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Theory and Empirics of Dynamic Matching

Paper Session

Friday, Jan. 4, 2019 10:15 AM - 12:15 PM

Atlanta Marriott Marquis, M103
Hosted By: American Economic Association
  • Chair: Valentin Verdier, University of North Carolina-Chapel Hill

How (Not) to Allocate Affordable Housing

Nick Arnosti
Columbia University
Peng Shi
University of Southern California


We study a setting in which items are dynamically assigned to waiting agents. The common practice of using independent lotteries encourages agents to enter many lotteries, resulting in inefficient matching. We consider several alternatives, and reach three main conclusions.

First, systems with very different descriptions can produce identical outcomes. In particular, Independent lotteries are equivalent to a waitlist in which participants lose their position if they reject an offer; Restricting agents to enter at most one lottery is equivalent to using a waitlist in which participants keep their position after rejecting an offer, and both are equivalent to using artificial currency.

Second, when an agent’s level of need is unobservable, there is often a tradeoff between matching (assigning agents to items that are a good fit) and targeting (assigning items to agents with the greatest need).

Third, it is generally preferable to prioritize good matching over effective targeting. The exception is when most participants have very little need, and the remainder are far more desperate. In such circumstances,effective targeting can be achieved by adding friction to the assignment system.

Our findings suggest that independent lotteries are rarely advisable. We discuss the implications of our work for the allocation of affordable housing, and of discounted tickets to Broadway shows.

The Public-Housing Allocation Problem: Theory and Evidence from Pittsburgh

Neil Thakral
Harvard University


We present a model of public-housing allocation, in which objects that arrive stochastically over time must be matched with applicants on a waiting list. Our framework delivers a strategy-proof, ex-ante efficient and envy-free mechanism which allows applicants to trade off their preferences for different units and waiting times by choosing among a set of waiting lists. A counterfactual change from existing mechanisms, in which applicants receive offers after units become available and can refuse only a limited number of times, to the proposed mechanism improves welfare by a lower bound of $6,429 per applicant in a sample of Pittsburgh households.

Welfare Effects of Dynamic Matching: An Empirical Analysis

Valentin Verdier
University of North Carolina-Chapel Hill
Carson Reeling
Western Michigan University


Assignment mechanisms that do not rely on monetary transfers lead to equitable access but may yield inefficient allocations. Theory suggests that introducing rationing when resources are allocated repeatedly over time can mitigate this issue, while the magnitude of the resulting efficiency gains is an empirical question in most settings. We study a dynamic assignment mechanism used by the Michigan Department of Natural Resources to allocate bear hunting permits and find that it yields a more efficient allocation than static mechanisms both by inducing participants to be more selective and by allowing participants with a higher preference for hunting to obtain permits more frequently. Our empirical analysis also highlights the importance of heterogeneity across participants and across allocated resources for determining the efficiency of a dynamic allocation mechanism.

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

Daniel Waldinger
New York University


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.
JEL Classifications
  • D4 - Market Structure, Pricing, and Design
  • C1 - Econometric and Statistical Methods and Methodology: General