Some researchers, for example, Koop (1992), and Sims (1988), advocated for Bayesian alternatives to unit-root testing over the classical approach using the augmented Dickey-Fuller test (ADF). This paper studies what Koop (1992) called the "Objective" Bayesian approach to unit-root testing. We apply the "objective" Bayesian unit-root test to a study of long-run purchasing power parity (PPP) for the post-Bretton Woods era. While the classical approach using the ADF test cannot reject the unit-root hypothesis, the Bayesian approach, on the other hand, suggests that the unit-root hypothesis is not strongly supported by the sample data. Rather, the trend-stationary hypothesis receives the highest posterior probability in all cases except for the Japanese yen/German mark real exchange rate where the stationary hypothesis receives the highest posterior probability. In two Monte Carlo simulations, however, we find that the "objective" Bayesian test have relatively low power in distinguishing between plausible alternatives, making it difficult to draw any conclusions concerning long-run PPP. We conclude that, at least for the "objective" Bayesian test, the Bayesian approach is not necessary better than the classical ADF approach.