Dr Hugo Kruiniger hugo.kruiniger@durham.ac.uk
Associate Professor
Large sample properties of GMM estimators under second-order identification
Kruiniger, Hugo
Authors
Abstract
Dovonon and Hall (Journal of Econometrics, 2018) proposed a limiting distribution theory for GMM estimators for a p - dimensional globally identified parameter vector {\phi} when local identification conditions fail at first-order but hold at second-order. They assumed that the first-order underidentification is due to the expected Jacobian having rank p-1 at the true value {\phi}_{0}, i.e., having a rank deficiency of one. After reparametrizing the model such that the last column of the Jacobian vanishes, they showed that the GMM estimator of the first p-1 parameters converges at rate T^{-1/2} and the GMM estimator of the remaining parameter, {\phi}_{p}, converges at rate T^{-1/4}. They also provided a limiting distribution of T^{1/4}({\phi}_{p}-{\phi}_{0,p}) subject to a (non-transparent) condition which they claimed to be not restrictive in general. However, as we show in this paper, their condition is in fact only satisfied when {\phi} is overidentified and the limiting distribution of T^{1/4}({\phi}_{p}-{\phi}_{0,p}), which is non-standard, depends on whether {\phi} is exactly identified or overidentified. In particular, the limiting distributions of the sign of T^{1/4}({\phi}_{p}-{\phi}_{0,p}) for the cases of exact and overidentification, respectively, are different and are obtained by using expansions of the GMM objective function of different orders. Unsurprisingly, we find that the limiting distribution theories of Dovonon and Hall (2018) for Indirect Inference (II) estimation under two different scenarios with second-order identification where the target function is a GMM estimator of the auxiliary parameter vector, are incomplete for similar reasons. We discuss how our results for GMM estimation can be used to complete both theories and how they can be used to obtain the limiting distributions of the II estimators in the case of exact identification under either scenario.
Citation
Kruiniger, H. (2022). Large sample properties of GMM estimators under second-order identification
Working Paper Type | Working Paper |
---|---|
Publication Date | 2022 |
Deposit Date | Oct 3, 2023 |
Publicly Available Date | Dec 12, 2023 |
Public URL | https://durham-repository.worktribe.com/output/1756436 |
Publisher URL | https://doi.org/10.48550/arXiv.2307.13475 |
Additional Information | Published Online: 25 July 2023 |
Files
Published Working Paper
(252 Kb)
PDF
You might also like
A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions
(2018)
Preprint / Working Paper
Further results on the estimation of dynamic panel logit models with fixed effects
(2023)
Preprint / Working Paper
Estimation of dynamic panel data models with a lot of heterogeneity
(2021)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search