Identification and Estimation of Auctions with Incomplete Contracts: A Structural Analysis of California Highway Construction Projects

We introduce a structural model of procurement auctions with incomplete contracts, where a procurer chooses an initial project specification endogenously. The contract between the procurer and the winner of the auction is incomplete in that the two parties may agree to adopt a new feasible specification later, and negotiate an additional transfer via Nash Bargaining where both parties’ disagreement values depend on the auction price. In a Perfect Bayesian Equilibrium, contractors competing in the auction take account of such incompleteness while quoting prices. We show that the model primitives are non-parametrically identified and propose a feasible estimation procedure. Using data from highway procurement auctions in California, we estimate the structural elements that determine the hold-up due to incompleteness, and infer how a contractor’s bargaining power and the mark-up in the price quoted vary with its characteristics and the features of the construction project. We also find that ignoring the existence of contract incompleteness in the structural analysis of the bidding data leads to substantial over-estimation of the mark-ups in the prices.