Do You Use P-Values and Confidence Intervals?

Unless your econometrics training has been true-blue Bayesian in nature, you'll have reported a lot of p-values, and constructed heaps of confidence intervals in your time.

Both of these concepts have been the centre of widespread controversy in the statistics literature since their inception. It's probably good to be aware of this - just so you don't go and "shoot yourself in the foot" at some stage.

Economist/econometrician Aris Spanos has published an interesting and readable piece about all of this In a recent issue of the journal, Ecology. His paper is titled, "Recurring Controversies About P Values and Confidence Intervals Revisited". You can read a summary on the Error Statistics blog, here.

I strongly recommend this paper.

© 2014, David E. Giles

New Award for David Hendry

It's difficult to imagine what our modern econometrics world would be like if it weren't for the numerous, seminal, contributions that Sir David Hendry has made over the course of his distinguished career.

So, it was wonderful to see this announcement two days ago from the Economic and Social Research Council:

"Professor Sir David Hendry has today received the ESRC Celebrating Impact Lifetime Achievement Award. Over five decades Professor Hendry has developed macroeconomic models capturing how economies work, which are now embedded in software widely used by policymakers and decision-makers."

You can read the full details of the award, and a related video, here.


© 2014, David E. Giles

Frequentist vs. Bayesian Analysis

"Statisticians should readily use both Bayesian and frequentist ideas."

So begins a 2004 paper by Bayarri and Berger, "The Interplay of Bayesian and Frequentist Analysis", Statistical Science, 19(1), 58-80.

Let's re-phrase that opening sentence: "Econometricians should readily use both Bayesian and frequentist ideas."

Before turning to economics, my undergraduate training was in statistics and pure mathematics. My statistical training (in the 1960's) came from professors who were staunchly Bayesian - at a time when it was definitely "them and us". With few exceptions, the attitude was that "if you're not with us, then you're against us". And this was true on both sides of the Frequentist-Bayesian divide.

Hardly a healthy situation - but we've seen similar philosophical divisions throughout the history of economics, and in pretty much every other discipline at some point.

After a very orthodox training in econometrics (based largely on the texts of Johnston, and Malinvaud) I ended up doing my Ph.D. dissertation on some problems in Bayesian econometrics - supervised by a wonderful man who probably didn't have a Bayesian bone in his body. My first J. Econometrics paper looked at some of the sampling properties of certain Bayes estimators. How non-Bayesian can you get?

So, I've always told students that they need to be flexible in their econometric thinking, and they need to be prepared to use both frequentist and Bayesian tools. Time has proved me right, I believe. Modern econometric practice takes advantage of a healthy mix of ideas and techniques drawn from both tool boxes.

Yes, this has been made possible by the considerable advances that we have seen in computing methods and power in recent decades. But it's also reflected something of a shift in the mind-set of statisticians and econometricians alike.

Here's the concluding section of the Bayarri and Berger paper, in its entirety (pp.77-78):

"It seems quite clear that both Bayesian and frequentist philosophy are here to stay, and that we should not expect either to disappear in the future. This is not to say that all Bayesian or all frequentist methodology is fine and will survive. To the contrary, there are many areas of frequentist methodology that should be replaced by (existing) Bayesian methodology that provides superior answers, and the verdict is still out on those Bayesian methodologies that have been exposed as having potentially serious frequentist problems. 

Philosophical unification of the Bayesian and frequentist positions is not likely, nor desirable, since each illuminates a different aspect of statistical inference. We can hope, however, that we will eventually have a general methodological unification, with both Bayesian and frequentists agreeing on a body of standard statistical procedures for general use"

I hope that student followers of this blog will take the time to read the Bayarri and Berger paper, and to learn more about Bayesian methods.

© 2014, David E. Giles

The Deviance Information Criterion

A few years ago - twelve, to be specific - an interesting paper appeared in the Journal of the Royal Statistical Society. That paper, "Bayesian measures of model complexity and fit", by Spiegelhalter et al., stirred up a good deal of controversy within the statistical community. That much is apparent even from the "discussion" that accompanied its publication. More than 4,600 Google Scholar citations later, it continues to attract widespread attention - though not that much among econometricians, as far as I can tell. An exception is the paper by Berg et al. (2004).

In their 2002 paper, Spiegelhalter et al. introduced a new measure of model fit. They termed it the "Deviance Information Criterion" (DIC). Briefly, here's how it's defined:

June Reading List

Put away that novel! Here's some really fun June reading:

• Berger, J., 2003. Could Fisher, Jeffreys and Neyman have agreed on testing?. Statistical Science, 18, 1-32.
• Canal, L. and R. Micciolo, 2014. The chi-square controversy. What if Pearson had R? Journal of Statistical Computation and Simulation, 84, 1015-1021.
• Harvey, D. I., S. J. Leybourne, and A. M. R. Taylor, 2014. On infimum Dickey-Fuller unit root tests allowing for a trend break under the null. Computational Statistics and Data Analysis, 78, 235-242.
• Karavias, Y. and E. Tzavalis, 2014. Testing for unit roots in short panels allowing for a structural breaks. Computational Statistics and Data Analysis, 76, 391-407.
• King, G. and M. E. Roberts, 2014. How robust standard errors expose methodological problems they do not fix, and what to do about it. Mimeo., Harvard University.
• Kuroki, M. and J. Pearl, 2014. Measurement bias and effect restoration in causal inference. Biometrika, 101, 423-437.
• Manski, C., 2014. Communicating uncertainty in official economic statistics. Mimeo., Department of Economics, Northwestern University.
• Martinez-Camblor, P., 2014. On correlated z-values in hypothesis testing. Computational Statistics and Data Analysis, in press.

© 2014, David E. Giles

It's Not A Blog .......

This gem from @AcademicSay on Twitter today:

"It's not a blog. It's an independent open-access journal with a dedicated submission agreement."

© 2014, David E. Giles

Questions About Granger Causality Testing - The Fine Print

Judging by the number of hits, comments, and questions that I've had in relation to my various posts on testing for Granger (Non-) Causality, this seems to be a topic that a lot of followers find interesting. For instance, see the posts here, here, here, and especially here.

In the comments, and in a large number of related emails that I've received, several questions seem to recur, and I thought it would be worth addressing them in one place - right here, to be specific!

The following discussion relates to the (usual) case where there is the possibility that one or more of the time-series variables under consideration may be non-stationary, and some of the variables may be cointegrated. In such cases we have to be especially careful when we apply tests for Granger causality. The reasons for this, and for adopting a modified testing procedure, such as that proposed by Toda and Yamamoto (1995), or that of Dolado and Lütkepohl  (1996) and Saikkonen and Lütkepohl (1996), are laid out in this earlier post, and I won't repeat them here. I'll make the bold assumption that you've done your homework.

Unit Root Testing: Sample Size vs. Sample Span

The more the merrier when it comes to the number of observations we have for our economic time-series data - right? Well, not necessarily. 

There are several reasons to be cautious, not the least of which include the possibility of structural breaks or regime-switching in the data-generating process. However, these are topics for future posts. Here, I want to discuss a different issue - namely, the impact of data frequency on the properties of tests for the stationarity of economic time-series.

To be specific, let's consider the following question: "Which is better when I'm applying the (augmented) Dickey-Fuller test - 20 annual observations for the series, or 80 quarterly observations?"

A. L. Nagar

Earlier this year I had a post in memory of the eminent statistician and econometrician, Anirudh Nagar. His passing was a great loss to our profession. 

Today, I was pleased to learn about this site that honours A. L. Nagar's life and contributions. 

The obituary by my friend, Aman Ullah, is especially noteworthy.

© 2014, David E. Giles

Correlation - NOT Causation

"Correlation is NOT the same as causation".

I don't know how many times I've said it (haven't we all?) in class, to the T.V. announcer, ...........

Tyler Vigen is a grad. student at Harvard Law School. He has a fun site called Spurious Correlations. Here are a couple of examples:

As of today, there are more than 23,000 spurious correlation charts on Tyler's site. You can even sign up to get an RSS feed of a new spurious correlation every day, if you're so inclined (or even if you're standing up)!

  

(r = 0.9357)

(r = 0.9805)

Yes, the sample sizes are small; and yes, I'd like to see more economic examples. However, I can still see myself using this material in class!

© 2014, David E. Giles