2.5 Problems and remedies
Below I discuss four different problems related to the applicability of the data for the testing methodology. The first problem is that the data set is small. The second is that bidders’ participation decisions are possibly endogenous. The third possible problem is bidder collusion, and the fourth is the applicability of the structural estimation method for this particular data.
I introduce pooling to the test procedure for two reasons. First, for some combina- tions of bidder types there are too few auctions for the purpose of subsampling. When the observations are pooled by treating the auctions with small numbers of bidders as belonging to one group and the auctions with large numbers of bidders as belonging to the other group, a larger part of the data set can be used. Typically, the results are also more robust to the choice of subsample size with larger samples. The second reason is that this pooling alleviates the problem of possible endogenous participation.
HHS tests assume that the number of bidders is exogenous and known to all bidders ex ante. HHS mention two ways in which endogenous participation may pose problems. First, if auctions with large numbers of bidders tend to be those where the contract is known by bidders to be particularly easy to operate, tests based on an assumption