I am by far no expert on time-series but these are my thoughts for what it is worth.
Hopefully someone else could add to this to help you further on your way.
Does it make sense?
To me it doesn't really make a lot of sense.
When I do panel data analysis I base the choice of my variables on the results in the literature. There should be a theoretical basis for your model.
I would just use the Granger causality test as a method of analysis.
This paper might be of interest of you, where they use a Granger test in a panel data setting.
If the time series are non-stationary could I run the Granger CT or should I have to make time series stationary with some cointegration process before?
Yes you should make the time-series stationary as the VAR-model that you use to do the test assumes that the data is stationary.
If your time-series has a unit root, often first differencing will eliminate this unit root.
How can I do it with Stata?
First differencing can be done by using the D-command (don't forget to time-set your data first)
So if you have your time-series called gdp then you first difference it by:
gen gdpdiff=D.gdp
You can set up the VAR model by using the var-command.
For help on this simply type
help var
So the command for your VAR-model could be:
var fdi gdpdiff
Use varsoc to test the optimal length of the number of lags that need to be included. So in the command below I test the first 20 lags.
varsoc, lag(20)
The run your model with the desired number of lags, for instance
var fdi gdpdiff, lag(1/10)
After fitting the var-model you can do the Granger causality test using:
vargranger
How can I interpret the results?
I found this post quite useful on how to conduct and interpret a Granger causality test (it is done in R).
Be aware that the null hypothesis is one on non Granger causality.
If there is cointegration, then there is (100% percent surely) G-causality, but not vice versa.
For stationarity check, one MUST use Narayan-Popp 2010 non-stationarity test that takes the possible existence of structural breaks in the data into account.
You have 1113 observations after adjustments. This implies about 3-year period. During that period, it is highly likely that crises/interventions occured. These are encoded as structural breaks.
For cointegration check, (in the case of possible structural breaks) one MUST use Johansen-Mosconi-Nielsen 2000 critical values rather than Osterwald-Lenum 1992 critical values.
So, I am of the opinion that if you employ true methods, you will most probably end up with either of the following cases:
1. Your variables are not all I(1); hence, cointegration is impossible.
2. Your variables are all I(1); but, they are not cointegrated.
If I had your data in my hand, I would be able to say which one of the cases is valid.
Note also that one-to-one applying of Joyeux 2007 method via R revealed that Eviews miscalculate cointegration check. Hence, use R no matter what...
Best Answer
Question 1: no, you apply the cointegration test on the original series (that you believe to be non-stationnary I(1) ). Regarding selection of lag, one would usually base the choice on a criterion like AIC indeed.
Question 2: again, you would run the cointegration test on the original series. Note that Granger causality does not imply/require cointegration: 2 series can have Granger causality among themselves if they are both I(0), both I(1), or cointegrated.