Essays on Empirical Two-Sided Matching Models with Unobserved Heterogeneity

This dissertation studies two structural frameworks in empirical studies of Industrial Organization: two-sided matching models and simultaneous auction/contest models. Both models involve two disjoint sides of players: matching occurs between firms and workers, schools and students, and so forth; in an auction or contest, there always exists an auctioneer or contest designer on one side and bidders or contestants on the opposite. First, empirical studies of two-sided matching markets reveal that sorting patterns between potential employers and employees may be driven by unobserved heterogeneity on both sides and preferences over multidimensional wage contracts. Therefore, in Chapter 2, I study a generalized matching model with Non-Transferrable Utility (NTU), i.e. a two-stage model where employers firstly set wage contracts for their jobs, workers then match with the jobs in a decentralized way. I propose a strategy that exploits the variation in agent- and match-specific characteristics from finite-sized repeated markets to identify and estimate the preference primitives in the presence of two-sided unobserved heterogeneity, assuming employers share a vertical preference over workers. I further suggest a likelihood-based estimation strategy that tackles the dimensionality issue emerging from the existence of global players of the repeated game, and show its performance via Monte Carlo simulation analyses. In Chapter 3, I apply the model and identification method developed in Chapter 2 to study recently fast-growing online labor markets that match skilled labor to short-term jobs using a contest-based mechanism. Despite the anecdotal evidence showing both firms and workers benefiting from largely decreased meeting friction and increased flexibility on the platform, it is economically substantial to quantitatively reveal the preference structure of both parties, which may include unobserved factors to researchers. I, therefore, adopt the two-stage model where firms set wage contracts for their jobs before programmers choose coding projects simultaneously. I then use the identification strategy that exploits the variation in agent- and matchspecific characteristics from finite-sized repeated markets to estimate workers' latent skill levels and jobs' latent complexity levels. Using individual-level data from a leading online tournament-based labor market, TopCoder.com, which matches workers worldwide with short-term software developing tasks, I find a multidimensional preference beyond cash motives when workers consider which jobs to take. Using the results from the estimation, I further study the elements regarding market design that could leverage off the matching mechanisms to improve the total surplus generated from such markets. While this "crowdsourcing" market can be modeled as a matching process between firms with temporary jobs and workers, I would also like to capture the strategic interaction of workers after they match with an individual job. Within the same job, workers exert e ort to win pre-determined cash prizes according to the rank order of their delivered work. This can be naturally modeled in a (multi-prize) contest environment. A central concern is to recover the underlying preferences of workers, which again requires the full knowledge of the unobserved heterogeneity, or types, of both workers and jobs. Chapter 4 develops a new method to identify and estimate primitives in simultaneous contests with multiple prizes. I establish a two-stage game where bidders/contestants first choose one among multiple auctions/contests, then in the second stage, they compete within each auction/contest by submitting their bids simultaneously, contributing their efforts to win over the pre-determined prize based on the rank order. I show that by observing their first-stage choice probability combined with the second-stage bidding strategy, I can non-parametrically identify the joint distribution of unobserved heterogeneity on both sides of the market. I then present an estimation strategy and show the performance of Monte Carlo experiments