Signal Extraction and Rational Inattention∗

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 are fixed exogenously in the SE and RI problems, respectively, the two environments lead to different policy and welfare implications. We also find that if the signal-to-noise ratio in the SE problem is fixed, the two theories generate the same policy implications in the univariate case, but different policy implications in the multivariate case. These results are robust to the presence of correlation between structural shocks and noise shocks and the presence of risk-sensitive preferences. Thus, while RI provides a microfoundation for the imprecise observations and noise in the SE problem it is difficult to specify the structure of the noise in the SE problem in a manner consistent with the efficiency conditions from RI. JEL Classification Numbers: C61, D81, E21.