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Nonparametric Tests for Treatment Effect Heterogeneity

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
File Function: First version, 2006
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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
Contact details of provider: Postal: P.O. Box 248126, Coral Gables, FL 33124-6550
Phone: (305) 284-5540
Fax: (305) 284-2985
Web page: http://www.bus.miami.edu/faculty-and-research/academic-departments/economics/index.html
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Keywords: average treatment effects; causality; unconfoundedness; treatment effect heterogeneity;

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Find related papers by JEL classification:
  • 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
  • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

References listed on IDEAS
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  1. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  2. Blundell, Richard & Costa Dias, Monica, 2008. "Alternative Approaches to Evaluation in Empirical Microeconomics," IZA Discussion Papers 3800, Institute for the Study of Labor (IZA).
  3. Hardle, W. & Mammen, E., 1990. "Comparing nonparametric versus parametric regression fits," CORE Discussion Papers 1990065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Marianne Bitler & Jonah Gelbach & Hilary Hoynes, 2003. "What Mean Impacts Miss: Distributional Effects of Welfare Reform Experiments," NBER Working Papers 10121, National Bureau of Economic Research, Inc.
  9. 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).
  10. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  11. 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.
  12. Haerdle,Wolfgang & Marron,J., 1987. "Semiparametric comparision of regression curve," Discussion Paper Serie A 93, University of Bonn, Germany.
  13. Michael Lechner, 2005. "Some practical issues in the evaluation of heterogeneous labour market programmes by matching methods," Labor and Demography 0505006, EconWPA.
  14. 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.
  15. 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.
  16. 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.
  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. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  19. 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.
  20. Sergio Firpo, 2004. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometric Society 2004 North American Summer Meetings 605, Econometric Society.
  21. 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.
  22. 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.
  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.
  24. 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.
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Cited by:

  1. 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.
  2. Marianne P. Bitler & Jonah B. Gelbach & Hilary W. Hoynes, 2014. "Can Variation in Subgroups' Average Treatment Effects Explain Treatment Effect Heterogeneity? Evidence from a Social Experiment," NBER Working Papers 20142, National Bureau of Economic Research, Inc.
  3. 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.
  4. 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.
  5. 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.
  6. Christian Volpe Martincus & Jerónimo Carballo & Pablo M. García, 2010. "Public Programs to Promote Firms' Exports in Developing Countries: Are There Heterogeneous Effects by Size Categories?," IDB Publications (Working Papers) 36764, Inter-American Development Bank.
  7. Timothy B. Armstrong & Shu Shen, 2013. "Inference on Optimal Treatment Assignments," Cowles Foundation Discussion Papers 1927, Cowles Foundation for Research in Economics, Yale University.
  8. 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.
  9. Słoczyński, Tymon, 2012. "New Evidence on Linear Regression and Treatment Effect Heterogeneity," MPRA Paper 39524, University Library of Munich, Germany.
  10. 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.
  11. Albrecht, Konstanze & von Essen, Emma & Parys, Juliane & Szech, Nora, 2013. "Updating, self-confidence, and discrimination," European Economic Review, Elsevier, vol. 60(C), pages 144-169.
  12. repec:mpr:mprres:7461 is not listed on IDEAS
  13. 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).
  14. 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.
  15. Philip M. Gleason & Alexandra M. Resch & Jillian A. Berk, 2012. "Replicating Experimental Impact Estimates Using a Regression Discontinuity Approach," Mathematica Policy Research Reports c7ecf8b35c8d402491d09b2d0, Mathematica Policy Research.

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