Granger test must be read as follows:
H0: endogenous variables do not Granger cause the dependent variable. In your case, consider the five tests for the first equation you have. The null hypothesis cannot be rejected for cases 1, 2 and 3 at the 1% C.I. Therefore, we cannot reject the hypothesis that pc_growth, pc_growth2 and unemp do not Granger cause inj_killed. The fifth test refers to the null that the coefficients of all the other endogenous variables are jointly zero. Since we reject it, we reject also the null hypothesis that pc_growth, pc_growth2, unemp and pop do not Granger cause inj_killed.
Unfortunately, Granger Wald test does not provide clear cut results, since the "Granger causality" should not be interpreted according to the normal meaning of "causality". In other words Granger causality does not imply real causality. I would say that Granger causality measures if statistically "A happens before B" rather than "A is the cause of B".
Hope this helps.
Emanuele Canegrati
> Date: Thu, 4 Sep 2008 12:19:43 +0100
> From: [email protected]
> To: [email protected]
> Subject: st: Interpreting A Granger Causality Test
>
>
> Hi
>
> I have run the following granger test but im not very familiar with using macro
> data, so i am unsure as how to interpret the results. Do the results suggest
> endogeneity? Should the lag of pc_growth be used rather than current
> pc_growth.
>
> . vargranger
>
> Granger causality Wald tests
> +------------------------------------------------------------------+
> | Equation Excluded | chi2 df Prob> chi2 |
> |--------------------------------------+---------------------------|
> | inj_killed pc_growth | 1.0731 2 0.585 |
> | inj_killed pc_growth2 | 4.8658 2 0.088 |
> | inj_killed unemp | 1.6206 2 0.445 |
> | inj_killed pop | 11.794 2 0.003 |
> | inj_killed ALL | 117.98 8 0.000 |
> |--------------------------------------+---------------------------|
> | pc_growth inj_killed | 6.78 2 0.034 |
> | pc_growth pc_growth2 | 10.664 2 0.005 |
> | pc_growth unemp | .21308 2 0.899 |
> | pc_growth pop | 6.8881 2 0.032 |
> | pc_growth ALL | 26.169 8 0.001 |
> |--------------------------------------+---------------------------|
> | pc_growth2 inj_killed | 11.296 2 0.004 |
> | pc_growth2 pc_growth | 1.1352 2 0.567 |
> | pc_growth2 unemp | .50434 2 0.777 |
> | pc_growth2 pop | 17.398 2 0.000 |
> | pc_growth2 ALL | 55.601 8 0.000 |
> |--------------------------------------+---------------------------|
> | unemp inj_killed | 2.1026 2 0.349 |
> | unemp pc_growth | .68276 2 0.711 |
> | unemp pc_growth2 | 8.7176 2 0.013 |
> | unemp pop | 8.6597 2 0.013 |
> | unemp ALL | 23.873 8 0.002 |
> |--------------------------------------+---------------------------|
> | pop inj_killed | 9.6661 2 0.008 |
> | pop pc_growth | .67368 2 0.714 |
> | pop pc_growth2 | 8.3789 2 0.015 |
> | pop unemp | 1.3414 2 0.511 |
> | pop ALL | 25.71 8 0.001 |
> +------------------------------------------------------------------+
>
> Any help would be much appreciated.
>
> Oli
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