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Non-nested Models and the likelihood Ratio Statistic: A Comparison of Simulation and Bootstrap-based Tests

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  • Kapetanios, G.
  • Weeks, M.

Abstract

We consider an alternative use of simulation in the context of using the Likelihood-Ratio statistic to test non-nested models. To date simulation has been used to estimate the Kullback-Leibler measure of closeness between two densities, which in turn ‘mean adjusts’ the Likelihood-Ratio statistic. Given that this adjustment is still based upon asymptotic arguments, an alternative procedure is to utilise bootstrap procedures to construct the empirical density. To our knowledge this study represents the first comparison of the properties of bootstrap and simulation-based tests applied to non-nested tests. More specifically, the design of experiments allows us to comment on the relative performance of these two testing frameworks across models with varying degrees of nonlinearity. In this respect although the primary focus of the paper is upon the relative evaluation of simulation and bootstrap-based nonnested procedures in testing across a class of nonlinear threshold models, the inclusion of a similar analysis of the more standard linear/log-linear models provides a point of comparison.

Suggested Citation

  • Kapetanios, G. & Weeks, M., 2003. "Non-nested Models and the likelihood Ratio Statistic: A Comparison of Simulation and Bootstrap-based Tests," Cambridge Working Papers in Economics 0308, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:0308
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    References listed on IDEAS

    as
    1. Kilian, L., 1998. "Pitfalls in Constructing Bootstrap Confidence Intervals for Asymptotically Pivotal Statistics," Papers 98-04, Michigan - Center for Research on Economic & Social Theory.
    2. Godfrey, Leslie G & McAleer, Michael & McKenzie, Colin R, 1988. "Variable Addition and LaGrange Multiplier Tests for Linear and Logarithmic Regression Models," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 492-503, August.
    3. J. L. Horowitz, 1995. "Bootstrap Methods In Econometrics: Theory And Numerical Performance," SFB 373 Discussion Papers 1995,63, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. N. Coulibaly & B. Wade Brorsen, 1999. "Monte carlo sampling approach to testing nonnested hypothesis: monte carlo results," Econometric Reviews, Taylor & Francis Journals, vol. 18(2), pages 195-209.
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    More about this item

    Keywords

    Non-nested tests; simulation-based inference; bootstrap tests; nonlinear threshold models;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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