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The Role of the Propensity Score in Fixed Effect Models

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  • Dmitry Arkhangelsky
  • Guido Imbens

Abstract

We develop a new approach for estimating average treatment effects in the observational studies with unobserved cluster-level heterogeneity. The previous approach relied heavily on linear fixed effect specifications that severely limit the heterogeneity between clusters. These methods imply that linearly adjusting for differences between clusters in average covariate values addresses all concerns with cross-cluster comparisons. Instead, we consider an exponential family structure on the within-cluster distribution of covariates and treatments that implies that a low-dimensional sufficient statistic can summarize the empirical distribution, where this sufficient statistic may include functions of the data beyond average covariate values. Then we use modern causal inference methods to construct flexible and robust estimators.

Suggested Citation

  • Dmitry Arkhangelsky & Guido Imbens, 2018. "The Role of the Propensity Score in Fixed Effect Models," NBER Working Papers 24814, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:24814
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    References listed on IDEAS

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    1. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, January.
    2. Joseph G. Altonji & Richard K. Mansfield, 2018. "Estimating Group Effects Using Averages of Observables to Control for Sorting on Unobservables: School and Neighborhood Effects," American Economic Review, American Economic Association, vol. 108(10), pages 2902-2946, October.
    3. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney K. Newey, 2016. "Double machine learning for treatment and causal parameters," CeMMAP working papers CWP49/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
    5. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    6. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291, Decembrie.
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    8. repec:hal:spmain:info:hdl:2441/etefo8s8r89oamhnhiclqr530 is not listed on IDEAS
    9. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, November.
    10. Kosuke Imai & In Song Kim, 2019. "When Should We Use Unit Fixed Effects Regression Models for Causal Inference with Longitudinal Data?," American Journal of Political Science, John Wiley & Sons, vol. 63(2), pages 467-490, April.
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    Cited by:

    1. Hye Yoon Chung & Youjin Hahn, 2021. "Work Transitions, Gender, and Subjective Well-Being," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 16(5), pages 2085-2109, October.
    2. Athey, Susan & Imbens, Guido W., 2022. "Design-based analysis in Difference-In-Differences settings with staggered adoption," Journal of Econometrics, Elsevier, vol. 226(1), pages 62-79.
    3. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Mar 2024.
    4. Dalia Ghanem & Pedro H. C. Sant'Anna & Kaspar Wüthrich, 2022. "Selection and Parallel Trends," CESifo Working Paper Series 9910, CESifo.
    5. Nagasawa, Kenichi, 2020. "Identification and Estimation of Group-Level Partial Effects," The Warwick Economics Research Paper Series (TWERPS) 1243, University of Warwick, Department of Economics.
    6. Yang, Yimin, 2022. "A correlated random effects approach to the estimation of models with multiple fixed effects," Economics Letters, Elsevier, vol. 213(C).
    7. Daniel Brüggmann & Michaela Kreyenfeld, 2023. "Earnings Trajectories After Divorce: The Legacies of the Earner Model During Marriage," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 42(2), pages 1-34, April.
    8. Dmitry Arkhangelsky & Guido W. Imbens, 2019. "Doubly Robust Identification for Causal Panel Data Models," Papers 1909.09412, arXiv.org, revised Feb 2022.
    9. Berger, Marius & Hottenrott, Hanna, 2021. "Start-up subsidies and the sources of venture capital," Journal of Business Venturing Insights, Elsevier, vol. 16(C).
    10. Myungkou Shin, 2022. "Finitely Heterogeneous Treatment Effect in Event-study," Papers 2204.02346, arXiv.org, revised Feb 2024.
    11. Kosuke Imai & In Song Kim, 2019. "When Should We Use Unit Fixed Effects Regression Models for Causal Inference with Longitudinal Data?," American Journal of Political Science, John Wiley & Sons, vol. 63(2), pages 467-490, April.
    12. Youmi Suk, 2024. "A Within-Group Approach to Ensemble Machine Learning Methods for Causal Inference in Multilevel Studies," Journal of Educational and Behavioral Statistics, , vol. 49(1), pages 61-91, February.
    13. Alejandro Sanchez-Becerra, 2022. "The Network Propensity Score: Spillovers, Homophily, and Selection into Treatment," Papers 2209.14391, arXiv.org.
    14. Laura Liu & Alexandre Poirier & Ji-Liang Shiu, 2021. "Identification and Estimation of Partial Effects in Nonlinear Semiparametric Panel Models," Papers 2105.12891, arXiv.org, revised May 2024.
    15. Dmitry Arkhangelsky & Guido W. Imbens & Lihua Lei & Xiaoman Luo, 2021. "Design-Robust Two-Way-Fixed-Effects Regression For Panel Data," Papers 2107.13737, arXiv.org, revised Mar 2024.
    16. Guido W. Imbens & Davide Viviano, 2023. "Identification and Inference for Synthetic Controls with Confounding," Papers 2312.00955, arXiv.org.
    17. Youmi Suk & Hyunseung Kang, 2022. "Robust Machine Learning for Treatment Effects in Multilevel Observational Studies Under Cluster-level Unmeasured Confounding," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 310-343, March.

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    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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