I have the following regression equation (panel data): $Y = f(X_1, X_2, X_3, X_4)$
After obtaining CIPS and CADF statistics, $X_1$ results to be stationary for both intercept and intercept + trend, whereas $X_2$ is stationary only for intercept + trend. $X_3$ and $X_4$ are contrariwise non stationary in neither case.
Because of these results, I was wondering whether running a co-integration test makes sense (since if I'm not wrong, all the variables should be $I(1)$).
Also, I was wondering whether to proceed with using a first difference for $X_2$, $X_3$ and $X_4$, or only for $X_3$ and $X_4$.
Thank you very much.