This paper replicates in a wider sense the unobserved components model of Laubach and Williams (Review of Economics and Statistics, 2003, 85, 1063-1070) to estimate the natural rate of interest (NRI) and investigates the role of model uncertainty. A stochastic Bayesian model selection procedure is employed to test the hypothesis of time variation in the NRI against a constant NRI. The model selection confirms time variation in the NRI as a result of changes in potential output growth, but other determinants of the NRI are found constant.