We consider identiﬁcation in a class of nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine standard exclusion restrictions with a requirement that each structural error enter through a “residual index” function. We provide constructive proofs of identiﬁcation under several sets of conditions, demonstrating tradeoﬀs between restrictions on the support of the instruments, shape restrictions on the joint distribution of the structural errors, and restrictions on the form of the residual index function.
Berry, Steven T. and Haile, Philip A., "Identification in a Class of Nonparametric Simultaneous Equations Models" (2011). Cowles Foundation Discussion Papers. 2128.