This paper presents a new monotonicity condition for unordered discrete choice models with multiple treatments. Unlike a less general version of mono-tonicity 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.
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