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

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C. Lanier Benkard
Steven Berry

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Abstract

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. Copyright The Econometric Society 2006.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2006.00711.x
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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 74 (2006)
Issue (Month): 5 (09)
Pages: 1429-1440
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Handle: RePEc:ecm:emetrp:v:74:y:2006:i:5:p:1429-1440

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
  2. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09. [Downloadable!] (restricted)
  3. Donald J. Brown & Rosa L. Matzkin, 1998. "Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand," Cowles Foundation Discussion Papers 1175, Cowles Foundation, Yale University. [Downloadable!]
  4. Angrist, Joshua D & Graddy, Kathryn & Imbens, Guido W, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," Review of Economic Studies, Blackwell Publishing, vol. 67(3), pages 499-527, July.
  5. Guido W. Imbens & Whitney K. Newey, 2002. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," NBER Technical Working Papers 0285, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  6. Susan Athey & Philip A. Haile, 2002. "Identification of Standard Auction Models," Econometrica, Econometric Society, vol. 70(6), pages 2107-2140, November. [Downloadable!] (restricted)
  7. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, 09. [Downloadable!] (restricted)
  8. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
  9. repec:att:wimass:1920013 is not listed on IDEAS
  10. Brown, Bryan W, 1983. "The Identification Problem in Systems Nonlinear in the Variables," Econometrica, Econometric Society, vol. 51(1), pages 175-96, January. [Downloadable!] (restricted)
  11. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09. [Downloadable!] (restricted)
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  1. Ivana Komunjer, 2008. "Global Identification In Nonlinear Semiparametric Models," University of California at San Diego, Economics Working Paper Series 2007-06R1, Department of Economics, UC San Diego. [Downloadable!]
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