Semiparametric Quantile Models for Ascending Auctions With Asymmetric Bidders

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.

本文提出了一种适用于独立私人价值（Independent Private Value）框架下不对称竞标者的简约且灵活的半参数分位数回归（semiparametric quantile regression）规范。不对称性通过母私人价值分布的幂函数进行参数化，而该母分布由分位数回归规范生成。正如坎蒂隆（Cantillon）所述，该规范覆盖并扩展了适用于同质竞标者间有效合谋、联合竞标与并购的各类模型。该规范可利用中标出价与中标者身份对升序拍卖进行估计，估计过程分为两个阶段：不对称参数可通过简单的最大似然估计程序，从中标者身份数据中估算得到；母分位数回归规范则可通过对吉梅内斯（Gimenes）方法的简单修改完成估计。本文同时考虑了规范检验程序。一项木材行业应用案例显示，弱势竞标者的中标概率较强势竞标者低30%。此外研究发现，在不对称升序拍卖中提升参与人数，其收益未必如对称场景下Bulow与Klemperer的经典结论所预期的那样，可媲美使用最优保留价的效果。