On the Nonparametric Identification of Nonlinear Simultaneous Equations

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. ∗We have had very helpful conversations with Pat Bayer, Don Brown, Yossi Feinberg, Guido Imbens, Yuliy Sannikov, Andy Skrzypacz, and Chris Timmons. Any remaining errors are our own.