Hello
I try to make a regression, with panel data over a period of eight years, in which I will investigate the relationship between crime and migration. My regression equation is as follows where crime is the number of registered violent crimes (dependent variable). Migrants are the number of asylum seekers (independent variable, main variable of interest) and four possible control variables represented by X in a region i in year t are used.



My questions are:
1) I have seen in papers that make a fixed or first difference regression often use e.g. year dummies and/or region dummies. In other papers they are given in the tables as fixed effect instead of dummies. What is the difference between e.g. a year dummy and a year fixed effect?

2) How important is it to include in such an estimation e.g. year dummies? or should one include year dummies and also region dummies?