This note revisits the identiﬁcation theorems of B. Brown (1983) and Roehrig (1988). We describe an error in the proofs of the main identiﬁcation theorems in these papers, and provide an important counterexample to the theorems on the identiﬁcation of the reduced form. Speciﬁcally, contrary to the theorems, the reduced form of a nonseparable simultaneous equations model is not identiﬁed even under the assumptions of those papers. We conclude the note with a conjecture that it may be possible to use classical exclusion restrictions to recover some of the key implications of the theorems.
Benkard, C. Lanier and Berry, Steven T., "On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: Comment on B. Brown (1983) and Roehrig (1988)" (2004). Cowles Foundation Discussion Papers. 1764.