Large sample properties for estimators based on the order statistics approach in auctions

• 成果类型: Article
• 署名作者: Menzel, Konrad; Morganti, Paolo
• 署名单位: New York University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE177
• 发表日期: 2013
• 页码: 329-375
• 关键词: Empirical auctions; order statistics; bounds; irregular identification; uniform consistency; C13; C14; D44

摘要

For symmetric auctions, there is a close relationship between distributions of order statistics of bidders' valuations and observable bids that is often used to estimate or bound the valuation distribution, optimal reserve price, and other quantities of interest nonparametrically. However, we show that the functional mapping from distributions of order statistics to their parent distribution is, in general, not Lipschitz continuous and, therefore, introduces an irregularity into the estimation problem. More specifically, we derive the optimal rate for nonparametric point estimation of, and bounds for, the private value distribution, which is typically substantially slower than the regular root-n rate. We propose trimming rules for the nonparametric estimator that achieve that rate and derive the asymptotic distribution for a regularized estimator. We then demonstrate that policy parameters that depend on the valuation distribution, including optimal reserve price and expected revenue, are irregularly identified when bidding data are incomplete. We also give rates for nonparametric estimation of descending bid auctions and strategic equivalents.