Estimating Long-Run Relationships between Observed Integrated Variables by Unobserved Component Methods

A regression including integrated variables yields spurious results if the residuals contain a unit root. Although the obtained estimates are unreliable, this does not automatically imply that there is no long-run relation between the included variables as the unit root in the residuals may be induced by omitted or unobserved integrated variables. This paper uses an unobserved component model to estimate the partial long-run relation between observed integrated variables. This provides an alternative to standard cointegration analysis. The proposed methodology is described using a Monte Carlo simulation and applied to investigate purchasing-power parity.