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We consider identiﬁcation in a class of nonseparable 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 some of the available tradeoﬀs between conditions on the support of the instruments, 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. 2130.