I am analyzing a panel dataset (n=1050, T=14) with individual effects modeled as fixed effects. The DV is a count variable. The DV and the independent variables (IVs) are non-stationary. After first differencing both the DV and the IVs, I have tested that they are all individually stationary (i.e., using xtunitroot in Stata to test for unit roots). My questions:
1) Do I need to conduct co-integration tests given that the individual series are stationary now (after differencing)? What's the benefit of the error correction model specifically? I have read that it gets at the long-run relationship but none of the books gave me a good example to help me decide if the short-run relationship is okay in my case.
2) Most of the books talking about the unit root tests and cointegration are focused on linear regressions. How do we do these tests with count variables?