If you are writing a paper, you usually use a fixed or double-fixed mode without thinking. However, if you are writing a big homework or the teacher asks for a test, you need to test the choice of mixed OLS, random effect and fixed effect.

The fixed effect model is called "fixed" because it can control the missing individual characteristic variables. In fact, the control method is to subtract the average value of individuals in the group or increase the virtual variables of individuals. It can be seen that the operation was written in two ways.

After deciding to use variable coefficient model, we still need to decide whether we should use random model or fixed effect model. In fact, from the theoretical analysis just now, we can know that random effect needs stronger hypothesis than fixed effect (because explanatory variables have nothing to do with individual missing characteristics), but in contrast, fixed effect loses more degrees of freedom (because more parameters need to be estimated), so we need to choose between the two.

In fact, it is also well understood that since individual characteristics are related to individuals and do not change with time, individual characteristics can be dealt with by certain means.