Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: May, 2018, Volume 86, Issue 3

Kernel-Based Semiparametric Estimators: Small Bandwidth Asymptotics and Bootstrap Consistency
p. 955-995

Matias D. Cattaneo, Michael Jansson

This paper develops asymptotic approximations for kernel‐based semiparametric estimators under assumptions accommodating slower‐than‐usual rates of convergence of their nonparametric ingredients. Our first main result is a distributional approximation for semiparametric estimators that differs from existing approximations by accounting for a bias. This bias is nonnegligible in general, and therefore poses a challenge for inference. Our second main result shows that some (but not all) nonparametric bootstrap distributional approximations provide an automatic method of correcting for the bias. Our general theory is illustrated by means of examples and its main finite sample implications are corroborated in a simulation study.

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Supplemental Material

Supplement to "Kernel-Based Semiparametric Estimators: Small Bandwidth Asymptotics and Bootstrap Consistency"

This zip contains the replication files for the manuscript as well as an online appendix with additional material not found within the manuscript.