Market Design

Members of the NBER's Market Design Working Group met in Cambridge on October 18-19. Research Associates Michael Ostrovsky of Stanford University and Parag A. Pathak of MIT organized the meeting. These researchers' papers were presented and discussed:

Liran Einav, Stanford University and NBER; Amy Finkelstein, MIT and NBER; Yunan Ji, Harvard University; and Neale Mahoney, University of Chicago and NBER

Voluntary Regulation: Evidence from Medicare Payment Reform

Government programs are often offered on an optional basis to market participants. Einav, Finkelstein, Ji, and Mahoney explore the economics of such voluntary regulation in the context of a Medicare payment reform, in which one medical provider receives a single ("bundled") payment for a sequence of related healthcare services, instead of separate service-specific payments. The program was originally implemented as a 5-year randomized trial, with mandatory participation by hospitals assigned to the new payment model, but after two years participation was unexpectedly made voluntary for half of these hospitals. Using detailed claim-level data the researchers document that voluntary participation is more likely for hospitals who can increase revenue without changing behavior ("selection on levels") and for hospitals that had large changes in behavior when participation was mandatory ("selection on slopes"). To assess outcomes under counterfactual regimes, they estimate a simple model of responsiveness to and selection into the program. The researchers find that the current voluntary regime generates inefficient transfers to hospitals and reduces social welfare compared to the status quo, but that alternative (feasible) designs could be welfare improving. The analysis highlights key design elements to consider under voluntary regulation.

Amanda Y. Agan, Rutgers University and NBER; Bo Cowgill, Columbia University; and Laura K. Gee, Tufts University

Salary Disclosure and Hiring: Field Experimental Evidence from a Two-Sided Audit Study

What is the effect of job candidates disclosing their wage history on callbacks and salary offers? If these effects differ by a job candidate's gender or the amount they disclose, then disclosure might also impact inequality in the labor market. Agan, Cowgill, and Gee implement a field experimental design they call a two-sided audit study, in which recruiters evaluate job applications with randomized characteristics under randomly assigned salary disclosure conditions. Researchers begin by estimating the effects of candidates' salary disclosure under a variety of settings. Then, Agan, Cowgill, and Ge combine their estimates to examine the likely effect of recent laws that ban employers from asking candidates for their salary history like those passed in Massachusetts, California, New York City, and Chicago.

Nicole Immorlica and Brendan Lucier, Microsoft Research; Jacob D. Leshno, University of Chicago; and Irene Y. Lo, Stanford University

Information Acquisition Costs in Matching Markets

Christina Aperjis, Power Auctions LLC; Lawrence Ausubel, University of Maryland; and Oleg V. Baranov, University of Colorado, Boulder

Supply Reduction in the Broadcast Incentive Auction

The FCC's Broadcast Incentive Auction incorporated a reverse auction for the voluntary clearing of broadcast stations. While aiming to be obviously strategy-proof, it maintained the fiction that stations were owned individually when many were part of station groups. Theoretically, this design creates severe supply-reduction incentives in stylized models, while alternative Vickrey-Clarke-Groves-based mechanisms would avoid these incentives yet still enable price discrimination. Empirically, the first analysis of the actual bidding data -- matched with ex post resale data -- reveals unmistakable instances of drop-out prices far exceeding station values. Both theoretically and empirically, Aperjis, Ausubel, and Baranov show that supply reduction posed a serious challenge to the reverse auction.

Yannai A. Gonczarowski, Microsoft Research; Lior Kovalio and Noam Nisan, Hebrew University of Jerusalem; and Assaf Romm, Hebrew University of Jerusalem and Stanford University

Matching for the Israeli "Mechinot" Gap-Year Programs: Handling Rich Diversity Requirements

Gonczarowski, Kovalio, Nisan, and Romm describe their experience with designing and running a matching market for the Israeli "Mechinot" gap-year programs. The main conceptual challenge in the design of this market was the rich set of diversity considerations. This market was run for the first time in January 2018 and matched 1,607 candidates (out of a total of 2,580 candidates) to 35 different programs.

Tayfun Sönmez and M. Bumin Yenmez, Boston College

Affirmative Action in India via Vertical and Horizontal Reservations

Built into the country's constitution, one of the world's most comprehensive affirmative action programs exists in India. Government jobs and seats at publicly funded educational institutions are allocated through a Supreme Court-mandated procedure that integrates a meritocracy-based system with a reservation system that provides a level playing field for disadvantaged groups through two types of special provisions. The higher level provisions, known as vertical reservations, are exclusively intended for backward classes that faced historical discrimination, and implemented on a "set aside" basis. The lower-level provisions, known as horizontal reservations, are intended for other disadvantaged groups (such as women, disabled, or the economically disadvantaged), and they are implemented on a "minimum guarantee" basis. Sönmez and Yenmez show that, the Supreme Court mandated procedure suffers from at least four major deficiencies. First and foremost, it is not well-defined when candidates can qualify for multiple horizontal reservations, a phenomenon that has been increasingly more common in recent years. Moreover, while a candidate can never lose a position to a less meritorious candidate from her own group under this procedure, she can lose a position to a less meritorious candidate from a higher privilege group. This loophole under the Supreme Court-mandated procedure causes widespread confusion in India, resulting in countless lawsuits, conflicting judgements on these lawsuits, and even defiance in some of its states. Sönmez and Yenmez propose an alternative procedure that resolves these two major deficiencies and two additional ones.

Marek Pycia, University of Zurich

Evaluating with Statistics: Which Outcome Measures Differentiate Among Matching Mechanisms?

The selection of mechanisms to allocate school seats in public school districts can be highly contentious. At the same time the standard statistics of student outcomes calculated from districts' data are very similar for many mechanisms. This paper contributes to the debate on mechanism selection by explaining the similarity puzzle as being driven by the invariance properties of the standard outcome statistics: outcome measures are approximately similar if and only if they are approximately anonymous.

Daniel C. Waldinger, New York University

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

Public housing benefits are rationed through waitlists. Waldinger argues that the range of allocation policies used across US cities involves a trade-off between two policy objectives: maximizing welfare gains for tenants, and targeting the most economically disadvantaged applicants. Using waitlist data from Cambridge, MA, Waldinger develops and estimates a model of public housing preferences in a setting where heterogeneous apartments are rationed through waiting time. Counterfactual simulations show that the preferred mechanism depends on social preferences for redistribution. However, many cities use systems that would be suboptimal in Cambridge for any value of redistribution.

Joshua Angrist and Parag A. Pathak, MIT and NBER, and Roman Zarate, MIT

Choice and Consequence: Assessing Mismatch at Chicago Exam Schools (NBER Working Paper 26137)

The educational mismatch hypothesis asserts that students are hurt by affirmative action policies that place them in selective schools for which they wouldn't otherwise qualify. Angrist, Pathak, and Zárate evaluate mismatch in Chicago's selective public exam schools, which admit students using neighborhood-based diversity criteria as well as test scores. Regression discontinuity estimates for applicants favored by affirmative action indeed show no gains in reading and negative effects of exam school attendance on math scores. These results hold for more selective schools and for applicants most likely to benefit from affirmative-action, a pattern suggestive of mismatch. However, exam school effects in Chicago are explained by schools attended by applicants who are not offered an exam school seat. Specifically, mismatch arises because exam school admission diverts many applicants from high-performing Noble Network charter schools, where they would have done well. Consistent with these findings, exam schools reduce Math scores for applicants applying from charter schools in another large urban district. Exam school applicants' previous achievement, race, and other characteristics that are sometimes said to mediate student-school matching play no role in this story.

Mohammad Akbarpour, Stanford University; Julien Combe, University College London; Yinghua He, Rice University; Victor Hiller, Université Paris 2; Robert Shimer, University of Chicago and NBER; and Olivier Tercieux, Paris School of Economics

Unpaired Kidney Exchange: Overcoming Double Coincidence of Wants without Money

Akbarpour, Combe, He, Hiller, Shimer, and Tercieux propose a new matching algorithm -- Unpaired kidney exchange -- to tackle the problem of double coincidence of wants without using money. The fundamental idea is that "memory" can serve as a medium of exchange. In a dynamic matching model with heterogeneous agents, the researchers prove that average waiting time under the Unpaired algorithm is close-to optimal, and substantially less than the standard pairwise and chain exchange algorithms. They evaluate this algorithm using a rich dataset of the kidney patients in France. Counterfactual simulations show that the Unpaired algorithm can match nearly 57% of the patients, with an average waiting time of 424 days (state-of-the-art algorithms match about 31% with an average waiting time of 675 days or more). The optimal algorithm performs only slightly better: it matches 58% of the patients and leads to an average waiting time of 410 days. The Unpaired algorithm confronts two incentive-related practical challenges. The researchers address those challenges via a practical version of the Unpaired algorithm that employs kidneys from the deceased donors waiting list. The practical version can match nearly 87% of patient-donor pairs, while reducing the average waiting time to about 141 days.

Gianluca Brero and Sven Seuken, University of Zurich, and Benjamin Lubin, Boston University

Machine Learning-Powered Iterative Combinatorial Auctions

Brero, Lubin, and Seuken present a machine learning-powered iterative combinatorial auction (CA). The main goal of integrating machine learning (ML) into the auction is to improve preference elicitation, which is a major challenge in large CAs. In contrast to prior work, this auction design uses value queries instead of prices to drive the auction. The ML algorithm is used to help the auction mechanism decide which value queries to ask in every iteration. While using ML inside an auction introduces new challenges, the researchers demonstrate how they obtain an auction design that is individually rational, has good incentives, and is computationally tractable. Via simulations, they benchmark the new auction against the well-known combinatorial clock auction (CCA). The results indicate that the ML-powered auction achieves higher allocative efficiency than the CCA, even with only a small number of value queries. Additionally, they explain how the parameters of the auction design can be used to make a conscious trade-off between efficiency and revenue.

Nick Arnosti, Columbia University, and Peng Shi, University of Southern California

Design of Lotteries and Waitlists for Affordable Housing Allocation

Arnosti and Shi study a setting in which dynamically arriving items are assigned to waiting agents, who have heterogeneous values for distinct items and heterogeneous outside options. An ideal match would both target items to agents with the worst outside options, and match them to items for which they have high value. The first finding is that two common approaches -- using independent lotteries for each item, and using a waitlist in which agents lose priority when they reject an offer -- lead to identical outcomes in equilibrium. Both approaches encourage agents to accept items that are marginal fits. The researchers show that the quality of the match can be improved by using a common lottery for all items. If participation costs are negligible, a common lottery is equivalent to several other mechanisms, such as limiting participants to a single lottery, using a waitlist in which offers can be rejected without punishment, or using artificial currency. However, when there are many agents with low need, there is an unavoidable tradeoff between matching and targeting. In this case, utilitarian welfare may be maximized by focusing on good matching (if the outside option distribution is light-tailed) or good targeting (if it is heavy-tailed). Using a common lottery achieves near-optimal matching, while introducing participation costs achieves near-optimal targeting.

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