DMCA
REGRESSION UNDER WEAK IDENTIFICATION
BibTeX
@MISC{Shi_regressionunder,
author = {Xiaoxia Shi and Peter C. B. Phillips and Xiaoxia Shi and Peter C. B. Phillips},
title = {REGRESSION UNDER WEAK IDENTIFICATION},
year = {}
}
Share
 |
 |
 |
 |
||
OpenURL
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 nonlin-ear 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 con-struct confidence intervals for the loading coefficient and the nonlinear transforma-tion parameter and show that these confidence intervals have correct asymptotic size. As in other cases of nonlinear estimation with integrated processes and unlike sta-tionary process asymptotics, the properties of the nonlinear transformations affect the asymptotics and, in particular, give rise to parameter dependent rates of con-vergence and differences between the limit results for integrable and asymptotically homogeneous functions. 1.
Keyphrases
regression weak identification nonlinear transformation integrated process finite-sample distribution loading coefficient confidence interval limit result correct asymptotic size asymptotic theory nonlinear function important technical component sta-tionary process asymptotics uniform weak convergence stochastic integral limit good approximation new result sample covariance dependent rate nonlin-ear function limit theory regression model nonlinear estimation nonlinear transforma-tion parameter square estimator weak identification arises misleading inference homogeneous function new local limit theory
