DP11237 The Rational Inattention Filter

Author(s): Bartosz Adam Mackowiak, Filip Matejka, Mirko Wiederholt
Publication Date: April 2016
Keyword(s): Kalman filter, Macroeconomics, rational inattention
JEL(s): C61, D83, E30
Programme Areas: Monetary Economics and Fluctuations
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=11237

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.