Local Identification of Nonparametric and Semiparametric Models

TL;DR

This paper extends classical local identification conditions from parametric models to nonparametric and semiparametric models, providing new criteria and applications for complex economic models.

Contribution

It derives an infinite-dimensional analog of the full rank condition for local identification in nonparametric models, including new criteria for several important economic models.

Findings

Established conditions for local identification in nonparametric models.

Provided restrictions on neighborhoods for identification.

Applied results to key economic models like IV and asset pricing.

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 the nonparametric, 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, single-index IV models, and semiparametric consumption-based asset pricing models.