The Normality of Joint and Marginal Distributions

I'm often surprised how many people are confused when it comes to joint and marginal normal distributions.

Most students of econometrics are taught that the marginal and conditional distributions associated with a multivariate normal random vector are themselves normal. That is, if

         p(x₁, x₂, ...., x_n) ~ MVN[μ₁, ....., μ_n ; V]              ;      where V = {v_ij}

then
         p(x_i) ~ N[μ_i ; v_ii]  .

Similarly, p(x₁ | x₂, x₃, ...., x_n), and all of the other conditional densities are normal.

However, what they don't seem to get taught is that the converse is not true. That is, if we have several random variables, each with normal marginal distributions, then the joint distribution of these variables is not necessarily normal.

It all depends on what copula is used to construct the joint distribution.


© 2014, David E. Giles

Arnold's "Signature"

Anonymity is part of the culture when it comes to refereeing papers submitted for possible publication in economics, econometrics, and statistics. Referees' names are typically "blinded", and some journals use a "double-blind" process, so that authors names are not know by the referees. Not all disciplines use this approach.

The double-blind approach is far from perfect, especially given how easy it often is to identify authors  by locating a "working paper" version of their article through an internet search. In addition, referees often effectively "reveal" their identity by insisting that authors include references to the referee's own work.

Sometimes, though, referees expose themselves quite unwittingly. Here's a case in point. 

Off to New Zealand in July

The New Zealand Association of Economists is holding its 55^th annual conference in early July of this year, in Auckland.

I'm delighted that I'll be there as a keynote speaker. 

The very first conference presentation that I made was at the meeting of the NZAE, in Palmerston North, in 1972. I'm very grateful to be participating this year!

© 2014, David E. Giles

Happy Birthday Sir Ronald Fisher

Ronald Aylmer Fisher.

Born: 17 February, 1890, in East Finchley, London, England 

Knighted: 1952

Other major Honours: Fellow of the Royal Society (1929), Royal Medal (1938), Guy Medal in Gold (1947), Copley Medal (1956), Darwin-Wallace Medal (1958)

Died: 29 July 1962, in Adelaide, S.A., Australia

If you're a student of Econometrics, think of:

• Maximum likelihood estimation
• Fisher's information
• Analysis of variance
• Sampling distributions (for various statistics)
• The null hypothesis
• The F distribution (sort of)

Some previous related posts:

• And in the Red Corner.....
• A Bayesian and Non-Bayesian Marriage
• On the Importance of Gong Global
• Whose F Distribution Was It?

The Fisher digital archives are housed in the University of Adelaide Library.


© 2014, David E. Giles

Sir Francis Galton

Sir Francis Galton, who gave us the concepts of both correlation, and regression, was born on this day, 16 February, in 1822. Galton was one of the great "polymaths" - he had a finger in every pie he could find - as is described in his Wikipedia entry.

We him a debt of gratitude for the role he played in The Origin of our Species.

It's a busy birthday month, with more to follow tomorrow!

© 2014, David E. Giles

Some Things You Should Know About the Jarque-Bera Test

What test do you usually use if you want to test if the errors of your regression model are normally distributed? I bet it's the Jarque-Bera (1982, 1987) test. After all, it's a standard feature in pretty well every econometrics package. And with very good reason.

However, there some things relating to this test that you may not have learned in your econometrics courses. Let's take a look at them.

P-Values ...... Again!

I've had posts about p-values in the past - e.g., see here, here, here, and here. Well, this pesky little devil is back in the news again. Every now and the the "p-value bashers" emerge from the swamp, and this past week it happened again - in Nature.

When I read this piece by Regina Nuzzo (and once the eye-rolling had subsided) I was very tempted to put together a post. I'm glad I didn't, because today Jeff Leek published a post on the Simply Statstics blog that is way, way better than anything I could have put together.

It's a must-read piece!

© 2014, David E. Giles

The World of Statistics

Many of you will know that 2013 was "The Year of Statistics". A large number of special events celebrated this fact. What you may not know is that the "Statistics2013 organisation has now been transformed into "The World of Statistics".

This recent piece in the AMSTAT News describes the reasons for this development:

"In the weeks since The World of Statistics was announced, feedback from Statistics2013 participating organizations has been unanimously supportive, with respondents agreeing that more time and effort are necessary to achieve the campaign’s goals, which are:

• Increase public awareness of the power and impact of statistics on all aspects of society.

• Nurture statistics as a profession, especially among young people. 

• Promote creativity and development in the sciences of probability and statistics.

The continuing movement also will help bring to reality the newly announced International Prize in Statistics, a “Nobel-like” prize in statistical science that will recognize the major achievement of an individual or team in the field of statistics."

You can follow The World of Statistics on  Twitter at @ASTATWORLD.

© 2014, David E. Giles

Bayesian Model Selection - A Worked Example

Choosing between non-nested models can be challenging. A lot of statisticians and econometricians find that a Bayesian approach has a lot to offer when it comes to addressing this challenge. I'm certainly of that view myself.

Let me take you through an empirical example of Bayesian model selection - it involves alternative regression models for the demand for beer in Australia - and it's one that I use, sometimes, in class.

An Interview With Bradley Efron

You've all heard about the bootstrap, and you all know that it was Bradley Efron (Statistics, Stanford) who came up with the idea. (If I'm wrong, you can check this earlier post.)

On Twitter yesterday, Joe Blitzstein (Statistics, Harvard; @stat110) drew attention to this great Youtube video interview in which Brad discusses what led him to develop the bootstrap.

I like his opening words when asked how it all came about:

"It's a story about having good colleagues..."

Well, it probably is, but I'd call that a pretty modest response!

Enjoy the video.


© 2014, David E. Giles

Modelling Olympic Medal Wins

With the Sochi Winter Olympics now well underway, I was reminded of the empirical literature that has attempted to model the number of medals that different countries win.

Back in 2006, one of our students, Glen Roberts, wrote an excellent paper, titled "Accounting for Achievement in Athens: A Count Data Analysis of National Olympic Performance", on this topic. Glen's work was based on a term project that he undertook for my ECON 546, "Themes in Econometrics" course. This is an elective course for M.A. students, and it emphasises the thematic content of econometric methods - MLE, IV/GMM, Bayesian inference, etc.

Glen found that the empirical analyses of Olympic medal wins largely ignored the "count data" aspect of the problem. You can find plenty of references in Glen's paper. He then set about rectifying this situation, as the abstract to his paper describes:

The Statsguys on Data Analytics

It's good to see that more and more students of econometrics are taking an interest in "Data Analytics" / "Big Data" /"Data Science" literature. As I've commented previously, there's a lot that we can all learn from each other. Moreover, many of "boundaries" are very soft, and are more perceived than real.

So, I was delighted to see the arrival of The Statsguys, last month. (Hat-tip to the team at Quandl for alerting me to this.

A Blast From the Past

Doesn't time fly! Around the end of August 1994 Lief Bluck and I put together a web site for our department. That may not sound very interesting, but let's put things in perspective.

Our University didn't have a web site - not many universities did. The Department of Physics & Astronomy here at Uvic had one - that was it. There were, I believe only 6 economics groups in the world that had a website when we got in on the act. The best known one was that run by Hal Varian - then at the University of Michigan - and now Chief Economist at Google.

Our site was a modest affair. Here's the kicker - we had to show people how to use it, and persuade them that this WWW thing may be around for a while!

Recently, Lief discovered a hard copy of this old memo. that he circulated to members of our department a few weeks after we got things going:

Vintage Years in Econometrics - The 1960's

Remember that saying - "if you can remember the 60's you probably weren't there"? Well, with that said, and continuing from my earlier posts about vintage years for econometrics in the 1930's, 1940's, and 1950's, here's my take on the 1960's.

Once again, let me note that "in econometrics, what constitutes quality and importance is partly a matter of taste - just like wine! So, not all of you will agree with the choices I've made in the following compilation."

Conference on Macro & Financial Economics/Econometrics

The 10th BMRC-DEMS Conference is being held at Brunel University, London (U.K.), at the end of May this year. Details can be found here.

The conference themes include a number of important topics:

• Recent developments in time-varying and nonlinear models
• Economic dynamics and smooth transition modeling
• Structural breaks in financial time series
• Dynamic structural financial and macroeconometric modeling
• Macro-financial modeling using mixed frequency data
• Monetary policy and risk taking
• Fiscal policy, financial development and growth
• Macro-finance interface
• Asset pricing models with time-varying moments
• Financial markets volatility and macroeconomic activity
• Financial crash, stock, bond and commodity prices
• Modeling dynamic correlations during financial crises
• Boom-bust cycles and the linkage between financial and real activity
• Early warning indicators of economic and financial instability

There's an impressive line-up of keynote speakers:

• R. Baillie (Michigan State University)
• V. CorradiI (University of Surrey)
• C. Francq (University of Lille 3)
• M. Hallin (ECARES, Brussels)
• A. Harvey (University of Cambridge)
• D. Hendry (University of Oxford)
• G. Melard (ECARES, Brussels)
• P. Minford (Cardiff University)
• R. Taylor (University of Essex)
• S. Wright (Birkbeck College, University of London)
• P. Zaffaroni (Imperial College, London)
• J.-M. Zakoian (CREST, Paris)

© 2014, David E. Giles

The February Reading List

As always - there's lots of interesting reading out there. Here are my suggestions for this month:

• Advani, A. and Tymon Słoczyński, 2013. Mostly harmless simulations? On the internal validity of empirical Monte Carlo studies.Discussion Paper No. 7874, IZA, Bonn.
• Flaig, G., 2012. Why we should use high values for the smoothing parameter of the Hodrick-Prescott filter.  CESifo Working Paper No. 3816, Department of Economics, University of Munich.
• Kiviet, J. F. and J. Niemzczyk, 2013.  On the limiting and empirical distribution of IV estimators when some of the instruments are actually endogenous. EGC Report No: 2013/11, Nanyang Techological University.
• Lütkepohl, H., A. Staszewska-Bystrova, and P. Winker, 2014. Confidence bands for impulse responses: Bonferroni versus Wald. (Updated.) SFB 649 Discussion Paper 2014-007.
• Lv, J. and J. S. Liu, 2013. Model selection principles in misspecified models. Journal of the Royal Statistical Society, B, 76, 141-167. 
• Skeels, C. L. and L. W. Taylor, 2013. Prediction after estimation. Economics Letters, 122, 420-422.
• Tserkezos, K., 2013. Temporal aggregation and Ramsey's (RESET) test for functional form: Results from empirical and Monte Carlo experiment. Mimeo., Department of Economics, University of Crete.

© 2014, David E. Giles

Econometrics at Monash University

My first academic position was in the (then) Department of Econometrics and Operations Research at Monash University ( in Melbourne, Australia). I was there for nine wonderful years from the mid 1970's to the mid 1980's.

Now re-named the Department of Econometrics and Business Statistics, the Monash group continues to rank among the very best in the world, as is evidenced by this recent score from IDEAS.

This makes me feel really good.

Great job!

© 2014, David E. Giles