Excess Demand and Rationing in Equilibrium in the Market for Public Housing∗

Science Conference in Savannah for comments and suggestions. We would also like to thank the Housing Authority of the City of Pittsburgh for providing us with some of the data used in this study. Finally, we acknowledge financial support by the National Science Foundation grant SBR-0617844. We develop a model for the market of public housing that captures excess demand for public housing and rationing in equilibrium. We characterize the equilibrium and show that a unique equilibrium exists if the housing authority follows an equal treatment policy and does not discriminate based on current residence. We then develop a maximum likelihood estimator for the parameters of the model. The estimator accounts for enriched sampling and imposes all equilibrium conditions in estimation. We estimate the parameters of the model based on a unique restricted use panel data set of low-income households in Pitts-burgh. We find that for each household that leaves public housing there are on average 14 households that would like to move into the vacated unit. Demolitions of existing units increase the degree of rationing and are likely to result in welfare losses