What should I do when I found out that my variables are stationary in first differencies? Should I estimate model in differencies? How unit root is related with cointegration? Thx for answers.
Estimating a model in differences is one way to proceed. A unit root doesn't itself indicate cointegration is possible. How it works is this;
If your dependent and independent variables share a common stochastic trend, they may cointegrate. Two series cointegrate in case of a genuine long run relationship between the two, i.e. they are both determined by the same DGP. If this is the case, and the vars do cointegrate, then, given y = I(1) and x = I(1), you can set a value of B such that (Y-BX) = I(0). B is your cointegrating vector. For this to be a possibility, BOTH your dep.var and indep.var(s) must be of the same order of integration, i.e. they must contain the same number of unit roots. Cointegration requires unit roots, unit roots don't require cointegration.
For panel cointegration tests, look at those by Pedroni and by Westerlund.