Difference between Granger causality and VAR(1)?

For my VAR(1) I get that the causal variable in each equation is statistically significant at 10%. But for Granger causality at 10% I only get that 1 variable granger causes the other and not the other way round. How is that possible?

Edit:

VAR:

x = 2y + u

y = 3x + u

Granger Causality:

x g-causes y

y does not g-cause x

So, why does y not g-cause x?

• Could you edit the post to include the output of your VAR model estimation and Granger causality test? Apr 19 '21 at 13:28
• This is not a model that could be used for testing Granger causality. You need a full VAR model, and this is not it; own lags are missing. (I hope you are using lagged variables on the right hand side, but your equations do not indicate that.) Apr 23 '21 at 19:18
• @RichardHardy its own lags were not significant at 10% therefore I didn't include them. Apr 23 '21 at 22:20
• The point is not to exclude insignificant variables from the model but to have them in and to test for their significance. This is how the Granger causality test works. Apr 24 '21 at 6:30
• @RichardHardy I don't get it. Why would we test for significance of something that we know is not significant? Apr 25 '21 at 22:23

If it is the same variable that is statistically significant at 10% in each equation, why are you surprised? For Granger causality of (1) $$x\xrightarrow{Granger}y$$ and (2) $$y\xrightarrow{Granger}x$$, you would look at different variables in different equations:
• For (1), you would look at lagged $$x$$ in the equation of $$y$$.
• For (2), you would look at lagged $$y$$ in the equation of $$x$$.