Dear all,

I am working with a cross-section cross-time panel dataset with N = 15 (country) and T = 23 (year), with percentage of right-wing votes as the independent variabel and citizenship law score as the dependent variabel, plus four control variabels. The dependent variable is lagged (one year ahead) to ensure X being ahead in time of Y.
I have non-stationary panels and therefore apply first differencing to my regression model to solve this problem. I also deal with heteroskedasticity and serial correlation (however not serial correlation when I apply first differencing to the regression model and run the test again).

I have a couple of questions on how to proceed, which I cannot seem to solve by reading, so I hope you can help out.

1) First of all, is it correct to assume there is no longer serial correlation because I applied first differencing to the model, and I therefore do not need to handle it by applying -cluster(country_var)- to my estimation model?

2) Is it possible to apply both first differencing AND fixed effects estimation to the model? I have read in multiple books, e.g. Wooldridge (2014), that either fixed effects estimation or first differencing can be applied to handle the same type of problems/difficulties with panel data, but I can't seem to find anywhere it states that it is impossible to use both in the same model. So, is it actually possible to apply first differencing to handle the stationary problem, but also apply fixed-effects estimation to the same model? Or is this simply just meaningless?

My apologies if the questions seems pointless, I am not great with statistics and this is quite advanced compared to what I have been taught so far academically.

Best regards,
Laura