# st: RE: help on granger causality

 From "Gustavo Sanchez" <[email protected]> To <[email protected]> Subject st: RE: help on granger causality Subject help on granger causality Date Tue, 28 Jun 2005 11:58:12 -0500

```Rashmi <[email protected]> wants to know how to interpret the -vargranger-
output.  Specifically, Rashmi would like to interpret

>. vargranger
>    Granger causality Wald tests
>   +------------------------------------------------------------------+
>   |          Equation           Excluded |   chi2     df Prob > chi2 |
>   |--------------------------------------+---------------------------|
>   |          bp_level           lnpetrol |  14.108     4    0.007    |
>   |          bp_level          lndomcred |  6.0917     4    0.192    |
>   |          bp_level                ALL |  19.279     8    0.013    |
>   |--------------------------------------+---------------------------|
>   |          lnpetrol           bp_level |  5.9199     4    0.205    |
>   |          lnpetrol          lndomcred |  5.4121     4    0.248    |
>   |          lnpetrol                ALL |  10.121     8    0.257    |
>   |--------------------------------------+---------------------------|
>   |         lndomcred           bp_level |   49.78     4    0.000    |
>   |         lndomcred           lnpetrol |  7.3881     4    0.117    |
>   |         lndomcred                ALL |  57.215     8    0.000    |
>   +------------------------------------------------------------------+

Variable A is said to Granger cause variable B, if the lags of A can improve
a forecast for variable B.  In a VAR model, under the null hypothesis that
variable A does not Granger cause variable B, all the coefficients on the
lags of variable A will be zero in the equation for variable B.  A Wald test
is commonly used to test for Granger causality.

Each row of the above table reports a Wald test that the coefficients on the
lags of the variable in the "excluded" column are zero in the equation for
the variable in the "equation" column.  For example, the small p-value in
the first row is evidence that the coefficients on the lags of lnpetrol are
not jointly zero in the equation for bp_level, indicating that the evidence
favors the alternative that lnpetrol Granger causes bp_level.

As another example, the second row corresponds to the Wald test that the
coefficients on the lags of lndomcred in the equation for bp_level are
jointly zero.  In this case we cannot reject the null hypothesis that
lndomcred does not Granger cause bp_level.

--David                 --Gustavo
[email protected]      [email protected]

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```