标题： 拍卖中截断交易价格的识别 显示英文标题

标题： Identification in Auctions with Truncated Transaction Prices

摘要： 许多带有保留价的拍卖数据集不包含低于保留价的出价。 本文在一系列信息结构下，当交易价格因具有约束力的保留价而被截断时，建立了第一价格和第二价格拍卖中的非参数识别结果。 在最简单的情况下——所有拍卖中潜在投标人的数量是固定且已知的——如果只观察到交易价格，那么在第二价格拍卖中投标人的私人价值分布是可以识别的，但在第一价格拍卖中则不能。 如果观察到活跃投标人的数量（即出价超过保留价的投标人）或没有成交的拍卖数量（所有出价都低于保留价），则可以在第一价格拍卖中实现识别。 当潜在投标人的数量在不同拍卖中变化且未知时，只要同时观察到交易价格和活跃投标人的数量，那么在第一价格拍卖中投标人的私人价值分布是可以识别的，但在第二价格拍卖中则不能。 最后，我将这些结果扩展到存在进入成本的拍卖，当缺少未进入的潜在投标人的数据时，这些拍卖会面临类似的截断问题。 显示英文摘要

摘要： Many auction datasets with reserve prices do not include bids that fall below the reserve. This paper establishes nonparametric identification results in first- and second-price auctions when transaction prices are truncated by a binding reserve price under a range of information structures. In the simplest case-where the number of potential bidders is fixed and known across all auctions-if only the transaction price is observed, the bidders' private-value distribution is identified in second-price auctions but not in first-price auctions. Identification in first-price auctions can be achieved if either the number of active bidders (those whose bids exceed the reserve) or the number of auctions with no sales (all bids below the reserve) is observed. When the number of potential bidders varies across auctions and is unknown, the bidders' private-value distribution is identified in first-price auctions but not in second-price auctions, provided that both the transaction price and the number of active bidders are observed. Finally, I extend these results to auctions with entry costs, which face a similar truncation issue when data on potential bidders who do not enter are missing.