I am making model to analyze migration from third countries (together 20) to Slovakia, Hungary, Poland and Czechia.
I created panel dataset for each pair of country. For example Ukraine-Slovakia, Ukraine-Hungary. This way I got 80 cross section ids. Time dimension is yearly and I have together 11 points of time.
My dependant variable is number of migrants from third countries. So basically each pair of countries has his own value for number of migrants. At the same time each of these pair of countries has several explanatory variables. I used ratio as follows:
HDI slovakia / HDI Ukraine
This way I am able to directly compare both countries. But I also have explanatory variables which are only for final country due to missing observations for third countries. For example I have social transfer which is only used for Slovakia without third countries. It means that the same value is multiple times in more cross sections ID.
My first question is, if this is correct way how to create panel data set and if I can use this dataset for Panel regression?
My second question is concerning the estimation of regression itself. It seems that everything is working properly when I try to estimate model using pooled OLS. All assumptions are correct and model seems fine after tests.
The problem starts when I try to estimate model using Fixed effects. It seems that diff_HDI is not correct. The values of coefficients of this variable are really high. HDI seems stationary after tests. Can it behave like this due to the fact that HDI is index which can have values from 0 to 1? Because for example, if I replace HDI with GDP (also calculated as ratio in pair of country) it seems that model is correct (no extreme coefficients). I cannot replace HDI with GDP due to the fact, that HDI is my hypothesis.
Please if anyone knows the answer, it would be very helpful!