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Granger causality test

gcausevar1var2[ifexp] [inrange],lags(#)[exog(varlist)regress]

gcauseis for use with time-series data. You musttssetyour data before using this commands; see help tsset.

Description

gcauseperforms a Granger causality test to investigate whether lagged values of a variable,var2, help in forecasting another variable,var1. SeeMethods &Formulasbelow.

Options

lags(#)is not optional. It specifies the number of lags ofvar1andvar2to include in the regression.

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

regressrequests the display of the output from the unrestricted regression.

Methods & FormulasGranger-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

ppy_t=c_1 + SUMa_i*y_t-i+ SUMb_i*x_t-i+ D_t+ u_ti=1i=1(

t= 1,...,T)where y_

tand x_trespectively refer tovar1andvar2ingcause's syntax diagram and D_tcorresponds to other variables that need to be controlled for, if any, specified atexog().pis determined bylags().The null hypothesis that x_

tdoes not Granger-cause y_tamounts to testing whetherb_i= 0 fori= 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

py_t=c_0 + SUMg_i*y_t-i+ D_t+ e_ti=1using 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_1which is distributed as a chi2(

p) variable.

ReferencesHamilton, J. D. (1994).

Time Series Analysis. Princeton University Press. 799 p.

AcknowledgementsThanks to Carol Miu for helpful comments.

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

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