Hi everyone,

I was facing a question regarding the intention for including a quadratic variable in a fixed effects regression model. For instance, if there originally exists a quadratic relationship between two variables X and Y, we need to include a quadratic form of the variable to take that into account. However, in fixed effects regression model, the variables are demeaned, that is, the mean is subtracted from the original values and then the regression takes place. So, just in case of fixed effects, is there any need to enter the quadratic form because the quadratic relationship does not exist after the variable is demeaned. I would be thankful for a response!