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This dissertation studies one-to-one matching between workers and assets in a market where financial securities are offered. The quality of an asset is publicly known, but a worker's productivity is private information. The asset side first posts contracts, under which the payment is contingent on the realized output. Then the workers direct their search based on the offers. Production exhibits complementarity so that the efficient allocation features positive assortative matching (PAM).I consider a frictionless setting in the first chapter. First, I characterize the sufficient and necessary conditions for decentralizing PAM. For any distribution of types, these conditions ensure that the set of posted contracts not only induces the workers to sort assortatively but also precludes the asset owners from poaching. In comparison with the case of full information, the asset side's share of the matching surplus is always greater and increases with the asset quality at a faster rate in equilibrium. Second, I show that all asset owners will always be better off if the feasible contracts are replaced with steeper ones, which cost better workers more than weaker workers. The second chapter focuses on the class of output sharing contracts. I study how it affects the matching efficiency and sorting pattern in the presence of search friction. The unique equilibrium features inefficient PAM. The matched pairs fully separate into a continuum of markets, where the queue length in each market still maximizes the expected surplus given the worker's equilibrium payoff. However, regardless of the distribution of types, all but the best workers pair up with better assets compared to the Second Best allocation. There is either an excessive entry of workers or an insufficient entry of assets. Sorting is inefficient because a reduction in the output share costs less to weaker workers than better workers. This handicaps their competition for better assets, driving up the output share of the best assets. These asset owners then induce an inefficiently long queue of workers to increase their matching probability.