Dynamic Rational Inattention: Analytical Results

This paper presents analytical results for dynamic rational inattention problems as in Sims (2003). The agent tracks an optimal action that follows a Gaussian process. The agent chooses the properties of the signals that he receives, so as to minimize the mean squared difference between his action and the optimal action, subject to a constraint on information flow. We prove that the optimal signal is a one-dimensional signal about the elements of the state vector, which typically has non-zero signal weights on all elements of the state vector. The intuition for these results is that an agent with memory and limited attention wants to learn about the current optimal action and the best predictors of future optimal actions. Hence, in a dynamic economy, rational inattention creates a combination of delay in actions due to noise in the optimal signal and forward-looking actions due to forward-looking information choice. We illustrate these analytical results in a macroeconomic model of price-setting and a business cycle model with news shocks.