LOCAL IDENTIFICATION OF NONPARAMETRIC AND SEMIPARAMETRIC MODELS by
نویسندگان
چکیده
In parametric models a su cient condition for local identi cation is that the vector of moment conditions is di erentiable at the true parameter with full rank derivative matrix. We show that there are corresponding su cient conditions for nonparametric models. A nonparametric rank condition and di erentiability of the moment conditions with respect to a certain norm imply local identi cation. 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 su cient conditions with endogenous quantile and single index examples. We also consider a semiparametric habitbased, consumption capital asset pricing model. There we nd the rank condition is implied by an integral equation of the second kind having a one-dimensional null space. JEL Classi cation: C12, C13, C23
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Local Identification of Nonparametric and Semiparametric Models∗
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