Identification in Auction Models with Interdependent Costs

This paper provides a positive identification result for first-price procurement models with asymmetric bidders, statistically dependent private signals,
and interdependent costs. When bidders are risk neutral, the model’s payoff-relevant primitives are: (i) the joint distribution of private signals and (ii) each bidder’s full-information cost—the expected cost conditional on own and competitors’ signals. Because bidding strategies are monotone in signals, the joint distribution of bids identifies the joint distribution of signals. First-order conditions identify the expected cost conditional on tying with at least one competitor for the lowest bid. The set of signals that induce such a tie can be recovered from the marginal distributions of bids. In the model, this conditioning set depends on competitors’ cost shifters that are excluded from the bidder’s own full-information cost. I show that variation in competitors’ cost shifters can be used to identify each bidder’s full-information cost for all configurations of own and rivals’ signals. Using data from Highway Procurements in Michigan and exploiting variation in contractors’ distance to each project, I estimate the payoff-relevant primitives and evaluate policies that affect the severity of the winner’s curse.