Quantitative Economics

Journal Of The Econometric Society

Edited by: Stéphane Bonhomme • Print ISSN: 1759-7323 • Online ISSN: 1759-7331

Quantitative Economics: Jul, 2024, Volume 15, Issue 3

Specification Testing for Conditional Moment Restrictions under Local Identification Failure

https://doi.org/10.3982/QE2242
p. 849-891

Prosper Dovonon, Nikolay Gospodinov

In this paper, we study the asymptotic behavior of specification tests in conditional moment restriction models under first‐order local identification failure with dependent data. More specifically, we obtain conditions under which the conventional specification test for conditional moment restrictions retains its standard normal limit when first‐order local identification fails but global identification is still attainable. In the process, we derive some novel intermediate results that include extending the first‐ and second‐order local identification framework to models defined by conditional moment restrictions, establishing the rate of convergence of the GMM estimator and characterizing the asymptotic representation for degenerate U‐statistics under strong mixing dependence. Importantly, the specification test is robust to first‐order local identification failure regardless of the number of directions in which the Jacobian of the conditional moment restrictions is degenerate and remains valid even if the model is first‐order identified.


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Supplemental Material

Supplement to "Specification Testing for Conditional Moment Restrictions under Local Identification Failure"

Prosper Dovonon and Nikolay Gospodinov

This supplement contains material not found within the manuscript.

Supplement to "Specification Testing for Conditional Moment Restrictions under Local Identification Failure"

Prosper Dovonon and Nikolay Gospodinov

The replication package for this paper is available at https://doi.org/10.5281/zenodo.11098557. The authors were granted an exemption to publish parts of their data because either access to these data is restricted or the authors do not have the right to republish them. Therefore, the replication package only includes the codes and the parts of the data that are not subject to the exemption. However, the authors provided the Journal with (or assisted the Journal to obtain) temporary access to the restricted data. The Journal checked the provided and restricted data and the codes for their ability to reproduce the results in the paper and approved online appendices.