Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

تمرين 18

Suppose that Y i = X i , + u i where ( u i ,-, X i , ) satisfy the Gauss-Markov conditions given in Equation (5.31).
a. Derive the least squares estimator of and show that it is a linear function of Y i ,..., Y n.
b. Show that the estimator is conditionally unbiased.
c. Derive the conditional variance of the estimator.
d. Prove that the estimator is BLUE.