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Unordered Monotonicity
Author(s) -
Heckman James J.,
Pinto Rodrigo
Publication year - 2018
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta13777
Subject(s) - monotonic function , counterfactual conditional , estimator , mathematics , identification (biology) , discrete choice , mathematical economics , binary number , econometrics , statistics , counterfactual thinking , arithmetic , mathematical analysis , philosophy , botany , epistemology , biology
This paper defines and analyzes a new monotonicity condition for the identification of counterfactuals and treatment effects in unordered discrete choice models with multiple treatments, heterogeneous agents, and discrete‐valued instruments. Unordered monotonicity implies and is implied by additive separability of choice of treatment equations in terms of observed and unobserved variables. 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 characterize IV estimators of counterfactuals as solutions to discrete mixture problems.