Publication Type
Journal Article
Version
acceptedVersion
Publication Date
6-2012
Abstract
An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the finite-sample distributions of nonlinear least squares estimators, resulting in potentially misleading inference. A new local limit theory is developed that approximates the finite-sample distributions of the estimators uniformly well irrespective of the strength of the identification. An important technical component of this theory involves new results showing the uniform weak convergence of sample covariances involving nonlinear functions to mixed normal and stochastic integral limits. Based on these asymptotics, we construct confidence intervals for the loading coefficient and the nonlinear transformation parameter and show that these confidence intervals have correct asymptotic size. As in other cases of nonlinear estimation with integrated processes and unlike stationary process asymptotics, the properties of the nonlinear transformations affect the asymptotics and, in particular, give rise to parameter dependent rates of convergence and differences between the limit results for integrable and asymptotically homogeneous functions.
Keywords
Integrated process, Local time, Nonlinear regression, Uniform weak convergence, Weak identification
Discipline
Econometrics | Economic Theory
Research Areas
Econometrics
Publication
Econometric Theory
Volume
28
Issue
3
First Page
509
Last Page
547
ISSN
0266-4666
Identifier
10.1017/S0266466611000648
Publisher
Cambridge University Press
Citation
SHI, Xiaoxia and PHILLIPS, Peter C. B..
Nonlinear Cointegrating Regression under Weak Identification. (2012). Econometric Theory. 28, (3), 509-547.
Available at: https://ink.library.smu.edu.sg/soe_research/1825
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1017/S0266466611000648