On the distribution of bids for construction contract auctions

The statistical distribution representing bid values constitutes an essential part of many auction models and has involved a wide range of assumptions, including the Uniform, Normal, Lognormal and Weibull densities. From a modelling point of view, its goodness is defined by how well it enables the probability of a particular bid value to be estimated – a past bid for ex-post analysis and a future bid for ex-ante (forecasting) analysis. However, there is no agreement to date of what is the most appropriate form and empirical work is sparse. Twelve extant construction data-sets from four continents over different time periods are analysed in this paper for their fit to a variety of candidate statistical distributions assuming homogeneity of bidders (ID not known). The results show there is no one single fit-all distribution, but that the 3p Log-Normal, Fréchet/2p Log-Normal, Normal, Gamma and Gumbel generally rank the best ex-post and the 2p Log-Normal, Normal, Gamma and Gumbel the best ex-ante – with ex-ante having around three to four times worse fit than ex-post. Final comments focus on the results relating to the third and fourth standardized moments of the bids and a post hoc rationalization of the empirical outcome of the analysis.