Any econometrics whizzes here?

[Jules]

Any thoughts on how to attack this problem?

[Eli]

Sounds fun.

[Jules]

Oh, tons!

[Gangerolf]

sorry, I don't speak greek

[Kidlicious]

hehe. just glad i didn't go for my graduate degree

[Sten Sture]

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...

[Jules]

Classroom. This is graduate-level economics stuff.

[ixnay]

o_O

[yavoon]

the math doesnt' look complicated u just need someone who knows the lingo.

[Jaguar]

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.

[Jules]

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.

[TCO]

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.

[Urban Ranger]

I think the V function is a common one, so there's no definition of it. Perhaps some kind of tests.

[Jules]

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:

[Jules]

And that's as much as I've been able to figure out so far.