Guided by matching theory, school choice markets are designed to generate stable matchings. The entry and exit of educational programs poses a barrier to stability if a long horizon is required for students to learn their preferences. In this paper, we study how entry and exit affect learning about a payoff relevant feature of educational programs: student quality. Theoretically, we show how entry and exit can inhibit stability. Empirically, using data from the college admissions market in New South Wales, Australia, we find gradual within-program convergence to stability and show how the persistent churn of programs in this marketplace inhibits overall-market convergence, leading to an unstable matching. This instability is primarily experienced by lower-ability students and those from marginalized groups, thus potentially increasing inequality.

School-choice clearinghouses often advise students to "rank their true preferences" despite not allowing students to express preferences over peers. We evaluate the consequences of doing so. Empirically, we find students have preferences over relative peer ability in the college admissions market in New South Wales, Australia. Theoretically, we show stable matchings exist even with peer preferences under mild conditions, but finding one via one-shot mechanisms is unlikely. The status quo procedure frequently employed by clearinghouses is to inform applicants about the assignment of students in the previous cohort, inducing a tâtonnement process which potentially provides useful information about likely peers in the current cohort. We theoretically argue this process likely leads to an unstable outcome, and we find instability in our empirical setting. We propose a mechanism that yields stability and incentivizes truthful reporting in the presence of peer preferences.

We consider sequential search by an agent who cannot observe the quality of goods but can acquire information by buying signals from a profit-maximizing principal with limited commitment power. The principal can charge higher prices for more informative signals in any period, but high prices in the future discourage continued search by the agent, thereby reducing the principal's future profits. A unique stationary equilibrium outcome exists, and we show that the principal (i) induces the socially efficient stopping rule, (ii) extracts the full surplus, and (iii) persuades the agent against settling for marginal goods, extending the duration of surplus extraction. However, introducing an additional, free source of information can lead to inefficiency in equilibrium.

Equal pay laws increasingly require that workers doing “similar” work are paid equal wages within firm. We study such “equal pay for similar work” (EPSW) policies theoretically and test our model’s predictions empirically using evidence from a 2009 Chilean EPSW. When EPSW only binds across protected class (e.g., no woman can be paid less than any similar man, and vice versa), firms segregate their workforce by gender. When there are more men than women in a labor market, EPSW increases the gender wage gap. By contrast, EPSW that is not based on protected class can decrease the gender wage gap. 

Mechanisms used to derive optimal allocations are typically designed assuming agents fully know their preferences. It is often impossible to duplicate optimal allocations when agents imperfectly observe object characteristics. I present a crowdsourcing mechanism to approximate optimal allocations under imperfect observations. To ensure truth-telling, agents are punished when their reports differ from the “wisdom-of-the-crowd.” Under mild conditions, this crowdsourcing-with-punishment mechanism replicates the full-information optimal allocation with probability exponentially converging to one in the size of the market, with small waste. No alternative mechanism can meaningfully do better. The proposed mechanism can be applied in many settings, including two-sided matching markets.

The public discourse around pay transparency has focused on the direct effect: how workers seek to rectify pay inequities through renegotiation. The question of how wage-setting and employment practices of the firm respond has received less attention. To study these equilibrium outcomes, we test our model of bargaining under incomplete information with an analysis of pay transparency mandates in the context of the U.S. private sector. Our model predicts that transparency reduces the individual bargaining power of workers, leading to lower average wages. A key insight is that employers credibly refuse to pay high wages to any one worker to avoid costly renegotiations with others under transparency. In situations where workers do not have individual bargaining power, such as under a collective bargaining agreement or in markets with posted wages, greater transparency has a muted impact on average wages. We test these predictions by evaluating the adoption of U.S. state legislation protecting the right of workers to inquire about the salaries of their coworkers. Consistent with our prediction, the laws lead wages to decline by approximately 2% overall, but effects are muted when workers have low individual bargaining power. Our model provides a unified framework to analyze a wide range of transparency policies, and reconciles effects of transparency mandates documented in a variety of countries and contexts. 

Consider indivisible-object allocation with contracts, such as college admissions where contracts specify majors. Can a designer guarantee a stable and (student) efficient matching? I show that contracts put stability and efficiency at odds; a necessary condition to ensure these properties is student-lexicographic priorities—schools must rank contracts from "second-tier" students consecutively. I present the weakest restriction guaranteeing stability and efficiency, and characterize necessary and sufficient conditions for any mechanism within a general class to deliver a stable and efficient matching in an incentive compatible manner. I apply this result to two well-known mechanisms: deferred acceptance and top trading cycles.

Decisions agents make before and after matching can be strategically linked through the match. We demonstrate this linkage in a game where universities either force students to commit to majors before matriculating or allow students to pick majors during their studies. The interaction between "matching forces" (competition for higher quality students) and "principal-agent forces" (moral hazard and adverse selection) leads to two equilibria that mirror the admissions systems in the US and England. With monetary transfers, our model provides insights into athletic scholarships. Payment caps that restricts transfers to potential athletes who decide not to play sports can maximize welfare.