Signal Extraction and Rational Inattention

Abstract

In this paper we examine the implications of two theories of informational frictions, signal extraction (SE) and rational inattention (RI), for optimal decisions and economic dynamics within the linear-quadratic-Gaussian (LQG) setting. We first show that if the variance of the noise and channel capacity (or marginal information cost) are fixed exogenously in the SE and RI problems, respectively, the two environments lead to di¤erent policy and equilibrium asset pricing implications. Second, we find that if the signal-to-noise ratio and capacity in the SE and RI problems are fixed, respectively, the two theories generate the same policy implications in the univariate case, but different policy implications in the multivariate case. We also show that our results do not depend on the presence of correlation between fundamental and noise shocks. We then discuss the applications to macroeconomic models of permanent income and price-setting.