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Estimating Marginal Treatment Effects in Heterogeneous Populations


  • Robert Moffit


This paper proposes a nonparametric method of estimating marginal treatment effects in heterogeneous populations. Building upon an insight of Heckman and Vytlacil, the conventional treatment effects model with heterogeneous effects is shown to imply that outcomes are a nonlinear function of participation probabilities. The degree of this nonlinearity, and hence the shape of the marginal response curve, can be estimated with series methods such as power series or splines. An illustration is provided for the returns to higher education in the U.K, indicating that marginal returns to higher education fall as the proportion of the population with higher education rises, thus providing evidence of heterogeneity in returns.

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  • Robert Moffit, 2007. "Estimating Marginal Treatment Effects in Heterogeneous Populations," Economics Working Paper Archive 539, The Johns Hopkins University,Department of Economics.
  • Handle: RePEc:jhu:papers:539

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    References listed on IDEAS

    1. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics,in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366 Elsevier.
    2. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College," NBER Working Papers 9546, National Bureau of Economic Research, Inc.
    3. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    4. Barbara Sianesi & John Van Reenen, 2003. "The Returns to Education: Macroeconomics," Journal of Economic Surveys, Wiley Blackwell, vol. 17(2), pages 157-200, April.
    5. Lorraine Dearden & Barbara Sianesi, 2001. "Estimating the Returns to Education: Models, Methods and Results," CEE Discussion Papers 0016, Centre for the Economics of Education, LSE.
    6. Carneiro, Pedro & Hansen, Karsten T. & Heckman, James J., 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," IZA Discussion Papers 767, Institute for the Study of Labor (IZA).
    7. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    8. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
    9. Lee, Lung-Fei, 1979. "Identification and Estimation in Binary Choice Models with Limited (Censored) Dependent Variables," Econometrica, Econometric Society, vol. 47(4), pages 977-996, July.
    10. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
    11. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    12. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    13. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
    14. Card, David, 1999. "The causal effect of education on earnings," Handbook of Labor Economics,in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 30, pages 1801-1863 Elsevier.
    15. Philip Oreopoulos, 2006. "Estimating Average and Local Average Treatment Effects of Education when Compulsory Schooling Laws Really Matter," American Economic Review, American Economic Association, vol. 96(1), pages 152-175, March.
    16. Richard Blundell & Lorraine Dearden & Barbara Sianesi, 2005. "Evaluating the effect of education on earnings: models, methods and results from the National Child Development Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(3), pages 473-512.
    17. Lang, Kevin, 1993. "Ability Bias, Discount Rate Bias and the Return to Education," MPRA Paper 24651, University Library of Munich, Germany.
    18. Aakvik, Arild & Heckman, James J. & Vytlacil, Edward J., 2005. "Estimating treatment effects for discrete outcomes when responses to treatment vary: an application to Norwegian vocational rehabilitation programs," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 15-51.
    19. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-1160, September.
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    Cited by:

    1. Richard Blundell & Monica Costa Dias, 2009. "Alternative Approaches to Evaluation in Empirical Microeconomics," Journal of Human Resources, University of Wisconsin Press, vol. 44(3).

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