On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: Comment on B. Brown (1983) and Roehrig (1988)∗

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, the reduced form of a nonseparable simultaneous equations model is not identified even under the assumptions of these papers. We provide conditions under which the reduced form is identified and is recoverable using the distribution of the endogenous variables conditional on the exogenous variables. However, these conditions place substantial limitations on the structural model. 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 in more general settings. ∗We have had helpful conversations with Pat Bayer, Don Brown, Yossi Feinberg, Guido Imbens, Yuliy Sannikov, Andy Skrzypacz, and Chris Timmons. We also thank the editor and four anonymous referees for their useful comments. Any remaining errors are our own.