# Re: st: help on granger causality

 From "Michael S. Hanson" To statalist@hsphsun2.harvard.edu Subject Re: st: help on granger causality Date Tue, 28 Jun 2005 12:11:17 -0400

```On Jun 27, 2005, at 4:56 PM, Rashmi Shankar wrote:

```
Hi, all: After running a var in first differences, 4 lags, I use vargranger to
run a pair-wise causality test. The output is as follows. How do I interpret
the causality test result?

. var bp_level lnpetrol lndomcred if cnum==1,lags(1/4)
```	[output deleted]

```
```. 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    |
+------------------------------------------------------------------+
```
"Granger causality" tests -- or more correctly perhaps, Granger non-causality tests -- are statistical tests of "causality" in the sense of determining whether lagged observations of another variable have incremental forecasting power when added to a univariate autoregressive representation of a variable.

The test itself is just an F-test (or, as above, a chi-squared test) of the joint significance of the other variable(s) in a regression that includes lags of the dependent variable. For example: in your above results, at traditional levels of significance, one would reject the null hypothesis that 'lnpetrol' does not "Granger cause" 'bp_level'. On the other hand, at traditional significance levels, one would reject Granger causality of either 'bp_level' or 'lndomcred' for 'lnpetrol'. That is, neither of these variables appear to have incremental forecasting power for 'lnpetrol' once one conditions on 4 of its own lags.

It is very important to understand what Granger causality is _not_. First, it cannot establish causality in a theoretical sense. In a classic example, a rooster may "Granger cause" the sunrise. Second, Granger causality tests may be misleading if, for example, the processes determining the variables of interest involve expectations. Third, Granger causality is not a test for strict exogeneity. For these issues and additional critiques of the (mis-)use of Granger causality, consult any of the textbooks mentioned in the [TS] entry for -vargranger-, such as Luetkepohl (1993), pp. 35-43, Hamilton (1994), pp. 302-309, or Enders (2004), pp. 283-287 and 357-358.

-- Mike

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