The study of Ireland (J Monet Econ 44:279–291, 1999) derives the restrictions imposed by Barro and Gordon’s theory of time-consistent monetary policy on a bivariate time-series model for US inflation and unemployment rate. The model is then estimated via maximum likelihood techniques using quarterly data from 1960q1 to 1997q2. In this study, we reproduce the central results of Ireland (1999) using the Metropolis–Hastings algorithm. Although we apply Bayesian instead of classical estimation, posterior parameter estimates are similar to maximum likelihood parameter estimates reported in Ireland (1999).