Hello!
For my panel data in STATA I am using a set of 6 countries for a time period of 20 years. I am examining the effect of FDI (% of GDP) on economic growth (GDP pc), and including some control variables which are backed up by economic literature (e.g. years of schooling/ physical investment etc etc). I wanted to run the OLS, FE and RE models, then check which one is most applicable by using the Hausman Test. Nonetheless, what I am noticing is that there seems to be a non-linear relationship between the dependent variable and FDI (% of GDP). Would that mean that I should include a quadratic term of FDI too?(FDI^2). My aim was to have a simple double log-linear Cobb-Douglass production function, meaning that GDP pc is transformed to a natural log, as well as all other variables. Would this mean that when I now add the squared term into the regression it doesn't make much sense anymore?
I cannot seem to find anything on a bell shaped relationship in panel data analysis in STATA (especially in regard to running FE models), help would be appreciated!!

*(Moreover, as well as having an overall effect on the 6 countries combined, what is the best (and easiest) STATA command/method to check the effect of FDI (with the control variables) on economic growth for the individual 6 countries?? Is including country dummies a way to go?)*

Thank you so much in advance!
Marti