Re: [Gretl-users] p-values tests
On Wed, 4 Apr 2012, alexkakashi(a)libero.it wrote:
I have analyzed a trivariate system X,Y,Z. In particular I have
studied
Granger causality from X to Y. I have the following result:
ols Y const Y(-1) X(-1) Z(-1)
# Granger-type restriction for p=1
restrict
b[1,3] = 0
end restrict
Statistica test: F(1, 51) = 1,88323, con p-value = 0,175973
Then, I have also applied this command using VAR model (estimated by OLS):
sys <- system
equation Y const Y(-1) X(-1) Z(-1)
equation X const Y(-1) X(-1) Z(-1)
equation Z const Y(-1) X(-1) Z(-1)
end system
# Granger-type restriction
restrict sys
b[1,3] = 0
end restrict
estimate sys method=ols
Test F per i vincoli specificati:
F(1,153) = 1,88323 [0,1720]
The test statistics are equal, but the p-values are slightly
different.
Yes: in the second case the restriction is being treated as
applying to the entire system, and the F-distribution to which
the test is referred has greater degrees of freedom in the
denominator -- which is actually wrong in this case since the
regressors are identical across the equations and the
estimator is equation-by-equation. We should probably be using
the chi-square form of the test to avoid this dof problem.
But note that if you use the "var" command you get the same
p-value for the Granger F-tests as if you do single equation
OLS -- since "var" knows about the structure of VARs.
Allin Cottrell