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

39 Pages Posted: 7 Jul 2008

See all articles by James J. Heckman

James J. Heckman

University of Chicago - Department of Economics; National Bureau of Economic Research (NBER); American Bar Foundation; Institute for the Study of Labor (IZA); CESifo (Center for Economic Studies and Ifo Institute)

Sergio Urzua

Northwestern University

Edward Vytlacil

Yale University - Department of Economics; National Bureau of Economic Research (NBER)

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.

Keywords: treatment effects, multinomial, nonparametric

JEL Classification: C31

Suggested Citation

Heckman, James J. and Urzua, Sergio Samuel and Vytlacil, Edward J., Instrumental Variables in Models with Multiple Outcomes: The General Unordered Case. , Vol. , pp. -, . Available at SSRN: https://ssrn.com/abstract=1155839 or http://dx.doi.org/10.1111/j.0042-7092.2007.00700.x

James J. Heckman (Contact Author)

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Sergio Samuel Urzua

Northwestern University ( email )

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Edward J. Vytlacil

Yale University - Department of Economics ( email )

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