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ASYMPTOTICALLY EFFICIENT ESTIMATION OF WEIGHTED AVERAGE DERIVATIVES WITH AN INTERVAL CENSORED VARIABLE

Published online by Cambridge University Press:  23 September 2016

Hiroaki Kaido
Hiroaki Kaido*
Affiliation:
Boston University
*
*Address correspondence to Hiroaki Kaido, Dept. of Economics, Boston University 270 Bay State Road, Boston, MA 02215, USA; e-mail: hkaido@bu.edu.
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Abstract

This paper studies the identification and estimation of weighted average derivatives of conditional location functionals including conditional mean and conditional quantiles in settings where either the outcome variable or a regressor is interval-valued. Building on Manski and Tamer (2002, Econometrica 70(2), 519–546) who study nonparametric bounds for mean regression with interval data, we characterize the identified set of weighted average derivatives of regression functions. Since the weighted average derivatives do not rely on parametric specifications for the regression functions, the identified set is well-defined without any functional-form assumptions. Under general conditions, the identified set is compact and convex and hence admits characterization by its support function. Using this characterization, we derive the semiparametric efficiency bound of the support function when the outcome variable is interval-valued. Using mean regression as an example, we further demonstrate that the support function can be estimated in a regular manner by a computationally simple estimator and that the efficiency bound can be achieved.

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 5 , October 2017 , pp. 1218 - 1241
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

The author thanks the editor and anonymous referees for comments that helped improve this paper. The author thanks Iván Fernández-Val, Arthur Lewbel, Francesca Molinari, Pierre Perron, Zhongjun Qu, Andres Santos, Jörg Stoye, and seminar participants at BU, Cornell, Brown, Yale and participants of BU-BC Joint Econometrics Conference, the CEMMAP Workshop (New Developments in the Use of Random Sets in Economics), the 2012 International Symposium on Econometric Theory and Applications, and CEME 2014 for helpful comments. The author acknowledges excellent research assistance from Michael Gechter. Financial support from NSF Grants SES-1230071 and SES-1357643 is gratefully acknowledged.

References

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