Testing subspace Granger causality

The methodology of multivariate Granger non-causality testing at various horizons is extended to allow for inference on its directionality. Empirical manifestations of these subspaces are presented and useful interpretations for them are provided. Simple vector autoregressive models are used to estimate these subspaces and to find their dimensions. The methodology is illustrated by an application to empirical monetary policy, where a conditional form of Okun's law is demonstrated as well as a statistical monetary policy reaction function to oil price changes.