RE is inconsistent (biased) if Xit and αi are correlated. Cov(Xit, αi) = 0 is required. This assumption is often violated.
We can test for RE vs. FE models: Hausman test H0: Cov(Xit, αi) = 0 (thus, RE is valid) If the null is rejected, we’d use FE.
因为random effect需要Cov(Xit, αi) = 0 ,如果违背的话,其估计值就会有偏
hausman test 就是利用这一点,如果Cov(Xit, αi) = 0 他等于零的话,我们就可以用re,否则,我们就用fe
明白了吗