Distinguishing incentive from selection effects in auction-determined contracts

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.