Piecewise Pseudo-Maximum Likelihood Estimation in Empirical Models of Auctions
针对博弈论在拍卖应用中的估计难题，提出分段伪极大似然估计法，并给出其一致性和渐近分布条件，适合研究拍卖实证方法的学者参考。
In applications of game theory to auctions, researchers assume that players choose strategies based upon a commonly known distribution of the latent characteristics. Rational behaviour, within an assumed class of distributions for the latent process, imposes testable restrictions upon the data generating process of the equilibrium strategies. Unfortunately, the support of the distribution of equilibrium strategies often depends upon all of the parameters of the distribution of the latent characteristics, making the standard application of maximum likelihood estimation procedures inappropriate. We present a piecewise pseudo-maximum likelihood estimator as well as the conditions for its consistency and its asymptotic distribution. In empirical applications of game theory to auctions, researchers assume that the distribution of latent (or unobserved) characteristics is common knowledge to the players of the game. For example, in the independent private values model of an auction, the distribution of valuations is known to all bidders. Moreover, each bidder knows that his opponents know the distribution of valuations, and his opponents know that he knows, etc. Based upon their knowledge of the distribution of latent characteristics, and given their realization from that valuation distribution, players are assumed to choose bids which maximize their expected pay-offs from winning the auction. Given this informational structure, the equilibrium of the game can be characterized by appealing to a particular concept of equilibrium (e.g., Bayesian-Nash).