Sunday, May 24, 2015

John Nash, 1928 - 2015

John & Alicia Nash
Tragically, John and Alicia Nash died as the result of a road accident on New Jersey yesterday.

Just days previously, Nash was the co-recipient of the 2015 Abel Prize for his contributions to the theory of nonlinear partial differential equations. He was the only person to be awarded both the Abel Prize and a Nobel Prize (Economics, 1994).

It would be impertinent of me to try and comment meaningfully, here, on Nash's contributions to Game Theory.

I was, however, taken by one comment on Twitter this morning:


Ferdinando is referring to Nash's Ph.D. dissertation, "Non-Cooperative Games", completed at Princeton University in May of 1950. Yes, it was just 27 pages long. One of the only two references was to von Neumann and Morgenstern's classic 1944 book, Theory of Games and Economic Behavior. The other was to Nash's own paper, published in the Proceedings of the National Academy of Sciences in 1950. It spanned just two pages, but was actually less than one page long!

Yes, sometimes it really is the case that, "Less is more". (Ludwig Mies van der Rohe)



(Suggested reading: "How Long Should My Thesis Be?".)


© 2015, David E. Giles

Friday, May 22, 2015

Maximum Likelihood Estimation & Inequality Constraints

This post is prompted by a question raised by Irfan, one of this blog's readers, in some email correspondence with me a while back.

The question was to do with imposing inequality constraints on the parameter estimates when applying maximum likelihood estimation (MLE). This is something that I always discuss briefly in my graduate econometrics course, and I thought that it might be of interest to a wider audience.

Here's the issue.

Wednesday, May 20, 2015

A Pleasant Surprise

I could scarcely believe my good fortune when I opened the following email earlier today:

Dear Dr Giles,

Congratulations, your paper “Being ‘in’ assessment: The ontological layer(ing) of assessment practice” published in Journal of Applied Research in Higher Education has been selected by the journal’s editorial team as the Outstanding Paper of 2014. We aim to increase dissemination of such a high quality article as much as possible and aim to promote your paper by making it freely available for one year. I will confirm once the free access has gone live so that you will be able to let others know. This will be in the next couple of weeks. As a winner you will receive a certificate. Where possible, we like to organise for you to be presented with your certificate in person. We will be in touch with you shortly (next few weeks) in the hope that we can organize a presentation. Again, many congratulations on your award. We will be in touch with you regarding our plans to promote and present your award very soon. Please do not respond to this mail asking about when your chapter will be made freely available or about possible presentations. I will be in touch soon with all the details!! 

Best regards,
Jim Bowden
Academic Relations Manager | Emerald Group Publishing Limited 
Tel: +44 (0)1274 785013 | Fax: +44 (0)1274 785200

Now, I must confess that I had some difficulty recalling the details of what I'd written to deserve this unexpected honour. But it must have been pretty darned good!

So, to refresh my memory I took a quick look at the 2014 volume of the journal in question. (Bookmark this link for future free access!)

Sure enough, there I it was - not the lead article, but close enough (apparently):


For reasons that I simply can't fathom, our library doesn't subscribe to this journal. For reasons that I definitely can fathom, neither do I! The promised free access has not yet "gone live", so I'll have to spare you the pleasure of a replication of the full text of the article here.

However, by way of recompense, here's the abstract:

Abstract:

Purpose
– Current discourses on educational assessment focus on the priority of learning. While this intent is invariably played out in classroom practice, a consideration of the ontological nature of assessment practice opens understandings which show the experiential nature of “being in assessment”. The purpose of this paper is to discuss these issues.

Design/methodology/approach

– Using interpretive and hermeneutic analyses within a phenomenological inquiry, experiential accounts of the nature of assessment are worked for their emergent and ontological themes.

Findings

– These stories show the ontological nature of assessment as a matter of being in assessment in an embodied and holistic way.

Originality/value

– Importantly, the nature of a teacher's way-of-being matters to assessment practices. Implications exist for teacher educators and teacher education programmes in relation to the priority of experiential stories for understanding assessment practice, the need for re-balancing a concern for professional knowledge and practice with a students’ way of being in assessment, and the pedagogical implications of evoking sensitivities in assessment.



I can hardly believe I wrote that!

(I have replied to Mr. Bowden, expressing my gratitude but suggesting that a certain David Giles in the School of Education at Flinders University in Australia may be even more pleased to hear from him than I was.)


© 2015, David E. Giles

Friday, May 15, 2015

Mark Thoma Interviews Koen Jochmans

The Denis Sargan Econometrics Prize is awarded annually by the Royal Economic Society for "the best (unsolicited) article published in The Econometrics Journal in a given year by anyone who is within five years of being awarded their doctorate."

The prize was first awarded last year to Fabrizio Ferriani.

This year, the Sargan Prize for papers published during 2013 was awarded to Koen Jochmans (Sciences Po, Paris) for his paper, "Pairwise-Comparison Estimation With Non-parametric Controls". The announcement and award took place at the 125th Meeting of the Society, held in Manchester a few weeks ago.


Mark Thoma (Economist's View blog) interviewed Koen about his research, and econometrics more generally. The resulting excellent video can be viewed here.

Congratulations to Koen on this award, and thanks to Mark for the video interview.

It's also worth mentioning that videos of the the various special sessions that were held at the 2015 RES conference are also available. These include The Sargan Lecture, by Michael Keane; and a session on "The Econometrics of Matching".


© 2015, David E. Giles

Tuesday, May 12, 2015

Alternative Tests for Serial Independence

The following question arose in a (fairly) recent email from Daumantas:
"I wonder if you could give any references -- or perhaps make a new blog post -- about testing for serial correlation: Breusch-Godfrey versus Ljung-Box test. I have no problem finding material on the two tests (separately), but I am interested in a comparison of the two. Under what conditions should one test be favoured over the other? What pitfalls should one be aware of before choosing one or the other test? Or perhaps both of them should be put to rest in favour of some new, more general, more robust or more powerful test?"
Daumantas apparently raised the same question on stackexchange, and got some sensible responses.

If this interests you, the response there that refers to Chapter 2 of Fumio Hayashi's, Econometrics, is right on target. There's no point in me repeating it here.

Rob Hyndman also had an interesting and useful post about the L-B test.

My recommendation - stick with the Breusch-Godfrey test if you're testing regression residuals.


© 2015, David E. Giles

Monday, May 11, 2015

Teaching Causality

Arguably, Judea Pearl is the most influential "Causality Specialist" of our time. (My term, not his!)

If you don't subscribe to his blog (Causal Analysis in Theory and Practice) and newsletter already, I'd suggest that you do so.

Judea also has several very informative video interviews that should be of interest to economists and econometricians. For example:



© 2015, David E. Giles

Friday, May 8, 2015

Yeah ............ That'd Be Great

"Bill Lumbergh" will continue to terrorize the office via my tweets at @DEAGiles:


p.s.: Actually, I do own a "Swingline" stapler, and I'm thinking of re-spraying it fire-engine red.


© 2015, David E. Giles

Thursday, May 7, 2015

On the Invariance of MLE's

The Maximum Likelihood Estimator (MLE) is extremely widely used in statistics, and in the various "metrics" disciplines such as econometrics. This is because this estimator has several highly desirable properties, as long as the sample size is sufficiently large.

For example, under fairly weak ("regularity") conditions, the MLE is weakly consistent, asymptotically efficient, and asymptotically normal.

In small samples, the MLE may or may not have good "sampling properties". For instance, it may be biased or unbiased, depending on the estimation problem under consideration.

When teaching this material, instructors invariably mention another nice property of the MLE: it's an "invariant estimator".

What does this actually mean?

Some econometrics texts (e.g., Greene, 2012, p.521) define the invariance property as follows: "If θ* is the MLE of θ, and f( . ) is a 1-1 function, then f(θ*) is the MLE of f(θ)."

In fact, this statement of the property is unduly strong. The function, f( . ), simply needs to be continuous - it doesn't need to be 1-1. (The proof of the result is especially simple if f is 1-1.)

In support of this more general result, I usually refer my students to the note by Zehna (1966). Recently, I became aware of some other important references when I read a paper by Olive (2004).

In particular, Berk's  (1967) review of Zehna's paper provides a simple proof of the general result.

An obvious implication of the generality of the invariance theorem is that if σ*2 is the MLE of the population variance, σ2, then √(σ*2) is the MLE of σ. This wouldn't be the case if the theorem was restricted to just 1-1 transformations!

Olive's paper will definitely be on my reading guide for students in future courses that I teach.


References

Berk, R., 1967. Review 1922 of ‘Invariance of maximum likelihood estimators’ by Peter W. Zehna. Mathematical Reviews, 33, 342-343.

Greene, W. H., 2012. Econometric Analysis, 7th ed.. Prentice Hall.

Olive, D. J., 2004. Does the MLE maximize the likelihood? Mimeo., Department of Mathematics, Southern Illinois University. (Also included in D. J. Olive, 2014, Statistical Theory and Inference, Springer.)

Zehna, P. W., 1966. Invariance of maximum likelihood estimators. Annals of Mathematical Statistics, 37, 744.

© 2015, David E. Giles

Friday, May 1, 2015

Reading for the Merry Month of May

While you're dancing around the Maypole (or whatever else it is that you get up to), my recommendations are:
  • Claeskens, G., J. Magnus, A. Vasnev, and W. Wang, 2014. The forecast combination puzzle: A simple theoretical explanation. Tinbergen Institute Discussion Paper TI 2014 - 127/III. 
  • de Jong, R. M. and M. Sakarya, 2013. The econometrics of the Hodrick-Prescott filter. Forthcoming in Review of Economics and Statistics.
  • Honoré, B. E. and L. Hu, 2015. Poor (wo)man’s bootstrap. Working Paper 2015-01, Federal Reserve Bank of Chicago.
  • King, M. L. and S. Sriananthakumar, 2015. Point optimal testing: A survey of the post 1987 literature. Working Paper 05/15, Department of Econometrics and Business Statistics, Monash University.
  • Meintanis, S. G. and E. Tsionas, 2015. Approximately distribution-free diagnostic tests for regressions with survival data. Statistical Theory and Practice, 9, 479-488. 
  • Piironen, J. and A. Vehtari, 2015. Comparison of Bayesian predictive methods for model selection. Mimeo.
  • Yu, P., 2015. Consistency of the least squares estimator in threshold regression with endogeneity. Economics Letters, 131, 41-46.

© 2015, David E. Giles

Thursday, April 30, 2015

Introduction to Applied Econometrics With R

I came across a January post from David Smith at Revolution Analytics, in his Revolutions blog. It's titled, An Introduction to Applied Econometrics With R, and it refers to a very useful resource that's been put together by Bruno Rodrigues of the University of Strasbourg. It's called Introduction to Programming Econometrics With R, and you can download it from here.

Bruno's material is a work in progress, but it's definitely worth checking out if you're looking for something to help economics students learn about R in an introductory statistics/econometrics course.


© 2015, David E. Giles