Independence , Monotonicity , and Latent Index Models : an Equivalence Result

A common problem in economics is to evaluate the effect of a treatment when individuals self-select whether to receive the treatment. This problem arises when trying to evaluate the union/nonunion wage differential, the effect of job training on earnings, and the returns to schooling, where being unionized or making a human capital investment is the treatment. One standard approach to this problem is the use of a selection model as first proposed by Heckman (1976). Under this approach, the researcher models selection into the program by a latent index crossing a threshold, where the latent index is interpreted as the expected net utility of selecting into treatment. However, some statisticians have criticized or even dismissed the use of selection models to estimate treatment effects, arguing that such analysis is inherently driven by distributional and functional form assumptions.2 This sentiment has been echoed within economics. The local average treatment effect (LATE) framework is a form of linear instrumental variables (IV) analysis developed by Imbens and Angrist (1994).3 However, like the