Abstract
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.
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