A Simple Adjustment for Bandwidth Snooping

108 Pages Posted: 31 Jul 2015

See all articles by Timothy Armstrong

Timothy Armstrong

Yale University - Cowles Foundation

Michal Kolesár

Princeton University

Multiple version iconThere are 4 versions of this paper

Date Written: July 21, 2015

Abstract

Kernel-based estimators are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals may not have correct coverage, even if the estimator is unbiased. This paper proposes a simple adjustment that gives correct coverage in such situations: replace the Normal quantile with a critical value that depends only on the kernel and ratio of the maximum and minimum bandwidths the researcher has entertained. We tabulate these critical values and quantify the loss in coverage for conventional confidence intervals. For a range of relevant cases, a conventional 95% confidence interval has coverage between 70% and 90%, and our adjustment amounts to replacing the conventional critical value 1.96 with a number between 2.2 and 2.8. A Monte Carlo study confirms that our approach gives accurate coverage in finite samples. We illustrate our approach with two empirical applications.

Keywords: Nonparametric estimation, Multiple testing, Regression discontinuity

JEL Classification: C01, C14

Suggested Citation

Armstrong, Timothy and Kolesar, Michal, A Simple Adjustment for Bandwidth Snooping (July 21, 2015). Cowles Foundation Discussion Paper No. 1961R, Available at SSRN: https://ssrn.com/abstract=2637469 or http://dx.doi.org/10.2139/ssrn.2637469

Timothy Armstrong (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Michal Kolesar

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

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