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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 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, single-index IV models, and semiparametric consumption-based asset pricing models.
Chen, Xiaohong; Chernozhukov, Victor; Lee, Sokbae; and Newey, Whitney, "Local Identification of Nonparametric and Semiparametric Models" (2011). Cowles Foundation Discussion Papers. 2139.