# When only half of the independent variables are non stationary, does it make sense to run a cointegration test?

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.

Kodi