To the best of my knowledge nothing can be done. It is very usual to make hypothesis on residuals in econometric methods, without checking them. Some sofwares can propose some solution but only with full panel data. (data for entire time series and cross section)
I suggest that you do a graph of a kernel-smoothed distribution of your residuals in order to see how they might depart from normal. If, as I suspect, the distribution has long tails, then consider using a robust procedure, such as quantile regression, as the method of estimation. I have pursued this extensively with cross-section data, and there is no reason that it cannot be used with panel data. Details can be found in Chapters 3 and 9 of the Third Edition of my book with H.S. Houthakker, Consumer Demand in The United States (Springer-Verlag, 2010).. Good luck in your research.