30-04-2003 03:15									#1
	Any econometrics whizzes here? Support Apolyton buy from Amazon

Any thoughts on how to attack this problem?

Attachment: econ_problem2.jpg
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	30-04-2003 03:16									#2
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Sounds fun.

	30-04-2003 03:17									#3
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Oh, tons!

	30-04-2003 03:20									#4
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sorry, I don't speak greek

	30-04-2003 03:45									#5
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hehe. just glad i didn't go for my graduate degree

	30-04-2003 04:29									#6
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CFA or classroom?

There are a couple of stats guys who can breeze this stuff, but I don't seen them around right now.

I am supposed to know, but it has been too long...

	30-04-2003 05:00									#7
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Classroom. This is graduate-level economics stuff.

	30-04-2003 05:08									#8
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o_O

	30-04-2003 05:20									#9
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the math doesnt' look complicated u just need someone who knows the lingo.

	30-04-2003 06:02									#10
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I asked my sister, an econ major at Yale, but she didn't know. She's never taken econometrics so she doesn't know all the lingo. Sorry, I can't help you.

	30-04-2003 06:49									#11
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Thanks anyway, Jag.

Is your sister an undergrad? If so, I'm not surprised she hasn't had this kind of thing. Econometrics at the undergraduate level is usually a "how to" course. "Here's how we analyze data and draw conclusions from it. Just let the computer do the heavy-lifting." You spend a lot of time looking up numbers from tables in the back of the book . At the graduate level, we study where these empirical techniques come from, the heavy-duty mathematical theory behind it, and why these techniques have desirable properties. Tough stuff.

	30-04-2003 07:56									#12
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It really just looks like a bit of algebra. Can't tell for sure. But if you take the matrices and expand them into their algebraic forms, can you just set up inequalities and prove this with basic pre-calc math?

I don't know a couple terms: what does "worse than" mean. Also, what does V(beta) mean. I don't see an algebraic definition of the V function. Is it a misprint?

Finally, you might want to think a bit about the implications of this in terms of actual problems.

	30-04-2003 08:38									#13
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I think the V function is a common one, so there's no definition of it. Perhaps some kind of tests.

	30-04-2003 08:46									#14
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V(.) refers to the variance of the argument in parentheses. Sigma-squared-epsilon is the variance of the error term, epsilon. By "worse then," I'm assuming this means "in the variance." In other words, the variance of the GLS estimates (beta-tildes) are no greater than the variance of the ordinary least squares (OLS) estimates (beta-hats).

Also keep in mind that X1 and X2 are matrices of appropriate dimension. The betas are vectors, y is a vector, epsilon and u are vectors. So think of it this way: we have T observations, K regressor variables (represented by the X's) so that we have K regression parameters (betas) that we are trying to estimate. We partition the T x K matrix of regressors into one set of regressors X1 (T x K1) and another set X2 (T x K2), K1 + K2 = K. So beta-one is a K1 x 1 vector and beta-two is K2 x 1; y is a T x 1 vector of the dependent variable. Sigma-squared-epsilon is scaler, so the regression errors are homoskedastic. Note then that "I" in the partitioned matrix expression is the identity matrix and is K1 x K1.

Now by the Frisch-Waugh-Lovell Theorem, the OLS estimate of beta-one (beta-one-hat) in the partitioned regression is given by:

Attachment: econ_problem3.jpg
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	30-04-2003 08:47									#15
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And that's as much as I've been able to figure out so far.

	30-04-2003 08:52									#16
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Read the bloody textbook

	30-04-2003 09:05									#17
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I may have to keep doing that.

	30-04-2003 10:11									#18
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Jules, try writing out some of it in algebra. Or at least explicity putting down some of the words into algebra. Worse than is an inequality.

Also, can you think through the problem in scalers? I.e. ignore for a minute that beta is a vector and X a matrix. What would it be if this were just a normal, garden variety regression in Excel.

Also, I don't understand how you can have variance of an estimate. I mean does beta correspond to the coefficent in a regression? And X to a variable?

	30-04-2003 10:26									#19
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Where is DrSpike to tell us that everyone should learn this in undergrad Econ 101?

My solution is to buy the bond with the most convexity, but that may not be helpful...

Good luck

	30-04-2003 11:28									#20
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ECONOMETRICS!!!!! AAAAAAAAAAAARRRRGHHHHHH!!!!!! My eyes! My eyes!

In fact, in Vilnius Uni, I passed it only from the third try, mainly due to fooling around with my current wife

	30-04-2003 12:22									#21
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*jaw drops*

	30-04-2003 12:46									#22
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AHHHHH!

Like Sava, I've been blinded!

I thought I left that behind a few years ago!

You bastard, Jules! YOU BASTARD!

	30-04-2003 13:04									#23
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My name is Saras, Mr.Siddiqui.

	30-04-2003 13:06									#24
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Saras, Sava no difference - one can't drive and the other can't form logical thoughts (I'll let you decide which is which)

	30-04-2003 13:38									#25
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*Runs Imran over with his super duper beamer*

	30-04-2003 13:38									#26
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Damn it, one semester of statistics and this still is Greek to me.

	30-04-2003 13:43									#27
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quote: Originally posted by Saras *Runs Imran over with his super duper beamer*

Oh Good! My first case where I get to extract loads of money from the other party .

	30-04-2003 13:54									#28
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*Zips away at 250 km/h to a non-extradiction country*

	30-04-2003 15:57									#29
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quote: Originally posted by Kropotkin Damn it, one semester of statistics and this still is Greek to me.

Because it's in Greek, more or less

	30-04-2003 20:07									#30
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The guts of this problem is showing that adding additional unbiased information to an estimator can't make you any worse off (ie no greater variance).

Write out the variance for the GLS estimator.
Write out the variance for the OLS estimators in partitioned form so the GLS and OLS variance matircies have the same dimensions.
Show that the difference between the OLS variance matrix and the GLS variance matrix is non-negative definite.
Remember that the OLS estimators are best linear unbiased estimators (BLUE), which tell you they have minimum variance for their part of the partioned matrix.