Suppose that the conditional variance is var(u_i|X_i)= λh(X_i)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 estimator in this case is 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. This is because the variance of the error term is proportional to h, and hence, by dividing by the square root of h, we can obtain a modified regression where the errors have constant variance. The choice A is incorrect as the fact that the function is known does not imply that the estimator will be the same as OLS. The choice B is incorrect as the number of observations is not related to the calculation of the estimator. The choice D is incorrect as dividing by h would increase the variance of the errors.

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

Suppose That the Conditional Variance Is Var(u_i|X_i)= λH(X_i)where λ Is