This article contrasts two auction formats often used in public procurement: first price auctions with ex post screening of bid responsiveness and average bid auctions (ABAs), in which the bidder closest to the average bid wins. The equilibrium analysis reveals that their ranking is ambiguous in terms of revenues, but the ABA is typically less efficient. Using a data set of Italian public procurement auctions run alternately under the two formats, a structural model of bidding is estimated for the subsample of first price auctions and used to quantify the efficiency loss under counterfactual ABAs. * Manuscript and Economic Research Association for bidders to collude; Chang et al. (2015) analyze the ABA in a common value environment; Galavotti et al. (2015) consider the IPV case, but through the framework of level-k thinking; and Eun (2015) analyzes bidding in a closely related procurement format used in Korea. Regarding the FPA with screening, this article is mostly related to the recent work of Bajari et al. (2014), who analyze bidding and adaptation costs in U.S. procurement auctions. The second contribution is to complement the theoretical comparison of ABAs and FPAs with screening with a quantitative analysis of their performance in a major procurement market. Auctions are typically very persistent institutions so that format changes are rarely observed. Only a few other studies, mostly involving public auctions in the United States, have presented this type of comparative analysis: Athey et al. (2011) compare open versus sealed bid auctions used for the sale of timber harvesting contracts, Lewis and Bajari (2011) compare first price versus scoring rule with time incentive auctions for the procurement of roadwork contracts, and Marion (2007) compares first price versus first price with small-business bid subsidy for roadwork contracts. 4 For Italian public procurement, two complementary studies, Decarolis (2014) and Branzoli and Decarolis (2015), present a difference-in-differences analysis of the effects of switching from ABAs to FPAs with screening on observable quantities: the winning bid and the ex post contractual performance in the first study and the entry and subcontracting choices in the second study. In this article, I structurally estimate firms' underlying costs from a sample of FPAs with screening and quantify the efficiency loss in counterfactual ABAs. 5 The findings in the aforementioned papers of Decarolis (2014) and Branzoli and Decarolis (2015), along with the results in Conley and Decarolis (2016) on collusion in ABAs, are used in this article to guide the complex construction of an appropriate counterfactual ABA. Methodologically, the article contributes by showing how the structural estimation can be performed by extending