Analytical Solutions to Rational Inattention Problems

This paper derives an analytical solution to a class of rational inattention problems. In Sims (2003) Section 4, the decision-maker chooses the process {Y} to track a Gaussian process {X} with loss E[(X-Y)^2] subject to a constraint on the information flow between the two processes. Sims (2003) solves this problem numerically. I derive an analytical solution to this problem in several special cases. Having an analytical solution has the following advantages. First, the analytical solution can be used to illustrate properties of the solution. Second, the analytical solution makes it easier to solve DSGE models in which agents face information flow constraints. Third, the analytical solution helps clarify the relation between rational inattention and signal extraction with exogenous signals.