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

16 Pages Posted: 8 Jun 2006

See all articles by C. Lanier Benkard

C. Lanier Benkard

Stanford Graduate School of Business; National Bureau of Economic Research (NBER)

Steven Berry

Yale University - Department of Economics; National Bureau of Economic Research (NBER); Yale University - Cowles Foundation

Date Written: April 19, 2006

Abstract

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.

Suggested Citation

Benkard, C. Lanier and Berry, Steven T., On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: Comment on B. Brown (1983) and Roehrig (1988) (April 19, 2006). Stanford University Graduate School of Business Research Paper No. 1868(R). Available at SSRN: https://ssrn.com/abstract=907123 or http://dx.doi.org/10.2139/ssrn.907123

C. Lanier Benkard (Contact Author)

Stanford Graduate School of Business ( email )

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National Bureau of Economic Research (NBER)

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Steven T. Berry

Yale University - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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United States

Yale University - Cowles Foundation

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New Haven, CT 06520-8281
United States

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