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Identifying Marginal Treatment Effects in the Presence of Sample Selection

Author

Listed:
  • Ot'avio Bartalotti
  • D'esir'e K'edagni
  • Vitor Possebom
Abstract
This article presents identification results for the marginal treatment effect (MTE) when there is sample selection. We show that the MTE is partially identified for individuals who are always observed regardless of treatment, and derive uniformly sharp bounds on this parameter under three increasingly restrictive sets of assumptions. The first result imposes standard MTE assumptions with an unrestricted sample selection mechanism. The second set of conditions imposes monotonicity of the sample selection variable with respect to treatment, considerably shrinking the identified set. Finally, we incorporate a stochastic dominance assumption which tightens the lower bound for the MTE. Our analysis extends to discrete instruments. The results rely on a mixture reformulation of the problem where the mixture weights are identified, extending Lee's (2009) trimming procedure to the MTE context. We propose estimators for the bounds derived and use data made available by Deb, Munking and Trivedi (2006) to empirically illustrate the usefulness of our approach.

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  • Ot'avio Bartalotti & D'esir'e K'edagni & Vitor Possebom, 2021. "Identifying Marginal Treatment Effects in the Presence of Sample Selection," Papers 2112.07014, arXiv.org.
    • Handle: RePEc:arx:papers:2112.07014
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    1. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    2. 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.
    3. David Arnold & Will Dobbie & Crystal S Yang, 2018. "Racial Bias in Bail Decisions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(4), pages 1885-1932.
    4. Mullahy, John, 2018. "Individual results may vary: Inequality-probability bounds for some health-outcome treatment effects," Journal of Health Economics, Elsevier, vol. 61(C), pages 151-162.
    5. Patrick Kline & Melissa Tartari, 2016. "Bounding the Labor Supply Responses to a Randomized Welfare Experiment: A Revealed Preference Approach," American Economic Review, American Economic Association, vol. 106(4), pages 972-1014, April.
    6. Xuan Chen & Carlos A. Flores, 2015. "Bounds on Treatment Effects in the Presence of Sample Selection and Noncompliance: The Wage Effects of Job Corps," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 523-540, October.
    7. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    8. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    9. Thomas Cornelissen & Christian Dustmann & Anna Raute & Uta Schönberg, 2018. "Who Benefits from Universal Child Care? Estimating Marginal Returns to Early Child Care Attendance," Journal of Political Economy, University of Chicago Press, vol. 126(6), pages 2356-2409.
    10. Patrick Kline & Christopher R. Walters, 2016. "Evaluating Public Programs with Close Substitutes: The Case of HeadStart," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1795-1848.
    11. Jack Mountjoy, 2022. "Community Colleges and Upward Mobility," American Economic Review, American Economic Association, vol. 112(8), pages 2580-2630, August.
    12. Partha Deb & Murat K. Munkin & Pravin K. Trivedi, 2006. "Bayesian analysis of the two‐part model with endogeneity: application to health care expenditure," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(7), pages 1081-1099, November.
    13. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    14. Charles F. Manski, 2011. "Policy Analysis with Incredible Certitude," Economic Journal, Royal Economic Society, vol. 121(554), pages 261-289, August.
    15. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    16. Christian N. Brinch & Magne Mogstad & Matthew Wiswall, 2017. "Beyond LATE with a Discrete Instrument," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 985-1039.
    17. 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.
    18. John Eric Humphries & Nicholas S. Mader & Daniel I. Tannenbaum & Winnie L. van Dijk, 2019. "Does Eviction Cause Poverty? Quasi-Experimental Evidence from Cook County, IL," NBER Working Papers 26139, National Bureau of Economic Research, Inc.
    19. Krueger, Alan B & Whitmore, Diane M, 2001. "The Effect of Attending a Small Class in the Early Grades on College-Test Taking and Middle School Test Results: Evidence from Project STAR," Economic Journal, Royal Economic Society, vol. 111(468), pages 1-28, January.
    20. German Blanco & Carlos A. Flores & Alfonso Flores-Lagunes, 2013. "Bounds on Average and Quantile Treatment Effects of Job Corps Training on Wages," Journal of Human Resources, University of Wisconsin Press, vol. 48(3), pages 659-701.
    21. Eric Helland & Jungmo Yoon, 2017. "Estimating the Effects of the English Rule on Litigation Outcomes," The Review of Economics and Statistics, MIT Press, vol. 99(4), pages 678-682, July.
    22. Raj Chetty & John N. Friedman & Nathaniel Hilger & Emmanuel Saez & Diane Whitmore Schanzenbach & Danny Yagan, 2011. "How Does Your Kindergarten Classroom Affect Your Earnings? Evidence from Project Star," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(4), pages 1593-1660.
    23. Suresh de Mel & David McKenzie & Christopher Woodruff, 2013. "The Demand for, and Consequences of, Formalization among Informal Firms in Sri Lanka," American Economic Journal: Applied Economics, American Economic Association, vol. 5(2), pages 122-150, April.
    24. Bartalotti, Otávio & Kédagni, Désiré & Possebom, Vitor, 2023. "Identifying marginal treatment effects in the presence of sample selection," Journal of Econometrics, Elsevier, vol. 234(2), pages 565-584.
    25. Martin Eckhoff Andresen, 2018. "Exploring marginal treatment effects: Flexible estimation using Stata," Stata Journal, StataCorp LP, vol. 18(1), pages 118-158, March.
    26. Martin Huber & Giovanni Mellace, 2015. "Sharp Bounds on Causal Effects under Sample Selection," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 129-151, February.
    27. Imai, Kosuke, 2008. "Sharp bounds on the causal effects in randomized experiments with "truncation-by-death"," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 144-149, February.
    28. Philip Oreopoulos & Daniel Lang & Joshua Angrist, 2009. "Incentives and Services for College Achievement: Evidence from a Randomized Trial," American Economic Journal: Applied Economics, American Economic Association, vol. 1(1), pages 136-163, January.
    29. Manuela Angelucci & Dean Karlan & Jonathan Zinman, 2015. "Microcredit Impacts: Evidence from a Randomized Microcredit Program Placement Experiment by Compartamos Banco," American Economic Journal: Applied Economics, American Economic Association, vol. 7(1), pages 151-182, January.
    30. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    31. 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.
    32. O. Ashenfelter & D. Card (ed.), 1999. "Handbook of Labor Economics," Handbook of Labor Economics, Elsevier, edition 1, volume 3, number 3.
    33. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    34. 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.
    35. Will Dobbie & Roland G. Fryer Jr., 2015. "The Medium-Term Impacts of High-Achieving Charter Schools," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 985-1037.
    36. Edward Vytlacil & James J. Heckman, 2001. "Policy-Relevant Treatment Effects," American Economic Review, American Economic Association, vol. 91(2), pages 107-111, May.
    37. 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.
    38. Lukas Laffers & Giovanni Mellace, 2017. "A note on testing instrument validity for the identification of LATE," Empirical Economics, Springer, vol. 53(3), pages 1281-1286, November.
    39. Joshua Angrist & Eric Bettinger & Michael Kremer, 2006. "Long-Term Educational Consequences of Secondary School Vouchers: Evidence from Administrative Records in Colombia," American Economic Review, American Economic Association, vol. 96(3), pages 847-862, June.
    40. Heckman, James J. & Lalonde, Robert J. & Smith, Jeffrey A., 1999. "The economics and econometrics of active labor market programs," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 31, pages 1865-2097, Elsevier.
    41. Altonji, Joseph G, 1993. "The Demand for and Return to Education When Education Outcomes Are Uncertain," Journal of Labor Economics, University of Chicago Press, vol. 11(1), pages 48-83, January.
    42. Junni L. Zhang & Donald B. Rubin & Fabrizia Mealli, 2008. "Evaluating the effects of job training programs on wages through principal stratification," Advances in Econometrics, in: Modelling and Evaluating Treatment Effects in Econometrics, pages 117-145, Emerald Group Publishing Limited.
    43. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    44. Firpo, Sergio & Ridder, Geert, 2019. "Partial identification of the treatment effect distribution and its functionals," Journal of Econometrics, Elsevier, vol. 213(1), pages 210-234.
    45. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1071-1102.
    46. Bjorklund, Anders & Moffitt, Robert, 1987. "The Estimation of Wage Gains and Welfare Gains in Self-selection," The Review of Economics and Statistics, MIT Press, vol. 69(1), pages 42-49, February.
    47. 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.
    48. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    49. Martin Huber & Lukas Laffers & Giovanni Mellace, 2017. "Sharp IV Bounds on Average Treatment Effects on the Treated and Other Populations Under Endogeneity and Noncompliance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 56-79, January.
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    Cited by:

    1. Bartalotti, Otávio & Kédagni, Désiré & Possebom, Vitor, 2023. "Identifying marginal treatment effects in the presence of sample selection," Journal of Econometrics, Elsevier, vol. 234(2), pages 565-584.
    2. Gayani Rathnayake & Akanksha Negi & Otavio Bartalotti & Xueyan Zhao, 2024. "Difference-in-Differences with Sample Selection," Papers 2411.09221, arXiv.org, revised Dec 2024.
    3. Rui Wang, 2023. "Point Identification of LATE with Two Imperfect Instruments," Papers 2303.13795, arXiv.org.
    4. Xiaolin Sun & Xueyan Zhao & D. S. Poskitt, 2024. "Partially Identified Heterogeneous Treatment Effect with Selection: An Application to Gender Gaps," Papers 2410.01159, arXiv.org, revised Oct 2024.
    5. Phillip Heiler, 2022. "Heterogeneous Treatment Effect Bounds under Sample Selection with an Application to the Effects of Social Media on Political Polarization," Papers 2209.04329, arXiv.org, revised Jul 2024.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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