I used Fixed Effects and First Difference on panel data but identified serial correlation from my continuous variables. I tried to include lagged dependent variable, and lagged independent variable to address the serial correlation; however i still have serial correlation. Also, looking at SAS fit diagnostic plot of residual vs quantile, i have a slight “s” shape curve likely indicating that the normality assumption is violated. Given my model has serial correlation and potentially violates normality assumption, does FE or FD still produce reliable estimated coefficients?

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