Optimal Stabilization Policy When the Private Sector Has Information Processing Constraints

This paper considers a linear-quadratic control problem and determines how optimal policy is affected when the private sector has finite (Shannon) capacity to process information. Such capacity constraints prevent private agents from perfectly observing the state variables and the policy choices. The first result is that the control problem when including these constraints remains to be of a linear-quadratic form, which makes the problem technically tractable. The main difference to a standard problem are the costs associated with the use of the policy instrument, which are now endogenous. Depending on parameters these costs might be either higher or lower and lead to less or more aggressive optimal policies, respectively. If shocks show persistence and are heteroskedastic then the costs of using the policy instrument are non-constant and generate either sluggish or overshooting optimal policy reactions.