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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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  1. Donald W.K. Andrews & Xiaoxia Shi, 2010. "Inference Based on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1761R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2011.
  2. Linton, Oliver & Maasoumi, Esfandiar & Whang, Yoon-Jae, 2003. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," SFB 373 Discussion Papers 2003,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves without Crossing," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
  4. 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.
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  6. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, 9.
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  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Davidson, Russell & Duclos, Jean-Yves, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Cahiers de recherche 9805, Université Laval - Département d'économique.
  13. 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.
  14. 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.
  15. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, Econometric Society, vol. 78(6), pages 2021-2042, November.
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  18. Sergio Firpo, 2004. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometric Society 2004 North American Summer Meetings 605, Econometric Society.
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  20. 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).
  21. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc.
  22. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
  23. Abadie, Alberto & Imbens, Guido W., 2011. "Bias-Corrected Matching Estimators for Average Treatment Effects," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 29(1), pages 1-11.
  24. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, vol. 93(2), pages 126-132, May.
  25. 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.
  26. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, Econometric Society, vol. 71(1), pages 71-104, January.
  27. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, Econometric Society, vol. 64(5), pages 1183-93, September.
  28. 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.
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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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