I need to use PVAR approach since I have multiple variables of interest that are endogenous in nature. Any suggestions about how to deal with the small N large T problem would be useful.
To derive informed insights into the estimations you intend to conduct, please share information on your research objective and specific variables you want to analyse, clearly stating the dependent variable versus independent variables, etc. Bearing in mind that panel VAR analysis is founded upon selecting the optimal lag order in both panel VAR specification and moment condition, please share your motivations for applying panel VAR – eg explore the endogenous interaction between variables, further examine causality to identify the direction of the link between variables, run impulse response functions (IRFs), etc. Such information would guide in providing informed inputs/suggestions.
Maximum likelihood (ML) estimators or approaches asymptotically equivalent to the Arellano and Bond (1991) estimator are considered better and strongly preferred in respect of finite sample performance when the number of cross-section observations (N) is small relative to time (T). The attached paper may provide additional great insights - All the best
For panels with T> N, I recommend the book TIME SERIES AND PANEL DATA ECONOMETRICS by Pesaran (2015). You can see the contents of the book at https://oxford.universitypressscholarship.com/view/10.1093/acprof:oso/9780198736912.001.0001/acprof-9780198736912?rskey=n1INi6&result=4