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?



   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?

  • $\begingroup$ Could you edit the post to include the output of your VAR model estimation and Granger causality test? $\endgroup$ Apr 19 '21 at 13:28
  • $\begingroup$ 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.) $\endgroup$ Apr 23 '21 at 19:18
  • $\begingroup$ @RichardHardy its own lags were not significant at 10% therefore I didn't include them. $\endgroup$ Apr 23 '21 at 22:20
  • $\begingroup$ 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. $\endgroup$ Apr 24 '21 at 6:30
  • $\begingroup$ @RichardHardy I don't get it. Why would we test for significance of something that we know is not significant? $\endgroup$ 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 $x$.
  • $\begingroup$ I edited my question to explain what I meant. $\endgroup$ Apr 23 '21 at 17:38

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