To estimate the causal effect of immigration flows on housing market variables in the medium-run, we address the key problem of immigrant sorting by exploiting exogenous variation from push-factor migration and a unique institutional setting that allocates refugee immigrants to municipalities on a quasi-random basis. Economic theory predicts that immigrant influx will increase demand for residential space, increasing house rents and prices as well as residential construction at the aggregate level, but will have ambiguous effects at the neighborhood level in case of native flight. We find a large positive impact on house rents and prices and little evidence of native flight at the municipal level. At the neighborhood level, we also find a positive impact on house rents and prices, albeit more modest, as well as evidence of native flight. We further provide evidence of inelastic supply. Our findings support economic policies that increase housing supply elasticities and re-distribute part of the gains from immigration to groups that bear the burden from immigration and thereby decrease political opposition to immigration.