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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.

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Bibliographic Info

Article provided by ENSAE in its journal Annals of Economics and Statistics.

Volume (Year): (2008)
Issue (Month): 91-92 ()
Pages: 151-174

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Handle: RePEc:adr:anecst:y:2008:i:91-92:p:08

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  1. Cameron, Stephen V & Heckman, James J, 1993. "The Nonequivalence of High School Equivalents," Journal of Labor Economics, University of Chicago Press, University of Chicago Press, vol. 11(1), pages 1-47, January.
  2. Gordon B. Dahl, 2002. "Mobility and the Return to Education: Testing a Roy Model with Multiple Markets," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 488, University of Rochester - Center for Economic Research (RCER).
  3. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, Econometric Society, vol. 73(3), pages 669-738, 05.
  4. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2009. "Understanding Instrumental Variables in Models with Essential Heterogeneity," Working Papers, Geary Institute, University College Dublin 200941, Geary Institute, University College Dublin.
  5. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, Elsevier, vol. 136(2), pages 341-396, February.
  6. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, Econometric Society, vol. 70(1), pages 331-341, January.
  7. Jean-Pierre Florens & James Heckman & Costas Meghir & Edward Vytlacil, 2002. "Instrumental variables, local instrumental variables and control functions," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP15/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. 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, University of Chicago Press, vol. 106(2), pages 262-333, April.
  9. Heckman, James J. & Vytlacil, Edward J., 2000. "The relationship between treatment parameters within a latent variable framework," Economics Letters, Elsevier, Elsevier, vol. 66(1), pages 33-39, January.
  10. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, Econometric Society, vol. 51(2), pages 507-12, March.
  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, University of Wisconsin Press, vol. 32(3), pages 441-462.
  12. 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, MIT Press, MIT Press, vol. 115(2), pages 651-694, May.
  13. 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, Department of Economics, University of Bergen 0599, Department of Economics, University of Bergen.
  14. 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, American Economic Association, vol. 98(2), pages 351-56, May.
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Cited by:
  1. Carneiro, Pedro & Heckman, James J. & Vytlacil, Edward, 2010. "Estimating Marginal Returns to Education," IZA Discussion Papers 5275, Institute for the Study of Labor (IZA).
  2. James Heckman & Sergio Urzua, 2010. "Comparing IV with structural models: what simple IV can and cannot identify," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP08/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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