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Partial Identification of Distributional Treatment Effects in Panel Data using Copula Equality Assumptions

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  • Heshani Madigasekara
  • D. S. Poskitt
  • Lina Zhang
  • Xueyan Zhao

Abstract

This paper aims to partially identify the distributional treatment effects (DTEs) that depend on the unknown joint distribution of treated and untreated potential outcomes. We construct the DTE bounds using panel data and allow individuals to switch between the treated and untreated states more than once over time. Individuals are grouped based on their past treatment history, and DTEs are allowed to be heterogeneous across different groups. We provide two alternative group-wise copula equality assumptions to bound the unknown joint and the DTEs, both of which leverage information from the past observations. Testability of these two assumptions are also discussed, and test results are presented. We apply this method to study the treatment effect heterogeneity of exercising on the adults' body weight. These results demonstrate that our method improves the identification power of the DTE bounds compared to the existing methods.

Suggested Citation

  • Heshani Madigasekara & D. S. Poskitt & Lina Zhang & Xueyan Zhao, 2024. "Partial Identification of Distributional Treatment Effects in Panel Data using Copula Equality Assumptions," Papers 2411.04450, arXiv.org.
    • Handle: RePEc:arx:papers:2411.04450
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    References listed on IDEAS

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    1. Callaway, Brantly, 2021. "Bounds on distributional treatment effect parameters using panel data with an application on job displacement," Journal of Econometrics, Elsevier, vol. 222(2), pages 861-881.
    2. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    3. Carlos A. Flores & Xuan Chen, 2018. "Average Treatment Effect Bounds with an Instrumental Variable: Theory and Practice," Springer Books, Springer, number 978-981-13-2017-0, December.
    4. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    5. Thomas M. Russell, 2021. "Sharp Bounds on Functionals of the Joint Distribution in the Analysis of Treatment Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 532-546, March.
    6. Brantly Callaway & Tong Li, 2019. "Quantile treatment effects in difference in differences models with panel data," Quantitative Economics, Econometric Society, vol. 10(4), pages 1579-1618, November.
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