On the J-test for nonnested hypotheses and Bayesian extension

Surekha Rao (skrao@iun.edu), Moheb Ghali and John Krieg

MPRA Paper from University Library of Munich, Germany

Abstract: 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.

Keywords: specification testing; non-nested hypotheses; Bayes factor; Bayesian Information Criteria; Marginal likelihood (search for similar items in EconPapers)
JEL-codes: C01 C11 C12 C52 (search for similar items in EconPapers)
Date: 2008-01
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