The role of liquidity constraints in the response of monetary policy to house prices

We analyse the optimal response of monetary policy to house prices in a New Keynesian framework. A positive wealth effect from housing is derived from liquidity constrained consumers. Housing equity withdrawal allows them to convert an increase in housing value into consumption and we show that monetary policy should react to house prices due to their effect on consumption by constrained agents. Moreover, we allow the share of liquidity constrained consumers to vary with house prices. Consequently, the optimal weights on expected inflation, the output gap and house prices in the optimal interest rate rule vary over time too.