Modelling the Phillips curve with unobserved components

The relationship between inflation and the output gap can be modelled simply and effectively by including an unobserved random walk component in the model. The dynamic properties match the stylized facts and the random walk component satisfies the properties normally required for core inflation. The model may be generalized so as to include a term for the expectation of next period's output, but it is shown that this is difficult to distinguish from the original specification. The model is fitted as a single equation and as part of a bivariate model that includes an equation for Gross Domestic Product (GDP). Fitting the bivariate model highlights some new aspects of Unobserved Components (UC) modelling. Single equation and bivariate models tell a similar story: an output gap 2% above trend is associated with an annual inflation rate that is 1% above core inflation.