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Semi-parametric estimation of multi-valued treatment effects for the treated:estimating equations and sandwich estimators

Author

Listed:
  • Zetterqvist, Johan

    (Karolinska institutet)

  • Waernbaum, Ingeborg

    (IFAU - Institute for Evaluation of Labour Market and Education Policy)

Abstract

An estimand of interest in empirical studies with observational data is the average treatment effect of a multi-valued treatment in the treated subpopulation. We demonstrate three estimation approaches: outcome regression, inverse probability weighting and inverse probability weighted regression, where the latter estimator holds a so called doubly robust property. Here, we define the estimators in the framework of partial M-estimation and derive corresponding sandwich estimators of their variances. The finite sample properties of the estimators and the proposed variance estimators are evaluated in simulations that reproduce designs from a previous simulation study in the literature of multi-valued treatment effects. The proposed variance estimators are investigated and compared to a bootstrap estimator.

Suggested Citation

  • Zetterqvist, Johan & Waernbaum, Ingeborg, 2020. "Semi-parametric estimation of multi-valued treatment effects for the treated:estimating equations and sandwich estimators," Working Paper Series 2020:4, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    • Handle: RePEc:hhs:ifauwp:2020_004
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    References listed on IDEAS

    as
    1. Cattaneo, Matias D., 2010. "Efficient semiparametric estimation of multi-valued treatment effects under ignorability," Journal of Econometrics, Elsevier, vol. 155(2), pages 138-154, April.
    2. S. Derya Uysal, 2015. "Doubly Robust Estimation of Causal Effects with Multivalued Treatments: An Application to the Returns to Schooling," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 763-786, August.
    3. Słoczyński, Tymon & Wooldridge, Jeffrey M., 2018. "A General Double Robustness Result For Estimating Average Treatment Effects," Econometric Theory, Cambridge University Press, vol. 34(1), pages 112-133, February.
    4. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    5. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    6. Matias D. Cattaneo, 2010. "multi-valued treatment effects," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
    7. Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
    8. Kosuke Imai & David A. van Dyk, 2004. "Causal Inference With General Treatment Regimes: Generalizing the Propensity Score," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 854-866, January.
    9. Shu Yang & Guido W. Imbens & Zhanglin Cui & Douglas E. Faries & Zbigniew Kadziola, 2016. "Propensity score matching and subclassification in observational studies with multi‐level treatments," Biometrics, The International Biometric Society, vol. 72(4), pages 1055-1065, December.
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    More about this item

    Keywords

    ATT; causal inference; inverse probability weighting; doubly robust; weighted ordinary least squares;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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