This all depends on your research objectives and your view of the data generating process. You might need to examine the stationarity of the data especially when you have a long time period (T). You can also check the cross sectional dependence and heterogeneity among the cross sectional units. If the variables are stationary at level and there's no evidence of Cross sectional dependence, You may proceed to using the conventional panel data methods such as fixed effect, random effect etc.

On the contrary, you may need to try methods like Augmented mean group(AMG), CCEMG, CS-ARDL, CS-DL.

All depending on your belief about if the long run differs from Short run, or short run is the same across countries but long run differs. If you are also believe there's non linearity or threshold effect, you can as well try the panel threshold regression..

If in a panel data set T>NT > NT>N (i.e., the time dimension is greater than the cross-sectional dimension), a fixed effects model or a dynamic panel model (such as the Arellano-Bond estimator) is typically appropriate to account for the time-series nature of the data and individual heterogeneity.

You could go the route of pooled mean group estimator or the newer version pooled bowley estimator by Pesaran if your N and T are relatively small. But for T > N in a relatively large enough data set, Pooled Mean Group is fine. Start with Cross sectional dependence test, Unit root, cointegtation test and then the PMG as compared to it MG, and DFE.

When T>NT > NT>N in panel data, where the number of time periods TTT is greater than the number of entities NNN, the Fixed Effects Model is often appropriate. This model accounts for individual-specific effects and is suitable when focusing on within-entity variations over time.