Inference based on Kotlarski's Identity

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 funct...

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Bibliographic Details
Published inarXiv.org
Main Authors Kato, Kengo, Sasaki, Yuya, Ura, Takuya
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.09.2019
Subjects
Computer simulation
Economic models
Error analysis
Inference
Monte Carlo simulation
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Summary: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.
ISSN:2331-8422