The standard view of housing markets holds that the flexibility of local housing supply— shaped by factors like geography and regulation—strongly affects the response of house prices, house quantities and population to rising housing demand. However, from 2000 to 2020, we find that higher income growth predicts the same growth in house prices, housing quantity, and population regardless of a city’s estimated housing supply elasticity. We find the same pattern when we expand the sample to 1980 to 2020, use different elasticity measures, and when we instrument for local housing demand. Using a general demand-and-supply framework, we show that our findings imply that constrained housing supply is relatively unimportant in explaining differences in rising house prices among U.S. cities. These results challenge the prevailing view of local housing and labor markets and suggest that easing housing supply constraints may not yield the anticipated improvements in housing affordability.