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Bootstrap Tests of Nonnested Linear Regression Models


  • Davidson, R.
  • Mackinnon, J.G.


The J test for nonnested regression models often works badly as an asypmtotic test, but it generally works very well when bootstrapped. We provide a theroretical analysis of the J test which explains both of these phenomena. We also propose a modified version of the test which works even better than the ordinary J test when bootstrapped. Using our theoretical results to make simulation much faster, we obtain extremely accurate Monte Carlo results which demonstrate just how well the bootstraped tests perform.

Suggested Citation

  • Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Tests of Nonnested Linear Regression Models," ASSET - Instituto De Economia Publica 170, ASSET (Association of Southern European Economic Theorists).
  • Handle: RePEc:fth:inecpu:170

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    References listed on IDEAS

    1. Russell Davidson & James G. MacKinnon, 1996. "The Size and Power of Bootstrap Tests," Working Papers 932, Queen's University, Department of Economics.
    2. M. H. Pesaran, 1974. "On the General Problem of Model Selection," Review of Economic Studies, Oxford University Press, vol. 41(2), pages 153-171.
    3. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    4. McAleer, Michael, 1995. "The significance of testing empirical non-nested models," Journal of Econometrics, Elsevier, vol. 67(1), pages 149-171, May.
    5. Russell Davidson & James G. Mackinnon, 1982. "Some Non-Nested Hypothesis Tests and the Relations Among Them," Review of Economic Studies, Oxford University Press, vol. 49(4), pages 551-565.
    6. Godfrey, Leslie G, 1983. "Testing Non-Nested Models after Estimation by Instrumental Variables or Least Squares," Econometrica, Econometric Society, vol. 51(2), pages 355-365, March.
    7. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
    8. Michelis, Leo, 1999. "The distributions of the J and Cox non-nested tests in regression models with weakly correlated regressors," Journal of Econometrics, Elsevier, vol. 93(2), pages 369-401, December.
    9. Godfrey, L. G. & Pesaran, M. H., 1983. "Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence," Journal of Econometrics, Elsevier, vol. 21(1), pages 133-154, January.
    10. Fisher, Gordon R. & McAleer, Michael, 1981. "Alternative procedures and associated tests of significance for non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 16(1), pages 103-119, May.
    11. Yanqin Fan & Qi Li, 1995. "Bootstrapping J-type tests for non-nested regression models," Economics Letters, Elsevier, vol. 48(2), pages 107-112, May.
    12. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    13. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    14. Godfrey, L. G., 1998. "Tests of non-nested regression models some results on small sample behaviour and the bootstrap," Journal of Econometrics, Elsevier, vol. 84(1), pages 59-74, May.
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    Cited by:

    1. Rao, Surekha & Ghali, Moheb & Krieg, John, 2008. "On the J-test for nonnested hypotheses and Bayesian extension," MPRA Paper 14637, University Library of Munich, Germany.
    2. Davidson, Russell & MacKinnon, James G., 2007. "Improving the reliability of bootstrap tests with the fast double bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3259-3281, April.
    3. Luger, Richard, 2006. "Exact permutation tests for non-nested non-linear regression models," Journal of Econometrics, Elsevier, vol. 133(2), pages 513-529, August.
    4. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    5. Han, Xiaoyi & Lee, Lung-fei, 2013. "Model selection using J-test for the spatial autoregressive model vs. the matrix exponential spatial model," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 250-271.
    6. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 123(1), pages 67-87, November.
    7. Hagemann, Andreas, 2012. "A simple test for regression specification with non-nested alternatives," Journal of Econometrics, Elsevier, vol. 166(2), pages 247-254.
    8. Yang, Ji-Chung, 2005. "Impact measurement for public investment evaluation: An application to Korea," Journal of Policy Modeling, Elsevier, vol. 27(5), pages 535-551, July.
    9. BHATTI, M.Ishaq & BODLA, Mahmud, A., 2008. "Empirical Power Comparison Of Non-Nested Tests For The Evm: Some Monte Carlo Evidence," International Journal of Applied Econometrics and Quantitative Studies, Euro-American Association of Economic Development, vol. 5(2).
    10. James G. MacKinnon, 2006. "Applications of the Fast Double Bootstrap," Working Papers 1023, Queen's University, Department of Economics.
    11. Rachida Ouysse, 2011. "Computationally efficient approximation for the double bootstrap mean bias correction," Economics Bulletin, AccessEcon, vol. 31(3), pages 2388-2403.
    12. Jin, Fei & Lee, Lung-fei, 2013. "Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 590-616.
    13. Jeffrey S. Racine & Christopher F. Parmeter, 2012. "Data-Driven Model Evaluation: A Test for Revealed Performance," Department of Economics Working Papers 2012-13, McMaster University.
    14. Russell Davidson & James MacKinnon, 2002. "Fast Double Bootstrap Tests Of Nonnested Linear Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 419-429.
    15. Hsin-Yi Lin, 2011. "A robust test for non-nested hypotheses," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(1), pages 93-111, March.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General


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