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Instrumental Variables in Models with Multiple Outcomes: The General Unordered Case

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  • James J. Heckman
  • Sergio Urzua
  • Edward Vytlacil

Abstract

This paper develops the method of local instrumental variables for models with multiple, unordered treatments when treatment choice is determined by a nonparametric version of the multinomial choice model. Responses to interventions are permitted to be heterogeneous in a general way and agents are allowed to select a treatment (e.g. participate in a program) with at least partial knowledge of the idiosyncratic response to the treatments. We define treatment effects in a general model with multiple treatments as differences in counterfactual outcomes that would have been observed if the agent faced different choice sets. We show how versions of local instrumental variables can identify the corresponding treatment parameters. Direct application of local instrumental variables identifies the marginal treatment effect of one option versus the next best alternative without requiring knowledge of any structural parameters from the choice equation or any large support assumptions. Using local instrumental variables to identify other treatment parameters requires either large support assumptions or knowledge of the latent index function of the multinomial choice model.

Suggested Citation

  • 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.
    • Handle: RePEc:adr:anecst:y:2008:i:91-92:p:151-174
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    References listed on IDEAS

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    1. Jay Bhattacharya & Azeem M. Shaikh & Edward Vytlacil, 2008. "Treatment Effect Bounds under Monotonicity Assumptions: An Application to Swan-Ganz Catheterization," American Economic Review, American Economic Association, vol. 98(2), pages 351-356, May.
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    7. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    8. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    9. James Heckman & Neil Hohmann & Jeffrey Smith & Michael Khoo, 2000. "Substitution and Dropout Bias in Social Experiments: A Study of an Influential Social Experiment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(2), pages 651-694.
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    11. James Heckman, 1997. "Instrumental Variables: A Study of Implicit Behavioral Assumptions Used in Making Program Evaluations," Journal of Human Resources, University of Wisconsin Press, vol. 32(3), pages 441-462.
    12. Aakvik, A. & Heckman, J.J. & Vytlacil, E.J., 1999. "Training Effects on Employment when the Training Effects are Heterogenous : an Application to Norwegian Vocational Rehabilitation Programs," Norway; Department of Economics, University of Bergen 0599, Department of Economics, University of Bergen.
    13. Jean-Pierre Florens & James Heckman & Costas Meghir & Edward Vytlacil, 2002. "Instrumental variables, local instrumental variables and control functions," CeMMAP working papers CWP15/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Heckman, James J. & Vytlacil, Edward J., 2000. "The relationship between treatment parameters within a latent variable framework," Economics Letters, Elsevier, vol. 66(1), pages 33-39, January.
    15. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
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    Cited by:

    1. James J. Heckman & John Eric Humphries & Gregory Veramendi, 2018. "The Nonmarket Benefits of Education and Ability," Journal of Human Capital, University of Chicago Press, vol. 12(2), pages 282-304.
    2. Carta, Francesca & Rizzica, Lucia, 2018. "Early kindergarten, maternal labor supply and children's outcomes: Evidence from Italy," Journal of Public Economics, Elsevier, vol. 158(C), pages 79-102.
    3. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    4. Heckman, James J. & Urzúa, Sergio, 2010. "Comparing IV with structural models: What simple IV can and cannot identify," Journal of Econometrics, Elsevier, vol. 156(1), pages 27-37, May.
    5. 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.
    6. Kamat, Vishal, 2019. "Identification with Latent Choice Sets," TSE Working Papers 19-1031, Toulouse School of Economics (TSE).
    7. 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.
    8. Heckman, James J. & Humphries, John Eric & Veramendi, Gregory, 2016. "Dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 191(2), pages 276-292.
    9. Heckman, James J. & Pinto, Rodrigo, 2022. "Causality and Econometrics," IZA Discussion Papers 15081, Institute of Labor Economics (IZA).
    10. Andrew Chesher & Adam M. Rosen, 2021. "Counterfactual Worlds," Annals of Economics and Statistics, GENES, issue 142, pages 311-335.
    11. Vishal Kamat, 2017. "Identifying the Effects of a Program Offer with an Application to Head Start," Papers 1711.02048, arXiv.org, revised Aug 2023.
    12. Kamat, Vishal, 2024. "Identifying the effects of a program offer with an application to Head Start," Journal of Econometrics, Elsevier, vol. 240(1).
    13. Fitzenberger, Bernd & Furdas, Marina & Sajons, Christoph, 2016. "End-of-year spending and the long-run employment effects of training programs for the unemployed," ZEW Discussion Papers 16-084, ZEW - Leibniz Centre for European Economic Research.
    14. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    15. Joseph G. Altonji & Ling Zhong, 2021. "The Labor Market Returns to Advanced Degrees," Journal of Labor Economics, University of Chicago Press, vol. 39(2), pages 303-360.
    16. Vishal Kamat & Samuel Norris & Matthew Pecenco, 2023. "Identification in Multiple Treatment Models under Discrete Variation," Papers 2307.06174, arXiv.org.
    17. Feng, Junlong, 2024. "Matching points: Supplementing instruments with covariates in triangular models," Journal of Econometrics, Elsevier, vol. 238(1).
    18. Aniket A. Kawatkar & Joel W. Hay & William Stohl & Michael B. Nichol, 2013. "Incremental Expenditure Of Biologic Disease Modifying Antirheumatic Treatment Using Instrumental Variables In Panel Data," Health Economics, John Wiley & Sons, Ltd., vol. 22(7), pages 807-823, July.
    19. Mario Fiorini & Katrien Stevens, 2021. "Scrutinizing the Monotonicity Assumption in IV and fuzzy RD designs," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(6), pages 1475-1526, December.
    20. Nibbering, Didier & Oosterveen, Matthijs & Silva, Pedro Luís, 2022. "Clustered Local Average Treatment Effects: Fields of Study and Academic Student Progress," IZA Discussion Papers 15159, Institute of Labor Economics (IZA).
    21. Gandil, Mikkel Høst, 2021. "Substitution Effects in College Admissions," Memorandum 3/2021, Oslo University, Department of Economics.
    22. Bhuller, Manudeep & Sigstad, Henrik, 2024. "2SLS with multiple treatments," Journal of Econometrics, Elsevier, vol. 242(1).
    23. Fernando Saltiel, 2023. "Multi-Dimensional Skills and Gender Differences in Stem Majors," The Economic Journal, Royal Economic Society, vol. 133(651), pages 1217-1247.

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    More about this item

    JEL classification:

    • 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

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