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Generalized Least Squares Model Averaging


  • Qingfeng Liu

    () (Otaru University of Commerce)

  • Ryo Okui

    () (Institute of Economic Research, Kyoto University)

  • Arihiro Yoshimura

    () (Kyoto University)


This paper proposes a method of averaging generalized least squares (GLS) estimators for linear regression models with heteroskedastic errors. We derive two kinds of Mallows' Cp criteria, calculated from the estimates of the mean of the squared errors of the tted value based on the averaged GLS estimators, for this class of models. The averaging weights are chosen by minimizing Mallows' Cp criterion. We show that this method achieves asymptotic optimality. It is also shown that the asymptotic optimality holds even when the variances of the error terms are estimated and the feasible generalized least squares (FGLS) estimators are averaged. Monte Carlo simulations demonstrate that averaging FGLS estimators yields an estimate that has a remarkably lower level of risk compared with averaging least squares estimators in the presence of heteroskedasticity, and it also works when heteroskedasticity is not present, in nite samples.

Suggested Citation

  • Qingfeng Liu & Ryo Okui & Arihiro Yoshimura, 2013. "Generalized Least Squares Model Averaging," KIER Working Papers 855, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:855

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    Cited by:

    1. Steel, Mark F. J., 2017. "Model Averaging and its Use in Economics," MPRA Paper 81568, University Library of Munich, Germany.
    2. Cong Li & Qi Li & Jeffrey Racine & DAIQIANG ZHANG, 2017. "Optimal Model Averaging Of Varying Coefficient Models," Department of Economics Working Papers 2017-01, McMaster University.

    More about this item


    model averaging; GLS; FGLS; asymptotic optimality; Mallows' Cp;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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