COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1795 Local Identification of Nonparametric and Semiparametric Models Xiaohong Chen, Victor Chernozhukov, Sokbae Lee and Whitney Newey April 2011 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. |
