Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2014, Volume 82, Issue 2

Local Identification of Nonparametric and Semiparametric Models
p. 785-809

Xiaohong Chen, Victor Chernozhukov, Sokbae Lee, Whitney K. Newey

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 , 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.

Log In To View Full Content

Supplemental Material

Supplement to "Local Identification of Nonparametric and Semiparametric Models"

This supplemental material gives proofs for the results of Sections 4 and 5 of the paper as well as some additional results and discussions.