Journal of Econometrics 98 (2000) 129 }161 Conditionally independent private information in OCS wildcat auctions Tong Li, Isabelle Perrigne*, Quang Vuong Indiana University, Los Angeles, USA Department of Economics, University of Southern California, Los Angeles 90089-0253, USA INRA, France Received 1 May 1998; received in revised form 1 October 1999; accepted 1 October 1999 Abstract 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. Speci"cally, we model each bidder's private information as the product of two unobserved independent components, one speci"c to the auctioned object and common to all bidders, the other speci"c 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 identi"ed from observed bids in the CIPV case. On the other hand, identi"cation 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 "rst 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.  2000 Elsevier Science S.A. All rights reserved. JEL classixcation: D44; C14; L70 * Corresponding author. Tel.: (213) 740 3528; fax: (213) 740 8543. E-mail address: perrigne@usc.edu (I. Perrigne). 0304-4076/00/$ - see front matter  2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 0 4 - 4 0 7 6 ( 9 9 ) 0 0 0 8 1 - 0