This paper considers the social costs implied by inefficient allocation of contracts in a first price, sealed bid procurement auction with asymmetric bidders. We adopt a constrained (piecewise linear) strategy equilibrium concept and estimate the structural parameters of the bidders distribution of costs. We estimate social costs defined as the predicted cost difference between the winning firm and the most efficient bidding firm. We also compare the expected procurement costs under two different auction formats. The data is collected from procurement auctions of road painting in Sweden during 1993-99. The results indicate that the social costs of inefficient contract allocation is about 1.7 per cent of total potential social cost and that an efficient second price auction would lower the expected procurement cost by 2.8 per cent.