Discrete Bids and Empirical Inference in Divisible Good Auctions

I examine a model of a uniform price auction of a perfectly divisible good with private information in which the bidders submit discrete bidpoints rather than continuous downward sloping demand functions. I characterize necessary conditions for equilibrium bidding. The characterization reveals a close relationship between bidding in multiunit auctions and oligopolistic behaviour. I demonstrate that a recently proposed indirect approach to the revenue comparisons of discriminatory and uniform price auctions is not valid if bid functions have steps. In particular, bidders may bid above their marginal valuation in a uniform price auction. In order to demonstrate that discrete bidding can have important consequences for empirical analysis I use my model to examine a data set consisting of individual bids in uniform price treasury auctions of the Czech government. I propose an alternative method for evaluating the performance of the employed mechanism. My results suggest that the uniform price auction performs well, both in terms of efficiency of the allocation and in terms of revenue maximization. I estimate that the employed mechanism failed to extract at most 3 basis points in terms of the annual yield of T-bills worth of expected surplus while implementing an allocation resulting in almost all the efficient surplus. Failing to account for discreteness of bids would in my application result in overestimating the unextracted revenue by more than 50%.