{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Pricing under RI with Endogenous Feedback"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"This example solves a pricing problem under rational inattention **with** endogenous feedback using the [DRIPs](https://github.com/afrouzi/DRIPs.jl) package."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"See [Afrouzi and Yang (2020)](http://www.afrouzi.com/dynamic_inattention.pdf) for background on the theory.\n",
"Include the solver and import packages for plots and performance:"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Contents\n",
"* Setup\n",
" * Problem\n",
" * Matrix Notation\n",
"* Initialization\n",
" * Assign Parameters\n",
" * A Function for Finding the Fixed Point\n",
"* Solution\n",
"* IRFs\n",
"* Measure Performance"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Setup\n",
"### Problem\n",
"Suppose now that there is general equilibrium feedback with the degree of strategic complementarity $\\alpha$: $$p_{i,t}^*=(1-\\alpha)q_t+\\alpha p_t$$ where\n",
"$$\n",
"\\begin{aligned}\n",
" \\Delta q_t&=\\rho \\Delta q_{t-1}+u_t,\\quad u_t\\sim \\mathcal{N}(0,\\sigma_u^2) \\\\\n",
" p_t&\\equiv \\int_0^1 p_{i,t}di\n",
"\\end{aligned}\n",
"$$\n",
"Note that now the state space representation for $p_{i,t}^*$ is no longer exogenous and is determined in the equilibrium. However, we know that this is a Guassian process and by Wold's theorem we can decompose it to its $MA(\\infty)$ representation:\n",
"$$\n",
"\\begin{aligned}\n",
" p_{i,t}^*=\\Phi(L)u_t\n",
"\\end{aligned}\n",
"$$\n",
"where $\\Phi(.)$ is a lag polynomial and $u_t$ is the shock to nominal demand. Here, we have basically guessed that the process for $p_{i,t}^*$ is determined uniquely by the history of monetary shocks which requires that rational inattention errors of firms are orthogonal (See [Afrouzi, 2020](http://www.afrouzi.com/strategic_inattetion.pdf)). Our objective is to find $\\Phi(.)$."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Since we cannot put $MA(\\infty)$ processes in the computer, we approximate them with truncation. In particular, we know for stationary processes, we can arbitrarily get close to the true process by truncating $MA(\\infty)$ processes to $MA(T)$ processes. Our problem here is that $p_{i,t}^*$ has a unit root and is not stationary. We can bypass this issue by re-writing the state space in the following way:\n",
"$$\n",
"\\begin{aligned}\n",
" p_{i,t}^*=\\phi(L)\\tilde{u}_t,\\quad \\tilde{u}_t=(1-L)^{-1}u_t =\\sum_{j=0}^\\infty u_{t-j}\n",
"\\end{aligned}\n",
"$$\n",
"here $\\tilde{u}_{t-j}$ is the unit root of the process and basically we have differenced out the unit root from the lag polynomial, and $\\phi(L)=(1-L)\\Phi(L)$. Notice that since the original process was difference stationary, differencing out the unit root means that $\\phi(L)$ is now in $\\ell_2$, and the process can now be approximated arbitrarily precisely with truncation."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Matrix Notation"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"For a length of truncation $L$, let $\\vec{x}_t\\equiv (\\tilde{u}_t,\\tilde{u}_{t-1},\\dots,\\tilde{u}_{t-(L+1)})\\in\\mathbb{R}^L$. Then, note that $p_{i,t}^*\\approx \\mathbf{H} '\\vec{x}_{t}$ where $\\mathbf{H}\\in \\mathbb{R}^L$ is the truncated matrix analog of the lag polynominal, and is endogenous to the problem. Our objective is to find the general equilibrium $\\mathbf{H}$ along with the optimal information structure that it implies."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Moreover, note that $$q_t=\\mathbf{H}_q'\\vec{x}_t,\\quad \\mathbf{H}_q'=(1,\\rho,\\rho^2,\\dots,\\rho^{L-1})$$"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We will solve for $\\phi$ by iterating over the problem. In particular, in iteration $n\\geq 1$, given the guess $\\mathbf{H}_{(n-1)}$, we have the following state space representation for the firm's problem\n",
"$$\n",
"\\begin{aligned}\n",
" \\vec{x}_{t}&\n",
" = \\underset{\\mathbf{A}}{\\underbrace{\\left[\\begin{array}{ccccc}\n",
" 1 & 0 & \\dots & 0 & 0\\\\\n",
" 1 & 0 & \\dots & 0 & 0\\\\\n",
" 0 & 1 & \\dots & 0 & 0\\\\\n",
" \\vdots & \\vdots & \\ddots & \\vdots & \\vdots\\\\\n",
" 0 & 0 & \\dots & 1 & 0\n",
" \\end{array}\\right]}}\\, \\vec{x}_{t-1}\n",
" + \\underset{\\mathbf{Q}}{\\underbrace{\\left[\\begin{array}{c}\n",
" \\sigma_u\\\\\n",
" 0\\\\\n",
" 0\\\\\n",
" \\vdots\\\\\n",
" 0\n",
" \\end{array}\\right]}}\\, u_t, \\\\\n",
" p_{i,t}^*&=\\mathbf{H}_{(n-1)}'\\vec{x}_{t}\n",
"\\end{aligned}\n",
"$$"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Then we can solve the rational inattention problem of all firms and get the new guess for $p_t^*$:\n",
"$$\n",
"\\begin{aligned}\n",
" p_t^* & = (1-\\alpha)q_t + \\alpha p_t \\\\\n",
" & = (1-\\alpha)\\sum_{j=0}^\\infty \\alpha^j q_t^{(j)}, \\\\\n",
" q_{t}^{(j)}&\\equiv \\begin{cases}\n",
"q_{t} & j=0\\\\\n",
"\\int_{0}^{1}\\mathbb{E}_{i,t}[q_{t}^{(j-1)}]di & j\\geq1\n",
"\\end{cases}\n",
"\\end{aligned}\n",
"$$"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"where $q_t^{(j)}$ is the $j$'th order belief of firms, on average, of $q_t$. Now, we need to write these higher order beliefs in terms of the state vector. Suppose, for a given $j$, there exists $\\mathbf{X}_j\\in \\mathbb{R}^{L\\times L}$ such that\n",
"$$\n",
"\\begin{aligned}\n",
"q_t^{(j)} = \\mathbf{H}_q'\\mathbf{X}_j \\vec{x}_t\n",
"\\end{aligned}\n",
"$$\n",
"This clearly holds for $j=0$ with $\\mathbf{X}_0=\\mathbf{I}$."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Now, note that\n",
"$$\n",
"\\begin{aligned}\n",
" q_{t}^{(j+1)} &= \\int_{0}^{1}\\mathbb{E}_{i,t}[q_{t}^{(j)}]di \\\\\n",
" &= \\mathbf{H}_{q}'\\mathbf{X}_{j}\\int_{0}^{1}\\mathbb{E}_{i,t}[\\vec{x}_{t}]di \\\\\n",
" &= \\mathbf{H}_{q}'\\mathbf{X}_{j}\\sum_{j=0}^{\\infty}[(\\mathbf{I}-\\mathbf{K}_{(n)}\\mathbf{Y}'_{(n)})\\mathbf{A}]^{j}\\mathbf{K}_{(n)}\\mathbf{Y}'_{(n)}\\vec{x}_{t-j} \\\\\n",
" &\\approx\\underset{\\equiv\\mathbf{X}_{(n)}}{\\mathbf{H}_{q}'\\mathbf{X}_{j}\\underbrace{\\left[\\sum_{j=0}^{\\infty}[(\\mathbf{I}-\\mathbf{K}_{(n)}\\mathbf{Y}'_{(n)})\\mathbf{A}]^{j}\\mathbf{K}_{(n)}\\mathbf{Y}'_{(n)}\\mathbf{M}'^{j}\\right]}}\\vec{x}_{t}=\\mathbf{H}_{q}'\\mathbf{X}_{j}\\mathbf{X}_{(n)}\\vec{x}_{t}\n",
"\\end{aligned}\n",
"$$\n",
"where the $(n)$ subscripts refer to the solution of the RI problem in the $(n)$'th iteration. Note that this implies\n",
"$$\n",
"\\begin{aligned}\n",
"\\mathbf{X}_{j}=\\mathbf{X}_{(n)}^j,\\forall j\\geq 0 \\Rightarrow q_t^{(j)}=\\mathbf{X}_{(n)}^{j}\\vec{x}_t\n",
"\\end{aligned}\n",
"$$"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"This gives us an updated guess for $\\mathbf{H}$:\n",
"$$\n",
"\\begin{aligned}\n",
" p_t^*&=(1-\\alpha)\\mathbf{H}_q'\\underset{\\equiv \\mathbf{X}_{p,(n)}}{\\underbrace{\\left[\\sum_{j=0}^\\infty \\alpha^j \\mathbf{X}_{(n)}^j\\right]}} \\vec{x}_t \\\\\n",
" &\\Rightarrow \\mathbf{H}_{(n)} = (1-\\alpha)\\mathbf{X}_{p,(n)}'\\mathbf{H}_q\n",
"\\end{aligned}\n",
"$$\n",
"We iterate until convergence of $\\mathbf{H}_{(n)}$."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Initialization\n",
"Include the package:"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using DRIPs;"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"### Assign Parameters"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"ρ = 0.6; #persistence of money growth\n",
"σ_u = 0.1; #std. deviation of shocks to money growth\n",
"α = 0.8; #degree of strategic complementarity\n",
"L = 40; #length of truncation\n",
"Hq = ρ.^(0:L-1); #state-space rep. of Δq"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"Specifying the primitives of the DRIP:"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using LinearAlgebra;\n",
"ω = 0.2;\n",
"β = 0.99;\n",
"A = [1 zeros(1,L-2) 0; Matrix(I,L-1,L-1) zeros(L-1,1)];\n",
"Q = [σ_u; zeros(L-1,1)];"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"### A Function for Finding the Fixed Point"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Let us now define a function that solves the GE problem and returns the solution in a `Drip` structure:"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"function ge_drip(ω,β,A,Q, #primitives of drip except for H because H is endogenous\n",
" α, #strategic complementarity\n",
" Hq, #state space rep. of Δq\n",
" L; #length of truncation\n",
" H0 = Hq, #optional: initial guess for H (Hq is the true solution when α=0)\n",
" maxit = 200, #optional: max number of iterations for GE code\n",
" tol = 1e-4) #optional: tolerance for iterations\n",
" err = 1;\n",
" iter = 0;\n",
" M = [zeros(1,L-1) 0; Matrix(I,L-1,L-1) zeros(L-1,1)];\n",
" while (err > tol) & (iter < maxit)\n",
" if iter == 0\n",
" global ge = Drip(ω,β,A,Q,H0, w = 0.9);\n",
" else\n",
" global ge = Drip(ω,β,A,Q,H0;Ω0 = ge.ss.Ω ,Σ0 = ge.ss.Σ_1,maxit=15);\n",
" end\n",
"\n",
" XFUN(jj) = ((I-ge.ss.K*ge.ss.Y')*ge.A)^jj * (ge.ss.K*ge.ss.Y') * (M')^jj\n",
" X = DRIPs.infinitesum(XFUN; maxit=L, start = 0); #E[x⃗]=X×x⃗\n",
"\n",
" XpFUN(jj) = α^jj * X^(jj)\n",
" Xp = DRIPs.infinitesum(XpFUN; maxit=L, start = 0);\n",
"\n",
" H1 = (1-α)*Xp'*Hq;\n",
" err= 0.5*norm(H1-H0,2)/norm(H0)+0.5*err;\n",
" H0 = H1;\n",
"\n",
" iter += 1;\n",
" if iter == maxit\n",
" print(\"GE loop hit maxit\\n\")\n",
" end\n",
" println(\"Iteration $iter. Difference: $err\")\n",
" end\n",
" return(ge)\n",
"end;"
],
"metadata": {},
"execution_count": 4
},
{
"cell_type": "markdown",
"source": [
"## Solution\n",
"Solve for benchmark parameterization:"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.376908 seconds (303.26 k allocations: 319.417 MiB, 9.06% gc time)\n"
]
}
],
"cell_type": "code",
"source": [
"using Suppressor; # suppresses printing of function. comment to see convergence details\n",
"@time @suppress ge = ge_drip(ω,β,A,Q,α,Hq,L); # remove suppress to see convergence log"
],
"metadata": {},
"execution_count": 5
},
{
"cell_type": "markdown",
"source": [
"## IRFs\n",
"Get IRFs:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.PyPlotBackend() n=3}",
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",
"text/html": [
""
],
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 6
}
],
"cell_type": "code",
"source": [
"geirfs = irfs(ge,T = L)\n",
"\n",
"M = [zeros(1,L-1) 0; Matrix(I,L-1,L-1) zeros(L-1,1)]; # shift matrix\n",
"dq = diagm(Hq)*geirfs.x[1,1,:]; # change in nominal demand\n",
"Pi = (I-M)*geirfs.a[1,1,:]; # inflation\n",
"y = inv(I-M)*(dq-Pi); # output\n",
"\n",
"using Plots, LaTeXStrings; pyplot();\n",
"p1 = plot(1:L,[dq,Pi],\n",
" label = [L\"Agg. Demand Growth ($\\Delta q$)\" L\"Inflation ($\\pi$)\"]);\n",
"\n",
"p2 = plot(1:L,y,\n",
" label = L\"Output ($y$)\");\n",
"\n",
"plot(p1,p2,\n",
" layout = (1,2),\n",
" xlim = (1,20),\n",
" lw = 3,\n",
" legend = :topright,\n",
" legendfont = font(12),\n",
" tickfont = font(12),\n",
" size = (900,370),\n",
" framestyle = :box)"
],
"metadata": {},
"execution_count": 6
},
{
"cell_type": "markdown",
"source": [
"## Measure Performance"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Solve and measure performance for random values of $\\omega$:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "BenchmarkTools.Trial: \n memory estimate: 282.72 MiB\n allocs estimate: 34098\n --------------\n minimum time: 194.207 ms (2.63% GC)\n median time: 200.155 ms (5.08% GC)\n mean time: 200.345 ms (3.88% GC)\n maximum time: 208.894 ms (2.45% GC)\n --------------\n samples: 25\n evals/sample: 1"
},
"metadata": {},
"execution_count": 7
}
],
"cell_type": "code",
"source": [
"using BenchmarkTools;\n",
"@suppress @benchmark ge_drip(ω,β,A,Q,α,Hq,L) setup = (ω=rand()) # solves and times the fixed point for different values of ω"
],
"metadata": {},
"execution_count": 7
},
{
"cell_type": "markdown",
"source": [
"---\n",
"\n",
"*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
],
"metadata": {}
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.4.1"
},
"kernelspec": {
"name": "julia-1.4",
"display_name": "Julia 1.4.1",
"language": "julia"
}
},
"nbformat": 4
}