Ordered Discrete-Choice Selection Models and Local Average Treatment Effect Assumptions: Equivalence, Nonequivalence, and Representation Results

This note shows that the local average treatment effect (LATE) assumptions of Angrist and Imbens are weaker than imposing an ordered, discrete-choice selection model if one imposes the standard assumption of constant thresholds in the latter. However, the note extends results of Vytlacil to show that the LATE assumptions are equivalent to an ordered, discrete-choice selection model if one allows for random thresholds in the latter. A nonparametric representation result for ordered, discrete-choice models is produced as a by-product of these results.