ESSAYS ON MATCHING MARKETS WITH INCOMPLETE INFORMATION

Abstract

This dissertation investigates matching markets with incomplete information. In chapter 1, I introduce a framework for studying transient matching in decentralized markets where workers learn about their preferences through their experiences. Limits on the number of available positions force workers to compete over matches. Each capacity-constrained firm employs workers whose match value exceeds a threshold. Since employment offers both payoff and information benefits, workers effectively face a multi-armed bandit problem. To them each firm acts as a bandit where the probability of ``success'' at the firm is driven by market competition. In such markets, aggregate demand for firms satisfies the gross substitutes condition which ensures equilibrium existence. The resulting search patterns match a variety of stylized facts from labor market data. High-quality workers search less and tenure increases with age. In general, equilibria are inefficient because competition depresses the level of search. Natural interventions designed to improve efficiency are effective in uncongested markets, but can fail when congestion is several. From a market design perspective, the utilization of headhunters has differential effects depending on workers’ quality, conclusively improving both outcomes for low-quality workers and overall efficiency. Reducing congestion through unemployment benefits, can depress search and may ultimately reduce match efficiency. Chapter 2, joint with Kwok Hao Lee and Luther Yap, considers the optimal allocation of public housing from the perspective of dynamic mechanism design. Novel in our setting: the designer can choose what types of apartments to supply, in response to earlier demand realizations. However, since the designer does not know which apartments are desired by households, she must trade-off learning about preferences with matching current demand. This control radically changes the optimal mechanism. In this mechanism, under-demanded housing is overproduced relative to a benchmark in which apartments are built in proportion to demand. Competition between housing applicants improves average match quality when the government controls supply. Competition can be artificially generated by batching applications, thus increasing market thickness. If the planner values match quality highly, the optimal mechanism features batching. Chapter 3, also joint with Lee and Yap, considers the design ofa large-scale public housing program where consumers face dynamic tradeoffs over apartments rationed via lotteries and prices. We show that changing rules complements increasing supply. By waiting for “better” developments arriving tomorrow, households forgo mediocre developments available today, raising vacancies. We formulate a dynamic choice model over housing lotteries and estimate it on data from Singapore. Under the existing mechanism, we find that increasing supply fails to lower wait times. However, when a strategyproof mechanism is implemented, vacancies and wait times fall, but prices on the secondary market rise. Under this new mechanism, building more apartments lowers wait times and reduces the upward pricing pressure on the secondary market.