Spherically Distributed Errors in Regression Models

Let's think about the standard linear regression model that we encounter in our introductory econometrics courses:

 

                                       y = Xβ + ε .                      (1)

 

By writing the model in this form, we've already made two assumptions about the stochastic relationship between the dependent variable, y, and the regressors (the columns of the X matrix). First, the relationship is a parametric one - hence the presence of the coefficient vector, β; and second, the relationship is a linear one. That's to say, the model is linear in these parameters. If it wasn't, we wouldn't be able to write the model in the form given in equation (1).

 

However, the model isn't fully specified until we lay out any assumptions that are being made about the regressors and the random error term, ε. Now, let's consider the full set of (rather stringent) assumptions that we usually begin with:

Dummy Variables - Again!

In a previous post (here) I had a few things to say about the dummy variables that we often use in regression analysis. I'm currently making changes to a related paper of mine that's at the "revise and re-submit" stage with a journal. So, to get further feedback, I presented the material in my department's Brown Bag seminar series earlier this week.

If you're interested, you can download the slides for that presentation from here.

© 2012, David E. Giles

Granger Causality Testing With Panel Data

Some of my previous posts on testing for Granger causality (for example, here, here, and here) have drawn quite a lot of interest. That being the case, I'm sure that readers of this blog will enjoy reading a new paper by two of my colleagues, and a former graduate student of theirs.

The paper, by Weichun Chen, Judith Clark, and Nilanjana Roy is titled "Health and Wealth: Short Panel Granger Causality Tests for Developing Countries". Here's the abstract of their paper:

Guy Medal for David Firth

At the recent annual conference of the Royal Statistical Society, the Guy Medal, in Silver, was awarded to Professor David Firth, Head of the Department of Statistics at of the University of Warwick.

Alert readers of this blog will recall David's name appearing in a recent post about bias correction. David, a Fellow of the British Academy, was previously awarded the Guy Medal, in Bronze, in 1998.

You can find a full list of all winners of the Guy medals, in Gold, Silver, and Bronze, here. Econometricians will see lost of very familiar names on the lists!

© 2012, David E. Giles

What's Your Favourite Data Analysis Cartoon?

This question was asked on the Stack Exchange Cross Validated  blog. Your choice!

Enjoy!

© 2012, David E. Giles

Using Integrated Likelihoods to Deal With Nuisance Parameters

There are more possibilities open to you when using maximum likelihood estimation than you might think.

When we're conducting inference, it's often the case that our primary interest lies with a sub-set of the parameters. and the other parameters are essentially what we call "nuisance parameters". They're part of the data-generating process, but we're not that interested in learning about them.

We can't just ignore these other parameters - that would amount to mis-specifying the model we're working with. However, in the context of maximum likelihood estimation, there are several things that we can do to make life a little easier.

NBER Summer Institute 2012

Recently, I checked out the site for the NBER Summer Institute 2012 - Econometric Methods for Demand Estimation.

 

There, you'll find eight videos of some of the lectures presented by Ariel Pakes (Harvard) and Aviv Nevo (Northwestern). The slides that accompany the lectures are also available for downloading.

 

The topics covered in the vieo lectures are:

 

Pakes -

• The primitives of static demand models
• Confronting the precision problem, the information in prices, implications for use of hedonics
• Incorporating micro data
• Moment inequalities in demand analysis

Nevo -

• Estimation of static discrete choice models using market level data
• Applications and choice of IV's
• Measurement of consumer welfare
• Dynamic demand

I learned a lot from these lectures, and I hope that you find them interesting too!

© 2012, David E. Giles

So, What is Econometrics?

Over the years there have been many attempts to define what we mean by the term "Econometrics". I guess we all have our favourites. Mine comes from one of the most influential econometricians of our time - David Hendry:

"Unfortunately, I must now try to explain what "econometrics" comprises. Do not confuse the word with "econo-mystics" or with "economic-tricks", nor yet with "icon-ometrics". While we may indulge in all of these activities, they are not central to the discipline. Nor are econometricians primarily engaged in measuring the heights of economists."
 

On Crime and Punishment

Quite regularly, I take a look at the "Graphic Detail" blog that's published each business day on The Economist's website. Many of the graphs, maps and infographics that they produce are rather interesting.

 

Today's one is taken from a recent study, "Divergent Effects of Beliefs in Heaven an Hell on National Crime Rates", published by Azim Shariff and Mijke Rhemtulla  in the open-access journal, Plos One.

 

Here's the abstract from that paper:

The Cauchy Estimator & Unit Root Tests

As we all know, there's more than one way to estimate a regression equation. Some of the estimators that we frequently use include OLS, GLS, IV, GMM, LAD, and ML. Some of these estimators are special cases of some of the others, depending on the circumstances.

But have you ever used the Cauchy estimator? Probably not, even though it's been around (at least) since 1836.