Measuring the Euro area output gap using multivariate unobserved components models containing phase shifts

This paper analyses the impact of using different macroeconomic variables and output decompositions to estimate the euro area output gap. We estimate twelve multivariate unobserved components models with phase shifts being allowed between individual cyclical components. As output decomposition plays a central role in all multivariate models, three different output decompositions are utilised; these are a first-order stochastic cycle combined with either a local linear trend or a damped slope trend, and a second-order cycle plus an appropriate trend specification (a trend following a random walk with a constant drift is generally preferred). We also extend the commonly used trivariate models of output, inflation and unemployment to incorporate a fourth variable, either investment or industrial production. We find that the four-variate model incorporating industrial production produces the most satisfactory output gap estimates, especially when the output gap is modelled as a first-order cycle. In addition, measuring phase shifts and calculating contemporaneous correlations between individual cyclical components provides a better understanding of the different gap estimates. We conclude that the output gap estimate in all models leads the cyclical components of inflation and unemployment, but lags those of industrial production and investment. Furthermore, the output gap estimates obtained from the four-variate model including investment present the longest leads-and-lags with respect to other cyclical components, implying that investment appears to be more of a leading indicator than a coincident variable for the euro area.