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SMOOTHED ESTIMATING EQUATIONS FOR INSTRUMENTAL VARIABLES QUANTILE REGRESSION

Published online by Cambridge University Press:  22 January 2016

David M. Kaplan  and
Yixiao Sun
David M. Kaplan*
Affiliation:
University of Missouri
Yixiao Sun
Affiliation:
University of California, San Diego
*
*Address correspondence to David M. Kaplan, Department of Economics, University of Missouri, 118 Professional Bldg, 909 University Ave, Columbia, MO 65211-6040; e-mail: kaplandm@missouri.edu.
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Abstract

The moment conditions or estimating equations for instrumental variables quantile regression involve the discontinuous indicator function. We instead use smoothed estimating equations (SEE), with bandwidth h. We show that the mean squared error (MSE) of the vector of the SEE is minimized for some h > 0, leading to smaller asymptotic MSE of the estimating equations and associated parameter estimators. The same MSE-optimal h also minimizes the higher-order type I error of a SEE-based χ2 test and increases size-adjusted power in large samples. Computation of the SEE estimator also becomes simpler and more reliable, especially with (more) endogenous regressors. Monte Carlo simulations demonstrate all of these superior properties in finite samples, and we apply our estimator to JTPA data. Smoothing the estimating equations is not just a technical operation for establishing Edgeworth expansions and bootstrap refinements; it also brings the real benefits of having more precise estimators and more powerful tests.

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Type
ARTICLES
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Econometric Theory , Volume 33 , Issue 1 , February 2017 , pp. 105 - 157
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

Thanks to Victor Chernozhukov (co-editor) and an anonymous referee for insightful comments and references, and thanks to Peter C. B. Phillips (editor) for additional editorial help. Thanks to Xiaohong Chen, Brendan Beare, Andres Santos, and active seminar and conference participants for insightful questions and comments.

References

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