TY  - RPRT
        AU  - Heckman, James J.
AU  - Pinto, Rodrigo
        TI  - Unordered Monotonicity
        PY  - 2017/Jun/
        PB  - Institute of Labor Economics (IZA)
        CY  - Bonn
        T2  - IZA Discussion Paper
        IS  - 10821
        UR  - https://www.iza.org/publications/dp10821
        AB  - 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.

        KW  - Generalized Roy Model
KW  - revealed preference
KW  - monotonicity
KW  - instrumental variables
KW  - selection bias
KW  - identification
KW  - binary matrices
KW  - discrete choice
KW  - discrete mixtures
        ER  -