Granger Causality Tests with Panel Data

[sanjeev]

Can we also estimate a Vector error correction model in a panel framework the way it is done in time series?

Thanks.
Regards.

[sanjeev]

Dear Tom,
I got following output when I ran granger causality tests.
Heterogeneous Panel Causality Test
Chi-Squared(7)= -27.329732 with Significance Level NA

1.000000 0.175 0.67536
1.000000 0.965 0.32605
1.000000 2.642 0.10410
1.000000 0.528 0.46743
1.000000 5.892 0.01521
1.000000 1.153 0.28300
1.000000 1.785 0.18149
OVERALL -27.330 NA
I can't figure out the reason.Could you please help?
Can it happen because of unbalanced data?

Thanks and Regards.

[TomDoan]

You clearly made a mess out of the program. You'll have to post what you did.

[sanjeev]

Please see the following:
Here Prod is my dependent variable while hk is the independent variable. I have more variables in my system and I am getting the right answers in case of all variables except for two variables,hk being one of those.

sweep(group=%indiv(t),var=hetero)
# dprod
# constant dprod{1 to p} dhk{1 to p}
compute loglunr=%logl,nregunr=%nregsystem
sweep(group=%indiv(t),var=hetero)
# dprod
# constant dprod{1 to p}
compute loglres=%logl,nregres=%nregsystem
cdf(title="Heterogeneous Panel Causality Test") chisqr 2.0*(loglunr-loglres) nregunr-nregres
compute jointtest=%cdstat,jointsignif=%signif
*
* Individual causality tests. The individual log likelihood ratios sum
* to the joint test.
*
report(action=define,title="Panel Causality Test")
do i=1,7
linreg(noprint,smpl=%indiv(t)==i) dprod
# constant dprod{1 to p} dhk{1 to p}
exclude(noprint)
# dhk{1 to p}
compute lr=log((1+p*%cdstat/%ndf))*%nobs
report(row=new,atcol=1) id(i) lr %chisqr(lr,p)
end do i
report(row=new,atcol=1) "OVERALL" jointtest jointsignif
report(atcol=2,tocol=2,action=format,picture="*.###")
report(atcol=3,tocol=3,action=format,picture="*.#####")
report(action=show)

[TomDoan]

DHK is probably missing some observations.

[sanjeev]

Thanks Tom for your reply! I had also thought so.But then does it imply that this test can't be conducted if we have missing observations for a certain cross-section?
Is the same thing also true for panel cointegration and FMOLS?

Thanks.
Regards.

[TomDoan]

You just have to be careful. The overall test is done using restricted and unrestricted regressions, and in this case, the unrestricted regression includes a variable which knocks data points out of the sample. You have to make sure both those regressions use the same set of entries. The single equation tests are Wald tests so they start out by doing the unrestricted regression and never actually try to do a separate restricted regression. You can either construct a SMPL series which gets common ranges for the restricted and unrestricted SWEEP instructions, or you can add up the individual test statistics to get the overall test statistic.

The Pedroni tests and procedures are all designed to work with unbalanced data.

[sanjeev]

Dear Tom,In continuation with my previous two mails,if I have missing observations for some variable in the model and I run a multivariate model and then conduct granger causality tests,then will the estimations be done for the maximum possible time period for each variable for each individual?
Also,can we also test for the significance of the error correction term along with lagged coefficients of the variable of interest?

Please reply!

Thanks.
Regards.

[TomDoan]

Dear Tom,In continuation with my previous two mails,if I have missing observations for some variable in the model and I run a multivariate model and then conduct granger causality tests,then will the estimations be done for the maximum possible time period for each variable for each individual?

The default behavior is to run any regression over the maximum number of entries possible, so yes.

Also,can we also test for the significance of the error correction term along with lagged coefficients of the variable of interest?

Yes.

[sanjeev]

Dear Tom,In continuation with my previous two mails,if I have missing observations for some variable in the model and I run a multivariate model and then conduct granger causality tests,then will the estimations be done for the maximum possible time period for each variable for each individual?

The default behavior is to run any regression over the maximum number of entries possible, so yes.

Also,can we also test for the significance of the error correction term along with lagged coefficients of the variable of interest?

Yes.

Could you please guide me on that?

[TomDoan]

Run the regression, do an EXCLUDE instruction. In a VECM equation, everything has standard asymptotics.

[sanjeev]

Thanks for your reply! But I am sorry,I don't know how to include the error correction term in the original regression itself.So,could you please help me a bit further as to what form of regression I should run first?

Thanks.

[sanjeev]

Dear Tom,
Can we actually use our results on panel granger causality tests along with panel group-mean FMOLS to show robustnness of our results?That is,can the two results be complementary to each other?

Regards.

[TomDoan]

Dear Tom,
Can we actually use our results on panel granger causality tests along with panel group-mean FMOLS to show robustnness of our results?That is,can the two results be complementary to each other?

FMOLS is an estimator, not a test, so I have no idea what you're asking. Can you do both of them on one data set? Yes. However, I'm not sure what value a simple causality test is going to have if you think the series are cointegrated. If they're cointegrated, one has to cause the other at a minimum and typically there's causality both ways. There's no real difference with it being a panel data set. If you don't understand how cointegration and error correction models work, you should study it in the standard time series literature.

[TomDoan]

Thanks for your reply! But I am sorry,I don't know how to include the error correction term in the original regression itself.So,could you please help me a bit further as to what form of regression I should run first?

Do you know how an error correction model is done? Differences on lagged differences and a lagged error correction term?