How should affordable housing be allocated?

As rents rise across the country, millions of families are struggling to find an affordable place to live. There are many important policy questions pertaining to affordable housing. How much housing should be built? Where should it go? How should it be financed? Who should be eligible to apply? In this article, we focus on the question: How should affordable housing be allocated?

We start by describing existing allocation systems, using the Providence Housing Authority Waitlist and the New York City Affordable Housing Lotteries as case studies. Neither of these systems allows applicants to influence which units they are offered. As a result, tenants needlessly face long commutes and separation from their communities. We believe that small changes to existing systems could greatly expand tenant choice. These changes would improve outcomes for families, and help communities get the most benefit from existing housing stock. 

Existing Systems

Public housing waitlists. Approximately 1.2 million families live in public housing in the United States. This housing is funded by the U.S. Department of Housing and Urban Development (HUD), but administered locally by approximately 3,300 public housing authorities (PHAs) [1]. Each PHA sets its own allocation policies. As one example, consider the following description of the policy in Providence, R.I. [2]:

The PHA maintains one central waiting list... When an applicant’s name reaches the top of the waiting list, he or she is offered a unit at the development with the highest number of vacancies, and anyone who refuses the unit goes back to the bottom of the waiting list.

This approach is representative of offer policies across the country. Although some PHAs allow applicants to maintain their position after refusing an offer, the HUD Public Housing Occupancy Guidebook states that housing authorities should make at most three offers before removing a family from the waitlist [3]. 

Affordable housing lotteries. An alternative to public housing is affordable housing provided through public-private partnerships. Cities offer tax credits (or exemptions to zoning laws) to developers that agree to rent some of their newly constructed units at below-market rates. Because demand for these units exceeds supply, they are typically allocated by lottery. For example, in New York City, approximately 5,300 affordable units were offered through HousingConnect lotteries in 2017 [4]. There is a separate lottery for each building, and prospective tenants may apply to as many lotteries as they want. In 2016, buildings averaged nearly 1,000 applications for every available unit [5]. 

Concerns with Existing Systems

Unfortunately, neither of the systems described above offers families much control over where they will live. Although an applicant for Public Housing may decline an offer, doing so entails losing his or her position on a years-long waitlist. As a result, families may accept units that are far from where they currently live, work or attend school. This causes long commutes and social disruption. Meanwhile, these same units may be perfectly suited for other families that are only a few positions lower on the waitlist.

Similarly, the long odds in New York’s affordable housing lotteries give prospective tenants the incentive to apply to as many lotteries as possible. A family that prefers to live on the north side of the city may nevertheless apply to units all over town. They might win the lottery for a building on the south side, at the same time as a family who seeks a southerly building is awarded a unit further north.

The fact is, by allocating apartments with little regard for family preferences, existing systems are wasting a precious resource. Given the shortage of affordable housing, it is important to put the limited housing supply to the best possible use.

A Model of Housing Allocation

Acknowledging imperfections in existing systems is one thing. Agreeing on an alternative is another. Any administrator making a change wants assurance that it will lead to better outcomes. Unfortunately, evaluating a new approach isn’t easy.

One reason for this is that (unlike in the digital world) experimentation is costly and slow. New PHA policies require new documentation to be written, approved by HUD and distributed to everyone on the waitlist. Even after this is done, it may take years to measure the effects. This measurement is especially challenging because data from different systems may not be comparable; changes in the allocation process also change what people will accept. A family that accepted a particular building might have rejected that same building if they expected another offer in the near future. Often, all that can be learned from a family’s decision to accept an apartment is that it was better than their current living situation.

In our paper “Design of Lotteries and Waitlists for Affordable Housing Allocation” (forthcoming in Management Science), we attempt to circumvent these challenges by studying a simplified model of reality. Our model captures the fact that families differ in their preferences: the building that is perfectly located for one family may entail a long commute for another. Furthermore, we allow family behavior to adjust to the system that is in place. For example, we assume that when deciding whether to accept an offer, a family will take into account the time until they next expect to receive an offer. This model allows us to evaluate and compare existing systems, as well as alternatives that may not have been used in practice.

Our model predicts that under the systems currently used in Providence and New York, families will apply for and accept buildings that they consider less than ideal. The greater the shortage of housing, the less selective families will be. If demand far exceeds supply, families will accept almost any offer. Somewhat surprisingly, our model predicts that these seemingly disparate systems – waitlists with a single offer and independent lotteries – will produce identical outcomes. By this, we mean that families will be equally selective (and equally likely to be housed) in both systems.

Alternatives that Offer Choice

Fortunately, there are many ways to modify the systems in Providence and New York to offer applicants more choice.

For example, instead of giving families a use-it-or-lose-it opportunity to apply to each building, New York’s housing lotteries could reward families who abstain from several lotteries with higher chances of winning the next lottery that they enter. This would allow families to increase their odds of winning the buildings that best fit their needs, while leaving other buildings to those who would appreciate them more.

Another possible change to New York’s housing lotteries would be to conduct a single “grand lottery” for many (or all) buildings, rather than holding separate lotteries for each building. Whereas the existing system essentially gives families a take-it-or-leave-it offer for a random building, winners of the grand lottery would be able to select among buildings scattered across the city.

Meanwhile, the Providence Housing Authority (and other PHAs across the country) could offer families more choice by allowing them to maintain their position on the list, even after rejecting several offers. This is in fact the approach used by public housing agencies in Amsterdam. Another alternative is to offer families information about waiting times, and allow them to indicate which buildings they would like to wait for.

Our model predicts that any of these changes would improve match quality, meaning that families would receive apartments better suited to their particular needs. 

Words of Caution

Of course, giving families more choice may have unintended consequences. For example, allowing families on the waitlist to reject offers with impunity might cause an increase in administrative overhead and delays in the allocation of vacant units. For this reason, we prefer allowing families to pre-specify the buildings or neighborhoods that they find suitable [6]. This would ensure high-quality matches, while also minimizing the time and effort required to fill vacancies.

Our research identifies a second unintended consequence of offering families more choice: this may affect which families receive apartments. While the changes suggested above would unambiguously benefit families for whom only a few options are acceptable, those who are willing to live anywhere might find their chance of winning an apartment reduced. In fact, our work shows that this concern is not specific to any particular proposal, but rather applies to any system that offers families more choice. In other words, the potential benefits of increased choice may not be shared equally across all families.

Nevertheless, we believe that giving families more say in where they live will result in a more efficient allocation. Concerns about the welfare of certain groups (i.e., single mothers, or those with especially low incomes) are best addressed by prioritizing these groups – not by removing choice from other applicants. 

Next Steps

We hope to work with housing agencies to craft plans that offer choice to families while ensuring that all recipients are truly in need of subsidized housing. Although there is no perfect solution, we believe that the small changes outlined in this article could offer families more control over their fate, improving outcomes for tens of thousands of people across the country at no additional cost to taxpayers or developers.

References

1. https://www.hud.gov/topics/rental_assistance/phprog
2. https://provhousing.org/about-pha/plans-policies/ (Providence PHA 2017 Annual Report, p.79)
3. https://www.hud.gov/sites/documents/DOC_10760.PDF (Chapter 8.1)
4. https://www1.nyc.gov/office-of-the-mayor/news/036-18/mayor-de-blasio-city-secured-more-affordable-housing-2017-in-any-prior-year#/0
5. https://www.nydailynews.com/new-york/2-5m-people-applied-nyc-2-600-affordable-housing-units-article-1.2633482
6. This is done, for example, in the city of Toronto: https://www.housingconnections.ca/pdf/application_form.pdf