Econometrica

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: Nov, 2022, Volume 90, Issue 6

Robust Empirical Bayes Confidence Intervals

https://doi.org/10.3982/ECTA18597
p. 2567-2602

Timothy B. Armstrong, Michal Kolesár, Mikkel Plagborg‐Møller

We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The intervals are centered at the usual linear empirical Bayes estimator, but use a critical value accounting for shrinkage. Parametric EBCIs that assume a normal distribution for the means (Morris (1983b)) may substantially undercover when this assumption is violated. In contrast, our EBCIs control coverage regardless of the means distribution, while remaining close in length to the parametric EBCIs when the means are indeed Gaussian. If the means are treated as fixed, our EBCIs have an average coverage guarantee: the coverage probability is at least 1 − α on average across the n EBCIs for each of the means. Our empirical application considers the effects of U.S. neighborhoods on intergenerational mobility.


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Supplemental Material

Supplement to "Robust Empirical Bayes Confidence Intervals"

Timothy B. Armstrong, Michal Kolesár and Mikkel Plagborg-Møller

This zip file contains the replication files for the manuscript.

Supplement to "Robust Empirical Bayes Confidence Intervals"

Timothy B. Armstrong, Michal Kolesár and Mikkel Plagborg-Møller

This supplement is organized as follows. Supplemental Appendix D gives proofs of the formal results in the main text and details on Assumption C.5. Supplemental Appendix E gives details on the simulations. Supplemental Appendix F discusses the power of tests based on our empirical Bayes confidence intervals (EBCIs), and Supplemental Appendix G works through examples of the general shrinkage estimators in Section 6.1.

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