Optimal Policy with General Signal Extraction

• Authors: Albert Marcet and Esther Hauk.
• BSE Working Paper: 110405 | October 16
• Keywords: optimal policy; partial information; separation; calculus of variations; fiscal policy
• JEL codes: C63, D82, E60, H60
• optimal policy; partial information; separation; calculus of variations; fiscal policy

We study optimal policy when the planner has partial information in a general setup where observed signals are endogenous to policy. In this context, signal extraction and policy have to be determined jointly. We derive a general non-standard first order condition of optimality from first principles and we use it to find numerical solutions. This first order condition allows us to identify widely-used special cases in the literature in which the signal extraction and the optimal decision problems can be solved separately, using the well-known separation principle. Our general setup, which does not feature any separation, is relevant for most available dynamic models in macro. We apply our results to a model of fiscal policy and show that optimal taxes are often a very non-linear function of observed hours, calling for tax smoothing in normal times, but for a strong fiscal reaction to output in a deeper recession. This non-linearity arises because signal extraction interacts differently with optimal policy depending on the range of observed signals. The non-linearity is stronger near the top of the Laffer curve or near a debt limit. In a fully dynamic model taxes react with a delay to adverse deficit shocks due to partial information, and this can lead to larger low-frequency fluctuations.