Global Representation of the Conditional LATE Model: A Separability Result

TL;DR

This paper provides a global representation of the conditional LATE model, revealing that under certain monotonicity conditions, the treatment choice equation must be separable between the instrument and covariates, with extensions to multiple treatment levels.

Contribution

It establishes a novel global representation theorem for the conditional LATE model, highlighting testable restrictions on covariate inclusion and extending to multiple treatment levels.

Findings

Monotonicity directions imply separability in treatment equations.

Testable restrictions on covariate effects are derived.

Representation extended to multiple ordered treatments.

Abstract

This paper studies the latent index representation of the conditional LATE model, making explicit the role of covariates in treatment selection. We find that if the directions of the monotonicity condition are the same across all values of the conditioning covariate, which is often assumed in the literature, then the treatment choice equation has to satisfy a separability condition between the instrument and the covariate. This global representation result establishes testable restrictions imposed on the way covariates enter the treatment choice equation. We later extend the representation theorem to incorporate multiple ordered levels of treatment.