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Simulation Encompassing: Testing Non‐nested Hypotheses

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  • Maozu Lu
  • Grayham E. Mizon
  • Chiara Monfardini

Abstract

This paper considers simulation‐based procedures to compute the Wald encompassing and the Cox test statistics for non‐nested models. These simulation estimation procedures are applied to both the encompassing contrast and its covariance matrix in the case of a Wald non‐nested test statistic, and both the numerator and the denominator in the Cox test statistic. The proposed procedures are illustrated by the example of comparing a linear with a log‐linear model. Monte Carlo studies are conducted for both examples and the results indicate that with simulated covariance matrices, the small sample behaviour of both test statistics is close to that of their asymptotic distributions.

Suggested Citation

  • Maozu Lu & Grayham E. Mizon & Chiara Monfardini, 2008. "Simulation Encompassing: Testing Non‐nested Hypotheses," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 781-806, December.
    • Handle: RePEc:bla:obuest:v:70:y:2008:i:s1:p:781-806
    DOI: 10.1111/j.1468-0084.2008.00530.x
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    References listed on IDEAS

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    1. Hashem Pesaran, M. & Pesaran, Bahram, 1993. "A simulation approach to the problem of computing Cox's statistic for testing nonnested models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 377-392.
    2. Hendry, David F. & Richard, Jean-Francois, 1982. "On the formulation of empirical models in dynamic econometrics," Journal of Econometrics, Elsevier, vol. 20(1), pages 3-33, October.
    3. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-678, May.
    4. Pesaran, M H & Deaton, Angus S, 1978. "Testing Non-Nested Nonlinear Regression Models," Econometrica, Econometric Society, vol. 46(3), pages 677-694, May.
    5. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    6. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    7. James G. MacKinnon, 1983. "Model Specification Tests Against Non-Nested Alternatives," Working Paper 573, Economics Department, Queen's University.
    8. M. H. Pesaran, 1974. "On the General Problem of Model Selection," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(2), pages 153-171.
    9. Christophe Bontemps & Grayham E. Mizon, 2008. "Encompassing: Concepts and Implementation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 721-750, December.
    10. Aris Spanos & David F. Hendry & J. James Reade, 2008. "Linear vs. Log‐linear Unit‐Root Specification: An Application of Mis‐specification Encompassing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 829-847, December.
    11. Gwyn Aneuryn-Evans & Angus Deaton, 1980. "Testing Linear versus Logarithmic Regression Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 275-291.
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    Cited by:

    1. Luigi Ermini & David F. Hendry, 2008. "Log Income vs. Linear Income: An Application of the Encompassing Principle," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 807-827, December.
    2. Christophe Bontemps & Grayham E. Mizon, 2008. "Encompassing: Concepts and Implementation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 721-750, December.
    3. David F. Hendry & Massimiliano Marcellino & Chiara Monfardini, 2008. "Foreword," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 711-714, December.
    4. Aris Spanos & David F. Hendry & J. James Reade, 2008. "Linear vs. Log‐linear Unit‐Root Specification: An Application of Mis‐specification Encompassing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 829-847, December.

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