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From |
"Michael S. Hanson" <mshanson@mac.com> |

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]

"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.. 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 | +------------------------------------------------------------------+

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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**Follow-Ups**:**Re: st: help on granger causality***From:*Rashmi Shankar <rashmi@brandeis.edu>

**References**:**st: help on granger causality***From:*Rashmi Shankar <rashmi@brandeis.edu>

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