The bidder exclusion effect

We introduce a new, simple-to-compute test of independence of valuations and the number of bidders for ascending button auctions with symmetric, conditionally independent private values. The test involves estimating the expected revenue drop from excluding a bidder at random, which can be computed as a scaled sample average of a difference of order statistics. This object also provides a bound on counterfactual revenue changes from optimal reserve pricing or bidder mergers. We illustrate the approach using data from timber auctions, where we find some evidence that bidder valuations and the number of participants are not independent.