Optimal Policy with Endogenous Signal Extraction

This paper studies optimal policy in models with multidimensional uncertainty and endogenous observables. We first consider a very general setup where the policy-maker does not observe the realisations of the shocks that hit the economy, but only some aggregate variables that are endogenous with respect to policy, therefore standard first order conditions do not hold. We derive first order conditions of optimality from first principles and we illustrate why the estimation of the state of the economy cannot be separated from the determination of the optimal policy. In an optimal fiscal policy application with incomplete markets and endogenous Partial Information, we find that the optimal policy response to aggregate data can be quite non-linear: it calls for tax smoothing across states in normal times, but in some cases for a strong adjustment of fiscal positions during a slump. We show that policies that disregard the endogeneity of the filtering problem and hence these non-linearities can be quite wrong. Finally, our model can rationalise the fiscal response of some European countries to the Great Recession: a slow reaction, followed by large deficits and a delayed sharp fiscal adjustment that protracts the downturn.