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On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: Comment on Brown (1983) and Roehrig (1988)
Author(s) -
Benkard C. Lanier,
Berry Steven
Publication year - 2006
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/j.1468-0262.2006.00711.x
Subject(s) - counterexample , mathematical proof , identification (biology) , nonparametric statistics , mathematics , conjecture , conditional expectation , nonlinear system , mathematical economics , key (lock) , econometrics , calculus (dental) , computer science , pure mathematics , discrete mathematics , medicine , botany , geometry , physics , computer security , dentistry , quantum mechanics , biology
This note revisits the identification theorems of 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.