Bayesian routes and unit roots: de rebus prioribus semper est disputandum

This paper provides detailed responses to the following eight discussants of my paper `To criticize the critics: an objective Bayesian analysis of stochastic trends': Gary Koop and Mark Steel; Edward Leamer; In-Moo Kim and G. S. Maddala; Dale J. Poirier; Peter C. Schotman and Herman K. van Dijk; James H. Stock; David DeJong and Charles H. Whiteman; and Christopher Sims. This reply puts new emphasis on the call made in the earlier paper for objective Bayesian analysis in time-series; it underlines the need for a new approach, especially with regard to posterior odds testing; and it draws attention to a new methodology of Bayesian analysis developed in a recent paper by Phillips and Ploberger (1991a). Some new simulations that shed light on certain comments of the discussants are provided; new empirical evidence is reported with the extended Nelson--Plosser data supplied by Schotman and van Dijk; and the new Phillips-Ploberger posterior odds test is given a brief empirical illustration.