IDENTIFICATION IN TRIANGULAR SYSTEMS USING CONTROL FUNCTIONS
讨论了非参数连续三角系统中控制函数存在的充要条件，发现这些条件限制了未观测异质性的维度，表明在大多数应用中难以找到合理的控制函数。
This note discusses identification in nonparametric, continuous triangular systems. It provides conditions that are both necessary and sufficient for the existence of control functions satisfying conditional independence and support requirements. Confirming a commonly noticed pattern, these conditions restrict the admissible dimensionality of unobserved heterogeneity in the first-stage structural relation, or more generally the dimensionality of the family of conditional distributions of second-stage heterogeneity given explanatory variables and instruments. These conditions imply that no such control function exists without assumptions that seem hard to justify in most applications. In particular, none exists in the context of a generic random coefficient model.