Targeting In-Kind Transfers through Market Design: A Revealed Preference Analysis of Public Housing Allocation

In-kind transfer programs aim to provide valuable resources to beneficiaries while targeting those who most need assistance. This problem is particularly challenging for public housing authorities (PHAs), which allocate apartments to applicants who may differ in their outside options as well as their preferred apartment types. PHAs in the U.S. differ widely in the priority systems they use and how much choice they give potential tenants over where to live. This paper evaluates how these choice and priority systems affect two competing objectives: efficiency and redistribution. I use data on the submitted choices of public housing applicants to estimate a structural model of preferences for public housing in Cambridge, MA. I find substantial heterogeneity in applicants’ preferred housing developments and in their values of obtaining assistance. Counterfactual simulations suggest that the range of mechanisms used by PHAs involves a large trade-off between efficiency and redistribution. When applicants are allowed to choose where they live, tenants enjoy welfare gains equivalent to cash transfers of more than $6,500 per year. Removing choice would house applicants with worse outside options but provide low match quality, causing cost-adjusted welfare gains to fall by 30 percent. Prioritizing low-income applicants while allowing choice would improve targeting without lowering match quality. While several combinations of choice and priority are on the frontier of efficiency and redistribution, some commonly used mechanisms, such as prioritizing higher-income applicants without allowing choice, are never optimal. ∗I am very grateful to Nikhil Agarwal, Parag Pathak, Michael Whinston, and Amy Finkelstein for invaluable guidance and support. This paper benefited from feedback from Zarek Brot-Goldberg, Alonso Bucarey, Sydnee Caldwell, Glenn Ellison, Chishio Furukawa, Andrey Fradkin, Colin Gray, Arda Gitmez, Ingrid Gould Ellen, Jonathan Gruber, Ray Kluender, Jacob Leshno, Benjamin Marx, Pooya Molavi, Anders Munk-Nielsen, Scott Nelson, Alan Olivi, Christina Patterson, Otis Reid, Nancy Rose, Peng Shi, Michael Stepner, Neil Thakral, Heidi Williams, and Ariel Zucker, as well as seminar participants at the MIT Industrial Organization and Public Finance lunches. The Cambridge Housing Authority generously provided the applicant and tenant data used in this paper, with special thanks to Tara Aubuchon, Tito Evora, Michael Johnston, Jay Leslie, Hannah Lodi, and John Ziniewicz. All analysis and views expressed in this paper are my own and do not represent the views of the Cambridge Housing Authority. †MIT Economics. Email: dwalding@mit.edu. All mistakes are my own.