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Title: The Rational Inattention Filter

Author(s): Bartosz Adam Mackowiak, Filip Matejka and Mirko Wiederholt

Publication Date: April 2016

Keyword(s): Kalman filter, Macroeconomics and rational inattention

Programme Area(s): Monetary Economics and Fluctuations

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 {X(t),...,X(t-p+1)} and {e(t),... e(t-q+1)}, where X(t) denotes the variable of interest and e(t) 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.

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Bibliographic Reference

Mackowiak, B, Matejka, F and Wiederholt, M. 2016. 'The Rational Inattention Filter'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=11237