The Rational Inattention Filter

50 Pages Posted: 3 Feb 2017

See all articles by Bartosz Maćkowiak

Bartosz Maćkowiak

European Central Bank (ECB)

Filip Matějka

Charles University in Prague - CERGE-EI (Center for Economic Research and Graduate Education - Economics Institute)

Mirko Wiederholt

Northwestern University - Department of Economics

Date Written: January 31, 2017

Abstract

Dynamic rational inattention problems used to be difficult to solve. This paper provides simple, analytical results for dynamic rational inattention problems. We start from the benchmark rational inattention problem. An agent tracks a variable of interest that follows a Gaussian process. The agent chooses how to pay attention to this variable. The agent aims to minimize, say, the mean squared error subject to a constraint on information flow, as in Sims (2003). We prove that if the variable of interest follows an ARMA(p,q) process, the optimal signal is about a linear combination of {Xt,...,Xt-p 1} and {Et,...,Et-q 1}, where Xt denotes the variable of interest and Et denotes its period t innovation. The optimal signal weights can be computed from a simple extension of the Kalman filter: the usual Kalman filter equations in combination with first-order conditions for the optimal signal weights. We provide several analytical results regarding those signal weights. We also prove the equivalence of several different formulations of the information flow constraint. We conclude with general equilibrium applications from Macroeconomics.

Keywords: rational inattention, Kalman filter, Macroeconomics

JEL Classification: D83, E32

Suggested Citation

Maćkowiak, Bartosz and Matějka, Filip and Wiederholt, Mirko, The Rational Inattention Filter (January 31, 2017). ECB Working Paper No. 2007. Available at SSRN: https://ssrn.com/abstract=2910942

Bartosz Maćkowiak (Contact Author)

European Central Bank (ECB) ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314
Germany

Filip Matějka

Charles University in Prague - CERGE-EI (Center for Economic Research and Graduate Education - Economics Institute) ( email )

P.O. Box 882
7 Politickych veznu
Prague 1, 111 21
Czech Republic

HOME PAGE: http://www.cerge-ei.cz

Mirko Wiederholt

Northwestern University - Department of Economics ( email )

2001 Sheridan Road
Evanston, IL 60208
United States
(847) 491-8227 (Phone)
(847) 491-7001 (Fax)

HOME PAGE: http://faculty.wcas.northwestern.edu/~mwi774/

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