Panel Data Analysis, Help Urgently Needed! Fixed & Random effects, Fama MacBeth etc.


I have the following panel dataset: 11 years of annual data with a total of 250 observations. The panel is highly unbalanced, in the beginning years only few observations, while the last years make up the most of the observations. For instance, in year 1 I have only 6 observations, while in year 11 I have 50 observations.

I use a pooled panel regression with time and firm fixed effects for return estimation. Thereby, I account for many potential biases. My questions is whether the Fama Macbeth 2 stage regression model would work or would not work. What are the limitations? In specific, with respect to my data, why would it not work? Is there a certain amount of observations per time period that one needs?

The same question applies to the random coefficients model.

Also, what are the limitations of the approach that I use with both time and firm fixed effects?

Thanks for your help!