How exactly does identification of Granger Causality (or lack of) between variables affect my decision for what variables to include in my VAR or VECM model?
The motivation behind the question is such:
I've ran a couple of standard macroeconometric models testing the impact of interest rate on Inflation rate along side some other variables, and have rarely found granger causality betweeen any of the variables.
Yet I see them included in a number of models. specifically in the bank of canada's paper The M1 Vector-Error-Correction Model: Some Extensions and Applications.
Why is this the case?