Since you have the panel data set, have try to run f-test, BP-test and hausman test to see which model would be the best fit in your case?

Above test will help you to choose from OLS, FE and RE.

If you want, you also can proceed to more advance model, but depending on the nature of data. 

Actually, you can't choose a model, your data will choose its own best fit model. So try some pre-test of model specification. 

You need to go for traditional panel data analysis. You may choose among pooled OLS, fixed effect and random effect on the basis of Hausman test and Breusch Pagan LM test. You may also go for GMM for the robustness. 

Just pooled OLS because T is short but N is large.

Dynamic Panel Data analysis may be performeed

 One year  lag dynamic data  analysis  by  applying  OLS approach .  

If you are a novice using panel data, you can begin by running the basic panel models: Pooled OLS, Fixed Effects and Random Effects. Each model differs from the others depending on how we model country fixed effects (heterogeneity). However, we allow the data to decide which model is appropriate by applying appropriate specification tests: F-Test, Breush-Pagan Test and the Hausman Test. 

If you are an advanced user of panel data. You can go ahead and address panel data bias (endogeneity) by using either an Instrumental Variable estimator (Such as 2SLS) or the generalised method of moments (GMM). GMM is excellent in handling panel data bias but the theory behind it is a bit dense, so you will need above average statistical and econometric theory. 

you can use the traditional panel models.

Tatenda Maswedza

From my experience, I could say tjat the most appropriate model I found is Poisson pseudo maximum likelihood (PPML) estimator, that avoids heteroscedasticity in well-behaved error terms, deals with zero observations in the sample size, and yields consistent estimation with high goodness of fit