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help for gcause                                                        [P.Joly]
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Granger causality test

        gcause var1 var2 [if exp] [in range] , lags(#) [ exog(varlist) regress
                           ]


gcause is for use with time-series data.  You must tsset your data before using
this commands; see help tsset.


Description

gcause performs a Granger causality test to investigate whether lagged values
of a variable, var2, help in forecasting another variable, var1.  See Methods &
Formulas below.


Options

lags(#) is not optional.  It specifies the number of lags of var1 and var2 to
    include in the regression.

exog(varlist) for lack of a better name, specifies other conditioning variables
    which may enter the regression.  varlist may contain time-series operators
    which is particularly useful to add other lagged variables to the test
    regressions.

regress requests the display of the output from the unrestricted regression.


Methods & Formulas

Granger-causality tests are usually performed in the context of vector
autoregressions (VAR) or more specifically, individual equations within VAR
systems.  Individual equations in VARs are known as autoregressive distributed
lag (ADL) relationships and may be represented as

                 p                p
    y_t = c_1 + SUM a_i *y_t-i + SUM b_i *x_t-i + D_t + u_t
                i=1              i=1

    (t = 1,...,T )

where y_t and x_t respectively refer to var1 and var2 in gcause's syntax
diagram and D_t corresponds to other variables that need to be controlled for,
if any, specified at exog().  p is determined by lags().

The null hypothesis that x_t does not Granger-cause y_t amounts to testing
whether b_i = 0 for i = 1,...,p.  The rationale for conducting such a test is
simple.  If event X is seen as causing event Y, then event X should precede Y
(Hamilton, p.303).  The test statistic is calculated from the sum of squared
residuals (RSS) of the unrestricted equation (above) and restricted equation

                 p
    y_t = c_0 + SUM g_i *y_t-i + D_t + e_t
                i=1

using the formula for joint-significance tests given by

    F = (RSS_0 - RSS_1)/p
        ------------------
        RSS_1 /(T -2p -1)

which is distributed as an F (p,T -2p -1) variable.  RSS_0 (RSS_1) is the
residual sum of squares of the restricted (unrestricted) regression.

The above test in only valid asymptotically due to the presence of a lagged
dependent variable in the regression.  An asymptotically equivalent test is
given by,

    F_a = T (RSS_0 - RSS_1)
          -----------------
               RSS_1

which is distributed as a chi2(p) variable.


References

Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press. 799
  p.


Acknowledgements

Thanks to Carol Miu for helpful comments.


Author

Patrick Joly, Industry Canada
pat.joly@utoronto.ca


Also see

On-line:  help for test, vecar (if installed)