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Robust Empirical Bayes Confidence Intervals

Author

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

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.

Suggested Citation

  • Timothy B. Armstrong & Michal Kolesár & Mikkel Plagborg‐Møller, 2022. "Robust Empirical Bayes Confidence Intervals," Econometrica, Econometric Society, vol. 90(6), pages 2567-2602, November.
    • Handle: RePEc:wly:emetrp:v:90:y:2022:i:6:p:2567-2602
    DOI: 10.3982/ECTA18597
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    1. Raj Chetty & Nathaniel Hendren, 2018. "The Impacts of Neighborhoods on Intergenerational Mobility II: County-Level Estimates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1163-1228.
    2. Timothy B. Armstrong & Michal Kolesár, 2018. "Optimal Inference in a Class of Regression Models," Econometrica, Econometric Society, vol. 86(2), pages 655-683, March.
    3. Thomas J. Kane & Douglas O. Staiger, 2008. "Estimating Teacher Impacts on Student Achievement: An Experimental Evaluation," NBER Working Papers 14607, National Bureau of Economic Research, Inc.
    4. Raj Chetty & Nathaniel Hendren, 2018. "The Impacts of Neighborhoods on Intergenerational Mobility I: Childhood Exposure Effects," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1107-1162.
    5. Laura Liu & Hyungsik Roger Moon & Frank Schorfheide, 2023. "Forecasting with a panel Tobit model," Quantitative Economics, Econometric Society, vol. 14(1), pages 117-159, January.
    6. Hansen, Bruce E., 2016. "Efficient shrinkage in parametric models," Journal of Econometrics, Elsevier, vol. 190(1), pages 115-132.
    7. Raj Chetty & John N. Friedman & Jonah E. Rockoff, 2014. "Measuring the Impacts of Teachers I: Evaluating Bias in Teacher Value-Added Estimates," American Economic Review, American Economic Association, vol. 104(9), pages 2593-2632, September.
    8. Yoav Benjamini & Daniel Yekutieli, 2005. "False Discovery Rate-Adjusted Multiple Confidence Intervals for Selected Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 71-81, March.
    9. Roger Koenker & Ivan Mizera, 2014. "Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 674-685, June.
    10. Stéphane Bonhomme & Martin Weidner, 2021. "Posterior average effects," CeMMAP working papers CWP36/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Stéphane Bonhomme & Martin Weidner, 2019. "Posterior average effects," CeMMAP working papers CWP43/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Xianchao Xie & S. C. Kou & Lawrence D. Brown, 2012. "SURE Estimates for a Heteroscedastic Hierarchical Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1465-1479, December.
    13. Alberto Abadie & Maximilian Kasy, 2019. "Choosing Among Regularized Estimators in Empirical Economics: The Risk of Machine Learning," The Review of Economics and Statistics, MIT Press, vol. 101(5), pages 743-762, December.
    14. Joshua D. Angrist & Peter D. Hull & Parag A. Pathak & Christopher R. Walters, 2017. "Leveraging Lotteries for School Value-Added: Testing and Estimation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(2), pages 871-919.
    15. T. Tony Cai & Mark Low & Zongming Ma, 2014. "Adaptive Confidence Bands for Nonparametric Regression Functions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1054-1070, September.
    16. Brian A. Jacob & Lars Lefgren, 2008. "Can Principals Identify Effective Teachers? Evidence on Subjective Performance Evaluation in Education," Journal of Labor Economics, University of Chicago Press, vol. 26(1), pages 101-136.
    17. Koenker, Roger & Mizera, Ivan, 2014. "Convex Optimization in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i05).
    18. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    19. Bradley Efron, 2015. "Frequentist accuracy of Bayesian estimates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(3), pages 617-646, June.
    20. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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