Optimal Policy with General Signal Extraction

This paper studies optimal policy with partial information in a general setup where observed signals are endogenous to policy. In this case, signal extraction about the state of the economy cannot be separated from the determination of the optimal policy. We derive a non-standard first order condition of optimality from first principles and we use it to find numerical solutions. We show how previous results based on linear methods, where separation or certainty equivalence obtains, arise as special cases. We use as an example 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 when a recession is quite certain and the economy is near the top of the Laffer curve or near a debt limit.