Potential output, the natural rate of unemployment, and the Phillips Curve in a multivariate structural time series framework

We propose a bivariate structural time series framework to decompose GDP and the unemployment rate into their trend, cyclical, and irregular components. We implement Okun's law by a generalised version of the common cycles restriction allowing for a phase shift between the two cycles and add a price-wage block to the system. We estimate by maximum likelihood Phillips curve-type equations, where the particular cycles enter the wage and price equations in levels though the trends are modelled as non-stationary stochastic processes. The extended models provide an improved estimate of the current cyclical position, compared to univariate estimates and the HP filter.