Wednesday, September 26, 2012

My "Must Read" List

I have to confess that the number of items on my list of papers that I really must read (very soon) is rather large. My excuse is the same as everyone else's - too many papers, too little time. However, here's a small selection of of some of the papers that I've added to that list recently:

Monday, September 24, 2012

The Journal of Econometric Methods

The first issue of the Journal of Econometric Methods is available online, and you can register for a FREE trial access if your library doesn't already subscribe to a package that includes this journal.

Edited by Jason Abrevaya, Bo Honoré, Atsushi Inoue, Jack Porter, and Jeff Wooldridge, the Journal of Econometric Methods promises to be a "must read" publication. For now, issues will be published once a year.

Here's an extract from the "Editorial" of the first issue:

Sunday, September 23, 2012

Different Views on Significance Testing

Econ Journal Watch is an online resource that provides "scholarly comments on academic economics". If you don't follow it, or at least browse it from time to time, then I urge you to do so. Yes, that includes econometricians!
In the September 2012 issue you'll find a piece by Thomas Mayer. It's titled, "Ziliak & McCloskey's Criticisms of Significance Tests: An Assessment", and you can download a pdf version of the full article for free.

 Here's the abstract of his article:

Sunday, September 16, 2012

Confidence Regions for Regression Coefficients

Let’s consider the usual linear regression model, with the full set of assumptions:

                     y = Xβ + ε ;    ε ~ N[0 , σ2In] , (1)

where X is a non-random (n × k) matrix with full column rank.

Recall that, under our usual set of assumptions for the linear regression model, the OLS coefficient estimator,  b = (X'X)-1X'y, has the following sampling distribution:

               b ~ N[β ,σ2(X'X)-1] .          (2)

From the form of the covariance matrix for the b vector, we see that, in general:

(i) The leading diagonal elements will not all be the same, so each element of b will usually have a different variance.

(ii) There is no reason for the off-diagonal elements of the covariance matrix to be zero in value, so the elements of the b vector will be pair-wise correlated with each other.

You'll also remember that when we develop a confidence interval for one of the elements of β, say βi, we start off with the following probability statement:

                  Pr.[-tc < (bi - βi) / s.e.(bi) < tc] = (1 - α) ,        (3)

where tc is chosen to ensure that the desired probability of (1 - α) is achieved. Equation (3) is then re-written (equivalently) as:

                 Pr.[βi - tcs.e.(bi) < bi < βi +tcs.e.(bi)] = (1 - α),       (4)

and we then manipulate the event whose probability of occurrence we were interested in, until we ended up with the following random interval which, if constructed many, many times, would cover the true (but unobserved) βi, 100(1 - α)% of the time:

                 [bi - tcs.e.(bi) , bi + tcs.e.(bi)] .          (5)

Notice that this interval is centered at bi. Making the interval symmetric about this point ensures that we get the shortest (and hence most informative) interval for any fixed values of n, the sample size, and α. (See here and here for more details.)

Now, suppose that we want to generalize the concept of a confidence interval (that applies to a single element of b) to that of a confidence region, that can be associated with two elements of b at once.

Saturday, September 15, 2012

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:

Friday, September 14, 2012

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

Thursday, September 13, 2012

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:

Monday, September 10, 2012

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!


© 2012, David E. Giles

Sunday, September 9, 2012

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.

Saturday, September 8, 2012

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

Friday, September 7, 2012

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."

Monday, September 3, 2012

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: