Minimum MSE Estimation of a Regression Model

Students of econometrics encounter the Gauss-Markhov Theorem (GMT) at a fairly early stage - even if they don't see a formal proof to begin with. This theorem deals with a particular property of the OLS estimator of the coefficient vector, β, in the following linear regression model:

                        y = Xβ + ε  ;  ε ~ [0 , σ² I_n] ,

where X is (n x k), non-random, and of rank k.

The GMT states that among all linear estimators of β that are also unbiased estimators, the OLS estimator of β is most efficient. That is, OLS is the BLU estimator for β.

EViews Tutorials

If you're a student who is just learning to use the EViews econometrics package, the tutorials that IHS (the supplier of EViews) has made available should be very helpful. You'll find them here.

There are 13 tutorials at this time, ranging from "EViews basics" to "Forecasting".

"The tutorials are split into self-contained sessions, although we recommend that new users of EViews work their way through the tutorials one by one.

Each tutorial is accompanied by data files so that you may follow the tutorials in your own copy of EViews. The data files are available in the Supporting Files side bar of each tutorial. Each tutorial is available in Microsoft Powerpoint® format, along with the data files, bundled together in a Zip file, in the Download Package area of of the side bar of each tutorial. 

You should note that the tutorials are written based on EViews 8, however the vast majority of material covered in them is applicable to earlier versions of EViews too."

Certainly, these tutorial won't tell you everything you'll want to know,  but they're a good start.

© 2013, David E. Giles

Variance Estimators That Minimize MSE

In this post I'm going to look at alternative estimators for the variance of a population. The following discussion builds on a recent post, and once again it's really directed at students. Well, for the most part.

Actually, some of the results relating to populations that are non-Normal probably won't be familiar to a lot of readers. In fact, I can't think of a reference for where these results have been assembled in this way previously. So, I think there's some novelty here. But we'll get to that in due course.

I can just imagine you smacking your lips in anticipation!

Camp(s) Econometrics

The New York Camp Econometrics VIII was held in Bolton Landing, NY, last month. I recall Badi Baltagi (one of the Camp Econometrics organisers) telling me about this great annual event a few years ago. The Texas Econometrics 2013 was held in Lost Pines back in February. This was the 18^th Camp for the group in Texas.

I also seem to recall that there used to be another regular Camp Econometrics in Southern California some years ago. If my neurons are still firing in the right order, I believe that Denis Aigner was one of the leaders of that venture. 

Back to the NY Camp:

"This event is a gathering of econometricians and empirical economists whose successful goal is to: (1) Bring together a group of econometricians/empirical economists and guests of host universities to discuss issues in econometrics, both applied and theoretical; (2) Present papers for comments by participants; (3) Stimulate student interest in econometrics; (4) Help students develop their technical presentation skills by encouraging the students of host universities to participate in the meetings and present papers."

Events like the Camp(s) Econometrics, and The Econometric Game, in the Netherlands, really are great ventures!

© 2013, David E. Giles

Cookbook Econometrics - Reprise

A few days ago I was looking at my copy of Econometric Foundations, written by Ron Mittelhammer, George Judge, and Doug Miller. It's an excellent book, by the way.

I noticed, for the first time, that on p.xxviii of the Preface they have the following to say, under the heading of "A Comment":

I Know What You Did Last Summer!

O.K., I know that I stole that title! It was absolutely blatant.

The other day, some colleagues and I were discussing the issue of students (including our own offspring), and their summer jobs - or no jobs, as the case may be. I'm not passing judgement here in what follows, by the way. 

When I was a student I had to earn enough money over the summer to live off for the rest of the year. That's just the way it was. Period! My parents were great - I could live at home over the summer at no cost to me. But that was it. They lived in a very small rural town in New Zealand, a long way from where I attended university. The upside of this was that, being a rural area (in the mid/late 1960's through to the early 1970's), there were some seriously good work opportunities.

So, what did I do each summer?

What's the Variance of a Sample Variance?

This post is really pitched at students who are taking a course or two in introductory economic statistics. It relates to a couple of estimators of the variance of a population that we all meet in such courses - plus another one that you might not have met. In addition, I'll be emphasising the fact that some "standard" results depend crucially on certain assumptions. Not surprisingly - but  not always made clear by instructors and text books.

Top Economics Blogs

Nice to be on the list - thanks, INOMICS!

© 2013, David E. Giles

What's Your Favourite Estimator?

It's interesting to dwell on the popularity of different estimators that econometricians use. Some estimators are "in vogue" for a period, and then give way to others as new developments come along. Different topics have captured the attention of theoreticians and practitioners alike at different times in history.

Here's a Google Ngram showing the extent to which some familiar estimators for simultaneous equations models have been mentioned in books since 1960:

Not too surprisingly, good old OLS just goes on and on:

I was going to include the GMM estimator in these plots, but this acronym has meanings other than the obvious one that comes to mind. So, the results would have been misleading. To be safe, let's use the full phrase Generalized Method of Moments and allow for case sensitivity:

Interestingly, the phrase appeared in some books before the publication of Hansen's classic 1982 paper.

© 2013, David E. Giles

Flowers for Mom - From Quandl

Today being Mothers' Day in many parts of the world, I thought that flowers would be appropriate. Well, a price index for (Gardens, Plants, and) Flowers. Specifically, a harmonized price index for these goods for 27 European Union countries.

I retrieved the monthly data for the period January 2006 to March 2013 from Quandl.com - a really nice resource that I posted about recently.  As well as downloading the data in various formats, reading the data from R, etc., you can also embed an interactive chart of the data directly into a document such as this one, and make the data visible to viewers. (Just click on the graph.) For instance: