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Partial identification of distributional and quantile treatment effects in difference-in-differences models

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  • Fan, Yanqin
  • Yu, Zhengfei

Abstract

In this paper, we supplement the identification results for the mean treatment effect for the treated in the difference-in-differences framework studied by Abadie (2005) by establishing partial identification results for the distribution and quantile of the counterfactual outcome and of the treatment effect for the treated. Unlike the mean treatment effect which is identifiable from either the panel or the repeated cross sectional data, we show that the distribution/quantile of either the counterfactual outcome or of the treatment effect is only partially identified and in general the identified interval is tighter with panel than with the repeated cross sectional data. We further illustrate this gain from the panel via a numerical example.

Suggested Citation

  • Fan, Yanqin & Yu, Zhengfei, 2012. "Partial identification of distributional and quantile treatment effects in difference-in-differences models," Economics Letters, Elsevier, vol. 115(3), pages 511-515.
    • Handle: RePEc:eee:ecolet:v:115:y:2012:i:3:p:511-515
    DOI: 10.1016/j.econlet.2012.01.001
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    References listed on IDEAS

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    1. Firpo, Sergio Pinheiro & Ridder, Geert, 2010. "Bounds on functionals of the distribution treatment effects," Textos para discussão 201, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
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    4. Abbring, Jaap H. & Heckman, James J., 2007. "Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72, Elsevier.
    5. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 1-19.
    6. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 487-535.
    7. Fan, Yanqin & Park, Sang Soo, 2012. "Confidence intervals for the quantile of treatment effects in randomized experiments," Journal of Econometrics, Elsevier, vol. 167(2), pages 330-344.
    8. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    9. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," Econometrica, Econometric Society, vol. 66(5), pages 1017-1098, September.
    10. Stéphane Bonhomme & Ulrich Sauder, 2011. "Recovering Distributions in Difference-in-Differences Models: A Comparison of Selective and Comprehensive Schooling," The Review of Economics and Statistics, MIT Press, vol. 93(2), pages 479-494, May.
    11. Yanqin Fan & Sang Soo Park, 2009. "Partial identification of the distribution of treatment effects and its confidence sets," Advances in Econometrics, in: Nonparametric Econometric Methods, pages 3-70, Emerald Group Publishing Limited.
    12. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(3), pages 931-951, June.
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    Cited by:

    1. 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.
    2. David Bounie & Youssouf Camara, 2020. "Card-Sales Response to Merchant Contactless Payment Acceptance," Post-Print hal-02296302, HAL.
    3. Callaway, Brantly & Li, Tong & Oka, Tatsushi, 2018. "Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods," Journal of Econometrics, Elsevier, vol. 206(2), pages 395-413.
    4. Andrea Ciaccio, 2024. "Distributional Difference-in-Differences Models with Multiple Time Periods: A Monte Carlo Analysis," Papers 2408.01208, arXiv.org.
    5. David Bounie & Youssouf Camara, 2019. "Card-Sales Response to Merchant Contactless Payment Acceptance: Causal Evidence," Working Papers hal-02296302, HAL.
    6. Wang, Zheng-Xin & Jv, Yue-Qi, 2022. "A smooth difference-in-differences model for assessing gradual policy effects: Revisiting the impact of banking deregulation on income distribution," Finance Research Letters, Elsevier, vol. 50(C).
    7. Bounie, David & Camara, Youssouf, 2020. "Card-sales response to merchant contactless payment acceptance," Journal of Banking & Finance, Elsevier, vol. 119(C).

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