Nonparametric identification of first-price auction with unobserved competition: A density discontinuity framework

We consider nonparametric identification of independent private value first-price auction models, in which the analyst only observes winning bids. Our benchmark model assumes an exogenous number of bidders N. We show that, if the bidders observe N, the resulting discontinuities in the winning bid density can be used to identify the distribution of N. The private value distribution can be identified in a second step. A second class of models considers endogenously determined N, due to a reserve price or an entry cost. If bidders observe N, these models are also identifiable using winning bid discontinuities. If bidders cannot observe N, however, identification is not possible unless the analyst observes an instrument which affects the reserve price or entry cost. Lastly, we derive some testable restrictions for whether bidders observe the number of competitors and whether endogenous participation is due to a reserve price or entry cost. An application to USFS timber auction data illustrates the usefulness of our theoretical results for competition analysis, showing that nearly one bid out of three can be non competitive. It also suggests that the risk aversion bias caused by a mismeasured competition can be large.