We develop a new dynamic equilibrium model with heterogeneous households that captures the most important frictions that arise in housing rental markets and explains the political popularity of affordable housing policies. We estimate the model using data collected by the New York Housing Vacancy Survey in 2011. We find that there are significant adjustment costs in all markets as well as serious search frictions in the market for affordable housing. Moreover, there are large queuing frictions in the market for public housing. Having access to rent-stabilized housing increases household welfare by up to $65,000. Increasing the supply of affordable housing by 10% significantly improves the welfare of all renters in the city. Progressive taxation of higher-income households that live in public housing can also be welfare improving.