Structural Estimation of the Affiliated Private Value Auction Model

Abstract

price sealed-bid auctions. The model allows for bidders' individual efficiencies and opportunity costs, while permitting dependence among bidders' private values through affiliation. We establish the nonparametric identification of the APV model, characterize its theoretical restrictions, and propose a computationally convenient and consistent two-step nonparametric estimation procedure for estimating the joint private value distribution from observed bids. Using simulated bid data we provide a step by step guide on how to implement our procedure and show the good behavior of our estimator in small samples.

Structural Econometric Methods in Auctions: A Guide to the Literature

“…Moreover, CIPV can rationalize a sample of bids if and only if the inverse-bid function is monotonic. As in Li et al (2002), the power of this last result lies in the fact that their estimation procedure allows for verification of monotonicity, which in turn implies that the CIPV assumption is partially testable (subject, of course, to other sources of model misspecification).…”

“…The authors showed their estimator of the joint density of private values achieves the optimal uniform rate of convergence for a two-step nonparametric estimatorà la GPV-that is, the joint density of private values can be estimated at the same rate as the marginal density of private values. The copula parameterization allows for this asymptotic gain as the dimension of the joint density of private values is reduced to one which avoids the curse of dimensionality problem concerning the number of bidders and associated with the nonparametric approach of Li et al (2002). The extra copula-related work in the first step appears to pay dividends in small samples: they used Monte Carlo experiments to show their estimator is on par with GPV when data are independent and that their estimator performs well on affiliated data, even if the researcher chooses the wrong copula.…”

“…Hong and Shum (2002) also adopted the log-additive specification of firm costs considered by Wilson (1998), although with some differences from Li et al (2002). Here, firm costs have both idiosyncratic and common components, and are given by C i = A i V. Furthermore, firms do not directly observe their costs, but rather a noisy signal of costs S i = C i e i , where e i is a positive error term.…”

“…If these two components are independent of each other and, when multiplied, comprise the bidders' valuations, identification obtains as long as two bids are observed at each auction. By assuming multiplicatively-separable components, she was able to relate her work to and leverage results from Li and Vuong (1998) as well as Li et al (2002).…”

“…In a PV environment, these distributions should not vary with the number of bidders, whereas the CV alternative implies a first-order stochastic dominance relation. Of course, it is impossible to compare distributions of bidders' expectations, conditional on N , so they relied on nonparametric methods developed by GPV, Li et al (2000Li et al ( , 2002, as well as Hendricks et al (2003) to compare empirical distributions of estimates of these expectations. First, under the null hypothesis of PV, the nonparametric methods mentioned above are employed to estimate pseudoprivate values that underly each one of the bids.…”