SummaryA common concern in the empirical study of auctions is the likely presence of auction-specific factors that are common knowledge among bidders but unobserved to the econometrician. Such unobserved heterogeneity confounds attempts to uncover the underlying structure of demand and information, typically a primary feature of interest in an auction market. Unobserved heterogeneity presents a particular challenge in first-price auctions, where identification arguments rely on the econometrician’s ability to reconstruct from observables the conditional probabilities that entered each bidder’s equilibrium optimization problem. When bidders condition on unobservables, it is not obvious that this is possible. Here we discuss several approaches to identification developed in recent work on first-price auctions with unobserved heterogeneity. Despite the special challenges of this setting, all of the approaches build on insights developed in other areas of econometrics, including those on control functions, measurement error, and mixture models. Because each strategy relies on different combinations of model restrictions, technical assumptions, and data requirements, their relative attractiveness will vary with the application. However, this varied menu of results suggests both a type of robustness of identifiability and the potential for expanding the frontier with additional work.

中文翻译：

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拍卖中未观察到的异质性

总结拍卖的实证研究中普遍关注的一个问题是可能存在竞标特定因素，这些因素是投标人之间的常识，但计量经济学家却没有注意到。这种无法观察到的异质性混淆了试图揭示需求和信息的底层结构的尝试，这通常是拍卖市场感兴趣的主要特征。未观察到的异质性在首次价格拍卖中提出了一个特殊的挑战，识别论据依赖于计量经济学家从可观察到的事物中重构进入每个投标人均衡优化问题的条件概率的能力。当投标人以不可观察的条件为条件时，这是不可能的。在这里，我们讨论了最近的关于具有未观察到的异质性的首次价格拍卖中开发的识别方法。尽管在这种情况下存在特殊挑战，但所有方法都建立在计量经济学其他领域的见解之上，包括对控制功能，测量误差和混合模型的见解。由于每种策略都依赖于模型限制，技术假设和数据要求的不同组合，因此它们的相对吸引力将随应用程序而变化。但是，这种多样化的结果菜单既表明了一种可识别性的鲁棒性，又表明了通过其他工作扩展边界的潜力。和数据要求，它们的相对吸引力会随应用程序而变化。但是，这种多样化的结果菜单既表明了一种可识别性的鲁棒性，又表明了通过其他工作扩展边界的潜力。和数据要求，它们的相对吸引力会随应用程序而变化。但是，这种多样化的结果菜单既表明了一种可识别性的鲁棒性，又表明了通过其他工作扩展边界的潜力。