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A Bayesian Extension of the J-Test for Non-Nested Hypotheses

  • Moheb Ghali
  • John M. Krieg
  • K. Surekha Rao

It is a common practice to use the Davidson and MacKinnon's J-test in empirical applications to test non-nested model specifications. However, when the alternate specifications fit the data well the J- test may fail to distinguish between the true and false models: the J-test will either reject, or fail to reject both specifications. We show that it is possible to use the information generated by the J-test and combine it with the Bayesian posterior odds approach that would yield an unequivocal and acceptable solution for non-nested hypotheses. We show that the approximations of Schwarz and Bayesian Information Criterion based on classical estimates for the J- test yield the Bayesian posterior odds without any need for the specification of the prior distributions and the onerous Bayesian computations.

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Article provided by The Indian Econometric Society in its journal Journal of Quantitative Economics.

Volume (Year): 9 (2011)
Issue (Month): 1 ()
Pages: 53-72

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Handle: RePEc:jqe:jqenew:v:9:y:2011:i:1:p:53-72
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  1. Ben S. Bernanke & Henning Bohn & Peter C. Reiss, 1985. "Alternative Nonnested Specification Tests of Time Series Investment Models," NBER Technical Working Papers 0049, National Bureau of Economic Research, Inc.
  2. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  3. Pesaran, M. H. & Weeks, M., 1999. "Non-nested Hypothesis Testing: An Overview," Cambridge Working Papers in Economics 9918, Faculty of Economics, University of Cambridge.
  4. 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.
  5. McAleer, Michael, 1995. "The significance of testing empirical non-nested models," Journal of Econometrics, Elsevier, vol. 67(1), pages 149-171, May.
  6. Michael C. Lovell, 1963. "Seasonal Adjustment of Economic Time Series and Multiple Regression," Cowles Foundation Discussion Papers 151, Cowles Foundation for Research in Economics, Yale University.
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