Nonparametric identification of first-price auction with unobserved competition: A density discontinuity framework
中文摘要
本文研究独立私人价值一价拍卖模型的非参数识别问题,其中分析者仅能观测到中标出价。我们的基准模型假设竞标者人数 N 为外生。我们证明,若竞标者能观测到 N,则中标出价密度中由此产生的断点可用于识别 N 的分布;私人价值分布可在第二步中得到非参数识别。在可检验的识别条件下,该结果可扩展至 N 为潜在买家数量的情形,此时潜在买家以某一未知概率出价。当存在由某些参数分布抽取的加性不可观测异质性时,识别结果依然成立。
Abstract
We consider nonparametric identification of independent private value first-price auction models, in which the analyst only observes winning bids. Our benchmark model assumes an exogenous number of bidders N. We show that, if the bidders observe N, the resulting discontinuities in the winning bid density can be used to identify the distribution of N. The private value distribution can be nonparametrically identified in a second step. This extends, under testable identification conditions, to the case where N is a number of potential buyers, who bid with some unknown probability. Identification also holds in presence of additive unobserved heterogeneity drawn from some parametric distributions.