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INFERENCE ON TWO-COMPONENT MIXTURES UNDER TAIL RESTRICTIONS

Published online by Cambridge University Press:  04 April 2016

Koen Jochmans ,
Marc Henry  and
Bernard Salanié
Koen Jochmans*
Affiliation:
Sciences Po
Marc Henry
Affiliation:
The Pennsylvania State University
Bernard Salanié
Affiliation:
Columbia University
*
*Address correspondence to Koen Jochmans, Sciences Po, Department of Economics, 28 rue des Saints Pères 75007, Paris, France, e-mail. koen.jochmans@sciencespo.fr.
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Abstract

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Many econometric models can be analyzed as finite mixtures. We focus on two-component mixtures, and we show that they are nonparametrically point identified by a combination of an exclusion restriction and tail restrictions. Our identification analysis suggests simple closed-form estimators of the component distributions and mixing proportions, as well as a specification test. We derive their asymptotic properties using results on tail empirical processes and we present a simulation study that documents their finite-sample performance.

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 3 , June 2017 , pp. 610 - 635
Copyright
Copyright © Cambridge University Press 2016 

Footnotes

We are grateful to Peter Phillips, Arthur Lewbel, and three referees for comments and suggestions, and to Victor Chernozhukov and Yuichi Kitamura for fruitful discussions. Parts of this paper were written while Henry was visiting the University of Tokyo Graduate School of Economics and while Salanié was visiting the Toulouse School of Economics. The hospitality of both institutions is gratefully acknowledged. Jochmans’ research has received funding from the SAB grant “Nonparametric estimation of finite mixtures”. Henry’s research has received funding from the SSHRC Grants 410-2010-242 and 435-2013-0292, and NSERC Grant 356491-2013. Salanié thanks the Georges Meyer endowment. Some of the results presented here previously circulated as part of Henry, Kitamura, and Salanié (2010), whose published version (Henry et al., 2014) only contains results on partial identification.

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