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Estimating Marginal Treatment Effects in Heterogeneous Populations

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  • Robert Moffitt

Abstract

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.

Suggested Citation

  • Robert Moffitt, 2008. "Estimating Marginal Treatment Effects in Heterogeneous Populations," Annals of Economics and Statistics, GENES, issue 91-92, pages 239-261.
    • Handle: RePEc:adr:anecst:y:2008:i:91-92:p:239-261
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    File URL: http://www.jstor.org/stable/27917247
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    Cited by:

    1. John Engberg & Dennis Epple & Jason Imbrogno & Holger Sieg & Ron Zimmer, 2009. "Estimation of Causal Effects in Experiments with Multiple Sources of Noncompliance," NBER Working Papers 14842, National Bureau of Economic Research, Inc.
    2. Belskaya, Olga & Peter, Klara Sabirianova & Posso, Christian, 2014. "College Expansion and the Marginal Returns to Education: Evidence from Russia," IZA Discussion Papers 8735, Institute of Labor Economics (IZA).
    3. Pedro Carneiro & James J. Heckman & Edward J. Vytlacil, 2011. "Estimating Marginal Returns to Education," American Economic Review, American Economic Association, vol. 101(6), pages 2754-2781, October.
    4. Ivar Kolstad & Arne Wiig, 2015. "Education and entrepreneurial success," Small Business Economics, Springer, vol. 44(4), pages 783-796, April.
    5. Gong, Jie & Lu, Yi & Xie, Huihua, 2020. "The average and distributional effects of teenage adversity on long-term health," Journal of Health Economics, Elsevier, vol. 71(C).
    6. Xiang Zhou & Yu Xie, 2016. "Propensity Score–based Methods Versus MTE-based Methods in Causal Inference," Sociological Methods & Research, , vol. 45(1), pages 3-40, February.
    7. Pedro Carneiro & Sokbae Lee, 2011. "Trends in Quality-Adjusted Skill Premia in the United States, 1960-2000," American Economic Review, American Economic Association, vol. 101(6), pages 2309-2349, October.
    8. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    9. Sylvain Chassang & Gerard Padro I Miquel & Erik Snowberg, 2012. "Selective Trials: A Principal-Agent Approach to Randomized Controlled Experiments," American Economic Review, American Economic Association, vol. 102(4), pages 1279-1309, June.
    10. Tymon S{l}oczy'nski, 2018. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," Papers 1810.01576, arXiv.org, revised May 2020.
    11. Yuya Sasaki & Takuya Ura, 2018. "Estimation and Inference for Policy Relevant Treatment Effects," Papers 1805.11503, arXiv.org, revised Jul 2020.
    12. Sasaki, Yuya & Ura, Takuya, 2023. "Estimation and inference for policy relevant treatment effects," Journal of Econometrics, Elsevier, vol. 234(2), pages 394-450.
    13. John Engberg & Dennis Epple & Jason Imbrogno & Holger Sieg & Ron Zimmer, 2014. "Evaluating Education Programs That Have Lotteried Admission and Selective Attrition," Journal of Labor Economics, University of Chicago Press, vol. 32(1), pages 27-63.
    14. Matthias Westphal & Daniel A Kamhöfer & Hendrik Schmitz, 2022. "Marginal College Wage Premiums Under Selection Into Employment," The Economic Journal, Royal Economic Society, vol. 132(646), pages 2231-2272.
    15. Bernhard Eckwert & Itzhak Zilcha, 2020. "The role of colleges within the higher education sector," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 315-336, March.
    16. Adriana Camacho & Julián Messina & Juan Pablo Uribe, 2017. "The Expansion of Higher Education in Colombia: Bad Students or Bad Programs?," Documentos CEDE 15352, Universidad de los Andes, Facultad de Economía, CEDE.
    17. Kolstad, Ivar & Wiig, Arne & Moazzem, Khondaker Golam, 2014. "Returns to education among entrepreneurs in Bangladesh," Journal of Asian Economics, Elsevier, vol. 34(C), pages 54-65.
    18. Rentocchini, Francesco & D'Este, Pablo & Manjarrés-Henríquez, Liney & Grimaldi, Rosa, 2014. "The relationship between academic consulting and research performance: Evidence from five Spanish universities," International Journal of Industrial Organization, Elsevier, vol. 32(C), pages 70-83.
    19. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    20. Richard Dorsett & Lucy Stokes, 2022. "Pre‐apprenticeship training for young people: Estimating the marginal and average treatment effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 37-60, January.
    21. Sloczynski, Tymon, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," IZA Discussion Papers 11866, Institute of Labor Economics (IZA).
    22. Shao-Hsun Keng & Chun-Hung Lin & Peter F. Orazem, 2017. "Expanding College Access in Taiwan, 1978-2014: Effects on Graduate Quality and Income Inequality," Journal of Human Capital, University of Chicago Press, vol. 11(1), pages 1-34.
    23. Caio Waisman & Brett R. Gordon, 2023. "Multi-cell experiments for marginal treatment effect estimation of digital ads," Papers 2302.13857, arXiv.org, revised Jan 2024.
    24. Sarrias, Mauricio, 2021. "A two recursive equation model to correct for endogeneity in latent class binary probit models," Journal of choice modelling, Elsevier, vol. 40(C).

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