Introductory Econometrics 4th Edition by Jeffrey Wooldridge

تمرين 5

Let denote the sample average from a random sample with mean and variance 2. Consider two alternative estimators of : W 1 = [(n-1)/n] and W 2 = /2.
(i) Show that W 1 and W 2 are both biased estimators of and find the biases. What happens to the biases as n Comment on any important differences in bias for the two estimators as the sample size gets large.
(ii) Find the probability limits of W 1 and W 2. {Hint: Use Properties PLIM.1 and PLIM.2; for W 1 , note that plim [(n-1)/n] = 1.} Which estimator is consistent
(iii) Find Var(W 1 ) and Var(W 2 ).
(iv) Argue that W 1 is a better estimator than if is gcloseh to zero. (Consider both bias and variance.)