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.

A growing literature establishes that high quality early childhood interventions targeted toward disadvantaged children have substantial impacts on later life outcomes. Little is known about the mechanisms producing these impacts. This paper uses longitudinal data on cognitive and personality traits from an experimental evaluation of the influential Perry Preschool program to analyze the channels through which the program boosted both male and female participant outcomes. Experimentally induced changes in personality traits explain a sizable portion of adult treatment effects.