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Efficient propensity score regression estimators of multi-valued treatment effects for the treated

Author

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  • Ying-Ying Lee
Abstract
We study the role of the propensity scores in estimating treatment effects for the treated with a multi-valued treatment. Assume assignment to one of the multiple treatments is random given observed characteristics. Valid causal comparisons for the subpopulation who has been treated a particular treatment level are based on two propensity scores - one for the treatment level and one for the counterfactual level. In contrast to the binary treatment case, these two propensity scores do not add up to one. This is the key feature that allows us to distinguish different roles of the propensity scores and to provide new insight in well-known paradoxes in the binary treatment effect and missing data literature. We formally show that knowledge of the propensity scorefor the treated level decreases the semiparametric efficiency bound, regardless of knowledge of the propensity score for the counterfactual level. We propose efficient kernel regression estimators that project on a nonparametrically estimated propensity score for the counterfactual level and the true propensity score for the treated level. A surprising result is implied for the binary treatment effect for the treated: when the propensity scores are known, using one estimated propensity score is not efficient. Our efficient estimator regresses on a normalized propensity score that utilizes the information contained in the nonparametrically estimated and the true propensity scores.

Suggested Citation

  • Ying-Ying Lee, 2015. "Efficient propensity score regression estimators of multi-valued treatment effects for the treated," Economics Series Working Papers 738, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:738
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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. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    3. 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.
    4. Bryan S. Graham, 2011. "Efficiency Bounds for Missing Data Models With Semiparametric Restrictions," Econometrica, Econometric Society, vol. 79(2), pages 437-452, March.
    5. Matias Busso & John DiNardo & Justin McCrary, 2014. "New Evidence on the Finite Sample Properties of Propensity Score Reweighting and Matching Estimators," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 885-897, December.
    6. Jinyong Hahn & Geert Ridder, 2013. "Asymptotic Variance of Semiparametric Estimators With Generated Regressors," Econometrica, Econometric Society, vol. 81(1), pages 315-340, January.
    7. Donald, Stephen G. & Hsu, Yu-Chin, 2014. "Estimation and inference for distribution functions and quantile functions in treatment effect models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 383-397.
    8. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    9. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    10. Matias D. Cattaneo, 2010. "multi-valued treatment effects," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
    11. Sergio Firpo & Cristine Pinto, 2016. "Identification and Estimation of Distributional Impacts of Interventions Using Changes in Inequality Measures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(3), pages 457-486, April.
    12. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    13. Stephen G. Donald & Yu‐Chin Hsu & Garry F. Barrett, 2012. "Incorporating covariates in the measurement of welfare and inequality: methods and applications," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 1-30, February.
    14. 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.
    15. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    16. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
    17. Michael Lechner, 2002. "Program Heterogeneity And Propensity Score Matching: An Application To The Evaluation Of Active Labor Market Policies," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 205-220, May.
    18. Busso, Matias & DiNardo, John & McCrary, Justin, 2009. "New Evidence on the Finite Sample Properties of Propensity Score Matching and Reweighting Estimators," IZA Discussion Papers 3998, Institute of Labor Economics (IZA).
    19. Rajeev H. Dehejia & Sadek Wahba, 2002. "Propensity Score-Matching Methods For Nonexperimental Causal Studies," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 151-161, February.
    20. Heckman, James J. & Lalonde, Robert J. & Smith, Jeffrey A., 1999. "The economics and econometrics of active labor market programs," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 31, pages 1865-2097, Elsevier.
    21. 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.
    22. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, vol. 137(2), pages 674-707, April.
    23. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(2), pages 261-294.
    24. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.
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    3. Young-Min Ju & Myoung-Jae Lee, 2017. "Control Function Approach for Partly Ordered Endogenous Treatments: Military Rank Premium in Wage," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(6), pages 1176-1194, December.

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    More about this item

    Keywords

    propensity score; multi-valued treatment; semiparametric efficiency bound; unconfoundedness; generated regressor;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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