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Identifying Treatment Effects Under Data Combination

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  • Yanqin Fan
  • Robert Sherman
  • Matthew Shum

Abstract

We consider the identification of counterfactual distributions and treatment effects when the outcome variables and conditioning covariates are observed in separate data sets. Under the standard selection on observables assumption, the counterfactual distributions and treatment effect parameters are no longer point identified. However, applying the classical monotone rearrangement inequality, we derive sharp bounds on the counterfactual distributions and policy parameters of interest.

Suggested Citation

  • Yanqin Fan & Robert Sherman & Matthew Shum, 2014. "Identifying Treatment Effects Under Data Combination," Econometrica, Econometric Society, vol. 82(2), pages 811-822, March.
    • Handle: RePEc:wly:emetrp:v:82:y:2014:i:2:p:811-822
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    File URL: http://hdl.handle.net/10.1111/ecta.2014.82.issue-2.x
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    Citations

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    Cited by:

    1. Wooyoung Kim & Koohyun Kwon & Soonwoo Kwon & Sokbae Lee, 2018. "The identification power of smoothness assumptions in models with counterfactual outcomes," Quantitative Economics, Econometric Society, vol. 9(2), pages 617-642, July.
    2. Mullahy, John, 2018. "Individual results may vary: Inequality-probability bounds for some health-outcome treatment effects," Journal of Health Economics, Elsevier, vol. 61(C), pages 151-162.
    3. Xavier D'Haultf{oe}uille & Christophe Gaillac & Arnaud Maurel, 2022. "Partially Linear Models under Data Combination," Papers 2204.05175, arXiv.org, revised Aug 2023.
    4. Pablo Lavado & Gonzalo Rivera, 2016. "Identifying Treatment Effects with Data Combination and Unobserved Heterogeneity," Working Papers 79, Peruvian Economic Association.
    5. Jiannan Lu & Peng Ding & Tirthankar Dasgupta, 2018. "Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds," Journal of Educational and Behavioral Statistics, , vol. 43(5), pages 540-567, October.
    6. Firpo, Sergio & Galvao, Antonio F. & Parker, Thomas, 2023. "Uniform inference for value functions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1680-1699.
    7. Xavier D'Haultfoeuille & Christophe Gaillac & Arnaud Maurel, 2018. "Rationalizing Rational Expectations? Tests and Deviations," NBER Working Papers 25274, National Bureau of Economic Research, Inc.
    8. Fan, Yanqin & Guerre, Emmanuel & Zhu, Dongming, 2017. "Partial identification of functionals of the joint distribution of “potential outcomes”," Journal of Econometrics, Elsevier, vol. 197(1), pages 42-59.
    9. Takahiro Hoshino & Keisuke Takahata, 2018. "Identification of heterogeneous treatment effects as a function of potential untreated outcome under the nonignorable assignment condition," Keio-IES Discussion Paper Series 2018-005, Institute for Economics Studies, Keio University.
    10. John Mullahy, 2017. "Individual Results May Vary: Elementary Analytics of Inequality-Probability Bounds, with Applications to Health-Outcome Treatment Effects," NBER Working Papers 23603, National Bureau of Economic Research, Inc.
    11. Xavier D'Haultfoeuille & Christophe Gaillac & Arnaud Maurel, 2021. "Rationalizing rational expectations: Characterizations and tests," Quantitative Economics, Econometric Society, vol. 12(3), pages 817-842, July.
    12. Martyna Kobus & Radoslaw Kurek, 2017. "Copula-based measurement of interdependence for discrete distributions," Working Papers 431, ECINEQ, Society for the Study of Economic Inequality.
    13. Fan Yanqin & Sherman Robert & Shum Matthew, 2016. "Estimation and Inference in an Ecological Inference Model," Journal of Econometric Methods, De Gruyter, vol. 5(1), pages 17-48, January.
    14. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    15. Fan, Yanqin & Henry, Marc, 2023. "Vector copulas," Journal of Econometrics, Elsevier, vol. 234(1), pages 128-150.
    16. Pablo Lavado, "undated". "Identifying Treatment Effects and Counterfactual Distributions using Data Combination with Unobserved Heterogeneity," Working Papers 13-25, Departamento de Economía, Universidad del Pacífico.
    17. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Pablo Lavado & Gonzalo Rivera, 2015. "Identifying treatment effects and counterfactual distributions using data combination with unobserved heterogeneity," Working Papers 15-14, Centro de Investigación, Universidad del Pacífico.
    19. D'Haultfoeuille, Xavier & Gaillac, Christophe & Maurel, Arnaud, 2024. "Linear Regressions with Combined Data," TSE Working Papers 24-1602, Toulouse School of Economics (TSE).
    20. Sarah Moon, 2024. "Partial Identification of Individual-Level Parameters Using Aggregate Data in a Nonparametric Model," Papers 2403.07236, arXiv.org, revised May 2024.
    21. Atsushi Inoue & Tong Li & Qi Xu, 2021. "Two Sample Unconditional Quantile Effect," Papers 2105.09445, arXiv.org.
    22. Nathan Kallus & Xiaojie Mao & Angela Zhou, 2022. "Assessing Algorithmic Fairness with Unobserved Protected Class Using Data Combination," Management Science, INFORMS, vol. 68(3), pages 1959-1981, March.
    23. Yechan Park & Yuya Sasaki, 2024. "The Informativeness of Combined Experimental and Observational Data under Dynamic Selection," Papers 2403.16177, arXiv.org.

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