Unit roots versus other types of time heterogeneity, parameter time dependence and superexogeneity

This paper stresses the restrictive nature of the standard unit root/cointegration assumptions and examines a more general type of time heterogeneity, which might characterize a number of economic variables, and which results in parameter time dependence and misleading statistical inference. We show that in such cases ‘operational’ models cannot be obtained, and the estimation of time-varying parameter models becomes necessary. For instance, economic processes subject to endemic change can only be adequately modelled in a state space form. This is a very important point, because unstable models will break down when use for forecasting purposes. We also discuss a new test for the null of cointegration developed by Quintos and Phillips, which is based on parameter constancy in cointegrating regressions. Finally, we point out that, if it is possible to condition on a subset of superexogenous variables, parameter instability can be handled by estimating a restricted system.