Local Identification of Nonparametric and Semiparametric Models
Yale University - Cowles Foundation
Massachusetts Institute of Technology (MIT) - Department of Economics; New Economic School
University College London
Whitney K. Newey
Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)
April 25, 2011
Cowles Foundation Discussion Paper No. 1795
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.
Number of Pages in PDF File: 31
Keywords: Identification, Local identification, Nonparametric models, Asset pricing
JEL Classification: C12, C13, C23working papers series
Date posted: April 25, 2011
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