Unordered Monotonicity

48 Pages Posted: 19 Jun 2017

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)

Rodrigo R. Pinto

University of Chicago - Department of Economics

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Abstract

This paper presents a new monotonicity condition for unordered discrete choice models with multiple treatments. Unlike a less general version of monotonicity in binary and ordered choice models, monotonicity in unordered discrete choice models along with other standard assumptions does not necessarily identify causal effects defined by variation in instruments, although in some cases it does. Our condition implies and is implied by additive separability of the choice equations in terms of observables and unobservables. These results follow from properties of binary matrices developed in this paper. We investigate conditions under which Unordered Monotonicity arises as a consequence of choice behavior. We represent IV estimators of counterfactuals as solutions to discrete mixture problems.

Keywords: instrumental variables, monotonicity, revealed preference, Generalized Roy Model, binary matrices, discrete choice, selection bias, identification, discrete mixtures

JEL Classification: I21, C93, J15, V16

Suggested Citation

Heckman, James J. and Pinto, Rodrigo R., Unordered Monotonicity. IZA Discussion Paper No. 10821. Available at SSRN: https://ssrn.com/abstract=2988168

James J. Heckman (Contact Author)

University of Chicago - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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American Bar Foundation

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Institute for the Study of Labor (IZA)

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CESifo (Center for Economic Studies and Ifo Institute)

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Rodrigo R. Pinto

University of Chicago - Department of Economics ( email )

1126 East 59th Street
Chicago, IL 60637
United States

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