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.

中文翻译：

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条件 LATE 模型的全局表示：可分离性结果*

本文研究了条件 LATE 模型的潜在指标表示，明确了协变量在治疗选择中的作用。我们发现，如果单调性条件的方向在条件协变量的所有值上都相同，这在文献中经常假设，那么治疗选择方程必须满足工具和协变量之间的可分离性条件。这种全局表示结果对协变量进入治疗选择方程的方式施加了可检验的限制。我们稍后扩展表示定理以包含多个有序级别的处理。