We document that the effect of monetary policy on housing prices varies substantially by local housing market. We show that this heterogeneity across local housing markets can be partly explained by variation in housing supply conditions – housing prices are typically more sensitive to changes in interest rates in areas where land is more expensive. But other factors are important too. Specifically, we find the sensitivity is greater in areas where incomes are relatively high, households are more indebted and there are more investors. Taken together, this suggests that the state of the economy can affect the sensitivity of housing prices to monetary policy. We also directly explore how monetary policy affects housing wealth inequality. We find that housing prices in more expensive areas are more sensitive to changes in interest rates than in cheaper areas. This suggests that lower interest rates increase housing wealth inequality, while higher rates do the opposite. However, these effects appear to be temporary.