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

Author

Listed:
  • Heckman, James J.

    (University of Chicago)

  • Urzua, Sergio

    (University of Maryland)

  • Vytlacil, Edward

    (Yale University)

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

  • Heckman, James J. & Urzua, Sergio & Vytlacil, Edward, 2008. "Instrumental Variables in Models with Multiple Outcomes: The General Unordered Case," IZA Discussion Papers 3565, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp3565
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    References listed on IDEAS

    as
    1. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    2. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    3. 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.
    4. Cameron, Stephen V & Heckman, James J, 1993. "The Nonequivalence of High School Equivalents," Journal of Labor Economics, University of Chicago Press, vol. 11(1), pages 1-47, January.
    5. 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.
    6. 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.
    7. 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.
    8. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-512, March.
    9. 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.
    10. 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.
    11. Gordon B. Dahl, 2002. "Mobility and the Return to Education: Testing a Roy Model with Multiple Markets," Econometrica, Econometric Society, vol. 70(6), pages 2367-2420, November.
    12. Stephen V. Cameron & James J. Heckman, 1998. "Life Cycle Schooling and Dynamic Selection Bias: Models and Evidence for Five Cohorts of American Males," Journal of Political Economy, University of Chicago Press, vol. 106(2), pages 262-333, April.
    13. 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.
    14. Hsiao,Cheng & Morimune,Kimio & Powell,James L. (ed.), 2001. "Nonlinear Statistical Modeling," Cambridge Books, Cambridge University Press, number 9780521662468, June.
    15. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    nonparametric; treatment effects; multinomial;
    All these keywords.

    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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