Robust Empirical Bayes Confidence Intervals
Timothy B. Armstrong, Michal Kolesár, Mikkel Plagborg-Møller
Econometrica · 2022 · Volume 90 · Issue 6
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 −αon average across thenEBCIs for each of the means. Our empirical application considers the effects of U.S. neighborhoods on intergenerational mobility.
Keywords
Average coverage, empirical Bayes, confidence interval, shrinkage
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