Suppose that the conditional variance is var(ui|Xi)= λh(Xi)where λ is a constant and h is a known function.The WLS estimator is
A)the same as the OLS estimator since the function is known
B)can only be calculated if you have at least 100 observations
C)the estimator obtained by first dividing the dependent variable and regressor by the square root of h and then regressing this modified dependent variable on the modified regressor using OLS
D)the estimator obtained by first dividing the dependent variable and regressor by h and then regressing this modified dependent variable on the modified regressor using OLS

Question

Quizplus · Accepted Answer

The WLS (weighted least squares) estimator in this scenario is obtained by weighting the observations based on the inverse of the conditional variance, which in this case is 1/h(Xi). Therefore, we can modify the dependent variable and regressor by dividing them by the square root of h(Xi), yielding the transformed model: y* = y / sqrt(h(Xi)) and X* = X / sqrt(h(Xi)). We can then regress y* on X* using OLS to obtain the WLS estimator.

Suppose That the Conditional Variance Is Var(ui|Xi)= λH(Xi)where λ Is