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Posterior average effects

Author

Listed:
  • Stéphane Bonhomme

    (Institute for Fiscal Studies and University of Chicago)

  • Martin Weidner

    (Institute for Fiscal Studies and University College London)

Abstract

Economists are often interested in estimating averages with respect to distributions of unobservables, such as moments of individual fixed-effects, or average partial effects in discrete choice models. For such quantities, we propose and study posterior average effects (PAE), where the average is computed conditional on the sample, in the spirit of empirical Bayes and shrinkage methods. While the usefulness of shrinkage for prediction is well-understood, a justification of posterior conditioning to estimate population averages is currently lacking. We show that PAE have minimum worst-case specification error under various forms of misspecification of the parametric distribution of unobservables. In addition, we introduce a measure of informativeness of the posterior conditioning, which quantifies the worst-case specification error of PAE relative to parametric model-based estimators. As illustrations, we report PAE estimates of distributions of neighborhood effects in the US, and of permanent and transitory components in a model of income dynamics.

Suggested Citation

  • Stéphane Bonhomme & Martin Weidner, 2021. "Posterior average effects," CeMMAP working papers CWP36/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:36/21
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    File URL: https://www.cemmap.ac.uk/publication/posterior-average-effects-3/
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    Cited by:

    1. Bonhomme, Stéphane & Denis, Angela, 2024. "Estimating heterogeneous effects: Applications to labor economics," Labour Economics, Elsevier, vol. 91(C).
    2. Timothy B. Armstrong & Michal Kolesár & Mikkel Plagborg‐Møller, 2022. "Robust Empirical Bayes Confidence Intervals," Econometrica, Econometric Society, vol. 90(6), pages 2567-2602, November.
    3. Manuel Arellano & Stéphane Bonhomme, 2023. "Recovering Latent Variables by Matching," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 693-706, January.
    4. Stéphane Bonhomme & Martin Weidner, 2022. "Minimizing sensitivity to model misspecification," Quantitative Economics, Econometric Society, vol. 13(3), pages 907-954, July.
    5. Omry Yoresh & Weijian Zou, 2026. "The lifecycle of judicial bias," IFS Working Papers W26/12, Institute for Fiscal Studies.
    6. Omry Yoresh & Weijian Zou, 2026. "The lifecycle of judicial bias," CEP Discussion Papers dp2159, Centre for Economic Performance, LSE.
    7. Timothy B. Armstrong & Michal Koles'ar & Mikkel Plagborg-M{o}ller, 2020. "Robust Empirical Bayes Confidence Intervals," Papers 2004.03448, arXiv.org, revised May 2022.
    8. Stéphane Bonhomme & Angela Denis, 2025. "Fixed Effects and Beyond. Bias Reduction, Groups, Shrinkage and Factors in Panel Data," Working Papers 2526, Banco de España.
    9. Stéphane Bonhomme & Kerstin Holzheu & Thibaut Lamadon & Elena Manresa & Magne Mogstad & Bradley Setzler, 2023. "How Much Should We Trust Estimates of Firm Effects and Worker Sorting?," Journal of Labor Economics, University of Chicago Press, vol. 41(2), pages 291-322.
    10. Pengzhou Wu & Kenji Fukumizu, 2021. "$\beta$-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap," Papers 2110.05225, arXiv.org.
    11. David Arnold & Will Dobbie & Peter Hull, 2022. "Measuring Racial Discrimination in Bail Decisions," American Economic Review, American Economic Association, vol. 112(9), pages 2992-3038, September.
    12. J. Carter Braxton & Kyle Herkenhoff & Jonathan Rothbaum & Lawrence Schmidt, 2025. "Changing Income Risk across the US Skill Distribution: Evidence from a Generalized Kalman Filter," American Economic Review, American Economic Association, vol. 115(12), pages 4438-4475, December.

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