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Least Squares Model Averaging by Prediction Criterion

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  • Tian Xie

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    Abstract

    This paper proposes a new estimator for least squares model averaging. A model average estimator is a weighted average of common estimates obtained from a set of models. We propose computing weights by minimizing a model average prediction criterion (MAPC). We prove that the MAPC estimator is asymptotically optimal in the sense of achieving the lowest possible mean squared error. For statistical inference, we derive asymptotic tests for single hypotheses and joint hypotheses on the average coefficients for the "core" regressors. These regressors are of primary interest to us and are included in every approximation model. To improve the finite sample performance, we also consider bootstrap tests. In simulation experiments the MAPC estimator is shown to have significant efficiency gains over existing model selection and model averaging methods. We also show that the bootstrap tests have more reasonable rejection frequency than the asymptotic tests in small samples. As an empirical illustration, we apply the MAPC estimator to cross-country economic growth models.

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    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1299.pdf
    File Function: First version 2012
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    Bibliographic Info

    Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1299.

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    Length: 41 pages
    Date of creation: Nov 2012
    Date of revision:
    Handle: RePEc:qed:wpaper:1299

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    Related research

    Keywords: Model Averaging; MAPC; Convex Optimization; Optimality; Statistical Inference;

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    References

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    1. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    2. 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.
    3. Barro, Robert J, 1991. "Economic Growth in a Cross Section of Countries," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 407-43, May.
    4. David F. Hendry & Bent Nielsen, 2007. "Preface to Econometric Modeling: A Likelihood Approach
      [Econometric Modeling: A Likelihood Approach]
      ," Introductory Chapters, Princeton University Press.
    5. Chun Liu & John M. Maheu, 2009. "Forecasting realized volatility: a Bayesian model-averaging approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 709-733.
    6. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    7. Hendry, David F., 1976. "The structure of simultaneous equations estimators," Journal of Econometrics, Elsevier, vol. 4(1), pages 51-88, February.
    8. Pagan, Adrian, 1987. " Three Econometric Methodologies: A Critical Appraisal," Journal of Economic Surveys, Wiley Blackwell, vol. 1(1), pages 3-24.
    9. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    10. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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