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Local identification of nonparametric and semiparametric models

Authors: Xiaohong Chen , Victor Chernozhukov , Sokbae Lee and Whitney K. Newey
Date: 01 March 2014
Type: Journal Article, Econometrica, Vol. 82, No. 2, pp. 785--809
DOI: 10.3982/ECTA9988

Abstract

In parametric, nonlinear structural models, a classical sufficient condition for local identification, like Fisher (1966) and Rothenberg (1971), is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We derive an analogous result for thenonparametric, nonlinear structural models, establishing conditions under which an infinite dimensional analog of the full rank condition is sufficient for local identification. Importantly, we show that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities overwhelming linear effects. We give restrictions on a neighborhood of the true value that are sufficient for local identification. We apply these results to obtain new, primitive identification conditions in several important models, including nonseparable quantile instrumental variable (IV) models and semiparametric consumption-based asset pricing models.

Previous version:
Xiaohong Chen, Victor Chernozhukov, Sokbae Lee and Whitney K. Newey November 2012, Local identification of nonparametric and semiparametric models, cemmap Working Paper, CWP37/12

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