Semiparametric Quantile Models for Ascending Auctions With Asymmetric Bidders

Abstract

The article proposes a parsimonious and flexible semiparametric quantile regression specification for asymmetric bidders within the independent private value framework. Asymmetry is parameterized using powers of a parent private value distribution, which is generated by a quantile regression specification. As noted in Cantillon, this covers and extends models used for efficient collusion, joint bidding and mergers among homogeneous bidders. The specification can be estimated for ascending auctions using the winning bids and the winner’s identity. The estimation is in two stage. The asymmetry parameters are estimated from the winner’s identity using a simple maximum likelihood procedure. The parent quantile regression specification can be estimated using simple modifications of Gimenes. Specification testing procedures are also considered. A timber application reveals that weaker bidders have 30% less chances to win the auction than stronger ones. It is also found that increasing participation in an asymmetric ascending auction may not be as beneficial as using an optimal reserve price as would have been expected from a result of Bulow and Klemperer valid under symmetry.