Dear all,

The square term of my core predictor is positive in OLS & GMM, but it is negative in FE. The level term is always positive. All of them are statistically significant. What's more, I do not use LSDV or xtreg, fe but create the variables of deviation scores from within-group mean manually because my panel is unbalanced and the predictors are at different levels (macro & micro). I completely followed the instructions of Allison (2009) and Prof. Richard Williams's handouts. I believe my variables and approach are correct.

Can I understand that the relationship is like waves? Is this interpretation correct -- "when differences are examined starting from 0, there is a U-shaped relationship of convexity. While moving to estimating from the average level, the U-shaped relationship becomes concavity"?

Or it just simply implies that my results are inconsistent?