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Deconvolution from Two Order Statistics

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  • JoonHwan Cho
  • Yao Luo
  • Ruli Xiao

Abstract

Economic data are often truncated by ranking and contaminated by measurement errors. We study the identification of the distributions of a latent variable of interest and its measurement errors using a subvector of order statistics of repeated measurements. Kotlarski's lemma is inapplicable due to dependence in the order statistics of measurement errors. Exploiting the ratio of characteristic functions of order statistics, we show observing two order statistics are sufficient to identify the underlying distributions nonparametrically. We adapt an existing simulated sieve estimator to our setting and illustrate its performance in finite samples.

Suggested Citation

  • JoonHwan Cho & Yao Luo & Ruli Xiao, 2022. "Deconvolution from Two Order Statistics," Working Papers tecipa-739, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-739
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    References listed on IDEAS

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    Cited by:

    1. Yao Luo & Ruli Xiao, 2019. "Identification of Auction Models Using Order Statistics," Working Papers tecipa-630, University of Toronto, Department of Economics.
    2. Luo, Yao & Xiao, Ruli, 2023. "Identification of auction models using order statistics," Journal of Econometrics, Elsevier, vol. 236(1).

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    More about this item

    Keywords

    Measurement Error; Order Statistics; Nonparametric Identification; Spacing; Cross-Sum;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

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