We characterise the evolution of the U.S. unemployment-inflation trade-off since the late XIX century era via a Bayesian time-varying parameters structural VAR. The Great Inflation episode appears as historically unique along several dimensions. In particular, the shape of the ‘Phillips loop’–which is defined in terms of the impulse-response functions of inflation and unemployment’s deviations from equilibrium–was, during those years, clearly out of line with respect to the rest of the sample period for all structural innovations except money demand shocks. During the Great Depression, on the other hand, the Phillips trade-off did not exhibit any peculiar qualitative feature, so that, when seen through these lenses, the 1930s only stand out because of the sheer size of the macroeconomic fluctuation. The historical evolution of the Phillips trade-off exhibits virtually no connection with the evolution of the extent of trade openness of the U.S. economy. Although, by itself, this does not rule out a possible impact of globalisation on the slope of the trade-off in recent years, it clearly suggests that, historically, the evolution of the trade-off has been dominated by factors other than trade openness.