The intensity of boom-and-bust cycles in house prices differs markedly between the member countries of the Euro Area. We provide empirical evidence that links the heterogeneity in country-wise house price responses to monetary policy shocks to a proxy for housing supply elasticities. We then construct a model of a currency area where (i) structural heterogeneity in countries' ability to quickly produce many new housing units and (ii) subjective private sector house price expectations in the form of capital gain extrapolation interact to endogenously generate inefficient boom-bust cycles in house prices that differ in their intensity between countries. To solve the model, we propose a new method for linearizing models with asset price learning. Specifically, we explicitly solve for the subjectively optimal plan of households to first order, given that they hold subjective expectations over house prices and rational expectations elsewhere. Our model qualitatively matches empirical patterns and uncovers new challenges for the monetary authority in a currency area.