Gauss-Markov assumptions part 1
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- Опубліковано 27 тра 2013
- This video details the first half of the Gauss-Markov assumptions, which are necessary for OLS estimators to be BLUE.
i, in this video I am going to be talking about the Gauss-Markov assumptions in econometrics, and what their significance is. So, the Gauss-Markov assumptions are a set of criteria which were first created by the mathematicians Carl-Friedrich Gauss, and Andrei Markov, which if they are upheld, then that says something about our ability to use Least-Squared estimators on the sample data. Well, it says that those Least-squares estimators are in fact BLUE. But, what does it mean for an estimator to be BLUE? Well, it means that there are no other linear unbiased estimators which have a lower sampling variance than that particular estimator. So, I can illustrate this graphically, imagine I have a sampling distribution of one estimator which looks like that. And then I have another one which has the same sort of centre as the first one, except that it is slightly steeper towards the centre of the distribution. So, assuming that both of these are unbiased, so they are both centered around the true population parameter, we can see that the second estimator has a lower sampling variance that the first. Well, that means that, more often than not when I use my Least-squared estimators - when I apply my Least-squared estimators to the sample data, they are going to more often than not provide estimates of the true population parameter 'beta p', which are closer to 'beta p' than I would have got by using the first type of estimator. So, that's the significance in econometrics of the Gauss-Markov assumptions. But, what are the Gauss-Markov assumptions? There's no particular order to the Gauss-Markov assumptions, but I am going to label them here so that means that I can refer to them in the future. The first Gauss-Markov assumption has to do with the population process, so assuming that there is some population process which connects wages with the number of years of education, although education doesn't exactly determine wages, because there's some sort of error term here. This is an example of a model which is linear in parameters, so that means that it's linear in alpha and beta. So this is the first Gauss-Markov assumption which says that our population process has to be linear in parameters. Note that if I had this type of model where I had wages equal to alpha times beta times the number of years of education plus alpha...well just alpha on its own - this would be nonlinear in parameters because this implies some sort of multiplicative effect between alpha and beta. Or if I had beta-squared here, that would also be nonlinear in parameters. Note that however that being linear in parameters does not mean that I cannot have a variable in our model which is nonlinear. So, actually just having education squared in our model, rather than just education, that is absolutely fine under the assumption of 'linearity in parameters'. It just means that I am not allowed to have a model which has nonlinear parameters within it. So, that's the first Gauss-Markov condition - the second condition is that we have a set of sample data - x and y which are a random sample from the population. So what does that actually mean? Well, it means that within our population, a random sample occurs if each individual within our population is equally likely to be picked, when I take the sample. That's what we mean by a random sample. But, it also implicitly means that not only are each person in the population equally likely to be picked, but it means that all of our points come from the same population. So they come from the same population process which in this context might be wages being equal to alpha plus beta times education. plus some error. The third condition is perhaps the most important of the Gauss-Markov conditions, which is the zero conditional mean of errors. So what does this actually mean? Well mathematically it means that the expectation of our error term in our population given our x term, which in this case is education has got to be equal to zero. Well, what does this mean practically? Well it means that if I know someone's level of education that does not help me to predict whether they will be above or below the average population regression line. So that's what it means for there to be a zero conditional mean of error. And this is perhaps the most important of the Gauss-Markov assumptions, for reasons which we'll come onto later. So, that concludes our first video looking into the Gauss-Markov assumptions. I'm going to, in the next video, explain the next three Gauss-Markov assumptions. Check out ben-lambert.com/econometrics-... for course materials, and information regarding updates on each of the courses. - Навчання та стиль
Dear Ben Lambert,
It is now exam season at the University of Birmingham. As a second year who hates economics, you are currently my rock and my hope to pass my Econometrics exam. You are a hero, a true legend, a life saviour. If I pass this year, I will dedicate my dissertation to you and if you're ever in Birmingham, let me buy you food.
WRITTEN WITH ALL MY LOVE
and several cans of spar budget energy drink
Hi Eva, thanks for your message, and (overly) kind words. Glad to hear that the videos have been useful. Good luck with the spar energy drinks (although perhaps upgrade them to LIDL/Tesco), and your exams and dissertation! Best, Ben
Thank You so much Ben for your tutorials . These tutorials have motivated me to explore the ideas of econometrics deeply.
just making a pause after some 30 videos... you have a wondurful vision of econometrics, everything is so consistent (...). It is just sometimes a bit complicated for a french guy to understand your Manchester accent...but after some vids it sounds like music of econometrics 😉 thank you so much!
you make someone who hates econometric now think that it is actually fun, wish there are more great teaching videos on UA-cam like yours. thanks a lot!!
This course is great and a super useful refresher!
I like the lehnea parameters part
Just found ur channel which i find pretty useful :D Thnx a lot Ben ^^
Thank you so much for this course..
Very helpful explanation. Distracting pron of linear
Thank you. Very useful for me to prepare my quant interview. Reading takes more time
so touching for an excellent video
What is the point of these assumptions, what is their significance?
If a function is non linear in parameters like y = alpha + beta squared times x + u, couldnt i simply substitute beta squared with another variable say, gamma, and we would get y = alpha + gamma x + u? Wouldn't it be linear then?
Following the outline of Gauss-Markov theorem proof
ua-cam.com/video/yHXjZTUjzgE/v-deo.html
I noticed that one suggests an alternative linear estimator.
This alternative linear estimator is then shown to have larger variance of the LS estimator.
This suggested alternative estimator is not only an estimator of a model which is linear in parameters (parameters==LS estimators), but also linear in the dependent variable observations or can be made to be linear in these observations.
In the hope I am not misleading any reader, each of the linearity constraints seem to imply the other .
Why would you make fun of our econometrics lord and savior
Plz do videos on estimability and identifiability
Why is random sampling important? (asking more for panel data)
2019 January studying for my CAT tommorow 31st.
how did you do it can you share with me , thank you
2:44 I thought that if there is a multiple that the equation is still linear?
+sltr1 It think you are right since a product of 2 constants is just another constant. Thus, the parameter is still linear
@@NhatLinhNguyen82 how is variable different then parameters? It said variables can be non-linear
Does the second assumption mean Cov(xi,ui)=0?
No that is the 6th assumption
Lin-e-ar
cool !!!
Привет из России) its best explanation i ve found
When the word "hero" comes to mind, the first person I remember is Ben Lambert
Econometrics be eating my ass.. respect man
excellent, except maybe the way you say linear ;)
Kandungan anda sangat menyentuh
laneeerrrr??????
do not see why we choose to pay so much to go to university while learning everything from Ben Lambert
axuming and lin-eer. great vid though
Lin-eer? Are you kidding? Great vid otherwise
Beeeeeta
so touching for an excellent video
Following the outline of Gauss-Markov theorem proof
ua-cam.com/video/yHXjZTUjzgE/v-deo.html
I noticed that one suggests an alternative linear estimator.
This alternative linear estimator is then shown to have larger variance of the LS estimator.
This suggested alternative estimator is not only an estimator of a model which is linear in parameters (parameters==LS estimators), but also Linear in the dependent variable.
So linearity of BLUE estimators has both constraints:
A. The model is linear in the estimators.
B. The estimators are linear in the dependent variable observations.
so touching for an excellent video