Rational inattention in the frequency domain

Abstract

This paper solves a dynamic rational inattention problem by formulating it in the frequency domain. The main result is a rational inattention version of the classical Wiener-Kolmogorov filter. This filter permits an infinite-dimensional state vector, provides a new line of attack for obtaining closed-form solutions, and can be implemented numerically using a simple iterative algorithm. The frequency-domain approach also sheds new light on why rational inattention produces forward-looking behavior: inattentive agents are willing to accept more uncertainty about the timing of disturbances in exchange for less uncertainty about fluctuations at the most important frequencies.