Granger Causality Testing in R

Today just gets better and better!

I had an email this morning from Christoph Pfeiffer, who follows this blog. Christoph has put together some nice R code that implements the Toda-Yamamoto method for testing for Granger causality in the context of non-stationary time-series data.

Given the ongoing interest in the various posts I have had (here, here, here & here) on testing for Granger causality, I'm sure that Christoph's code will be of great interest to a lot of readers.

Thanks for sharing this with us, Christoph.

© 2012, David E. Giles

Former Students

It's always great to see our former grad. students making great progress with their chosen careers. Singling out individuals for special mention may be a little risky. But what the heck!!!

Bayesian Exercises

In the Advanced Topics in Econometrics course that I'm teaching this semester, one of the topics we're covering is Bayesian Econometrics. I've blogged a little on this topic before - e.g., here, here, here, and here.

If you want some practice exercises on Bayesian inference, you may be interested in this set of problems, as well as the assignment that my class is working on currently.

There's not much "econometric" content to the questions - they're more broadly statistical in nature. However, they cover some of the key ideas associated with this topic. Solutions will be posted later.

We're also looking at computational issues, such as MCMC. More on the latter in a different post, perhaps.

© 2012, David E. Giles

Listening to your Data

The latest issue of Significance Magazine (a joint publication of the Royal Statistical Society, and the American Statistical Association), includes an interesting article by Ethan Brown and Nick Bearman. It's titled, "Listening to Uncertainty: Information That Sings". 

The article is about "sonification" - listening to your data!

Some Properties of Non-linear Least Squares

You probably know that when we have a regression model that is non-linear in the parameters, the Non-Linear Least Squares (NLLS) estimator is generally biased, but it's weakly consistent. This is the case even if the model has non-random regressors and an additive error term that satisfies all of the usual assumptions.

In addition, even if the model’s errors are normally distributed, the NLLS estimator will have a sampling distribution that is non-normal in finite samples, and the usual t-statistics will not be Student-t distributed in finite samples.

In this post I'll illustrate these, and some other results, by using a simple Monte Carlo experiment.

Central Limit Theorems

When we first encounter asymptotic (large sample) theory in econometrics, one of the most important results that we learn about is the Central Limit Theorem.  Loosely speaking we learn that if we aggregate together enough values that are sampled randomly from the same distribution, with a finite mean and variance, then this aggregate starts to behave as if it is normally distributed.

However, too few courses make it clear that this "classical" central limit theorem is just one of several such results. The one that assumes independently and identically distributed values is actually the Lindeberg-Lévy Central Limit Theorem. There are other, related, results that deal with less restrictive situations.

Viren Srivastava

Recently, a reader of this blog asked I could provide some information about the late V.K. Srivastava, and the substantial contributions that he made to econometrics and to statistics generally.

I'm more than happy to oblige, as Virendra (Viren) was a good friend of mine, a treasured co-author, and a very caring and humble individual.

Jobs for Econometricians

My impression is that there is a strong  international market for economists who have strong skills in econometrics. I'm not talking just jobs in the academic community, but also about positions in the private, public, and non-profit sectors too.

 

This blog has a page that list a very small selection of such jobs. This list has never been meant to be exhaustive. That's not what this blog is about. Rather, the jobs listed on that page are meant to be illustrative of some of the various jobs that are available to econometricians.

 

If you're looking seriously for an academic position, especially at the entry level, then the obvious place to start is Job Openings for Economists (JOE). This is sponsored by the American Economics Association, but handles jobs internationally. Although the focus is on academic positions, jobs in other sectors appear in JOE too.

 

Another website that may interest you is econometricsjobs.com. This is a commercial site that lists positions specific to econometrics. It also has international coverage, and covers all sectors of the workforce. Just browsing some of the jobs that are advertised there may broaden your perception of the opportunities that are available to econometricians.

 

There are other sites too, of course. Perhaps some of these will get mentioned in comments to this post. 

© 2012, David E. Giles

Mathgen

H/T to my colleague, Martin Farnham, for drawing my attention to Mathgen.

 

Thanks to Nate Eldridge, a mathematician at Cornell University, who blogs at That's Mathematics!, you can randomly generate your own mathematics research paper!

 

In fact, a Mathgen-generated was recently accepted for publication at one of those pseudo-journals that seem to have sprouted with a vengeance of late. If you weren't convinced already that these publishing outlets should be avoided like the plague, this ought to do it for you!

 

Just for funzies, I decided to solicit Mathgen's assistance in writing my own paper. It took just a few seconds, and you can read it here. Constructive comments are welcomed, of course. Just don't ask me what the title means.

I have a feeling that this is going to be a particularly productive weekend!

 

(As Martin suggested to me, this is every journal editor's new nightmare!)

 

© 2012, David E. Giles

Let's be Consistent

One of the standard, large-sample, properties that we hope our estimators will possess is "consistency". Indeed, most of us take the position that if an estimator isn't consistent, then we should probably throw it away and look for one that is!

When you're talking about the consistency of an estimator, it's a really good idea to be quite clear regarding the precise type of consistency you have in mind - especially if you're talking to a statistician! For example, there's "weak consistency", "strong consistency", "mean square consistency", and "Fisher consistency", at least some of which you'll undoubtedly encounter from time to time as an econometrician.