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Nonparametric Tests for Treatment Effect Heterogeneity

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Author Info

  • Richard K. Crump

    (University of California at Berkeley)

  • V. Joseph Hotz

    (University of California at Los Angeles)

  • Guido W. Imbens

    (University of California at Berkeley)

  • Oscar A. Mitnik

    ()
    (Department of Economics, University of Miami)

Abstract

A large part of the recent literature on program evaluation has focused on estimation of the average effect of the treatment under assumptions of unconfoundedness or ignorability following the seminal work by Rubin (1974) and Rosenbaum and Rubin (1983). In many cases however, researchers are interested in the effects of programs beyond estimates of the overall average or the average for the subpopulation of treated individuals. It may be of substantive interest to investigate whether there is any subpopulation for which a program or treatment has a nonzero average effect, or whether there is heterogeneity in the effect of the treatment. The hypothesis that the average effect of the treatment is zero for all subpopulations is also important for researchers interested in assessing assumptions concerning the selection mechanism. In this paper we develop two nonparametric tests. The first test is for the null hypothesis that the treatment has a zero average effect for any subpopulation defined by covariates. The second test is for the null hypothesis that the average effect conditional on the covariates is identical for all subpopulations, in other words, that there is no heterogeneity in average treatment effects by covariates. Sacrificing some generality by focusing on these two specific null hypotheses we derive tests that are straightforward to implement.

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File URL: http://ftp.iza.org/dp2091.pdf
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Bibliographic Info

Paper provided by University of Miami, Department of Economics in its series Working Papers with number 0609.

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Length: 34 pages
Date of creation: Apr 2006
Date of revision:
Publication status: Published in the Institute for the Study of Labor, Bonn, German
Handle: RePEc:mia:wpaper:0609

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Keywords: average treatment effects; causality; unconfoundedness; treatment effect heterogeneity;

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References

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  1. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
  2. Haerdle,Wolfgang & Marron,J., 1987. "Semiparametric comparision of regression curve," Discussion Paper Serie A 93, University of Bonn, Germany.
  3. Crump, Richard K. & Hotz, V. Joseph & Imbens, Guido W. & Mitnik, Oscar A., 2006. "Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand," IZA Discussion Papers 2347, Institute for the Study of Labor (IZA).
  4. Marianne P. Bitler & Jonah B. Gelbach & Hilary W. Hoynes, 2003. "What Mean Impacts Miss: Distributional Effects of Welfare Reform Experiments," Working Papers 109, RAND Corporation Publications Department.
  5. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  6. Guido W. Imbens, 2003. "Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review," NBER Technical Working Papers 0294, National Bureau of Economic Research, Inc.
  7. de Jong, R.M. & Bierens, H.J., 1994. "On the Limit Behavior of a Chi-Square Type Test if the Number of Conditional Moments Tested Approaches Infinity," Econometric Theory, Cambridge University Press, vol. 10(01), pages 70-90, March.
  8. V. Joseph Hotz & Guido W. Imbens & Jacob A. Klerman, 2006. "Evaluating the Differential Effects of Alternative Welfare-to-Work Training Components: A Reanalysis of the California GAIN Program," Journal of Labor Economics, University of Chicago Press, vol. 24(3), pages 521-566, July.
  9. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, 01.
  10. V. Joseph Hotz & Guido W. Imbens & Julie H. Mortimer, 1999. "Predicting the Efficacy of Future Training Programs Using Past Experiences," NBER Technical Working Papers 0238, National Bureau of Economic Research, Inc.
  11. Guido Imbens, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometric Society World Congress 2000 Contributed Papers 1166, Econometric Society.
  12. 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.
  13. 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.
  14. Richard Blundell & Mónica Costa Dias, 2008. "Alternative Approaches to Evaluation in Empirical Microeconomics," CEF.UP Working Papers 0805, Universidade do Porto, Faculdade de Economia do Porto.
  15. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2006. "Moving the Goalposts: Addressing Limited Overlap in the Estimation of Average Treatment Effects by Changing the Estimand," NBER Technical Working Papers 0330, National Bureau of Economic Research, Inc.
  16. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  17. Joseph Hotz, V. & Imbens, Guido W. & Mortimer, Julie H., 2005. "Predicting the efficacy of future training programs using past experiences at other locations," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 241-270.
  18. Michael Lechner, 2002. "Some practical issues in the evaluation of heterogeneous labour market programmes by matching methods," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(1), pages 59-82.
  19. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  20. Xiaohong Chen & Han Hong & Alessandro Tarozzi, 2008. "Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects," Cowles Foundation Discussion Papers 1644, Cowles Foundation for Research in Economics, Yale University.
  21. Guido W. Imbens & Whitney Newey & Geert Ridder, 2006. "Mean-squared-error Calculations for Average Treatment Effects," IEPR Working Papers 06.57, Institute of Economic Policy Research (IEPR).
  22. Alberto Abadie & Joshua D. Angrist & Guido W. Imbens, 1998. "Instrumental Variables Estimation of Quantile Treatment Effects," NBER Technical Working Papers 0229, National Bureau of Economic Research, Inc.
  23. 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.
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Citations

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Cited by:
  1. Hotz, V. Joseph & Crump, Richard K. & Mitnik, Oscar A. & Imbens, Guido, 2009. "Dealing with Limited Overlap in Estimation of Average Treatment Effects," Scholarly Articles 3007645, Harvard University Department of Economics.
  2. Ferraro, Paul J. & Miranda, Juan José, 2013. "Heterogeneous treatment effects and mechanisms in information-based environmental policies: Evidence from a large-scale field experiment," Resource and Energy Economics, Elsevier, vol. 35(3), pages 356-379.
  3. 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.
  4. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2006. "Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand," Working Papers 0608, University of Miami, Department of Economics.
  5. Słoczyński, Tymon, 2012. "New Evidence on Linear Regression and Treatment Effect Heterogeneity," MPRA Paper 39524, University Library of Munich, Germany.
  6. Philip M. Gleason & Alexandra M. Resch & Jillian A. Berk, 2012. "Replicating Experimental Impact Estimates Using a Regression Discontinuity Approach," Mathematica Policy Research Reports 7461, Mathematica Policy Research.
  7. Christian Volpe Martincus & Jer�nimo Carballo & Pablo M. Garcia, 2012. "Public programmes to promote firms’ exports in developing countries: are there heterogeneous effects by size categories?," Applied Economics, Taylor & Francis Journals, vol. 44(4), pages 471-491, February.
  8. 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.
  9. Albrecht, Konstanze & Von Essen, Emma & Parys, Juliane & Szech, Nora, 2011. "Updating, Self-Confidence and Discrimination," IZA Discussion Papers 6203, Institute for the Study of Labor (IZA).
  10. Manuel S. Santos & Juan Pablo Rincon-Zapatero, 2007. "Moving the Goalposts: Differentiability of the Value Function without Interiority Assumptions," Working Papers 0614, University of Miami, Department of Economics.
  11. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2006. "Moving the Goalposts: Addressing Limited Overlap in the Estimation of Average Treatment Effects by Changing the Estimand," NBER Technical Working Papers 0330, National Bureau of Economic Research, Inc.
  12. Paul Ferraro & Merlin Hanauer, 2011. "Protecting Ecosystems and Alleviating Poverty with Parks and Reserves: ‘Win-Win’ or Tradeoffs?," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 48(2), pages 269-286, February.
  13. Timothy B. Armstrong & Shu Shen, 2013. "Inference on Optimal Treatment Assignments," Cowles Foundation Discussion Papers 1927, Cowles Foundation for Research in Economics, Yale University.

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