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Paneldata Analysis-Steps to follow

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Hello,
for my research I have to do a paneldata analysis and I would like to know if there are steps to follow in order to get valid and robust results. I have paneldata for a time period of 50 years and five independent variables.
What I did until now is the following:
1. xtreg y x i e z u, re robust (Random effects regression)
2.Xttest0 (Test if pooled OLS is appropriate)
3. Xtoverid (Test if fixed effects or random reffects to choose)
As result I got that I have to choose the fixed effects model. How can I check now for these points in my panel data in order to obtain unbiased results:

4. Multicollinearity
5. Homoscedasticity
6. Autocorrelation
7. Normally distributed error term
8. How can I decide whether or not to include time-fixed effects?
9. Is there something like a model specification test which says that my model is appropriate?

Thank you for your help

Christian


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