Leaning against housing prices as robustly optimal monetary policy

We analytically characterize optimal monetary policy for an augmented New Keynesian model with a housing sector. In a setting where the private sector has rational expectations about future housing prices and inflation, optimal monetary policy can be characterized without making reference to housing price developments: commitment to a "target criterion" that refers to inflation and the output gap only is optimal, as in the standard model without a housing sector. When the policymaker is concerned with potential departures of private sector expectations from rational ones and seeks to choose a policy that is robust against such possible departures, then the optimal target criterion must also depend on housing prices. In the empirically realistic case where housing is subsidized and where monopoly power causes output to fall short of its optimal level, the robustly optimal target criterion requires the central bank to "lean against" housing prices: following unexpected housing price increases, policy should adopt a stance that is projected to undershoot its normal targets for inflation and the output gap, and similarly aim to overshoot those targets in the case of unexpected declines in housing prices. The robustly optimal target criterion does not require that policy distinguish between "fundamental" and "non-fundamental" movements in housing prices.