Optimal Policy with General Signal Extraction

Most available results on optimal decisions under partial information are derived under “separation”. But this principle does not always hold. We derive a non-standard first order condition of optimality from first principles when signal extraction and optimal policy must be jointly determined. This allows us to solve a model of optimal fiscal policy where separation does not apply. Tax smoothing prevails in normal times, but taxes respond strongly in recessions. This non-linearity arises because signal extraction interacts differently with optimal policy depending on the value of the observed signals. Existing results based on the “separation principle” follow as special cases.