Local Identification of Nonparametric and Semiparametric Models

Details Local Identification of Nonparametric and Semiparametric Models Local Identification of Nonparametric and Semiparametric Models

2011-05-16

arxiv.org/abs/1105.3007v1

Mathematics

Statistics Theory

Scientific paper

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.

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