Job Market Paper|
Equilibrium Effects of Pay Transparency in Bargaining Environments (with Zoe Cullen)
The policy debate around increasing pay transparency has paid little attention to equilibrium
effects, namely how firms change hiring and wage setting policies and how workers adjust
bargaining strategies. We assess the costs and benefits of increasing pay transparency along three
dimensions: Does it lead to higher employment? Does it result in more equal wages for similarly
productive workers? How does it affect the division of surplus between firm and worker? We
investigate by introducing a dynamic wage bargaining game with asymmetric information
between workers and a firm in which the level of transparency is modeled as the rate at which
workers learn the pay of their peers, and test the model's predictions using administrative data and
a field experiment in online labor platforms. We find the expected employment maximizing level
of transparency as a function of market parameters, and show that this is neither full transparency
nor full secrecy. Higher transparency compresses the earnings of employed workers. In
expectation, the firm benefits from pay transparency at the expense of workers. Regulation may
be necessary to achieve a desirable transparency outcome, as endogenous firm selection of the
transparency level unravels to a fully transparent pay structure regardless of market parameters.
Equal Pay for Equal Work? Evidence from the Renegotiation of Short-Term Contracts (with Zoe Cullen)
We show empirically why employers pay similar wages to heterogeneous workers. Three facts come from administrative data of a labor platform specializing in short-term contracts. First, for a particular multi-worker job, pay among workers differs on average by over fifty percent when workers are the first to propose a price. Second, when workers are in the same location, employers deliberately raise the pay of lower bidders, reducing dispersion, irrespective of differences in assessed productivity or reservation values. Finally, the same employer that compresses pay when workers are co-located will allow disparities when workers are physically separated. The important distinction between settings is the transparency of relative pay. The impact of pay transparency on pay equalization is consistent with a pure information channel where knowledge of co-worker pay changes the bargaining position of the worker. The employer may also find it efficient to equalize pay when relative allocations enter directly into the worker's utility function. We conduct a field experiment that underscores the contribution of both these channels to the equilibrium behavior of employers we observe in administrative data from the same environment.
Strategic Disaggregation in Matching Markets (with Stephen Nei)--Non-technical summary
Matching theory has not adequately studied what happens after agents match. Post-match
information arrival and actions can affect the value of a partner, which leads to previously unexplained strategic behavior
during and leading up to the matching process. We introduce a game in which
universities can force students to commit to majors before matriculating
or to allow students to pick their majors during their studies. Students
are initially uncertain about their preferred majors but can resolve
this uncertainty before matching by paying a cost. Fine-tuning the direct matching mechanism does not lead to drastically different outcomes, while pre- and post-match considerations are of first-order importance. The interaction between competition
for better students, moral hazard and adverse selection leads to two different equilibria
mirroring the American and English admissions systems.
With monetary transfers, our model provides new insight into whether
student athletes should be paid. Price competition removes the surplus
to enrolling top students, making it impossible to sustain the American
admissions equilibrium without an exogenous transfer cap. We show that properly
designed transfer caps can achieve the first-best welfare outcome, and can lead to Pareto improvements over the status quo.
Crowdsourcing and Optimal Market Design
Suppose an optimal allocation in a market depends on characteristics of goods which are imperfectly observed by agents. How well can a mechanism aggregate information in a way that induces agents to be truthful? I show that it is possible to achieve nearly the same allocation as in a full-information market by first aggregating the information of all agents and then running an optimal full-information mechanism. To ensure proper incentives, agents are punished when their reports do not match up with the “wisdom of the crowd.” The punishment scheme is independent of the desired allocation, and can be enacted with or without monetary transfers. Even when the number of objects being assessed is much larger than the number of assessors, the proposed mechanism asymptotically correctly identifies every object's quality, while imposing a worst-case total punishment that converges exponentially to zero. Therefore, I am able to generate nearly optimal allocations in two-sided matching markets with interdependent preferences, a setting for which impossibility results exist. I give necessary and sufficient conditions for recovering desirable properties when information acquisition is endogenous and costly.
Stable and Efficient Resource Allocation With Contracts
Consider a model of indivisible-object allocation with contracts, such as college admissions in which contracts specify majors. Does including contracts in a market allow designers to guarantee a stable and (student) efficient matching? I find that it is difficult to ensure both properties, as adding contracts can often put stability and efficiency at odds. Theorem 1 shows that a necessary condition to secure these properties is student-lexicographic priorities—colleges must rank all contracts from “second-tier” students consecutively. I develop a new framework to analyze a broad class of mechanisms with contracts. The main result characterizes the restriction which guarantees efficiency, stability and group strategy-proofness for this class of mechanisms. I use this framework to apply the main result to two famous mechanisms, deferred acceptance and top trading cycles. I conclude by extending the main result to many-to-many matching and substitutable college priorities.
Work in Progress
Hiding Large Orders: From Tarantino to Finance (with Mohammad Akbarpour and Shengwu Li)
How does a buyer with high demand and high value purchase goods in a market when sellers are not sure of her presence? If she buys too much at once she tips her hand to sellers, who respond by raising the price. If she delays, she misses out on consuming. We model a dynamic game between a long-lived Big Buyer, and myopic small buyers and sellers. Sellers and small buyers live for only one instant and attempt to maximize profit. Small buyers arrive stochastically, and so the Big Buyer optimally restricts demand at each time to hide in the crowd. We characterize the optimal pricing strategy of the sellers and the optimal buying strategy of the Big Buyer and small buyers. In equilibrium, the Big Buyer demands more when sellers either have a very low belief or a very high belief of her presence. Sellers almost surely learn of the Big Buyer’s existence in the market over time. We study optimal information revelation in this market.