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Lamy, Laurent; Patnam, Manasa; Visser, Michael
Journal of econometrics, 08/2023, Volume: 235, Issue: 2Journal Article
This paper develops a novel approach to estimate how contract and principal-agent characteristics influence a post-auction outcome when the matching between agents and principals derives from an auction process. We propose a control-function approach to account jointly for the endogeneity of contracts and matching. This consists of, first, estimating the primitives of an interdependent values auction model-which is shown to be non-parametrically identified from the bidding data-second, constructing control functions based on the distribution of the unobserved private signals conditional on the auction outcome. A Monte Carlo study shows that our augmented outcome equation corrects the endogeneity biases well, even in small samples. We apply our methodology to a labor market application and estimate the effect of sports players' auction-determined wages on their individual performances. We also use our structural estimates to evaluate the strength of matching inefficiencies and assess counterfactual reservation wage policies.
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