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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?

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    $\begingroup$ What do you mean by identification Granger Causality? My overall impression is that you are dealing with pure Granger causality in this question. Also, be aware that the purpose of the model also determines the model selection strategy. E.g. if the purpose of your model is to test for Granger causality, then you would of course include the variables regardless of what the outcome of the test is. Besides, in model selection people also employ theoretical subject-matter considerations extra to the statistical tools. $\endgroup$ – Richard Hardy Jan 30 '18 at 9:20
  • $\begingroup$ @RichardHardy I edited my question. You seem to be answering it in an effective way. $\endgroup$ – EconJohn Jan 30 '18 at 16:09
  • $\begingroup$ I see this question as a special case of using significance testing for model selection. This has been discussed extensively in other threads and could be found by searching for the right keywords. (Sorry about not providing direct links.) It has also been discussed in Rob J. Hyndman's blog post "Statistical tests for variable selection". $\endgroup$ – Richard Hardy Jan 30 '18 at 18:22
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As far as I know, Granger causality on its own is not typically used in economics for model-building.

Cointegration is more widely used, where time series tests like the ADF and Johansen tests are used to identify cointegrated relationships between variables. (Note that other tests may be used, some more rigorous than others).

The two concepts are related: the presence of a cointegrated relationship implies Granger causality in one or both directions.

For a cointegrated series, you may then model the relationship using a VECM on differences or a VAR on levels. (I'll leave it as general as that, since it depends on what exactly you're modelling and various other properties of the series.)

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