Should the Exchange Rate be in a Monetary Policy Objective Function?

Following from Woodford’s derivation of a benevolent monetary policy maker’s objective function from agents utility, a number of papers have suggested that policy in an open economy should have the same objectives as in a closed economy, and in particular that the exchange rate should play no role. We show that this conclusion is not robust to the presence of any shocks to International Risk Sharing. When such shocks are important, the exchange rate appears alongside output and inflation in the social welfare function. However the form of this target is rather different from that used by a number of authors.