Unit roots and long-run causality: investigating the relationship between output, money and interest rates

Abstract

In this article we show that sufficient conditions for the unit roots found in the AR representations of time series to persist in bivariate or trivariate VARs amount to long-run non-causality restrictions among the variables involved. Furthermore, in first-order models long-run non-causality is also a necessary and sufficient condition for the autoregressive coefficients in the AR representations to be equal to the corresponding coefficients in the VAR. We also discuss causality inference in the presence of cointegration and show that the omission of an `important' variable results in invalid inference about the causality structure of the system, unless causality runs to the omitted variable but not vice-versa. These theoretical results can account for our empirical findings on causality between output and financial variables: whilst the bivariate analysis misleadingly suggests that causality runs primarily from M1 to output, the trivariate model implies that interest rates are a better predictor of output.