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Non-nested Hypothesis Testing: An Overview

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Abstract

In econometric analysis, non-nested models arise naturally when rival economic theories are used to explain the same phenomenon, such as unemployment, inflation or output growth. The authors examine the problem of hypothesis testing when the models under consideration are ‘non-nested’ or belong to ‘separate’ families of distributions in the sense that none of the individual models may be obtained form the remaining, either by imposition of parameter restrictions or through a limiting process. Although the primary focus is on non-nested hypothesis testing, the authors briefly discuss the problem of model selection and the differences and similarities between the two approaches. By using the linear regression model as a convenient framework, the authors examine three broad approaches to non-nested hypothesis testing: the modified (centred) long-likelihood ratio procedure, the comprehensive models approach, and the encompassing procedure. Finally, they consider a number of practical problems which arise in the application of non-nested tests to non-linear models such as the probit and logit qualitative response models.

Suggested Citation

  • Pesaran, M. H. & Weeks, M., 1999. "Non-nested Hypothesis Testing: An Overview," Cambridge Working Papers in Economics 9918, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:9918
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    File URL: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/nnest.pdf
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    References listed on IDEAS

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    1. Pesaran, M H, 1982. "A Critique of the Proposed Tests of the Natural Rate-Rational Expectations Hypothesis," Economic Journal, Royal Economic Society, vol. 92(367), pages 529-554, September.
    2. Hendry, David F, 1980. "Econometrics-Alchemy or Science?," Economica, London School of Economics and Political Science, vol. 47(188), pages 387-406, November.
    3. Pesaran, M. H., 1981. "Pitfalls of testing non-nested hypotheses by the lagrange multiplier method," Journal of Econometrics, Elsevier, vol. 17(3), pages 323-331, December.
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    Cited by:

    1. Fingleton, Bernard, 2008. "Competing models of global dynamics: Evidence from panel models with spatially correlated error components," Economic Modelling, Elsevier, vol. 25(3), pages 542-558, May.
    2. Moheb Ghali & John M. Krieg & K. Surekha Rao, 2011. "A Bayesian Extension of the J-Test for Non-Nested Hypotheses," Journal of Quantitative Economics, The Indian Econometric Society, vol. 9(1), pages 53-72.
    3. Otsu, Taisuke & Seo, Myung Hwan & Whang, Yoon-Jae, 2012. "Testing for non-nested conditional moment restrictions using unconditional empirical likelihood," Journal of Econometrics, Elsevier, pages 370-382.
    4. Jesús Crespo-Cuaresma & Balázs Egert & Ronald MacDonald, 2005. "Non-Linear Exchange Rate Dynamics in Target Zones: A Bumpy Road towards a Honeymoon - Some Evidence from the ERM, ERM2 and Selected New EU Member States," CESifo Working Paper Series 1511, CESifo Group Munich.
    5. John Geweke & Joel Horowitz & M. Hashem Pesaran, 2006. "Econometrics: A Bird’s Eye View," CESifo Working Paper Series 1870, CESifo Group Munich.
    6. Otsu, Taisuke & Whang, Yoon-Jae, 2011. "Testing For Nonnested Conditional Moment Restrictions Via Conditional Empirical Likelihood," Econometric Theory, Cambridge University Press, vol. 27(01), pages 114-153, February.
    7. Timo Teräsvirta & Ann-Charlotte Eliasson, 2001. "Non-linear error correction and the UK demand for broad money, 1878-1993," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 277-288.
    8. Li, Tong, 2009. "Simulation based selection of competing structural econometric models," Journal of Econometrics, Elsevier, vol. 148(2), pages 114-123, February.
    9. M. Genius & E. Strazzera, 2000. "Evaluation of likelihood based tests for non-nested dichotomus choice contingent valuation models," Working Paper CRENoS 200012, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    10. Shi, Xiaoxia, 2015. "Model selection tests for moment inequality models," Journal of Econometrics, Elsevier, vol. 187(1), pages 1-17.
    11. Mancini, Loriano & Ronchetti, Elvezio & Trojani, Fabio, 2005. "Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models," Journal of the American Statistical Association, American Statistical Association, pages 628-641.
    12. Genius, Margarita & Strazzera, Elisabetta, 2002. "A note about model selection and tests for non-nested contingent valuation models," Economics Letters, Elsevier, vol. 74(3), pages 363-370, February.
    13. Jesús Crespo Cuaresma & Maria Antoinette Silgoner, 2004. "Groth effects of inflation in Europe: How low is too low, how high is too high?," Vienna Economics Papers 0411, University of Vienna, Department of Economics.

    More about this item

    Keywords

    Non-nested hypotheses; Model selection; Cox’s test; Encompassing; Stochastic simulation; Kullback-Leibler divergence measure;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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