If the assumption that cov(x,e)= 0 is not true,what are the implications of least squares estimators?
A)still BLUE for all sample sizes
B)consistent and normally distributed in very large sample sizes
C)unbiased,but not BLUE for small samples
D)inconsistent;parameter estimates do not converge to true values regardless of sample size.

Question

Quizplus · Accepted Answer

The assumption that cov(x,e)=0 is a necessary condition for the least squares estimators to be unbiased and consistent. If this assumption is not true, the least squares estimators become inconsistent, meaning that they do not converge to the true parameter values even with very large sample sizes. Therefore, D is the correct choice.

If the Assumption That Cov(x,e)= 0 Is Not True,what Are