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BOOTSTRAPPING DENSITY-WEIGHTED AVERAGE DERIVATIVES

Published online by Cambridge University Press:  29 April 2014

Matias D. Cattaneo ,
Richard K. Crump  and
Michael Jansson
Matias D. Cattaneo
Affiliation:
Department of Economics, University of Michigan
Richard K. Crump
Affiliation:
Capital Markets Function, Federal Reserve Bank of New York
Michael Jansson
Affiliation:
Department of Economics, UC Berkeley and CREATES
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Abstract

We investigate the properties of several bootstrap-based inference procedures for semiparametric density-weighted average derivatives. The key innovation in this paper is to employ an alternative asymptotic framework to assess the properties of these inference procedures. This theoretical approach is conceptually distinct from the traditional approach (based on asymptotic linearity of the estimator and Edgeworth expansions), and leads to different theoretical prescriptions for bootstrap-based semiparametric inference. First, we show that the conventional bootstrap-based approximations to the distribution of the estimator and its classical studentized version are both invalid in general. This result shows a fundamental lack of “robustness” of the associated, classical bootstrap-based inference procedures with respect to the bandwidth choice. Second, we present a new bootstrap-based inference procedure for density-weighted average derivatives that is more “robust” to perturbations of the bandwidth choice, and hence exhibits demonstrable superior theoretical statistical properties over the traditional bootstrap-based inference procedures. Finally, we also examine the validity and invalidity of related bootstrap-based inference procedures and discuss additional results that may be of independent interest. Some simulation evidence is also presented.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 6 , December 2014 , pp. 1135 - 1164
Copyright
Copyright © Cambridge University Press 2014 

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