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Inference based on Kotlarski's Identity

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  • Kengo Kato
  • Yuya Sasaki
  • Takuya Ura

Abstract

Kotlarski's identity has been widely used in applied economic research. However, how to conduct inference based on this popular identification approach has been an open question for two decades. This paper addresses this open problem by constructing a novel confidence band for the density function of a latent variable in repeated measurement error model. The confidence band builds on our finding that we can rewrite Kotlarski's identity as a system of linear moment restrictions. The confidence band controls the asymptotic size uniformly over a class of data generating processes, and it is consistent against all fixed alternatives. Simulation studies support our theoretical results.

Suggested Citation

  • Kengo Kato & Yuya Sasaki & Takuya Ura, 2018. "Inference based on Kotlarski's Identity," Papers 1808.09375, arXiv.org, revised Sep 2019.
    • Handle: RePEc:arx:papers:1808.09375
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    Cited by:

    1. Adusumilli, Karun & Kurisu, Daisuke & Otsu, Taisuke & Whang, Yoon-Jae, 2020. "Inference on distribution functions under measurement error," Journal of Econometrics, Elsevier, vol. 215(1), pages 131-164.
    2. William Morrison & Dmitry Taubinsky, 2023. "Rules of Thumb and Attention Elasticities: Evidence from Under- and Overreaction to Taxes," The Review of Economics and Statistics, MIT Press, vol. 105(5), pages 1110-1127, September.
    3. Li, Siran & Zheng, Xunjie, 2020. "A generalization of Lemma 1 in Kotlarski (1967)," Statistics & Probability Letters, Elsevier, vol. 165(C).

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