If both the dependent and independent variables are stationary, then there is no need for cointegration tests. You directly test for direction of causality.

Straight no. Cointegration is for non-stationary variables of same order.

Dear Fatemeh Dehdar,

The unit root test is not required for conducting the causality. The causality analysis can be conducted without unit root test. Unit root test actually help us to select the appropriate method of coefficients estimation e.g. All I(0) leads to the use of OLS and ARDL, All I(1) with co-integration leads to the use of VECM and ARDL, All I(1) with cointegration leads to the use of VAR, a mix of I(0) and I(1) leads to the use of ARDL. However, for causality analysis, we don't need series to be stationary.

Best wishes,

You need non-stationary variables to test cointegration. As per your result, all variables shows I(0) means they don't share a common trend, thus they aren't cointegrated. Therefore, you're not required to test the cointegration. 

Thank you everybody for your valuable answers. I really appreciate your help.

The IPS test does not control for contemporaneous correlation, and may therefore give misleading results, quite possibly rejecting unit roots when it should not. Before deciding your variables are I(0) base on the IPS test, I suggest you apply the CIPS test of Pesaran (2007), which does control for contemporaneous correlation. Pesaran, M.H., 2007. A simple panel unit root test in the presence of cross-section dependence. Journal of Applied Econometrics 22, 265–312.

Dear Prof. David O. Cushman, thank you for your valuable answer. I have missing values and unbalanced data set. Do you think that this test is working with my data set?

Fatemeh,

A slightly more general answer is that cointegration refers to a case in which a linear combination of 2 or more non-stationary series is stationary. If all your series are stationary to begin with, then any linear combination of them will also be stationary, so cointegration has no substantive meaning.

No. You could make causality test inmediately. You need make fixed effects or random effects in the estimation of the model.

Good luck

Well, if T > N, we should go for nonstationary panel data analysis that includes FMOLS, DOLS, PMG, Panel VAR, Panel VECM.

Cross-check with David O. Cushman advice if still at level then use gmm which is good method for level variables.

Dear Fatemeh,

No need to test the cointegration. You can run causality test directly.