We study the role of institutional characteristics of mortgage markets in affecting the strength and timing of the effects of monetary policy shocks on house prices and consumption in a sample of OECD countries. We document three facts: (1) there is significant divergence in the structure of mortgage markets across the main industrialised countries; (2) at the business cycle frequency, the correlation between consumption and house prices increases with the degree of flexibility/development of mortgage markets; (3) the transmission of monetary policy shocks on consumption and house prices is stronger in countries with more flexible/developed mortgage markets. We then build a two-sector dynamic general equilibrium model with price stickiness and collateral constraints, where the ability of borrowing is endogenously linked to the nominal value of a durable asset (housing). We study how the response of consumption to monetary policy shocks is affected by alternative values of three key institutional parameters: (i) down-payment rate; (ii) mortgage repayment rate; (iii) interest rate mortgage structure (variable vs. fixed interest rate). In line with our empirical evidence, the sensitivity of consumption to monetary policy shocks increases with lower values of (i) and (ii), and is larger under a variable-rate mortgage structure.