Hi Muhammad;

In principle, do not use cointegration tests in the GMM method for Panel data.

The problem here is N>T. The only way I can think of is to impose strict constraints on model parameters, e.g. b(1) =b(2)=b(3); s(1)=s(2), etc. fewer time series parameters to estimate, less T is required. But I'm not confident how well this would work in practice. May depend on N, T, and characteristics of the data.

Truly, given a mixed unit root for the variables of I(0) and I(1), then, the appropriate panel cointegration according to Pesaran is Autoregressive Distributed Lags (ARDL). Further, ARDL is appropriate use when T>N and can also be use when both N and T are large. However, neither ARDL nor other panel cointegration estimators such as dynamic OLS (DOLS) and fully modified OLS (FMOLS) is applicable when N>T because of the degree of freedom insufficient, except both T and N are large sample sizes.

Lastly, we can test a panel cointegration if both T and N are large sample sizes.

Panel ARDL can be applied when NT, imposing restrictions on parameters might work but as Mr. Lawrence Raffalovich said, the efficiency of estimators would be questionable.