Local Identification of Nonparametric and Semiparametric Models

31 Pages Posted: 25 Apr 2011

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics

Sokbae Lee

University College London

Whitney K. Newey

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 2 versions of this paper

Date Written: April 25, 2011

Abstract

In parametric models a sufficient condition for local identification is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We show that there are corresponding sufficient conditions for nonparametric models. A nonparametric rank condition and differentiability of the moment conditions with respect to a certain norm imply local identification. It turns out these conditions are slightly stronger than needed and are hard to check, so we provide weaker and more primitive conditions. We extend the results to semiparametric models. We illustrate the sufficient conditions with endogenous quantile and single index examples. We also consider a semiparametric habit-based, consumption capital asset pricing model. There we find the rank condition is implied by an integral equation of the second kind having a one-dimensional null space.

Keywords: Identification, Local identification, Nonparametric models, Asset pricing

JEL Classification: C12, C13, C23

Suggested Citation

Chen, Xiaohong and Chernozhukov, Victor and Lee, Sokbae and Newey, Whitney K., Local Identification of Nonparametric and Semiparametric Models (April 25, 2011). Cowles Foundation Discussion Paper No. 1795, Available at SSRN: https://ssrn.com/abstract=1822264

Xiaohong Chen (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-262f
Cambridge, MA 02142
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617-253-4767 (Phone)
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HOME PAGE: http://www.mit.edu/~vchern/

Sokbae Lee

University College London ( email )

Gower Street
London
United Kingdom

Whitney K. Newey

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
E52-262D
Cambridge, MA 02142
United States
617-253-6420 (Phone)

National Bureau of Economic Research (NBER) ( email )

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Cambridge, MA 02138
United States

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