Econometrics question

GARY_BREEN

Could someone help me with this question im stuck with?

When the error terms in the data generating process are heteroskedastic, Weighted Least Squares is
more efficient than Ordinary Least Squares. Is this a violation of the Gauss-Markov Theorem? Explain
your answer.

Flamed Diving

GARY_BREEN wrote: »

Could someone help me with this question im stuck with?

When the error terms in the data generating process are heteroskedastic, Weighted Least Squares is
more efficient than Ordinary Least Squares. Is this a violation of the Gauss-Markov Theorem? Explain
your answer.

Actually, what level are you at?

GARY_BREEN

I'm in 3rd year of an Arts course economics my 2nd subject

Flamed Diving

GARY_BREEN wrote: »

I'm in 3rd year of an Arts course economics my 2nd subject

Ok, I recommend reading this book. It breaks down the jargon and explains things in an easier fashion.

http://wps.aw.com/aw_studenmund_useecon_5/

This doc should help for this question, as it is at undergrad level, even if the formatting of the document is awful.

http://www.shsu.edu/~icc_cmf/cj_789/weightedLeastSquares2.doc

The short answer is no. WLS should correct for the heteroskedastic residuals that the OLS regression suffers from. As a consequence, WLS should be BLUE, wheras OLS was LUE, in this case.

FD got their first but the first thing to do is to go and see what an efficient estimator is, then look up heteroscedasticty and see what effect this will have on an OLS estimatare in terms of its efficiency.

Then compare the above to an WLS estimate. The answer from this will give you the answer to the GM Theorem.

GARY_BREEN

Cheers guys!!!

Much appreciated!!!

Daithio

For these sort of questions I always found it really helpful to memorise the formulas for the estimators, estimated variance etc. Then you can deduce from the problem which ones will be affected.

With heteroskedasticity, depending on whether the variance is increasing or decreasing you will over or underestimate the variance. And if you've mis-estimated your variance, then you can't draw correct inferences. Your beta estimators are still unbiased, however, as the estimated variance isn't used to calculate them. You just won't be able to make inferences about their accuracy, as you need an accurate estimate of the variance to do this.