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Treatment effects with targeting instruments

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  • Sokbae (Simon) Lee
  • Bernard Salanie

Abstract

Multivalued treatments are commonplace in applications. We explore the use of discrete-valued instruments to control for selection bias in this setting. Our discussion revolves around the concept of targeting: which instruments target which treatments. It allows us to establish conditions under which counterfactual averages and treatment effects are point- or partially-identified for composite complier groups. We illustrate the usefulness of our framework by applying it to data from the Head Start Impact Study. Under a plausible positive selection assumption, we derive informative bounds that suggest less beneficial effects of Head Start expansions than the parametric estimates of Kline and Walters (2016).

Suggested Citation

  • Sokbae (Simon) Lee & Bernard Salanie, 2024. "Treatment effects with targeting instruments," CeMMAP working papers 23/24, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:23/24
    DOI: 10.47004/wp.cem.2024.2324
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    1. Semenova, Vira, 2025. "Generalized Lee bounds," Journal of Econometrics, Elsevier, vol. 251(C).
    2. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2008. "Instrumental Variables in Models with Multiple Outcomes: The General Unordered Case," Annals of Economics and Statistics, GENES, issue 91-92, pages 151-174.
    3. 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.
    4. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    5. Joshua Angrist & Andres Santos & Otávio Tecchio, 2025. "One Instrument, Many Treatments: Instrumental Variables Identification of Multiple Causal Effects," NBER Working Papers 34607, National Bureau of Economic Research, Inc.
    6. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    7. Huang, Liquan & Khalil, Umair & Yıldız, Neşe, 2019. "Identification and estimation of a triangular model with multiple endogenous variables and insufficiently many instrumental variables," Journal of Econometrics, Elsevier, vol. 208(2), pages 346-366.
    8. Zhenting Sun, 2020. "Instrument Validity for Heterogeneous Causal Effects," Papers 2009.01995, arXiv.org, revised Oct 2023.
    9. Magne Mogstad & Alexander Torgovitsky & Christopher R. Walters, 2021. "The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables," American Economic Review, American Economic Association, vol. 111(11), pages 3663-3698, November.
    10. Philipp Eisenhauer & James J. Heckman & Edward Vytlacil, 2015. "The Generalized Roy Model and the Cost-Benefit Analysis of Social Programs," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 413-443.
    11. Yuehao Bai & Shunzhuang Huang & Max Tabord-Meehan, 2024. "Sharp Testable Implications of Encouragement Designs," Papers 2411.09808, arXiv.org, revised Oct 2026.
    12. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    13. Kamat, Vishal, 2019. "Identification with Latent Choice Sets," TSE Working Papers 19-1031, Toulouse School of Economics (TSE).
    14. Leonard Goff, 2020. "A Vector Monotonicity Assumption for Multiple Instruments," Papers 2009.00553, arXiv.org, revised Mar 2024.
    15. Cattaneo, Matias D., 2010. "Efficient semiparametric estimation of multi-valued treatment effects under ignorability," Journal of Econometrics, Elsevier, vol. 155(2), pages 138-154, April.
    16. 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.
    17. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2024. "Contamination Bias in Linear Regressions," American Economic Review, American Economic Association, vol. 114(12), pages 4015-4051, December.
    18. Wallice Ao & Sebastian Calonico & Ying-Ying Lee, 2021. "Multivalued Treatments and Decomposition Analysis: An Application to the WIA Program," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 358-371, January.
    19. James Heckman, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    20. Vishal Kamat, 2017. "Identifying the Effects of a Program Offer with an Application to Head Start," Papers 1711.02048, arXiv.org, revised Aug 2023.
    21. 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.
    22. Vira Semenova, 2020. "Generalized Lee Bounds," Papers 2008.12720, arXiv.org, revised May 2025.
    23. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    24. Ismael Mourifié & Yuanyuan Wan, 2017. "Testing Local Average Treatment Effect Assumptions," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 305-313, May.
    25. Caetano, Carolina & Escanciano, Juan Carlos, 2021. "Identifying Multiple Marginal Effects With A Single Instrument," Econometric Theory, Cambridge University Press, vol. 37(3), pages 464-494, June.
    26. 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.
    27. Kamat, Vishal, 2024. "Identifying the effects of a program offer with an application to Head Start," Journal of Econometrics, Elsevier, vol. 240(1).
    28. Karthik Muralidharan & Mauricio Romero & Kaspar Wüthrich, 2025. "Factorial Designs, Model Selection, and (Incorrect) Inference in Randomized Experiments," The Review of Economics and Statistics, MIT Press, vol. 107(3), pages 589-604, May.
    29. Mogstad, Magne & Torgovitsky, Alexander & Walters, Christopher R., 2024. "Policy evaluation with multiple instrumental variables," Journal of Econometrics, Elsevier, vol. 243(1).
    30. 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.
    31. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    32. Désiré Kédagni & Ismael Mourifié, 2020. "Generalized instrumental inequalities: testing the instrumental variable independence assumption," Biometrika, Biometrika Trust, vol. 107(3), pages 661-675.
    33. Christine Blandhol & John Bonney & Magne Mogstad & Alexander Torgovitsky, 2022. "When is TSLS Actually LATE?," NBER Working Papers 29709, National Bureau of Economic Research, Inc.
    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. Goff, Leonard, 2024. "A vector monotonicity assumption for multiple instruments," Journal of Econometrics, Elsevier, vol. 241(1).
    36. Tymon Słoczyński, 2022. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," The Review of Economics and Statistics, MIT Press, vol. 104(3), pages 501-509, May.
    37. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn & Zhipeng Liao, 2014. "Asymptotic Efficiency of Semiparametric Two-step GMM," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(3), pages 919-943.
    38. Yuehao Bai & Shunzhuang Huang & Sarah Moon & Azeem M. Shaikh & Edward J. Vytlacil, 2024. "On the Identifying Power of Generalized Monotonicity for Average Treatment Effects," Papers 2405.14104, arXiv.org, revised Nov 2025.
    39. Edward Vytlacil & James J. Heckman, 2001. "Policy-Relevant Treatment Effects," American Economic Review, American Economic Association, vol. 91(2), pages 107-111, May.
    40. Vishal Kamat & Samuel Norris & Matthew Pecenco, 2023. "Identification in Multiple Treatment Models under Discrete Variation," Papers 2307.06174, arXiv.org, revised Jan 2026.
    41. 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.
    42. James J. Heckman & Vytlacil, Edward J., 2007. "Econometric Evaluation of Social Programs, Part I: Causal Models, Structural Models and Econometric Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 70, Elsevier.
    43. Orazio Attanasio & Sarah Cattan & Emla Fitzsimons & Costas Meghir & Marta Rubio-Codina, 2020. "Estimating the Production Function for Human Capital: Results from a Randomized Controlled Trial in Colombia," American Economic Review, American Economic Association, vol. 110(1), pages 48-85, January.
    44. Jack Mountjoy, 2022. "Community Colleges and Upward Mobility," American Economic Review, American Economic Association, vol. 112(8), pages 2580-2630, August.
    45. Feng, Junlong, 2024. "Matching points: Supplementing instruments with covariates in triangular models," Journal of Econometrics, Elsevier, vol. 238(1).
    46. repec:adr:anecst:y:2008:i:91-92:p:08 is not listed on IDEAS
    47. James J. Heckman & Rodrigo Pinto, 2018. "Unordered Monotonicity," Econometrica, Econometric Society, vol. 86(1), pages 1-35, January.
    48. 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.
    49. Frolich, Markus, 2007. "Nonparametric IV estimation of local average treatment effects with covariates," Journal of Econometrics, Elsevier, vol. 139(1), pages 35-75, July.
    50. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2012. "A Practical Asymptotic Variance Estimator for Two-Step Semiparametric Estimators," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 481-498, May.
    51. Nibbering, Didier & Oosterveen, Matthijs & Silva, Pedro Luís, 2022. "Clustered Local Average Treatment Effects: Fields of Study and Academic Student Progress," IZA Discussion Papers 15159, IZA Network @ LISER.
    52. Matias D. Cattaneo, 2010. "multi-valued treatment effects," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
    53. Marx, Philip, 2024. "Sharp bounds in the latent index selection model," Journal of Econometrics, Elsevier, vol. 238(2).
    54. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    55. 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.
    56. Alexander Torgovitsky, 2015. "Identification of Nonseparable Models Using Instruments With Small Support," Econometrica, Econometric Society, vol. 83(3), pages 1185-1197, May.
    57. Bhuller, Manudeep & Sigstad, Henrik, 2024. "2SLS with multiple treatments," Journal of Econometrics, Elsevier, vol. 242(1).
    58. Junlong Feng, 2019. "Matching Points: Supplementing Instruments with Covariates in Triangular Models," Papers 1904.01159, arXiv.org, revised Jul 2020.
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    2. Eskil Heinesen & Christian Hvid & Lars Kirkebøen & Edwin Leuven & Magne Mogstad, 2026. "Instrumental Variables with Unordered Treatments: Theory and Evidence from Returns to Fields of Study," Journal of Labor Economics, University of Chicago Press, vol. 44(3), pages 823-854.
    3. Leonard Goff, 2024. "When does IV identification not restrict outcomes?," Papers 2406.02835, arXiv.org, revised Feb 2025.
    4. Ferreyra,Maria Marta & Galindo,Camila & Urzúa,Sergio, 2021. "Labor Market Effects of Short-Cycle Higher Education Programs : Lessons from Colombia," Policy Research Working Paper Series 9717, The World Bank.
    5. Goff, Leonard, 2024. "A vector monotonicity assumption for multiple instruments," Journal of Econometrics, Elsevier, vol. 241(1).
    6. Vishal Kamat & Samuel Norris & Matthew Pecenco, 2023. "Identification in Multiple Treatment Models under Discrete Variation," Papers 2307.06174, arXiv.org, revised Jan 2026.

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