i want to know; that how to proceed with the mentioned data set to capture the long run and short run association in panel data, thank you
N=8 is almost certainly too small for either standard fixed effects or random effects. Does your T = 15 refer to monthly, annual, or quarterly series. Even 15 years is too small to capture the long run in many economic processes.
You need a lot more data.
You should pay more attention to your economic theory. This should lead you to a sensible model you can test for specification and estimate. With a small sample, you need to pay more attention to your theory.
You can try any of the methods recommended by Jamal Tikouk but you will probably find that you fail to reject any sensible hypotheses. (This means that due to your small sample size, your tests have low power)r. Can you not simply present your data graphically and illustrate your ideas in a more simple manner.
John C Frain thank you, now i have changed it to N=7 and T=30 and i want to run DOLS for it
I presume that you are familiar with
https://www3.nd.edu/~nmark/wrkpaper/PDOLS_Oxford_Bulletin.pdf.
It is very difficult to give you a definite answer without some knowledge of your underlying economic theory, the model that you wish to estimate, your data, and the hypotheses that you want to test. Try it and see do you get sensible results.
Your data is indeed limited to capture short and long run, but with T > N we generally go for time series strategies such as ARDL rather than panel fixed effects. The choice more specifically will depend on your research question.