Document Type
Discussion Paper
Publication Date
12-1-2014
CFDP Number
1961R3
CFDP Revision Date
2017-07-01
CFDP Pages
54
Abstract
Kernel-based estimators such as local polynomial estimators in regression discontinuity designs 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. Our results also apply to other settings involving trimmed data, such as trimming to ensure overlap in treatment effect estimation. We illustrate our approach with three empirical applications.
Recommended Citation
Armstrong, Timothy B. and Kolesár, Michal, "A Simple Adjustment for Bandwidth Snooping" (2014). Cowles Foundation Discussion Papers. 2375.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/2375
Supplemental material
Comments
Supplement Materials, 46 pp