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Order Statistics Approaches to Unobserved Heterogeneity in Auctions

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  • Yao Luo
  • Peijun Sang
  • Ruli Xiao

Abstract

We establish nonparametric identification of auction models with continuous and nonseparable unobserved heterogeneity using three consecutive order statistics of bids. We then propose sieve maximum likelihood estimators for the joint distribution of unobserved heterogeneity and the private value, as well as their conditional and marginal distributions. Lastly, we apply our methodology to a novel dataset from judicial auctions in China. Our estimates suggest substantial gains from accounting for unobserved heterogeneity when setting reserve prices. We propose a simple scheme that achieves nearly optimal revenue by using the appraisal value as the reserve price.

Suggested Citation

  • Yao Luo & Peijun Sang & Ruli Xiao, 2022. "Order Statistics Approaches to Unobserved Heterogeneity in Auctions," Papers 2210.03547, arXiv.org.
  • Handle: RePEc:arx:papers:2210.03547
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    References listed on IDEAS

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    2. Yunmi Kong, 2020. "Not knowing the competition: evidence and implications for auction design," RAND Journal of Economics, RAND Corporation, vol. 51(3), pages 840-867, September.
    3. Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100, January.
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