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On the J-test for nonnested hypotheses and Bayesian extension

  • Rao, Surekha
  • Ghali, Moheb
  • Krieg, John

Abstract Davidson and MacKinnon’s J-test was developed to test non-nested model specification. In empirical applications, 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. In such cases we show that it is possible to use the information generated in the process of applying the J-test to implement a Bayesian approach that provides an unequivocal and acceptable solution. Jeffreys’ Bayes factors offer ways of obtaining the posterior probabilities of the competing models and relative ranking of the competing hypotheses. We further show that by using approximations of Schwarz Information Criterion and Bayesian Information Criterion we can use the classical estimates of the log of the maximum likelihood which are available from the estimation procedures used to implement the J test to obtain Bayesian posterior odds and posterior probabilities of the competing nested and non- nested specifications without having to specify prior distributions and going through the rigorous Bayesian computations.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 14637.

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Date of creation: Jan 2008
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Handle: RePEc:pra:mprapa:14637
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  1. Davidson, R. & Mackinnon, J. G., 1995. "Bootstrap Tests of Nonnested Linear Regression Models," G.R.E.Q.A.M. 97a25, Universite Aix-Marseille III.
  2. 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.
  3. Russell Davidson & James G. MacKinnon, 1980. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Working Papers 378, Queen's University, Department of Economics.
  4. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, July.
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