Robust Empirical Bayes Confidence Intervals

Author:

Armstrong Timothy B.1,Kolesár Michal2,Plagborg-Møller Mikkel2

Affiliation:

1. Department of Economics, University of Southern California

2. Department of Economics, Princeton University

Abstract

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.

Publisher

The Econometric Society

Subject

Economics and Econometrics

Reference44 articles.

1. Choosing among Regularized Estimators in Empirical Economics: The Risk of Machine Learning

2. Andrews, Isaiah, Toru Kitagawa, and Adam McCloskey (2021): “Inference on Winners,” Unpublished manuscript, Harvard University.

3. Leveraging Lotteries for School Value-Added: Testing and Estimation*

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5. Armstrong, Timothy B., Michal Kolesár, and Mikkel Plagborg-Møller (2020): “Robust Empirical Bayes Confidence Intervals,” arXiv:2004.03448v2.

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