Global Representation of the Conditional LATE Model: A Separability Result*
研究了条件LATE模型中协变量在处理选择中的作用，发现若单调性方向在所有协变量值上一致，则处理选择方程需满足工具变量与协变量的可分离性，这为协变量进入方程的方式提供了可检验约束。
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.