squares of a variable or demeaned product of the quadratic for fixed effect xtreg?

[Roxani Nikolaide]

I wanted to ask if for panel data with fixed effect is wrong to put in the regression the squares of some variables and not the demeaned product of the quadratic. Can I put just the squares of the variables without first removing the averages?

[Carlo Lazzaro]

Roxani:
no, as demeaning is the way the -fe- estimator works.

[Jeff Wooldridge]

I took the question to be more of should (x(i,t) - xbar)^2 be included, where xbar is the average over the entire sample, or is it okay to use just x(i,t)^2. It depends whether x(i,t) = 0 is a possible, or interesting, value. If not, I would center. But this is not demeaning by unit i. That demeaning is done to remove the fixed effects. The demeaning before squaring is to force the coefficient on x(i,t) to be the average marginal effect.