Persistence in macroeconomic time series: Is it a model invariant property?

This paper argues that persistence is not an invariant feature of a time series, but depends on the context in which the series is used: as the parameters of any dynamic model are defined relative to a particular information set, any change in the set of conditioning variables might affect the resulting estimates. We define persistence of a variable as the rate at which its autocorrelation function decays to zero, and show that inference about persistence of a variable is invariant to the addition of other conditioning variables only if those variables do not Granger-cause the variable of interest. Furthermore, we establish that measured persistence is a function of the model selected in a more fundamental way in the case of unstable systems. These findings suggest that, unless more restrictions derived from economic theory are imposed, issues such as the effectiveness of stabilisation policies cannot be settled empirically, and the debate between Keynesian and RBC theorists will remain inconclusive.