T < N or T>N is appropriate when you are making choice in difference and system GMM. In order to make a choice between Fixed Effect and Random Effect you have to apply Hausman test. Hausman test will direct you that either FE or RE is more appropriate for you analysis.

Thanks Haq, but if my memory does not fail me the difference or system-GMM estimators work best in "large N, small T" situations. For instance, N=70 and T=5. In my case both N and T are large. Hence, the choice between FE and RE may be appropriate.

Yes, the fixed effect model is appropriate for such an estimation. The fixed effect model is commonly used to analyze large N, large T panel data in sociology. It is also used to estimate panel data models for long panels where the number of time periods is relatively large.

Fixed effects estimation of a static model with robust or panel corrected standard errors is commonly used to model large N, large T panel data1. However, this approach is biased and inconsistent in the presence of dynamic misspecification, slope heterogeneity, and cross-sectional dependence. There are other methods that can be used to estimate models with large T and large N panel data. For example, semiparametric models with unobserved individual and time effects can be used.

Deeply appreciate you prof Chuck A Arize for the beautiful suggestion. Please can you recommend me any paper that used such an approach.