We use a structural Bayesian stochastic search variable selection VAR model to investigate the heterogeneous effects of housing demand shocks on economic and lending activities and the role of house prices in the monetary policy transmission across euro area countries, as well as the United Kingdom and the United States. A novel identification scheme which combines zero and sign restrictions based on benchmark models is proposed. We document significant asymmetries in the responses of house prices to monetary policy across euro area countries. We show that house prices and loans are more sensitive to changes in monetary policy in the euro area, characterised by bankcentric financial systems, than in the United States where the financial system is more market-oriented. House prices also play an important role in the availability of credit to households but a limited role in driving consumption in the euro area consistently with the restricted use of mortgage equity withdrawal. Overall, the housing wealth effect seems to be related to the development of the mortgage system.