a. In the fixed effects regression model, are the fixed entity effects, i, consistently estimated as n

Question:

a. In the fixed effects regression model, are the fixed entity effects, αi, consistently estimated as n → ∞ with T fixed?
b. If n is large (say, n = 2000) but T is small (say, T = 4), do you think that the estimated values of αi are approximately normally distributed? Why or why not?