Question

Question 1 Suppose that the conditional variance is var(WXi) = (x), where i is a constant and h is a known function. The WLS estimator: O A. is 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. O B. is the same as the OLS estimator since the function is known. O C. is 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. OD. can only be calculated if you have at least 100 observations.

can you help with these questions and briefly explain how you got to the answer. it would be a big help thank for your time.

Answer 1

When conditional variance is Vart i lx) = xh (xi), which is not constant, et violates the homoskedastic assumption of oLs. In seich cases, we need to breans form the dependent as well as regressored in such a way that the transformed model satisfies homoshedastic assumption. Consider an example, where Var filx) = xx . Dividing Yi and X; by x, the original model [yi= B + P2 Xit Hi] becomes : Z = B 1 + B2 = P. Tai + B2 WX; + Vi [where de dahil Now var (vi) X:)=E( (M) *2.Xi -^ [constant] Hence, the conditional variance becomes constant with abere transformation. Hence, correct answer is (C), sie. the WLs estimaton obtained by first dividing the dependent variable and regresson by the square root of h and then regressing this modified dependent variable on the modified regressor using oLs. For hypothesis testing wing t-test, we need the condition that the estimators are normally distributed. While normal distribution assumption of error terms is not essential for the essention essentials for the estimators to satisfy BLU property, the normality of error term ensures the normality of estimators and hence fercilitates hypothesis testing. On the other hand, if we dreap homoshedastic assumption, the estimaters are still De bes' linear and unbiased, only minimum variance property is not met. But we may still be able to pen forem hypothesis text. Hence, the concrect option in (b), lie. the conditional mean of Mi given is zero, (xiitilial....n are iid dreaws from their point distribution and the conditional distribution of Migiven x unormal The first and second assumptions in all three options are ampray required. The above three options are different only in terms of third assumption on the basis of above discussion, the normality is required to inference purpose. To the errors are heteroskadastic, then the minimum variamee property of the estimators doesn't hold. Hence, the estimate though. one of the BLUE properties. They are still linear and unbiased Irrespective of randomness of regressors, the presence of heteroshadastic exrore violates minimum variance property. Hence, the usual ous estimate can't be und, rather we use wls. Also, the peop problem of over identification or under identification is applicable for simultoneaus equation systems, not for single equations. Although heteroskedasticity can be a problem in simult. oneaus equation systems, still it doein't have any role to play in terms of identification of equations. Hence, correct option is (a), rie. the OLS estimator is not the B BLUE