Consider the model yit b1i b2xit eit (a) Show that the fixed effects estimator for b2 can be written as b^2; FE

Consider the model yit ¼ b1i þ b2xit þ eit

(a) Show that the fixed effects estimator for b2 can be written as b^2; FE ¼

N i¼1

T t¼1

ð Þ xit xi ð Þ yit yi

N i¼1

T t¼1

ð Þ xit xi 2

(b) Show that the random effects estimator for b2 can be written as b^2; RE ¼

N i¼1

T t¼1 xit a^ xi x
x   yit a^ yi y
y  

N i¼1

T t¼1 xit a^ xi x
x  2 where y and x are the overall means.

(c) Write down an expression for the pooled least squares estimator of b2.

Discuss the differences between the three estimators.