{
"cells": [
{
"cell_type": "markdown",
"id": "a40dfe7a-83c7-48da-bc4a-bdf4dc2da2ae",
"metadata": {},
"source": [
"# 1. Implement Real Business Cycle Model in MATLAB, Dynare, Python and Julia"
]
},
{
"cell_type": "markdown",
"id": "369bb94f-194a-452e-b238-24d9ee672b16",
"metadata": {},
"source": [
"DING Minjie, Spring 2025"
]
},
{
"cell_type": "markdown",
"id": "16c675fb-ace6-43bf-891a-9e5766962ef4",
"metadata": {},
"source": [
"In this tutorial, we will talk about:\n",
"\n",
"* 1. A Simple RBC Model Setting\n",
"* 2. RBC Model in MATLAB\n",
"* 3. Introduction to Dynare\n",
"* 4. RBC Model in Dynare\n",
"* 5. RBC Model with Occasional Binding\n",
"* 6. RBC Model in Python\n",
"* 7. RBC Model in Julia"
]
},
{
"cell_type": "markdown",
"id": "fbf24a6e-21a7-4602-9b01-6848010e3577",
"metadata": {},
"source": [
"_________________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "a1b5778d-678c-4f85-8ef3-495e6894aba8",
"metadata": {},
"source": [
"# 1. A Simple RBC Model Setting"
]
},
{
"cell_type": "markdown",
"id": "7b77c350-6ccb-4c4a-972c-a7abae915e01",
"metadata": {},
"source": [
"_________________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "7935e5fd-1449-47ad-917d-0f6854172914",
"metadata": {},
"source": [
"## Households\n",
"\n",
"The households maximize:\n",
"\n",
"$$\n",
"\\max E_{t}\\left[\\sum_{j=0}^{\\infty} \\beta^{j}\\left\\{\\frac{C_{t+j}^{1-1 / \\sigma}}{1-1 / \\sigma}-\\phi \\frac{N_{t+j}^{1+1 / \\eta}}{1+1 / \\eta}\\right\\}\\right],\n",
"$$\n",
"\n",
"where:\n",
"\n",
"- $C$ is consumption.\n",
"- $N$ is labor.\n",
"- $\\sigma$ is the intertemporal elasticity of substitution (IES).\n",
"- $\\eta$ is the Frisch elasticity of labor supply (the elasticity of hours worked to the wage rate). \n",
"\n",
"Households face two constraints:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\lambda: & C_{t}+I_{t}=W_{t} N_{t}+R_{t} K_{t} \\\\\n",
"q: & K_{t+1}=K_{t}(1-\\delta)+I_{t}\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"where:\n",
"\n",
"- $K$ is total investment in physical capital.\n"
]
},
{
"cell_type": "markdown",
"id": "dbbc512b-0848-40de-9851-b72c204463bb",
"metadata": {},
"source": [
"## Firm\n",
"\n",
"Firms maximize:\n",
"\n",
"$$\n",
"\\Pi_{t}=Y_{t}-W_{t} N_{t}-R_{t} K_{t}\n",
"$$\n",
"\n",
"where the production function is:\n",
"\n",
"$$\n",
"Y_{t}=A_{t} K_{t}^{\\alpha} N_{t}^{1-\\alpha}\n",
"$$\n",
"\n",
"We assume total factor productivity (TFP) evolves in an AR(1) process:\n",
"\n",
"$$\n",
"log(A_t) = \\rho log(A_{t-1}) + \\sigma \\epsilon_t\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"id": "5b2dff1b-4db7-483d-bb98-772c54298059",
"metadata": {},
"source": [
"## Recursive competitive equilibrium\n",
"\n",
"A Recursive Competitive Equilibrium consists of:\n",
"- Pricing functions: $W(K, A), R(K, A)$\n",
"- Policy functions of individual households: $K^{\\prime}(K, A), N(K, A), C(K, A)$\n",
"- Law of motion of TFP: $A^{\\prime} \\sim Q\\left(A^{\\prime} \\mid A\\right)$\n",
"\n",
"which satisfy:\n",
"1. Given $W(K, A), R(K, A)$ and rational expectations about future aggregates, $K^{\\prime}(K, A), N(K, A), C(K, A)$ are optimal.\n",
"2. Given $W(K, A), R(K, A)$, firms solve the maximization problem.\n",
"3. Markets clear: Labor market (trivial); Capital market (trivial); Goods market: $Y_{t}=C_{t}+I_{t}$.\n"
]
},
{
"cell_type": "markdown",
"id": "520db48c-4c8b-4e8c-b59b-e798ebd2089a",
"metadata": {},
"source": [
"An possible way to solve the model is to get a system of difference equations that govern the dynamical system, and then analyze those difference equations directly as we did before (without solving for the full equilibrium).\n",
"\n",
"In particular, from the first-order conditions (FOCs) from maximization problems and constraints (including goods market clearing condition), we can derive the following 9 equations for 9 endogenous variables: $ N_{t}, W_{t}, C_{t}, Y_{t}, I_{t}, K_{t+1}, Z_{t}, q_{t}, R_{t} $. Note that some of the variables can be consolidated $ N_{t}, W_{t}, Y_{t}, I_{t}, q_{t}, R_{t} $."
]
},
{
"cell_type": "markdown",
"id": "2155c936-3de0-40bc-ace7-ae81d8f5ff40",
"metadata": {},
"source": [
"## Optimality conditions consist of a system of 8 equations"
]
},
{
"cell_type": "markdown",
"id": "d44ad9f0-006a-4afe-ac84-1fbc08e83a80",
"metadata": {},
"source": [
"\n",
"\n",
"\n",
"FOCs from households' maximization problem:\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" C_{t}^{-1 / \\sigma} = \\beta \\mathbb{E} [(1+ R_t -\\delta) C_{t+1}^{-1 / \\sigma}] \\tag{1}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\phi N_{t}^{1 / \\eta} = W_{t} C_{t}^{-1 / \\sigma} \\tag{2}\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "f357742d-da10-47ed-88de-c0693cf2150f",
"metadata": {},
"source": [
"FOCs from firms' maximization problem:\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" Y_{t} = A_{t} K_{t}^{\\alpha} N_{t}^{1-\\alpha} \\tag{3}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" R_{t}K_t = \\alpha A_{t} K_{t}^{\\alpha} N_{t}^{1-\\alpha} = \\alpha Y_t \\tag{4}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"$$\n",
"\\begin{align*} \n",
"W_{t} N_t = (1-\\alpha) A_{t} K_{t}^{\\alpha} N_{t}^{1 -\\alpha} = (1-\\alpha) Y_t \\tag{5}\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "0c3c835d-922a-4b64-88a8-1eeab399ac8b",
"metadata": {},
"source": [
"Law of motions and market clearing:\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" K_{t+1} = K_{t}(1-\\delta) + I_{t} \\tag{6}\n",
" \\end{align*}\n",
" $$\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" Y_{t} = C_{t} + I_{t} \\tag{7}\n",
" \\end{align*}\n",
" $$\n",
"\n",
"$$\n",
"\\begin{align*} \n",
"log(A_t) = \\rho log(A_{t-1}) + \\sigma \\epsilon_t \\tag{8}\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "a95a337d-2e15-449d-a8be-f5e72bfd2b01",
"metadata": {},
"source": [
"Sometimes, law of motion of TFP is set as follows:\n",
"\n",
"- $A_{t+1} = \\rho A_{t} + (1-\\rho) \\bar{A} + \\varepsilon_{t+1} $"
]
},
{
"cell_type": "markdown",
"id": "55a20690-d342-4719-8a2d-b4815d2c6481",
"metadata": {},
"source": [
"## Calibration and solve steady state"
]
},
{
"cell_type": "markdown",
"id": "8a63db76-6ffb-434d-a57d-f6255647d4c2",
"metadata": {},
"source": [
"Usually, we try to solve steady state first, and then impulse response function.\n",
"\n",
"It is clear that the quantitative result of the model depends on the value of parameters used. So we need to \"calibrate\" these parameters appropriately.\n",
"\n",
"The central idea of calibration is to pin down as many deep parameters as possible.\n",
"- Directly estimated from the data: Hall's estimation about IES (0.2).\n",
" For simplicity, I set **$\\sigma=1$**, in this way $\\frac{1}{\\sigma}=1$ as well.\n",
"- Match the moments from the data: **$ \\beta=0.99 $** to match the capital-output ratio, which is about 10 in quarterly data.\n",
"- Commonly used parameter values (for a quarterly model):\n",
" - **$ \\delta=0.025 $** (10 percent annual depreciation rate).\n",
" - **$ \\alpha=0.35 $** (Share of labor income in the aggregate data).\n",
" - **$ \\rho=0.95 $** (TFP process is estimated to be very persistent).\n",
" - **$ \\eta=1 $** (for simplicity)."
]
},
{
"cell_type": "markdown",
"id": "1476afb8-d4ee-4213-aa20-ecbaa8f303bd",
"metadata": {},
"source": [
"How about **$\\phi$**? \n",
"\n",
"We set it so that $N$ equals to 1/3 in steady state. \n",
"\n",
"Besides, we set $A=1$ (sometimes people set $Y=1$)."
]
},
{
"cell_type": "markdown",
"id": "b89e5c27-d3d1-46be-b482-829d45c51d6e",
"metadata": {},
"source": [
"**Step 1: solve intertemporal price**\n",
"\n",
"From equation $2$, we have:\n",
"\n",
"$$\\beta * (1 + R - \\delta) = 1$$"
]
},
{
"cell_type": "markdown",
"id": "a4b82fc5-e8c8-44ad-9549-6ccc7d776a0a",
"metadata": {},
"source": [
"**Step 2: get ratio between $K$, $N$ and $Y$ in production side**\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "9f14041e-f6dd-406e-9951-922f0d173763",
"metadata": {},
"source": [
"Equation 4 over equation 3, and we get relation between capital $K$ and labor $N$:"
]
},
{
"cell_type": "markdown",
"id": "d7320846-bca9-4e07-b685-5c02023366cc",
"metadata": {},
"source": [
"$$\\frac{N}{K} = (\\frac{R}{A\\alpha})^{\\frac{1}{1-\\alpha}} = (\\frac{\\frac{1}{\\beta}+\\delta-1 }{A\\alpha})^{\\frac{1}{1-\\alpha}}$$"
]
},
{
"cell_type": "markdown",
"id": "ac5ec3ac-e9d2-41f2-8df8-33d93375bebf",
"metadata": {},
"source": [
"Combined with equation 3, we have relation between output $Y$, capital $K$ and labor $N$:"
]
},
{
"cell_type": "markdown",
"id": "4e860eeb-32aa-471f-ad5c-63300818dcdd",
"metadata": {},
"source": [
"$$\\frac{Y}{K} = A (\\frac{N}{K})^{1-\\alpha}$$"
]
},
{
"cell_type": "markdown",
"id": "be71ed89-4861-4cfd-9b17-6dd2155b0c4a",
"metadata": {},
"source": [
"**Step 3: together with $C$ in households**"
]
},
{
"cell_type": "markdown",
"id": "8f5a4e72-7fc7-473a-a6f1-70d08e98c2d9",
"metadata": {},
"source": [
"From equation 6 and equation 7, in steady state:"
]
},
{
"cell_type": "markdown",
"id": "8c1d7b1f-b3d3-4ff4-91fa-9eb65d4f2e71",
"metadata": {},
"source": [
"$$Y-C=\\delta K$$"
]
},
{
"cell_type": "markdown",
"id": "1acb138f-a087-4675-a161-d1eb39dc74f0",
"metadata": {},
"source": [
"Based on what we get in step 2:"
]
},
{
"cell_type": "markdown",
"id": "84fcac1e-d4ac-4a9e-97bb-352b2fad33a7",
"metadata": {},
"source": [
"$$\\frac{C}{K} = A (\\frac{N}{K})^{1-\\alpha}-\\delta $$"
]
},
{
"cell_type": "markdown",
"id": "8258d199-1902-46f0-9376-d02b9a4c4b32",
"metadata": {},
"source": [
"**Step 4: get $\\phi$**"
]
},
{
"cell_type": "markdown",
"id": "f5d6bf53-f8c4-4932-82af-6b4f438fa13f",
"metadata": {},
"source": [
"From equation 5:"
]
},
{
"cell_type": "markdown",
"id": "63e36a9d-678f-4e66-9eed-b04f4ca11f5b",
"metadata": {},
"source": [
"$$ W = (1-\\alpha) \\frac{Y}{N} = (1-\\alpha)\\frac{Y}{K} \\frac{K}{N}$$"
]
},
{
"cell_type": "markdown",
"id": "1a48beab-fb81-440e-bf16-91f1ad2384bd",
"metadata": {},
"source": [
"Add information from equation 2:"
]
},
{
"cell_type": "markdown",
"id": "22566356-de3f-44f0-8210-b48b686d4785",
"metadata": {},
"source": [
"$$\n",
"\\phi N^{\\frac{\\sigma}{\\eta}+1} = (1-\\alpha) A (\\frac{N}{K})^{1-\\alpha} \\frac{K}{C}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "82bd508a-ca86-430f-98a1-1b26088cac99",
"metadata": {},
"source": [
"The RHS right hand side is what we already know. \n",
"\n",
"The LHS, we have value for $\\sigma$ and $\\eta$.\n",
"\n",
"All we need is to choose a value for $\\phi$, so that $N=\\frac{1}{3}$."
]
},
{
"cell_type": "markdown",
"id": "e64751e5-3999-41f1-aced-15c44d4acc3a",
"metadata": {},
"source": [
"Now, we can get steady state.\n",
"\n",
"From $\\beta * (1 + R - \\delta) = 1$, $\\beta=0.99$, $\\delta=0.25$, we get: **$R=0.0351$**."
]
},
{
"cell_type": "markdown",
"id": "439a10f9-7ff7-4dde-8de7-839d037d2279",
"metadata": {},
"source": [
"From $\\frac{N}{K} = (\\frac{R}{A\\alpha})^{\\frac{1}{1-\\alpha}}$, $A=1$, $N=\\frac{1}{3}$, we have: $K=11.3$."
]
},
{
"cell_type": "markdown",
"id": "67800823-a86b-4d62-ae8a-a3d9b27f89f1",
"metadata": {},
"source": [
"From $\\frac{Y}{K} = A (\\frac{N}{K})^{1-\\alpha}$, we have: $Y=1.13$."
]
},
{
"cell_type": "markdown",
"id": "aa161c03-4b32-407e-b5aa-88d7fd57f43e",
"metadata": {},
"source": [
"From $Y-C=\\delta K$, we have: $C=0.86$."
]
},
{
"cell_type": "markdown",
"id": "5f22adae-3871-452b-ace7-603354cba5e1",
"metadata": {},
"source": [
"And then, $W=2.20$, $\\phi=7.8$."
]
},
{
"cell_type": "markdown",
"id": "7511d0d4-78f8-4e95-98f9-5c95cfa50b66",
"metadata": {},
"source": [
"_________________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "5528e0a8-c33e-4686-bca3-838d7c876014",
"metadata": {},
"source": [
"# 2. Real Business Cycle Model in MATLAB"
]
},
{
"cell_type": "markdown",
"id": "e578442a-4e66-49c7-97cb-48a6f7bfc02d",
"metadata": {},
"source": [
"_________________________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "70f8c7ef-fa20-40ae-9242-66b6b5087027",
"metadata": {},
"source": [
"Now I am going to implement RBC model in MATLAB."
]
},
{
"cell_type": "markdown",
"id": "badd8b19-8446-45fb-ba0c-7b23a4de6032",
"metadata": {},
"source": [
"You can skip this part if you prefer Dynare."
]
},
{
"cell_type": "markdown",
"id": "96c783fa-9d35-4466-897d-0bb95d86e031",
"metadata": {},
"source": [
"First, let's set the working directory and clear the environment."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5a55da18-15a3-407f-83a4-dcb47f152600",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"ans = 'C:\\Users\\ading\\A_TA_Notes'
"
],
"text/plain": [
"ans = 'C:\\Users\\ading\\A_TA_Notes'"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cd\"C:\\Users\\ading\\A_TA_Notes\"\n",
"pwd"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1ec4bd5f-269a-4ff1-a35b-5463c64c898d",
"metadata": {},
"outputs": [],
"source": [
"clear all;\n",
"clc;\n",
"close all;"
]
},
{
"cell_type": "markdown",
"id": "98b4f88b-f467-4d76-a696-efffe3b933dc",
"metadata": {},
"source": [
"Then, let's set the parameters."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1f215765-1dee-4a8a-8e70-9d3b0099395a",
"metadata": {},
"outputs": [],
"source": [
"nX = 8; % Number of variables\n",
"nEps = 1; % Number of epsilon variables\n",
"\n",
"% Define indices, which will be used for plot\n",
"% I arranged them according to the order \n",
"% in which they appear in the equilibrium solution\n",
"iA = 1; \n",
"iR = 2;\n",
"iN = 3;\n",
"iK = 4;\n",
"iY = 5;\n",
"iC = 6;\n",
"iI = 7;\n",
"iW = 8;"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5bfe8283-2d33-45d1-89c3-281670b7ec61",
"metadata": {},
"outputs": [],
"source": [
"% parameters \n",
"alpha = 0.35; % capital share\n",
"beta = 0.99; % discount factor\n",
"gamma = 1; % risk aversion\n",
"eta = 1; % labor elasticity\n",
"delta = 0.025; % depreciation rate\n",
"rho = 0.95; % TFP persistency\n",
"phi = 7.8; % labor disutility"
]
},
{
"cell_type": "markdown",
"id": "ae281e9a-9089-452f-a1e0-a23614e73889",
"metadata": {},
"source": [
"Here is steady state solution."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b640807b-52c3-43be-af93-c6bc847dcb39",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"File SteadyState.m created successfully.
"
],
"text/plain": [
"File SteadyState.m created successfully."
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%%file SteadyState.m\n",
"\n",
"function X = SteadyState(beta, delta, alpha, nX)\n",
" A = 1;\n",
" R = 1 / beta - 1 + delta;\n",
" N = 1/3;\n",
" K = N * (R/A/alpha)^(1/(alpha-1));\n",
" Y = A * K^alpha * N^(1-alpha);\n",
" C = Y - delta * K;\n",
" I = delta*K;\n",
" W = (1-alpha)*Y/N;\n",
"\n",
" X = zeros(nX, 1); % Initialize X as a column vector\n",
" X([1, 2, 3, 4, 5, 6, 7, 8]) = [A; R; N; K; Y; C; I; W]; % Assign values to X (adjust indices for MATLAB)\n",
"end\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "277af08e-d0cc-45ff-9a74-61473e3807d3",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Steady state: [1;0.0351010101010102;0.333333333333333;11.4660753507223;1.14991664772756;0.863264763959503;0.286651883768057;2.24233746306874]\n"
]
}
],
"source": [
"% Call the SteadyState function\n",
"X_SS = SteadyState(beta, delta, alpha, nX); % Ensure you provide the required parameters\n",
"\n",
"epsilon_SS = 0.0;\n",
"\n",
"% Display the steady state\n",
"fprintf('Steady state: %s\\n', mat2str(X_SS));"
]
},
{
"cell_type": "markdown",
"id": "e383910a-5107-4fdc-bc6c-994d4e51fc33",
"metadata": {},
"source": [
"Then, construct jacobian matrix. \n",
"\n",
"A_jacobian_raw measures how a small change in future variable affect system equilibrium.\n",
"\n",
"B_jacobian_raw measures how a small change in current variable affect system equilibrium.\n",
"\n",
"C_jacobian_raw measures how a small change in past variable affect system equilibrium.\n",
"\n",
"E_jacobian_raw measures how a small change in TFP shock affect system equilibrium."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5be30e37-8ec3-42d1-a675-89a06f47eaa5",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$A_jacobian_raw =\\left(\\begin{array}{cccccccc}\n",
"0 & 0 & 0 & 0 & 0 & -\\frac{C\\,{\\left(\\frac{99\\,R}{100}+\\frac{3861}{4000}\\right)}}{{C_P }^2 } & 0 & 0\\\\\n",
"0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/latex": [
"$B_jacobian_raw =\\begin{array}{l}\n",
"\\left(\\begin{array}{cccccccc}\n",
"0 & \\frac{99\\,C}{100\\,C_P } & 0 & 0 & 0 & \\frac{\\frac{99\\,R}{100}+\\frac{3861}{4000}}{C_P } & 0 & 0\\\\\n",
"0 & 0 & \\frac{39}{5} & 0 & 0 & \\frac{W}{C^2 } & 0 & -\\frac{1}{C}\\\\\n",
"{K_L }^{7/20} \\,N^{13/20} & 0 & \\frac{13\\,A\\,{K_L }^{7/20} }{\\sigma_1 } & 0 & -1 & 0 & 0 & 0\\\\\n",
"\\frac{7\\,N^{13/20} }{20\\,{K_L }^{13/20} } & -1 & \\frac{91\\,A}{400\\,{K_L }^{13/20} \\,N^{7/20} } & 0 & 0 & 0 & 0 & 0\\\\\n",
"\\frac{13\\,{K_L }^{7/20} }{\\sigma_1 } & 0 & -\\frac{91\\,A\\,{K_L }^{7/20} }{400\\,N^{27/20} } & 0 & 0 & 0 & 0 & -1\\\\\n",
"0 & 0 & 0 & -1 & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & 0 & 1 & -1 & -1 & 0\\\\\n",
"-\\frac{1}{A} & 0 & 0 & 0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)\\\\\n",
"\\mathrm{}\\\\\n",
"\\textrm{where}\\\\\n",
"\\mathrm{}\\\\\n",
"\\;\\;\\sigma_1 =20\\,N^{7/20} \n",
"\\end{array}$"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/latex": [
"$C_jacobian_raw =\\left(\\begin{array}{cccccccc}\n",
"0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & \\frac{7\\,A\\,N^{13/20} }{20\\,{K_L }^{13/20} } & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & -\\frac{91\\,A\\,N^{13/20} }{400\\,{K_L }^{33/20} } & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & \\frac{91\\,A}{400\\,{K_L }^{13/20} \\,N^{7/20} } & 0 & 0 & 0 & 0\\\\\n",
"0 & 0 & 0 & \\frac{39}{40} & 0 & 0 & 1 & 0\\\\\n",
"0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
"\\frac{19}{20\\,A_L } & 0 & 0 & 0 & 0 & 0 & 0 & 0\n",
"\\end{array}\\right)$"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/latex": [
"$E_jacobian_raw =\\left(\\begin{array}{c}\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"1\n",
"\\end{array}\\right)$"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"syms A R N K Y C I W A_P R_P N_P K_P Y_P C_P I_P W_P A_L R_L N_L K_L Y_L C_L I_L W_L epsilon\n",
"\n",
"residuals = [...\n",
" beta * (1+R-delta) * C_P^(-1/gamma) * C^(1/gamma) - 1.0; % Euler equation\n",
" phi * N^(1/eta) - W*C^(-1/gamma); \n",
" A * K_L^alpha * N^(1-alpha) - Y; % Production function\n",
" alpha * A * K_L^(alpha-1) * N^(1-alpha) - R; % MPK\n",
" (1-alpha) * A * K_L^alpha * N^(-alpha) - W; % MPN\n",
" (1 - delta) * K_L + I_L - K; % Aggregate resource constraint \n",
" % Do not use (1 - delta) * K + I - K_P\n",
" Y - C - I; % Aggregate resource constraint\n",
" rho * log(A_L) + epsilon - log(A) % TFP evolution\n",
" ];\n",
"\n",
"A_jacobian_raw = jacobian(residuals, [A_P,R_P,N_P,K_P,Y_P,C_P,I_P,W_P])\n",
"B_jacobian_raw = jacobian(residuals, [A, R, N, K, Y, C, I, W ])\n",
"C_jacobian_raw = jacobian(residuals, [A_L,R_L,N_L,K_L,Y_L,C_L,I_L,W_L]) % don't name it C, otherwise confused with consumption C\n",
"E_jacobian_raw = jacobian(residuals, epsilon)"
]
},
{
"cell_type": "markdown",
"id": "b1088b4a-54e1-4f20-815f-c99514bec569",
"metadata": {},
"source": [
"Plug in values to get jacobian matrix."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "85f7c235-b13a-41d9-af67-4b5a75ac75eb",
"metadata": {},
"outputs": [],
"source": [
"X = SteadyState(beta, delta, alpha, nX);\n",
"A_s = X(1);\n",
"R_s = X(2);\n",
"N_s = X(3);\n",
"K_s = X(4);\n",
"Y_s = X(5);\n",
"C_s = X(6);\n",
"I_s = X(7);\n",
"W_s = X(8);\n",
"\n",
"X_Lag = SteadyState(beta, delta, alpha, nX);\n",
"A_L_s = X_Lag(1);\n",
"R_L_s = X_Lag(2);\n",
"N_L_s = X_Lag(3);\n",
"K_L_s = X_Lag(4);\n",
"Y_L_s = X_Lag(5);\n",
"C_L_s = X_Lag(6);\n",
"I_L_s = X_Lag(7);\n",
"W_L_s = X_Lag(8);\n",
"\n",
"X_Prime = SteadyState(beta, delta, alpha, nX);\n",
"A_P_s = X_Prime(1);\n",
"R_P_s = X_Prime(2);\n",
"N_P_s = X_Prime(3);\n",
"K_P_s = X_Prime(4);\n",
"Y_P_s = X_Prime(5);\n",
"C_P_s = X_Prime(6);\n",
"I_P_s = X_Prime(7);\n",
"W_P_s = X_Prime(8);"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6179d757-9510-413a-89d5-cd28ce9e1b2b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"A_jacobian = 8×8 double\n",
" 0 0 0 0 0 -1.1584 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
""
],
"text/plain": [
"A_jacobian = 8×8 double\n",
" 0 0 0 0 0 -1.1584 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
"B_jacobian = 8×8 double\n",
" 0 0.9900 0 0 0 1.1584 0 0\n",
" 0 0 7.8000 0 0 3.0089 0 -1.1584\n",
" 1.1499 0 2.2423 0 -1.0000 0 0 0\n",
" 0.0351 -1.0000 0.0684 0 0 0 0 0\n",
" 2.2423 0 -2.3545 0 0 0 0 -1.0000\n",
" 0 0 0 -1.0000 0 0 0 0\n",
" 0 0 0 0 1.0000 -1.0000 -1.0000 0\n",
" -1.0000 0 0 0 0 0 0 0\n",
""
],
"text/plain": [
"B_jacobian = 8×8 double\n",
" 0 0.9900 0 0 0 1.1584 0 0\n",
" 0 0 7.8000 0 0 3.0089 0 -1.1584\n",
" 1.1499 0 2.2423 0 -1.0000 0 0 0\n",
" 0.0351 -1.0000 0.0684 0 0 0 0 0\n",
" 2.2423 0 -2.3545 0 0 0 0 -1.0000\n",
" 0 0 0 -1.0000 0 0 0 0\n",
" 0 0 0 0 1.0000 -1.0000 -1.0000 0\n",
" -1.0000 0 0 0 0 0 0 0\n"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
"C_jacobian = 8×8 double\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0.0351 0 0 0 0\n",
" 0 0 0 -0.0020 0 0 0 0\n",
" 0 0 0 0.0684 0 0 0 0\n",
" 0 0 0 0.9750 0 0 1.0000 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0.9500 0 0 0 0 0 0 0\n",
""
],
"text/plain": [
"C_jacobian = 8×8 double\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0 0 0 0.0351 0 0 0 0\n",
" 0 0 0 -0.0020 0 0 0 0\n",
" 0 0 0 0.0684 0 0 0 0\n",
" 0 0 0 0.9750 0 0 1.0000 0\n",
" 0 0 0 0 0 0 0 0\n",
" 0.9500 0 0 0 0 0 0 0\n"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
"E_jacobian = 8×1 double\n",
" 0\n",
" 0\n",
" 0\n",
" 0\n",
" 0\n",
" 0\n",
" 0\n",
" 1\n",
""
],
"text/plain": [
"E_jacobian = 8×1 double\n",
" 0\n",
" 0\n",
" 0\n",
" 0\n",
" 0\n",
" 0\n",
" 0\n",
" 1\n"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A_jacobian = subs(A_jacobian_raw, {A R N K Y C I W A_P R_P N_P K_P Y_P C_P I_P W_P A_L R_L N_L K_L Y_L C_L I_L W_L epsilon}, ...\n",
"{A_s R_s N_s K_s Y_s C_s I_s W_s A_P_s R_P_s N_P_s K_P_s Y_P_s C_P_s I_P_s W_P_s A_L_s R_L_s N_L_s K_L_s Y_L_s C_L_s I_L_s W_L_s 0});\n",
"A_jacobian = round(double(A_jacobian), 4)\n",
"\n",
"B_jacobian = subs(B_jacobian_raw, {A R N K Y C I W A_P R_P N_P K_P Y_P C_P I_P W_P A_L R_L N_L K_L Y_L C_L I_L W_L epsilon}, ...\n",
"{A_s R_s N_s K_s Y_s C_s I_s W_s A_P_s R_P_s N_P_s K_P_s Y_P_s C_P_s I_P_s W_P_s A_L_s R_L_s N_L_s K_L_s Y_L_s C_L_s I_L_s W_L_s 0});\n",
"B_jacobian = round(double(B_jacobian), 4)\n",
"\n",
"C_jacobian = subs(C_jacobian_raw, {A R N K Y C I W A_P R_P N_P K_P Y_P C_P I_P W_P A_L R_L N_L K_L Y_L C_L I_L W_L epsilon}, ...\n",
"{A_s R_s N_s K_s Y_s C_s I_s W_s A_P_s R_P_s N_P_s K_P_s Y_P_s C_P_s I_P_s W_P_s A_L_s R_L_s N_L_s K_L_s Y_L_s C_L_s I_L_s W_L_s 0});\n",
"C_jacobian = round(double(C_jacobian), 4)\n",
"\n",
"E_jacobian = subs(E_jacobian_raw, {A R N K Y C I W A_P R_P N_P K_P Y_P C_P I_P W_P A_L R_L N_L K_L Y_L C_L I_L W_L epsilon}, ...\n",
"{A_s R_s N_s K_s Y_s C_s I_s W_s A_P_s R_P_s N_P_s K_P_s Y_P_s C_P_s I_P_s W_P_s A_L_s R_L_s N_L_s K_L_s Y_L_s C_L_s I_L_s W_L_s 0});\n",
"E_jacobian = round(double(E_jacobian), 4)"
]
},
{
"cell_type": "markdown",
"id": "27a9f55e-3a8f-4d0e-a737-db331dd05ea5",
"metadata": {},
"source": [
"Then solve for P and Q.\n",
"\n",
"Here P satisfies: $C + B*P + A*P*P = 0$,\n",
"\n",
"and Q satisfies: $Q = -inv(B + A * P) * E $\n",
"\n",
"P measures how system absorbs changes over time.\n",
"\n",
"Q measures how eps shock affect system over time."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a5ed93b5-cf4c-4e0f-a13e-6a3ecb22b5fd",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"File SolveSystem.m created successfully.
"
],
"text/plain": [
"File SolveSystem.m created successfully."
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%%file SolveSystem.m\n",
"\n",
"function [P, Q] = SolveSystem(A, B, C, E)\n",
" % Solve the system using linear time iteration as in Rendahl (2017)\n",
" MAXIT = 1000; \n",
" P = zeros(size(A)); % Initialize P with the same size as A\n",
"\n",
" for it = 1:MAXIT\n",
" % Solve for P using least squares\n",
" P = - (B + A * P) \\ C; % Equivalent to np.linalg.lstsq in Python \n",
"\n",
" % Test the convergence condition\n",
" test = max(abs(C + B * P + A * P * P)); % Check C + B*P + A*P*P = 0\n",
" if test < 1e-7\n",
" break;\n",
" end\n",
" end\n",
"\n",
" % Impact matrix\n",
" % Solution is x_{t} = P*x_{t-1} + Q*eps_t\n",
" Q = -inv(B + A * P) * E ; % Q = - E * (B + A*P)\n",
"\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8aca5732-eb41-4a21-a9ec-8d34f54afae5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Matrix P:\n",
" 0.9500 0 0 0.0000 0 0 0.0000 0\n",
" 0.0444 0 0 -0.0024 0 0 -0.0008 0\n",
" 0.1611 0 0 -0.0052 0 0 -0.0121 0\n",
" 0 0 0 0.9750 0 0 1.0000 0\n",
" 1.4537 0 0 0.0234 0 0 -0.0272 0\n",
" 0.2564 0 0 0.0446 0 0 0.0424 0\n",
" 1.1973 0 0 -0.0212 0 0 -0.0695 0\n",
" 1.7508 0 0 0.0807 0 0 0.0285 0\n",
"\n",
"Matrix Q:\n",
" 1.0000\n",
" 0.0467\n",
" 0.1696\n",
" 0\n",
" 1.5302\n",
" 0.2699\n",
" 1.2604\n",
" 1.8430\n",
"\n"
]
}
],
"source": [
"\n",
"% Assuming A, B, C, and E are defined matrices\n",
"[P, Q] = SolveSystem(A_jacobian, B_jacobian, C_jacobian, E_jacobian);\n",
"\n",
"% Display the results\n",
"disp('Matrix P:');\n",
"disp(P);\n",
"\n",
"disp('Matrix Q:');\n",
"disp(Q);"
]
},
{
"cell_type": "markdown",
"id": "15534811-09b5-4905-b348-6261ca440e20",
"metadata": {},
"source": [
"Finally, let's plot the impulse response functions. "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a79f9146-11f4-4d11-b0ca-afc2cfe2ee7b",
"metadata": {},
"outputs": [],
"source": [
"% Assuming nX, Q, and P are defined\n",
"IRF_RBC = zeros(nX, 100); % Initialize IRF_RBC with zeros\n",
"IRF_RBC(:, 1) = Q * 0.01; % Set the first column\n",
"\n",
"for t = 2:100 % MATLAB indices start at 1\n",
" IRF_RBC(:, t) = P * IRF_RBC(:, t - 1); % Matrix multiplication\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dbe64f50-5f74-4b87-a12a-9001843702f3",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"figure('Position', [100, 100, 800, 400]); \n",
"\n",
"subplot(3,3,1)\n",
"plot(IRF_RBC(iA, :), 'blue', 'DisplayName', 'Impulse Response of Output'); % Plot the data\n",
"title('TFP shock'); xlabel('Time'); ylabel('Response');\n",
"\n",
"subplot(3,3,2)\n",
"plot(IRF_RBC(iY, :), 'blue', 'DisplayName', 'Impulse Response of Output'); % Plot the data\n",
"title('Output'); xlabel('Time'); ylabel('Response');\n",
"\n",
"subplot(3,3,3)\n",
"plot(IRF_RBC(iC, :), 'blue', 'DisplayName', 'Impulse Response of Output'); % Plot the data\n",
"title('Consumption'); xlabel('Time'); ylabel('Response');\n",
"\n",
"subplot(3,3,4)\n",
"plot(IRF_RBC(iK, :), 'blue', 'DisplayName', 'Impulse Response of Output'); % Plot the data\n",
"title('Capital'); xlabel('Time'); ylabel('Response');\n",
"\n",
"subplot(3,3,5)\n",
"plot(IRF_RBC(iN, :), 'blue', 'DisplayName', 'Impulse Response of Output'); % Plot the data\n",
"title('Labor'); xlabel('Time'); ylabel('Response');\n",
"\n",
"subplot(3,3,6)\n",
"plot(IRF_RBC(iW, :), 'blue', 'DisplayName', 'Impulse Response of Output'); % Plot the data\n",
"title('Wage'); xlabel('Time'); ylabel('Response');\n",
"\n",
"subplot(3,3,7)\n",
"plot(IRF_RBC(iI, :), 'blue', 'DisplayName', 'Impulse Response of Output'); % Plot the data\n",
"title('Investment'); xlabel('Time'); ylabel('Response');\n",
"\n",
"subplot(3,3,8)\n",
"plot(IRF_RBC(iR, :), 'blue', 'DisplayName', 'Impulse Response of Output'); % Plot the data\n",
"title('Interest Rate'); xlabel('Time'); ylabel('Response');"
]
},
{
"cell_type": "markdown",
"id": "fcc4fbb3-d38e-47a6-bd26-47a38202ee2e",
"metadata": {},
"source": [
"As we can see, almost all variable increase after a positive TFP shock.\n",
"\n",
"These figures are the same as what we will get by Dynare, except for the magnitute, since we plot absolute value here, and plot percentage change in Dynare."
]
},
{
"cell_type": "markdown",
"id": "59430225-2f49-4614-8045-fa239bf42685",
"metadata": {},
"source": [
"_________________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "56475dc0-c5e3-4c86-9351-90e0d4ed8b69",
"metadata": {},
"source": [
"# 3. Introduction to Dynare"
]
},
{
"cell_type": "markdown",
"id": "3f01e8f5-e855-4bc6-aef4-c18a6ff6fc6f",
"metadata": {},
"source": [
"_________________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "ff7fc3de-852b-4b2b-82d0-d384b3ab109f",
"metadata": {},
"source": [
"Dynare is a software platform for handling a wide class of economic models, in particular dynamic stochastic general equilibrium (DSGE) and overlapping generations (OLG) models. \n",
"\n",
"We can use Dynare to:\n",
"- compute the steady state of a model;\n",
"- compute the first, second order, or higher order approximation to solutions of stochastic models;\n",
"- estimate parameters of DSGE models using either a maximum likelihood or a Bayesian approach."
]
},
{
"cell_type": "markdown",
"id": "02dc84c1-9049-491e-a833-768e4b4bbe8e",
"metadata": {},
"source": [
"## Steps to install Dynare\n",
"- Install Matlab.\n",
"- Download at https://www.dynare.org/download/.\n",
"- Install (manual 2.2.1).\n",
"- Configure (manual 2.4)."
]
},
{
"cell_type": "markdown",
"id": "a8c4e6b0-61ae-4e4a-afb5-61c33e7719de",
"metadata": {},
"source": [
"To configure, personally I recommend to use 'addpath d:/dynare/6.2/matlab'\n",
"\n",
"Sometimes people will use menu entries: \n",
"\n",
"\"Set Path\" > \"Add Folder. . . \" > \n",
"\n",
"If you use this method, take care not to click \"Add Folder and Sub Folder...\""
]
},
{
"cell_type": "markdown",
"id": "f0587f6d-0333-4029-85b7-a2ab25927e0d",
"metadata": {},
"source": [
"## Version Choice\n",
"\n",
"Dynare now has updated to version 6. While some literature's replication package is based on version 4. \n",
"\n",
"A possible solution is to install MATLAB of different versions in your computer. \n",
"\n",
"For each MATLAB version, choose a Dynare version for it. \n",
"\n",
"In this way, you can replicate certain literature using Dynare 4, and try new functions using Dynare 6."
]
},
{
"cell_type": "markdown",
"id": "baf3ca43-c379-46f4-b8fc-708ff6849289",
"metadata": {},
"source": [
"## .mod file\n",
"\n",
"Structure of a .mod file:\n",
"- Preamble: parameters, variables\n",
"- Model\n",
"- Initial Value, End Value\n",
"- Steady State\n",
"- Shocks\n",
"- Computation\n",
"\n",
"To run a .mod code, type `dynare xxxx.mod` in the command window."
]
},
{
"cell_type": "markdown",
"id": "3f7d50c2-a83e-4eee-ad36-31058373e39c",
"metadata": {},
"source": [
"______________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "7545e296-6d67-4b9e-86db-f619ba9203ad",
"metadata": {},
"source": [
"# 4. Real Business Cycle Model in Dynare"
]
},
{
"cell_type": "markdown",
"id": "7a7d3902-1686-4d7f-a51e-02f7e8222a21",
"metadata": {},
"source": [
"______________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "880fb2f1-1d1a-4b2b-b5d6-afd80828786c",
"metadata": {},
"source": [
"We follow the model setting in part 1. "
]
},
{
"cell_type": "markdown",
"id": "00ab1ce7-252d-4e6f-9072-fbb78b318237",
"metadata": {},
"source": [
"A typical .mod file consist of 7 parts:\n",
"\n",
" 1. variable\n",
" 2. parameters\n",
" 3. model\n",
" 4. initial value\n",
" 5. shocks\n",
" 6. steady\n",
" 7. simulation"
]
},
{
"cell_type": "markdown",
"id": "274e4941-db73-4898-b83c-4a1634c908bd",
"metadata": {},
"source": [
"Here is an example. "
]
},
{
"cell_type": "markdown",
"id": "8d23fe2c-0495-4818-96f7-ed91cac29c76",
"metadata": {},
"source": [
"\n",
" \n",
"var y I k a c w R n;
\n",
"varexo e;\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"id": "f1ae0786-f811-44b3-93f2-15a339892dbe",
"metadata": {},
"source": [
"\n",
"\n",
"parameters alpha beta delta rho gamma sigmae eta phi;
\n",
"alpha=0.35;
\n",
"beta=0.99;
\n",
"delta=0.025;
\n",
"rho=0.95;
\n",
"gamma=1;
\n",
"sigmae=0.01;
\n",
"eta = 1;
\n",
"phi = 7.6;
\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"id": "4320c478-12a1-4dfd-a4af-139beb8527fa",
"metadata": {},
"source": [
"In model part, there are 8 equations. \n",
"\n",
"They are exactly the equilibiurm conditions we get in part 8. \n",
"\n",
"Remember the 8 equations in tag 1~8. "
]
},
{
"cell_type": "markdown",
"id": "3b3b2ebb-b05d-4cfd-9ed8-c0f02b00a8ed",
"metadata": {},
"source": [
"Note that here all variables are in log, so that we can get percentage change in the final result. "
]
},
{
"cell_type": "markdown",
"id": "1b691f66-0390-40c5-b945-7b5af9d683b4",
"metadata": {},
"source": [
"\n",
"\n",
"model;
\n",
"% equation 1
\n",
"exp(c)^(-1/gamma)=beta*exp(c(+1))^(-1/gamma)*(exp(R)+1-delta);\n",
"\n",
"% equation 2
\n",
"exp(c)^(-1/gamma)*exp(w)=phi*exp(n)^(1/eta);\n",
"\n",
"% equation 3
\n",
"exp(y)=exp(a)*exp(k(-1))^alpha*exp(n)^(1-alpha);\n",
"\n",
"% equation 4
\n",
"exp(R)=alpha*exp(a)*exp(k(-1))^(alpha-1)*exp(n)^(1-alpha);\n",
"\n",
"% equation 5
\n",
"exp(w)=(1-alpha)*exp(a)*exp(k(-1))^alpha*exp(n)^(-alpha);\n",
"\n",
"% equation 6
\n",
"exp(k)=exp(I(-1))+(1-delta)*exp(k(-1));\n",
"\n",
"% equation 7
\n",
"exp(y)=exp(c)+exp(I);\n",
"\n",
"% equation 8
\n",
"a=rho*a(-1)+e; \n",
"\n",
"end;\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"id": "ef6d5b18-5e48-4c3c-81d5-0c6b6df25c91",
"metadata": {},
"source": [
"We had better give initial value to Dynare, so that we can get reasonable solution when there are multiple solutions. \n",
"\n",
"It can be numbers assigned, or formula based on parameters. \n",
"\n",
"In the following code, it's the steady state that we get in part 1.\n",
"\n",
"Also, note that variables are in log. "
]
},
{
"cell_type": "markdown",
"id": "158e8f96-db52-4667-abbb-4bdb290bb5f1",
"metadata": {},
"source": [
"\n",
" \n",
"initval;
\n",
"\n",
"a = 0;
\n",
"n = log(1/3);
\n",
"R = log(1/beta - 1 + delta);
\n",
"k = log(exp(n)*(exp(R)/exp(a)/alpha)^(1/(alpha-1)));
\n",
"y = log(exp(a)*exp(k)^alpha*exp(n)^(1-alpha));
\n",
"I = log(delta)+k;
\n",
"c = log(exp(y)-exp(I));
\n",
"w = log(1-alpha) + y - n;
\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"id": "6d9ae9dd-82e5-42b0-ac36-c4567593ecbf",
"metadata": {},
"source": [
"\n",
"\n",
"shocks;
\n",
"var e = sigmae^2;
\n",
"end;
\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"id": "e86dc2b4-dd8b-4644-9fb9-1893c85ab01a",
"metadata": {},
"source": [
"\n",
"\n",
"steady;\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"id": "1cd99f64-2bf3-406a-988d-dad5ee04c1f2",
"metadata": {},
"source": [
"\n",
"\n",
"stoch_simul(order=1,irf=100);\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"id": "9f6ced3c-17ae-4e4e-8aff-c62d1dbc76e9",
"metadata": {},
"source": [
"Let's see the result from Dynare"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d0259ec3-e184-4920-abc0-142f00345b00",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"ans = 'C:\\Users\\ading\\A_TA_Notes'
"
],
"text/plain": [
"ans = 'C:\\Users\\ading\\A_TA_Notes'"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cd\"C:\\Users\\ading\\A_TA_Notes\"\n",
"pwd"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4cd416b9-d096-4d87-abc6-39eead3cbae8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Starting Dynare (version 6.2).\n",
"Calling Dynare with arguments: none\n",
"Starting preprocessing of the model file ... \n",
"Found 8 equation(s). \n",
"Evaluating expressions... \n",
"Computing static model derivatives (order 1). \n",
"Normalizing the static model... \n",
"Finding the optimal block decomposition of the static model... \n",
"2 block(s) found: \n",
" 1 recursive block(s) and 1 simultaneous block(s). \n",
" the largest simultaneous block has 7 equation(s) \n",
" and 7 feedback variable(s). \n",
"Computing dynamic model derivatives (order 1). \n",
"Normalizing the dynamic model... \n",
"Finding the optimal block decomposition of the dynamic model... \n",
"2 block(s) found: \n",
" 1 recursive block(s) and 1 simultaneous block(s). \n",
" the largest simultaneous block has 7 equation(s) \n",
" and 7 feedback variable(s). \n",
"Preprocessing completed. \n",
"Preprocessing time: 0h00m00s.\n",
"\n",
"STEADY-STATE RESULTS:\n",
"\n",
"a \t\t 0\n",
"y \t\t 0.0441673\n",
"c \t\t -0.226868\n",
"k \t\t 2.29508\n",
"n \t\t -1.08129\n",
"w \t\t 0.719991\n",
"I \t\t -1.3938\n",
"R \t\t -3.34953\n",
"\n",
"MODEL SUMMARY\n",
"\n",
" Number of variables: 8\n",
" Number of stochastic shocks: 1\n",
" Number of state variables: 3\n",
" Number of jumpers: 1\n",
" Number of static variables: 4\n",
"\n",
"\n",
"MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS\n",
"Variables e\n",
"e 0.000100\n",
"\n",
"POLICY AND TRANSITION FUNCTIONS\n",
" a y c k n w I R\n",
"Constant 0 0.044167 -0.226868 2.295080 -1.081289 0.719991 -1.393799 -3.349525\n",
"a(-1) 0.950000 1.271407 0.307186 0 0.482110 0.789297 4.368600 1.271407\n",
"k(-1) 0 0.212394 0.575213 0.975000 -0.181409 0.393803 -0.953025 -0.787606\n",
"I(-1) 0 -0.006815 0.013629 0.025000 -0.010222 0.003407 -0.072483 -0.006815\n",
"e 1.000000 1.338323 0.323354 0 0.507485 0.830838 4.598527 1.338323\n",
"\n",
"\n",
"THEORETICAL MOMENTS\n",
"VARIABLE MEAN STD. DEV. VARIANCE\n",
"a 0.0000 0.0320 0.0010\n",
"y 0.0442 0.0499 0.0025\n",
"c -0.2269 0.0378 0.0014\n",
"k 2.2951 0.0510 0.0026\n",
"n -1.0813 0.0114 0.0001\n",
"w 0.7200 0.0428 0.0018\n",
"I -1.3938 0.1139 0.0130\n",
"R -3.3495 0.0343 0.0012\n",
"\n",
"\n",
"\n",
"MATRIX OF CORRELATIONS\n",
"Variables a y c k n w I R\n",
"a 1.0000 0.9857 0.8143 0.6841 0.8043 0.9350 0.9508 0.4681\n",
"y 0.9857 1.0000 0.9002 0.7968 0.6933 0.9813 0.8854 0.3129\n",
"c 0.8143 0.9002 1.0000 0.9804 0.3103 0.9672 0.5947 -0.1316\n",
"k 0.6841 0.7968 0.9804 1.0000 0.1170 0.8982 0.4247 -0.3242\n",
"n 0.8043 0.6933 0.3103 0.1170 1.0000 0.5416 0.9488 0.9008\n",
"w 0.9350 0.9813 0.9672 0.8982 0.5416 1.0000 0.7794 0.1243\n",
"I 0.9508 0.8854 0.5947 0.4247 0.9488 0.7794 1.0000 0.7181\n",
"R 0.4681 0.3129 -0.1316 -0.3242 0.9008 0.1243 0.7181 1.0000\n",
"\n",
"\n",
"\n",
"COEFFICIENTS OF AUTOCORRELATION\n",
"Order 1 2 3 4 5\n",
"a 0.9500 0.9025 0.8574 0.8145 0.7738\n",
"y 0.9633 0.9307 0.8989 0.8679 0.8378\n",
"c 0.9958 0.9897 0.9818 0.9723 0.9613\n",
"k 0.9987 0.9952 0.9895 0.9821 0.9729\n",
"n 0.8952 0.8084 0.7275 0.6527 0.5834\n",
"w 0.9809 0.9625 0.9435 0.9241 0.9043\n",
"I 0.9146 0.8431 0.7760 0.7135 0.6553\n",
"R 0.9179 0.8350 0.7584 0.6873 0.6214\n"
]
},
{
"data": {
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"
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total computing time : 0h00m01s\n"
]
}
],
"source": [
"dynare rbc_8equations.mod"
]
},
{
"cell_type": "markdown",
"id": "fa378f71-acbc-440f-bc03-230b76fd10eb",
"metadata": {},
"source": [
"_________________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "19dd69a0-ba53-4370-b959-329858e2a8ea",
"metadata": {},
"source": [
"# 5. RBC Model with Occasional Binding"
]
},
{
"cell_type": "markdown",
"id": "e71f34fa-caaa-4548-91d2-5bfd059a17b2",
"metadata": {},
"source": [
"_________________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "024f6514-2df1-40ab-b49b-1be21bb1f50a",
"metadata": {},
"source": [
"Occasional Binding Constraints refer to situations in economic models where certain constraints are not always active but can become binding under specific conditions. "
]
},
{
"cell_type": "markdown",
"id": "6d82d878-23d3-46b3-8368-48072b913d8e",
"metadata": {},
"source": [
"OccBin is an important tool developed by Guerrieri and Iacoviello (JME, 2015).\n",
"\n",
"Dynare manual provides an example on how to set up occasional binding model."
]
},
{
"cell_type": "markdown",
"id": "e4d64bd4-08fd-4235-af18-1d1cdb42267a",
"metadata": {},
"source": [
"There are two occasionally binding constraints newly added into RBC model:\n",
" * 1. The INEG constraint implements quadratic capital adjustment costs if investment falls below its steady state. If investment is above steady state, there are no adjustment costs\n",
" * 2. The IRR constraint implements irreversible investment. Investment cannot be lower than a factor $phi$ of its steady state."
]
},
{
"cell_type": "markdown",
"id": "7dc6340e-b3ed-40c5-b661-223fc457d58c",
"metadata": {},
"source": [
"We list all variables first."
]
},
{
"cell_type": "markdown",
"id": "4e8a71f9-d613-4841-8c1b-ab3439747adc",
"metadata": {},
"source": [
"\n",
"\n",
"var A $A$ (long_name='TFP')
\n",
" C $C$ (long_name='consumption')
\n",
" Invest $I$ (long_name='investment')
\n",
" K $K$ (long_name='capital')
\n",
" Lambda $\\lambda$ (long_name='Lagrange multiplier')
\n",
" log_K ${\\hat K}$ (long_name='log capital')
\n",
" log_Invest ${\\hat I}$ (long_name='log investment')
\n",
" log_C ${\\hat C}$ (long_name='log consumption')
\n",
" ;\n",
"\n",
"varexo epsilon $\\varepsilon$ (long_name='TFP shock');\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"id": "6872afca-ea6b-4454-a493-cf5bb17020f4",
"metadata": {},
"source": [
"Then we set parameters."
]
},
{
"cell_type": "markdown",
"id": "d914d4d7-cbc2-47e4-9bc0-8cdf378562f1",
"metadata": {},
"source": [
"\n",
"parameters alpha $\\alpha$ (long_name='capital share')
\n",
" delta $\\delta$ (long_name='depreciation')
\n",
" beta $\\beta$ (long_name='discount factor')
\n",
" sigma $\\sigma$ (long_name='risk aversion')
\n",
" rho $\\rho$ (long_name='autocorrelation TFP')
\n",
" phi $\\phi$ (long_name='irreversibility fraction of steady state investment')
\n",
" psi $\\psi$ (long_name='capital adjustment cost')
\n",
" ;\n",
"\n",
"beta=0.96;
\n",
"alpha=0.33;
\n",
"delta=0.10;
\n",
"sigma=2;
\n",
"rho = 0.9;
\n",
"phi = 0.975;
\n",
"psi = 5;
\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"id": "a705b55a-34af-44d1-a98b-cee25aa553f5",
"metadata": {},
"source": [
"The model is set as follows. "
]
},
{
"cell_type": "markdown",
"id": "88547079-3270-4a30-bd7a-99e79e812485",
"metadata": {},
"source": [
"In equation 2, when INEG binds, there is extra adjustment cost: psi(K/K(-1)-1)^2.\n",
"\n",
"In equation 4, when IRR binds, investment equals to phi*investment_steadystate, investment can't be lower, and Lambda is larger than zero. "
]
},
{
"cell_type": "markdown",
"id": "05af75c1-d575-4bad-b579-25894fb80fbf",
"metadata": {},
"source": [
"\n",
"model;
\n",
"// 1.
\n",
"[name='Euler', bind = 'INEG']
\n",
"-C^(-sigma)*(1+2*psi*(K/K(-1)-1)/K(-1))+ beta*C(+1)^(-sigma)*((1-delta)-2*psi*(K(+1)/K-1)*
\n",
" (-K(+1)/K^2)+alpha*exp(A(+1))*K^(alpha-1))= -Lambda+beta*(1-delta)*Lambda(+1);
\n",
"\n",
"[name='Euler', relax = 'INEG']
\n",
"-C^(-sigma) + beta*C(+1)^(-sigma)*(1-delta+alpha*exp(A(+1))*K^(alpha-1))= -Lambda+beta*(1-delta)*Lambda(+1);
\n",
"\n",
"// 2.
\n",
"[name='Budget constraint',bind = 'INEG']
\n",
"C+K-(1-delta)*K(-1)+psi*(K/K(-1)-1)^2=exp(A)*K(-1)^(alpha);
\n",
"\n",
"[name='Budget constraint',relax = 'INEG']
\n",
"C+K-(1-delta)*K(-1)=exp(A)*K(-1)^(alpha);
\n",
"\n",
"// 3.
\n",
"[name='LOM capital']
\n",
"Invest = K-(1-delta)*K(-1);
\n",
"\n",
"// 4.
\n",
"[name='investment',bind='IRR,INEG']
\n",
"(log_Invest - log(phi*steady_state(Invest))) = 0;
\n",
"[name='investment',relax='IRR']
\n",
"Lambda=0;
\n",
"[name='investment',bind='IRR',relax='INEG']
\n",
"(log_Invest - log(phi*steady_state(Invest))) = 0;
\n",
"\n",
"// 5.
\n",
"[name='LOM TFP']
\n",
"A = rho*A(-1)+epsilon;
\n",
"\n",
"// Definitions
\n",
"[name='Definition log capital']
\n",
"log_K=log(K);
\n",
"[name='Definition log consumption']
\n",
"log_C=log(C);
\n",
"[name='Definition log investment']
\n",
"log_Invest=log(Invest);
\n",
"end;
\n",
"\n",
"occbin_constraints;
\n",
"name 'IRR'; bind log_Invest-log(steady_state(Invest))\n",
"name 'INEG'; bind log_Invest-log(steady_state(Invest))<-0.000001; %not exactly 0 for numerical reasons
\n",
"end;
\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"id": "06cfe868-98bd-4a58-a7d4-2838af60f468",
"metadata": {},
"source": [
"The steady state solution is here."
]
},
{
"cell_type": "markdown",
"id": "250f8b8b-9763-4a31-9e11-df6191d6fc82",
"metadata": {},
"source": [
"\n",
"steady_state_model;
\n",
"K = ((1/beta-1+delta)/alpha)^(1/(alpha-1));
\n",
"C = -delta*K +K^alpha;
\n",
"Invest = delta*K;
\n",
"log_K = log(K);
\n",
"log_C = log(C);
\n",
"log_Invest = log(Invest);
\n",
"Lambda = 0;
\n",
"A=0;
\n",
"end;
\n",
""
]
},
{
"cell_type": "markdown",
"id": "599931f3-3023-4922-b5b8-1d6c6b49fcd2",
"metadata": {},
"source": [
"Assume there is negative TFP shock at period 1-9, 10 and 50,\n",
"\n",
"there is positive TFP shock at period 90 and 130."
]
},
{
"cell_type": "markdown",
"id": "6699d08e-26ad-49c1-a08a-c405321b5423",
"metadata": {},
"source": [
"\n",
"shocks;
\n",
" var epsilon; stderr 0.015;
\n",
"end;
\n",
"\n",
"steady;
\n",
"\n",
"shocks(surprise);
\n",
"var epsilon;
\n",
"periods 1:9, 10, 50, 90, 130, 131:169;
\n",
"values -0.0001, -0.01,-0.02, 0.01, 0.02, 0;
\n",
"end;
\n",
"\n",
"occbin_setup;
\n",
"occbin_solver(simul_periods=200,simul_check_ahead_periods=200);
\n",
"\n",
"occbin_graph log_C epsilon Lambda log_K log_Invest A;
\n",
""
]
},
{
"cell_type": "markdown",
"id": "d7c745e7-70b6-4e5b-9026-195615db7588",
"metadata": {},
"source": [
"After 3 negative TFP shocks, at period 50, IRR condition binds, and there is difference between piecewise linear (occasional binding) and linear case. "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "aca2ef0d-fe45-49b3-b529-c1be689068a7",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"ans = 'C:\\Users\\ading\\A_TA_Notes'
"
],
"text/plain": [
"ans = 'C:\\Users\\ading\\A_TA_Notes'"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cd\"C:\\Users\\ading\\A_TA_Notes\"\n",
"pwd"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a1ca8287-0e66-4f49-aaa6-4a2e70e375db",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Starting Dynare (version 6.2).\n",
"Calling Dynare with arguments: none\n",
"Starting preprocessing of the model file ... \n",
"Found 8 equation(s). \n",
"Evaluating expressions... \n",
"Computing static model derivatives (order 1). \n",
"Normalizing the static model... \n",
"Finding the optimal block decomposition of the static model... \n",
"4 block(s) found: \n",
" 3 recursive block(s) and 1 simultaneous block(s). \n",
" the largest simultaneous block has 2 equation(s) \n",
" and 2 feedback variable(s). \n",
"Computing dynamic model derivatives (order 2). \n",
"Normalizing the dynamic model... \n",
"Finding the optimal block decomposition of the dynamic model... \n",
"3 block(s) found: \n",
" 2 recursive block(s) and 1 simultaneous block(s). \n",
" the largest simultaneous block has 5 equation(s) \n",
" and 4 feedback variable(s). \n",
"Preprocessing completed. \n",
"Preprocessing time: 0h00m00s.\n",
"\n",
"STEADY-STATE RESULTS:\n",
"\n",
"A \t\t 0\n",
"C \t\t 1.16335\n",
"Invest \t\t 0.353288\n",
"K \t\t 3.53288\n",
"Lambda \t\t 0\n",
"log_K \t\t 1.26211\n",
"log_Invest \t\t -1.04047\n",
"log_C \t\t 0.151306\n"
]
},
{
"data": {
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"
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total computing time : 0h00m02s\n"
]
}
],
"source": [
"dynare Occbin_example.mod"
]
},
{
"cell_type": "markdown",
"id": "d0baa43f-8ff8-43a9-9c11-4bd56ac8a6fc",
"metadata": {},
"source": [
"_____________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "cbee5bda-51e6-4539-a9e3-73cbb83069bc",
"metadata": {},
"source": [
"# Reference"
]
},
{
"cell_type": "markdown",
"id": "3a0a4377-c0b9-40cb-bdbc-8ba96b948d2f",
"metadata": {},
"source": [
"_________________________________________________________________________________________________________________________________________________"
]
},
{
"cell_type": "markdown",
"id": "2ff2a556-d8ca-4eed-806f-4b3db0fc2aab",
"metadata": {},
"source": [
"1. Dynare Manual, https://www.dynare.org/manual/"
]
},
{
"cell_type": "markdown",
"id": "606479d5-9095-4f53-b066-08c04fba4673",
"metadata": {},
"source": [
"2. Pontus Rendahl, \"Linear Time Iteration\", Institute for Advanced Studies"
]
},
{
"cell_type": "markdown",
"id": "42865207-b73e-4173-8b29-20444d59fdb6",
"metadata": {},
"source": [
"3. Alisdair Mckay, \"Computational Notes on Heterogeneous-Agent Macroeconomics\", https://alisdairmckay.com/Notes/HetAgentsV2/"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "MATLAB Kernel",
"language": "matlab",
"name": "jupyter_matlab_kernel"
},
"language_info": {
"file_extension": ".m",
"mimetype": "text/x-matlab",
"name": "matlab"
}
},
"nbformat": 4,
"nbformat_minor": 5
}