We consider a common value auction model with bidder participation determined jointly by nature and by bidder optimization. In this framework, an increase in the reserve price as two effects: it deters marginal bidders and it deters bidders from becoming informed. We then derive a test statistic for establishing when it is optimal to raise the reserve price. This statistic is independent of the distribution of valuations. We then apply the analysis to U.S. offshore oil sales and find evidence that the reserve price is dramatically too low.