[Luca Huber]

I was absolutely not sure: First, the hausman test told me to take RE - then, the results looked not bad (big R2 and signifikant effects). Now, I did the regression without the interaction term and I have to use fixed effects --> very low R2. That's why I made the cross sectional analysis first:

The residuals of the dependent variable look good (normalish). But the only (control)variable which has a significant influence on unemployment ist gdp_growth. So can I say that after my model, there is no evidence for an influence of immigration on unemployment (in the year for which I did the regression)?
Next step will be to include the interaction term (policy) in the regression, I think.

[Luca Huber]

And for this first panel analysis, do I have to check for homoscedasticity and multicollinearity as well? I know how to make that in the cross sectional case (hettest and imtest and vif)m but how can I check that in the Panel Regression?