We estimate an equilibrium model of housing demand and supply, quantifying the distributional effects of leverage regulation on mobility and access to high-quality housing. We match the population of households in Norway in 2010-2018, with demographic and financial characteristics, to the universe of housing transactions. Our model features households' dynamic renting and owning choices, investors' housing portfolio rebalancing, and equilibrium pricing. We recover households' willingness to pay for housing quality and moving costs. Our counterfactuals quantify the regressive effects of tighter loan-to-income (LTI) limits, documenting how these depend on household preferences and can be offset with housing subsidies.