Re: st: help on granger causality

["Michael S. Hanson" <mshanson@mac.com>]

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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