Copula as a Measure of Affiliation in First Price Auctions

Abstract

Estimating distribution of bidders' ex-ante valuation is an important structural parameter in corporate auctions design and setting the optimal reserve price. This parameter is unobserved to researcher as the observed bids are strategic response and at best is a monotonic function of bidders ex ante valuation. This paper presents a simple, copula based, two step semiparametric estimator for structural estimation of distributions of bidders' unobserved valuations in …first price auctions. In the …first step, the marginal distributions of "valuations" are non-parametrically estimated using the equilibrium distribution of bids. The second stage involves a simple maximum likelihood procedure to estimate the "copula" parameter which measures the association (affiliation) between the valuations. We apply our methodology to data from wildcat oil tract auctions. Wildcat auctions resembles a corporate auction where the target's value is highly uncertain and the market or industry provides a signal about the value of the target. The estimation and testing procedure rejects the hypothesis of independence of signals and opts for non-linear dependence structure in the tails of the distributions. This has important implications for auction choice and mechanism design. The methodology is well suited for corporate …nance and market microstructure applications with general informational assumptions. The estimated optimal reserve price found to be much higher than the actual reserve price.

Keywords: Auctions, Structural Estimation, Semi-Parametric Estimation, Copula

JEL Classification: C14, D44, D82