Conditionally independent private information in OCS wildcat auctions

In this paper, we consider the conditionally independent private information (CIPI) model which includes the conditionally independent private value (CIPV) model and the pure common value (CV) model as polar cases. Specifically, we model each bidder's private information as the product of two unobserved independent components, one specific to the auctioned object and common to all bidders, the other specific to each bidder. The structural elements of the model include the distributions of the common component and the idiosyncratic component. Noting that the above decomposition is related to a measurement error problem with multiple indicators, we show that both distributions are identified from observed bids in the CIPV case. On the other hand, identification of the pure CV model is achieved under additional restrictions. We then propose a computationally simple two-step nonparametric estimation procedure using kernel estimators in the first step and empirical characteristic functions in the second step. The consistency of the two density estimators is established. An application to the OCS wildcat auctions shows that the distribution of the common component is much more concentrated than the distribution of the idiosyncratic component. This suggests that idiosyncratic components are more likely to explain the variability of private information and hence of bids than the common component.