Rational inattention in the frequency domain

This paper solves the canonical dynamic rational inattention problem of Sims (2003) by formulating it in the frequency domain. The solution complements and extends existing results, which have been derived in the time domain. The paper provides a simple algorithm that quickly and accurately computes the solution numerically in the frequency domain, and shows how to obtain closed-form solutions when the target is an autoregressive moving average process. The key step to solve the problem is to correctly articulate the “no foresight” constraint. This constraint, often overlooked, restricts agents from processing information about future structural disturbances. The paper also analyzes the consequences of removing the no foresight constraint in a model of the real effects of nominal disturbances