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Estimation and Inference for Distribution Functions and Quantile Functions in Treatment Effect Models

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Abstract

We propose inverse probability weighted estimators for the distribution functions of the potential outcomes of a binary treatment under the unconfoundedness assumption. We also apply the inverse mapping on the distribution functions to obtain the quantile functions. We show that the proposed estimators converge weakly to zero mean Gaussian processes. A simulation method based on the multiplier central limit theorem is proposed to approximate these limiting Gaussian processes. The estimators in the treated subpopulation are shown to share the same properties. To demonstrate the usefulness of our results, we construct Kolmogorov-Smirnov type tests for stochastic dominance relations between the distributions of potential outcomes. We examine the finite sample properties of our tests in a set of Monte-Carlo simulations and use our tests in an empirical example which shows that a job training program had a positive effect on incomes.

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Bibliographic Info

Paper provided by Institute of Economics, Academia Sinica, Taipei, Taiwan in its series IEAS Working Paper : academic research with number 12-A016.

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Length: 43 pages
Date of creation: Dec 2012
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Handle: RePEc:sin:wpaper:12-a016

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Keywords: Hypothesis testing; stochastic dominance; treatment effects; propensity score;

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References

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  1. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2003. "Consistent testing for stochastic dominance under general sampling schemes," LSE Research Online Documents on Economics 2208, London School of Economics and Political Science, LSE Library.
  2. Guido Imbens & Jeffrey Wooldridge, 2008. "Recent developments in the econometrics of program evaluation," CeMMAP working papers CWP24/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Sergio Firpo, 2004. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometric Society 2004 North American Summer Meetings 605, Econometric Society.
  4. Oliver Linton & Kyungchul Song & Yoon-Jae Whang, 2009. "An improved bootstrap test of stochastic dominance," Economics Working Papers we094827, Universidad Carlos III, Departamento de Economía.
  5. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  6. 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 C1-C30, 02.
  7. Guido Imbens, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometric Society World Congress 2000 Contributed Papers 1166, Econometric Society.
  8. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile and probability curves without crossing," CeMMAP working papers CWP10/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
  10. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, 03.
  11. Heckman, James J & Ichimura, Hidehiko & Todd, Petra E, 1997. "Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 605-54, October.
  12. Donald W.K. Andrews & Xiaoxia Shi, 2011. "Nonparametric Inference Based on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1840RR, Cowles Foundation for Research in Economics, Yale University, revised Oct 2013.
  13. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
  14. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, October.
  15. 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.
  16. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
  17. James J. Heckman, 1989. "Choosing Among Alternative Nonexperimental Methods for Estimating the Impact of Social Programs: The Case of Manpower Training," NBER Working Papers 2861, National Bureau of Economic Research, Inc.
  18. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 261-94, April.
  19. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-20, September.
  20. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  21. Firpo, Sergio, 2010. "Identification and Estimation of Distributional Impacts of Interventions Using Changes in Inequality Measures," IZA Discussion Papers 4841, Institute for the Study of Labor (IZA).
  22. Sokbae Lee & Yoon-Jae Whang, 2009. "Nonparametric Tests of Conditional Treatment Effects," Cowles Foundation Discussion Papers 1740, Cowles Foundation for Research in Economics, Yale University.
  23. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
  24. Maier, Michael, 2011. "Tests for distributional treatment effects under unconfoundedness," Economics Letters, Elsevier, vol. 110(1), pages 49-51, January.
  25. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, vol. 93(2), pages 126-132, May.
  26. Abadie, Alberto & Imbens, Guido W., 2011. "Bias-Corrected Matching Estimators for Average Treatment Effects," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 1-11.
  27. Petra E. Todd & Jeffrey A. Smith, 2001. "Reconciling Conflicting Evidence on the Performance of Propensity-Score Matching Methods," American Economic Review, American Economic Association, vol. 91(2), pages 112-118, May.
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Cited by:
  1. 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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