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Asymptotic Efficiency Of The Ordinary Least Squares Estimator For Regressions With Unstable Regressors

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  • SHIN, DONG WAN
  • OH, MAN SUK

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.

Suggested Citation

  • Shin, Dong Wan & Oh, Man Suk, 2002. "Asymptotic Efficiency Of The Ordinary Least Squares Estimator For Regressions With Unstable Regressors," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1121-1138, October.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:05:p:1121-1138_18
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    Cited by:

    1. Shin, Dong Wan & Oh, Man-Suk, 2004. "Fully modified semiparametric GLS estimation for regressions with nonstationary seasonal regressors," Journal of Econometrics, Elsevier, vol. 122(2), pages 247-280, October.
    2. Dong Shin & Dai-Gyoung Kim & Han Kim, 2002. "Efficiency of the OLSE for regressions on two-dimensional grids with sinusoidal regressors and spatially correlated errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 56(3), pages 247-258, December.
    3. Yoshimasa Uematsu, 2011. "Asymptotic Efficiency of the OLS Estimator with Singular Limiting Sample Moment Matrices," Global COE Hi-Stat Discussion Paper Series gd11-208, Institute of Economic Research, Hitotsubashi University.
    4. Shin, Dong Wan & Joon Kim, Han & Jhee, Won-Chul, 2007. "Asymptotic efficiency of the ordinary least-squares estimator for sur models with integrated regressors," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 75-82, January.

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