Generalised Least Squares (GLS) Theory

[@prashant0104]

I cannot describe how grateful I am for your lectures. It's so clearly explained, and so well organized. This one sheet explains to me in a way that an entire chapter cannot. Thank you so much professor!

[@theseesztrzkoniczky9909]

I am a french student, your explanations are clear and smooth. I really like your work, +1 follower :)

[@stubill9298]

Very clear explanation as usual, thank you very much Ralf!

[@simobres]

Perfect explanation. Thank you so much

[@furkanbostanci8882]

Thank you very much ! It helped me a lot understand the logic behind it, very informative and explains a lot

[@bennetjanssen4037]

Excellent video! Best explanation so far 👌

[@simone24414]

I always wonder why good professors are always on youtube and not at Uni :D Thanks a lot for this video!

[@62294838]

I gave this question a serious thought in the shower for a while. The answer lies, of course, and it has to be, in the lack of competition at schools/universities. I know it's a boring answer, an answer that any economist would give, very predictable. But it's indeed undeniable that professors/lectures are not selected by students to teach, and have no power to substitute the poorly performed for the better.
But on TH-cam, it's a level playing field. Everyone faces the crude reality to have their video, when poorly made, sunk to the bottom; but, if well made, popularly circulated and reached a wider audience. This automatically performs the function to select the wheat from the chaff. The poor explainer stands not even a chance to have their video viewed. The number of views are now the new BoxOffice performance for professors/lecturers. What we are watching now are lectures that are explained by people who not only know their stuff but also are good presenters. Usually, one in a million chance he/she would be your teachers. But now we can easily listen to them at home.
This is the so called second printing revolution, with the first one brought about the 100 years War as a result of Protestants, with their newly printed bibles, having a different interpretation of God to the Catholicians. It's only these several years that people such as Jordan Peterson, Joe Rogan, Chris Do, Dr. Drew Pinsky come into fame for their intellectual offering, via speaking, not writing. In Econometrics, you for certain know another god-like chap called Ben Lambert.
Were you to be born 10 years earlier and doing an Economics master at an Ivy League, you would be dead by now. But the criteria these days to knowledge that were usually forbiddingly unwelcoming and difficult in the past is now becoming more available and easier as the mode of learning has revolutionised, thanks to the internet, hence, TH-cam.
Don't know why I am typing this. Enjoy

[@ttrn1]

@@62294838 Schools rankings such as US news are not based heavily on teaching quality, they focus on things like selectivity and research reputation. There is a free market, student select which college to attend, but most students will base their choice on those rankings that don't correlate to teaching quality. The result is that there is no financial reward to colleges for having high quality teaching. In a free market if you are not rewarded for good teaching but good teaching incurs a cost the obvious solution is to not fund good teaching.

[@kim8u96]

This is really well explained

[@geraldmashange985]

Thank you for the clear explanation.

[@antimoustique3175]

in (3), shouldn't the second Omega term be inverted as well as the first one ? if not, E(Bhat) is different from the true value of the parameter B.

[@ncwbr]

Yes you are right, I noticed that too. E(beta hat gls) and Var(beta hat gls) wouldn‘t be correct otherwise, which would destroy the whole purpose of gls.

[@AJ-et3vf]

Awesome video! Thank you!

[@shubhamrana7277]

Thanks for the video sir, I have one doubt GLS is also used when there is autocorrelation then variance covarianvr matrix would have non zero non diagonal terms then how will we proceed??

[@emanuelmuemadominic7288]

Very clear explanation, thanks.

[@LukasMaicher]

Incredibly well explained, thanks so much! As you denoted the GLS estimator in the end you did a minor mistake. The Variance-Covariance matrix is inverted in the brackets and also the second time.

[@byrusmx]

So this mean that given:
y = a + b1X1 + b2X2
the new model must be calculated as:
y/sd(y) = a/sd(a) + b1*1/sd(x1) + b2*1/sd(x2)
That is, observations are divided by the associated standard deviation? (e.g. observations for X1 are divided by the standard deviation for X1, observations for X2 are divided by sd for X2, and so on)
I'm really confused about this, hope you can help me.

[@rajudey1673]

Thank you for the nice lecture...one thing...If sigma i's are unknown parameters then how can we proceed to get an efficient estimator of beta as well as sigma i's

[@hadins1406]

where did he get the definitions at 10:05?

[@RalfBecker]

they are at 7:20

[@saudhayat959]

Sir, In my model the dependent variable is stock price and I have 7 independent variables. What will be the GLS equation for this model?

[@yuemengxu1882]

Thanks for the video! Omega should be sigma squared*I, not sigma * I -squared

[@RalfBecker]

oh yes, you are absolutely right! well spotted. Mistake at 0min 31sec, should read \sigma^2 * I

[@drdirk]

Thanks for the Video Ralf, but isn't this only a special case of GLS, namely "weighted least squares"?
I am pretty new to the topic, but as far as I understood your \Omega should be given by the covariance matrix, meaning that you approximated the off-diagonal elements while setting them to zero.

[@jambob7309]

Thank you sir.

[@eri6219]

Thank you so much! Studying for my stats exam right now lol

[@benediktfrey8018]

Genial!

[@27ajmirkhan61]

thank you sir

[@ositaonyejekwe]

You made a mistake in your lecture. towards the end of your derivation you should have Omega Inverse * Y and not just Omega * Y