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A plug-in averaging estimator for regressions with heteroskedastic errors

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  • LIU, CHU-AN

Abstract

This paper proposes a new model averaging estimator for the linear regression model with heteroskedastic errors. We address the issues of how to optimally assign the weights for candidate models and how to make inference based on the averaging estimator. We derive the asymptotic mean squared error (AMSE) of the averaging estimator in a local asymptotic framework, and then choose the optimal weights by minimizing the AMSE. We propose a plug-in estimator of the optimal weights and use these estimated weights to construct a plug-in averaging estimator of the parameter of interest. We derive the asymptotic distribution of the plug-in averaging estimator and suggest a plug-in method to construct confidence intervals. Monte Carlo simulations show that the plug-in averaging estimator has much smaller expected squared error, maximum risk, and maximum regret than other existing model selection and model averaging methods. As an empirical illustration, the proposed methodology is applied to cross-country growth regressions.

Suggested Citation

  • Liu, Chu-An, 2012. "A plug-in averaging estimator for regressions with heteroskedastic errors," MPRA Paper 41414, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:41414
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    File URL: https://mpra.ub.uni-muenchen.de/41414/1/MPRA_paper_41414.pdf
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    References listed on IDEAS

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    2. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February.
    3. Kabaila, Paul, 1998. "Valid Confidence Intervals In Regression After Variable Selection," Econometric Theory, Cambridge University Press, vol. 14(04), pages 463-482, August.
    4. Hansen, Bruce E., 2010. "Averaging estimators for autoregressions with a near unit root," Journal of Econometrics, Elsevier, vol. 158(1), pages 142-155, September.
    5. Andrews, Donald W. K., 1991. "Asymptotic optimality of generalized CL, cross-validation, and generalized cross-validation in regression with heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 359-377, February.
    6. DiTraglia, Francis J., 2016. "Using invalid instruments on purpose: Focused moment selection and averaging for GMM," Journal of Econometrics, Elsevier, vol. 195(2), pages 187-208.
    7. Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
    8. Leeb, Hannes & P tscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(02), pages 338-376, April.
    9. Yang Y., 2001. "Adaptive Regression by Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 574-588, June.
    10. Hansen, Bruce E., 2009. "Averaging Estimators For Regressions With A Possible Structural Break," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1498-1514, December.
    11. Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
    12. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
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    Cited by:

    1. Branko Urošević & Milan Nedeljković & Emir Zildžović, 2012. "Jackknife Model Averaging of the Current Account Determinants," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 59(3), pages 267-281, June.
    2. repec:ipf:psejou:v:41:y:2017:i:4:p:421-441 is not listed on IDEAS

    More about this item

    Keywords

    Local asymptotic theory; Model averaging; Model selection; Plug-in estimators;

    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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