Asymptotic efficiency of the ordinary least squares estimator for regressions with unstable regressors

Dong Wan Shin, Man Suk Oh

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

For regression models with general unstable regressors having characteristic roots on the unit circle and general stationary errors independent of the regressors, sufficient conditions are investigated under which the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has the same limiting distribution as the generalized least squares estimator (GLSE) under the same normalization. A key condition for the asymptotic efficiency of the OLSE is that one multiplicity of a characteristic root of the regressor process is strictly greater than the multiplicities of the other roots. Under this condition, the covariance matrix Γ of the errors and the regressor matrix X are shown to satisfy a relationship (ΓX = XC + V for some matrix C) for V asymptotically dominated by X, which is analogous to the condition (ΓX = XC for some matrix C) for numerical equivalence of the OLSE and the GLSE.

Original languageEnglish
Pages (from-to)1121-1138
Number of pages18
JournalEconometric Theory
Volume18
Issue number5
DOIs
StatePublished - Oct 2002

Fingerprint

Dive into the research topics of 'Asymptotic efficiency of the ordinary least squares estimator for regressions with unstable regressors'. Together they form a unique fingerprint.

Cite this