I am currently studying income inequality with a number of non-linear interaction and squared terms. While an initial fixed effects estimation looks good, there is evidence of non-stationarity and serial correlation in the idiosyncratic error term. I am unsure about how to go forward with my estimation because this is somewhat of a new field for me. Related papers use PGM or FMOLS estimation but I don't really get how to determine what is the appropriate way forward. I know it is difficult to provide advice without seeing the data, but did you encounter similar issues in research and how did you deal with it?
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