Robustly optimal monetary policy in a New Keynesian model with housing

We analytically characterize optimal monetary policy for an augmented New Keynesian model with a housing sector. With rational private sector expectations about housing prices and inflation, optimal monetary policy can be characterized by a standard 'target criterion' that refers to inflation and the output gap, without making reference to housing prices. When the policymaker is concerned with potential departures of private sector expectations from rational ones and seeks a policy that is robust against such possible departures, then the optimal target criterion must also depend on housing prices. For empirically realistic cases, the central bank should then 'lean against' housing prices, i.e., following unexpected housing price increases (decreases), policy should adopt a stance that is projected to undershoot (overshoot) its normal targets for inflation and the output gap. Robustly optimal policy does not require that the central bank distinguishes between 'fundamental' and 'non-fundamental' movements in housing prices.