We propose a framework for identification and estimation of a private values model with unobserved heterogeneity from bid data in English auctions, using variation in the number of bidders across auctions, and extend the framework to settings where the number of bidders is not cleanly observed in each auction. We illustrate our method on data from eBay Motors auctions. We find that unobserved heterogeneity is important, accounting for two thirds of price variation after controlling for observables, and that welfare measures would be dramatically misestimated if unobserved heterogeneity were ignored.

中文翻译：

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异质性不佳的英语拍卖的估计

我们提出了一个框架，用于识别和估计私人价值模型，该模型利用英国拍卖中竞标者数量的变化，从英国拍卖中的竞标数据中发现了未观察到的异质性，并将该框架扩展到在每个竞标者中都不干净地观察到竞标者数量的设置拍卖。我们用eBay汽车拍卖的数据说明了我们的方法。我们发现，未观察到的异质性很重要，占控制可观察物后价格变化的三分之二，如果忽略了未观察到的异质性，福利措施将被严重错误估计。