Testing for Unit Roots Cointegration in a Bayesian Framework

Classical tests for unit roots have been criticized of their unusual asymptotic theory leading to disconnected confidence intervals and their lack of power in small samples. Such critiques were initiated by SIMS (1998) who promoted a Bayesian approach to the question. Various papers then appeared, which took-up this idea. The present paper deals with the problem of testing for unit roots and cointegration in a Bayesian framework. The Bayesian approach is not exempt from criticism, as shown by PHILLIPS (1990). So great emphasis is given in this paper to the choice of an adequate parameterization for the model used for testing and of a prior density on the autoregressive parameter under test. These precautions are taken in order to get results which are as neutral as two hypotheses. Three empirical applications are provided concerning the tests of purchasing power parity theory, the presence of a unit root in GNP, and the French consumption function.