hspace{2mm} , \\hspace{2mm} p^1_{t,t+2} = 0.902 \\hspace{2mm} , \\hspace{2mm} p^1_{t,t+3} = 0.8369$$\n", "\n", "and in state 2, prices are:\n", "\n", "$$p^2_{t,t+1} = 0.9295 \\hspace{2mm} , \\hspace{2mm} p^2_{t,t+2} = 0.902 \\hspace{2mm} , \\hspace{2mm} p^2_{t,t+3} = 0.8769$$\n", "\n", "We will assume the same transition matrix and $G_t$ process as above." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# New model parameters\n", "H = 3\n", "p1 = np.array([[0.9695],[0.902],[0.8369]])\n", "p2 = np.array([[0.9295],[0.902],[0.8769]])\n", "Pi = np.array([[0.9,0.1],[0.1,0.9]])\n", "\n", "# Put penalty on different issuance across maturities\n", "c2 = 0.5\n", "\n", "A1,B1,C1,R1,Q1,W1 = LQ_markov_mapping_restruct(A22,C_2,Ug,H,p1,c2)\n", "A2,B2,C2,R2,Q2,W2 = LQ_markov_mapping_restruct(A22,C_2,Ug,H,p2,c2)\n", "\n", "# Small penalties on debt required to implement no-ponzi scheme\n", "R1[0,0] = R1[0,0] + 1e-9\n", "R1[1,1] = R1[1,1] + 1e-9\n", "R1[2,2] = R1[2,2] + 1e-9\n", "R2[0,0] = R2[0,0] + 1e-9\n", "R2[1,1] = R2[1,1] + 1e-9\n", "R2[2,2] = R2[2,2] + 1e-9\n", "\n", "#Sets up the two states of the world\n", "v1 = world(A=A1,B=B1,C=C1,R=R1,Q=Q1,W=W1)\n", "v2 = world(A=A2,B=B2,C=C2,R=R2,Q=Q2,W=W2)\n", "\n", "# Solve the model using the LQ_Markov class\n", "MJLQBarro3 = LQ_Markov(beta,Pi,v1,v2)\n", "\n", "x0 = np.array([[5000,5000,5000,1,10]])\n", "x,u,w,t = MJLQBarro3.compute_sequence(x0,ts_length=300)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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y2Il9Hm8c9cef53NwnVZbro7nP29mN+Kd37OBrWOeCbfgeuafZvb/8Li438Eb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plots of different maturities debt issuance\n", "\n", "plt.figure(figsize=(16,4))\n", "plt.subplot(141)\n", "plt.plot(u[0,:])\n", "plt.title('One-period debt issuance')\n", "plt.xlabel('Time')\n", "plt.subplot(142)\n", "plt.plot(u[1,:])\n", "plt.title('Two-period debt issuance')\n", "plt.xlabel('Time')\n", "plt.subplot(143)\n", "plt.plot(u[2,:])\n", "plt.title('Three-period debt issuance')\n", "plt.xlabel('Time')\n", "plt.subplot(144)\n", "plt.plot(u[0,:]+u[1,:]+u[2,:])\n", "plt.title('Total debt issuance')\n", "plt.xlabel('Time')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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boJnXk12WmSgUgxh0CSQiouAc5TSISA1ogDDeGFPgt3wydLz9C2YTDLKPAgA1jTHDnBeX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\nK6WsAR4BDqDKUTB/E2mSp5XAjCS7jNNmqJVSVlB9Z0dmaA9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot share of debt issuance which is short-term\n", "\n", "plt.plot(u[0,:]/(u[0,:]+u[1,:]+u[2,:]))\n", "plt.title('One-period debt issuance share')\n", "plt.xlabel('Time')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }