Tuesday, December 31, 2013

My Top 5 For 2013

Everyone seems to be doing it at this time of the year. So, here are the five most popular new posts on this blog in 2013:
  1. Econometrics and "Big Data"
  2. Ten Things for Applied Econometricians to Keep in Mind
  3. ARDL Models - Part II - Bounds Tests
  4. The Bootstrap - A Non-Technical Introduction
  5. ARDL Models - Part I

Thanks for reading, and for your comments.

Happy New Year!

© 2013, David E. Giles

Monday, December 30, 2013

A Cautionary Bedtime Story

Once upon a time, when all the world and you and I were young and beautiful, there lived in the ancient town of Metrika a young boy by the name of Joe.

Sunday, December 29, 2013

Happy Birthday, Econometric Society

The Econometric Society was founded 83 years ago today, as a result of a meeting held at the Stalton Hotel in Cleveland, Ohio.

One of my earliest posts was devoted to this aspect of the history of our discipline. If you haven't read it, this would certainly be an appropriate day to do so!

And if you want to look ahead, as well as back, keep in mind that the Econometric Society holds  a World Congress every five years. The 11th Congress is scheduled for 15 to 21 August 2015, in Montreal, Canada.

See you there!

© 2013, David E. Giles

Saturday, December 28, 2013

Statistical Significance - Again

With all of this emphasis on "Big Data", I was pleased to see this post on the Big Data Econometrics blog, today.

When you have a sample that runs to the thousands (billions?), the conventional significance levels of 10%, 5%, 1% are completely inappropriate. You need to be thinking in terms of tiny significance levels.

I discussed this in some detail back in April of 2011, in a post titled, "Drawing Inferences From Very Large Data-Sets". If you're of those (many) applied researchers who uses large cross-sections of data, and then sprinkles the results tables with asterisks to signal "significance" at the 5%, 10% levels, etc., then I urge you read that earlier post.

It's sad to encounter so many papers and seminar presentations in which the results, in reality, are totally insignificant!

© 2013, David E. Giles

Friday, December 27, 2013

Unbiased Estimation of a Standard Deviation

Frequently, we're interested in using sample data to obtain an unbiased estimator of a population variance. We do this by using the sample variance, with the appropriate correction for the degrees of freedom. Similarly, in the context of a linear regression model, we use the sum of the squared OLS residuals, divided by the degrees of freedom, to get an unbiased estimator of the variance of the model's error term.

But what if we want an unbiased estimator of the population standard deviation, rather than the variance?

Thursday, December 26, 2013

Solution to Regression Problem

O.K. - you've had long enough to think about that little regression problem I posed the other day. It's time to put you out of your misery!

Here's the problem again, with a solution.

Tuesday, December 24, 2013

Thought for the Day

As a number of writers have noted previously, sales of Christmas cards Granger-cause Christmas, but they certainly don't cause Christmas!

Best wishes for the holiday season.

© 2013, David E. Giles

Monday, December 23, 2013

A Simple Regression Problem

Here's a regression problem for student readers of this blog.

Suppose that we estimate the following regression model by OLS:

                     yi = α + β xi + εi .

The model has a single regressor, x, and the point estimate of β turns out to be 10.0.

Now consider the "reverse regression", based on exactly the same data:

                    xi = a + b yi + ui .

What can we say about the value of the OLS point estimate of b?
  • It will be 0.1.
  • It will be less than or equal to 0.1.
  • It will be greater than or equal to 0.1.
  • It's impossible to tell from the information supplied.

© 2013, David E. Giles

Thomas Bayes - 250 Years On

Two hundred and fifty years ago today a paper titled, "An Essay Towards Solving a Problem in the Doctrine of Chances", was presented to a meeting of the Royal Statistical Society in London. (Although, see here.)

The presenter - Richard Price. The author - (the late) Reverend Thomas Bayes.

Thus, we received "Bayes' Theorem".

A few days ago, the International Society for Bayesian Analysis held a celebratory conference to honour this momentous occasion in the history of statistical and scientific thinking.

Bayesian thinking has had a significant impact on the field of econometrics. My own Ph.D. dissertation (1975) was in Bayesian econometrics, and I was fortunate enough to have had Arnold Zellner as an external examiner.

I just wish I'd had access to the computational technology that's so freely available today!

© 2013, David E. Giles

Sunday, December 22, 2013

More on Student-t Regression Models

My recent post relating to maximum likelihood estimation of non-standard regression models in EViews included the case where the model's errors are independent Student-t distributed. In that example, the degrees of freedom for the Student-t distribution were assumed to be known. There was a good reason for making this assumption, as was spotted by Osman Dogan in his comment on that post.

If we relax this assumption and include the degrees of freedom parameter, v, of the t-distribution as another parameter that has to be estimated, then the likelihood function exhibits some unfortunate characteristics. Specifically, this function becomes unbounded at a boundary of the parameter space. Consequently, maximizing the likelihood function will generally result in us achieving only a local maximum, not a global maximum.

You might ask, "why would this matter?" Well, basically, if you want to be sure that your MLE achieves the good asymptotic properties that motivate us to use it in the first place, then you need to globally maximize the likelihood function.

I discussed this issue in some detail in an earlier post, here.

In the context of the multiple regression model with independent Student-t errors with an unknown degrees of freedom parameter, these issues have been discussed fully by Fernandez and Steel (1999), for example. In particular, those authors show how a Bayesian approach to this estimation problem can overcome the difficulties associated with MLE here.

The problem is very reminiscent of the "incidental parameters" problem that arises widely in statistics, as well as in certain econometric estimation problems. Good examples of this general type of problem in econometrics include "switching regression" models; as well as models of markets that are in disequilibrium; and stochastic frontier production functions.

It's well known that a Bayesian approach is productive in the case of the "incidental parameters" problem, so it shouldn't be too surprising that it's also helpful with the Student-t regression model.

So, if you want to estimate a regression model with independent Student-t errors, and the degrees of freedom parameter associated with that distribution is unknown, then don't use maximum likelihood estimation! The Bayesian estimator discussed by Fernandez and Steel (1999) is one alternative. Pianto (2010) suggests a bootstrap estimator; and another possibility  would be to consider method of moments estimation, which would result in estimates that are at least weakly consistent.


Fernandez, C, and M. F. J. Steel, 1999. Multivariate Student-t regression models: Pitfalls and inference. Biometrika, 86, 153-167. (Downloadable version here.)

Pianto, D. M., 2010. A bootstrap estimator for the Student-t regression model.

© 2013, David E. Giles

Saturday, December 21, 2013

What is an Econometric Model? Objectivity vs. Reflexivity

In response to my recent post, titled, "The History of Econometrics - An Alternative View", Judea Pearl  sent me a thoughtful and intriguing comment. The comment is posted already, but I think that it deserves more than just being tucked away at the bottom of another post.

So, I am giving Judea's comment additional attention here. I hope that you'll find it interesting, and that it will provoke some much-needed discussion.

Here's Judea's comment in its entirety:

Thursday, December 19, 2013

Maximum Likelihood Estimation in EViews

This post is all about estimating regression models by the method of Maximum Likelihood, using EViews. It's based on a lab. class from one of my grad. econometrics courses.

We don't go through all of the material below in class - PART 3 is left as an exercise for the students to pursue in their own time.

The data and the EViews workfile can be found on the data page and the code page for this blog.

The purpose of this lab. exercise is to help the students to learn how to use EViews to estimate the parameters of a regression model by Maximum Likelihood, when the model is of some non-standard type. Specifically, find lout how to estimate models of types that are not “built in” as a standard option in EViews. This involves setting up the log-likelihood function for the model, based on the assumption of independent observations; and then maximizing this function numerically with respect to the unknown parameters. 

First, to introduce the concepts and commands that are involved, we consider the standard  linear multiple regression model with normal errors, for which we know that the MLE of the coefficient vector is just the same as the OLS estimator. This will give us a “bench-mark” against which to check our understanding of what is going on. Then we can move on to some more general models.

Wednesday, December 18, 2013

The History of Econometrics - An Alternative View

There are different ways of looking at history.Professor Annie Cot reminds of this, in the context of econometrics, in one of her dissertations that has been made available here.
"Econometrics has become such an obvious, objective - almost natural - tool that economists often forget that it has a history of its own, a complex and sometimes problematic history. Two works - Morgan (1990) and Qin (1993) - constitute the Received View of the history of econometrics. Basing our analysis on Leo Corry's methodological (and historiographical) framework of image and body of knowledge, the main purpose of this dissertation is to provide a critical account of the Received View.
Our main criticism is that historians of econometrics have a particular image of knowledge that stems from within econometrics itself, generating a problem of reflexivity. This means that historians of econometrics would evaluate econometrics and its history from an econometrician point of view, determining very specific criteria of what should be considered as "true", what should be studied or what should be the questions that the scientific community should ask.
This reflexive vision has conducted the Received View to write an internalist and funnel-shaped version of the History of Econometrics, presenting it as a lineal process progressing towards the best possible solution: Structural Econometrics and Haavelmo's Probability Approach in Econometrics (1944). 
The present work suggests that a new history of econometrics is needed. A new history that would overcome the reflexivity problem yielding a certainly messier and convoluted but also richer vision of econometrics' evolution, rather than the lineal path towards progress presented by the Received View".
If you have a serious interest in the history of our discipline, this is for you.

© 2013, David E. Giles

Monday, December 16, 2013

Dennis Lindley Passes Away

The loss of Dennis Lindley, yesterday, will be received with sadness by Bayesians - econometricians included.

Dennis was a major driving force in the formalization and dissemination of Bayesian thought.

Two posts that comment on his many contributions can be found here and here.

I recall presenting a Bayesian paper at a statistics conference in New Zealand in the 1970's, with Dennis in the front row. It was an unnerving experience!

© 2013, David E. Giles

Sunday, December 15, 2013

Proxy Variables and Biased Estimation

Here's a problem from the exam. that one of my econometrics classes sat recently. It's to do with some of the consequences of mis-specifying a regression model, and then applying OLS estimation.

Specifically, let's suppose that data-generating process (the correct model specification) is actually of the form:

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

However, we can't observe the k variables in the X matrix, and instead we replace them with k "proxy variables" (substitutes) that we can observe. So, the model that we actually estimate is:

                      y = X*β + v .                                                     (2)

The students were asked to show that the usual (unbiased) estimator of σ2 is actually biased in this case; and they were asked if they could determine the "direction" of the bias.

Friday, December 13, 2013

On Staying Awake in Class

Pedagogy Unbound  is "A place for college teachers to share practical strategies for today's classrooms."

Their blog today contains a lovely piece by David Gooblar, titled " 'Trucker Tricks' for Keeping Students Awake". Not that any of you would have such problems on either side of the rostrum in econometrics classes, I'm sure!

David writes:
"Of all the tips that have been posted at Pedagogy Unbound since the site’s launch in August, the one that has been read the most—by far—is titled “Help your students stay awake in class.” This, it seems, is what professors are most concerned about. Not student writing. Not the plague of plagiarism. Not even students who don’t participate in discussions. No, the most pressing problem facing college teachers today is merely getting their students to stay conscious for an hour and 15 minutes.
.......The tip is one (from an associate professor who) worked as a truck driver when he was a college student and now, as a teacher, he passes on his “trucker tricks” for staying awake to his students. 
......Crucially, (he) follows up these tips by inviting the students, at any time during class throughout the term, to stand up if they feel like they are getting sleepy. They can take their notebooks and stand at the back or side of the classroom. He tells them he’d much prefer a class full of standing students to one full of sleeping, or even just drowsy, students. 
.......So ask your students to stand up if they feel they are in danger of falling asleep. If it turns out that a number of them take you up on the offer, you can tell yourself that you’re getting a standing ovation." 
I'm going to try it out!

© 2013, David E. Giles

Thursday, December 12, 2013

Time for Some More Reading!

With the weekend upon us once again, it's time to settle down with the papers - the econometrics research papers, that is. Here are my latest picks:
  • Cook, S., D. Watson, and L. Parker, 2014. New evidence on the importance of gender and asymmetry in the crime-unemployment relationship. Applied Economics, 46, 119-126.
  • Fan, J., F. Han, and H. Liu, 2013. Challenges of big data analysis. Mimeo.
  • Hashmi, A. R., 2014. Competition and innovation: The inverted-U relationship revisited. Review of Economics and Statistics, in press.
  • Juselius, K., N. F. Moller, and F. Tarp, 2104. The long-run impact of foreign aid in 36 African countries: Insights from multivariate time series analysis. Oxford Bulletin of Economics and Statistics, in press.
  • Li, R., D. K. J. Lin, and B. Li, 2013. Statistical inference in massive data sets. Applied Stochastic Models in Business and Industry, 29, 399-409.
  • Sanderson, E. and F. Windmeijer, 2013. A weak instrument F-test in linear IV models with multiple endogenous variables. CEMMAP Working Paper CWP58/13, The Institute for Fiscal Studies.

© 2013, David E. Giles

Data Do Not Imply Science

As a follow-up to my recent post on Big Data, I recommend today's post by Jeff Leek on the Simply Statistics blog. It's titled. 'The key word in "Data Science is not Data, it is Science'.

Jeff says:
"Most people hyping data  science have focused on the first word: data. They care about volume and velocity and whatever other buzzwords describe data that is too big for you to analyze in Excel. .........
But the key word in data science is not "data"; it is "science". Data science is only useful when the data are used to answer a question. That is the science part of the equation. The problem with this view of data science is that it is much harder than the view that focuses on data size or tools. It is much, much easier to calculate the size of a data set and say "My data are bigger than yours"......"
Right on, Jeff!

© 2013, David E. Giles

When Everything Old is New Again

We see it with clothing styles. Not just hemline lengths, but also the widths of jacket lapels and guy's ties. How wide should the trouser legs be? Cuffs or no cuffs? Leave your clothes in the closet long enough, and there's a good chance they'll be back in style some day!

And so it is with econometrics. Here are just a few examples:

Monday, December 9, 2013

Random Variable?

A big HT to Ryan MacDonald for drawing this quote to my attention:
"While writing my book (Stochastic Processes, 1953) I had an argument with Feller. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won."

Joe Doob, in Statistical Science 12 (1997), No. 4, page 307.

Added - thanks to Arthur Charpentier for this link..

© 2013, David E. Giles

Friday, December 6, 2013

The Washing Machine Repairman

Here's a fun quote.
"As I remember, Bill X fixed my washing machine. My husband, Harry X, brought him home to talk economics after a Cambridge dinner in hall and they walked in on my frustration with the washer. I met a slight-statured, quiet man who modestly asked if he could help. He tried something with a screw-driver which may have worked - or perhaps it didn't work - and went back to talking economics'"

Who were  "Harry" and Bill?

© 2013, David E. Giles

Thursday, December 5, 2013

Econometrics and "Big Data"

In this age of "big data" there's a whole new language that econometricians need to learn. Its origins are somewhat diverse - the fields of statistics, data-mining, machine learning, and that nebulous area called "data science".

What do you know about such things as:
  • Decision trees 
  • Support vector machines
  • Neural nets 
  • Deep learning
  • Classification and regression trees
  • Random forests
  • Penalized regression (e.g., the lasso, lars, and elastic nets)
  • Boosting
  • Bagging
  • Spike and slab regression?

Probably not enough!

If you want some motivation to rectify things, a recent paper by Hal Varian will do the trick. It's titled, "Big Data: New Tricks for Econometrics", and you can download it from here. Hal provides an extremely readable introduction to several of these topics.

He also offers a valuable piece of advice:
"I believe that these methods have a lot to offer and should be more widely known and used by economists. In fact, my standard advice to graduate students these days is 'go to the computer science department and take a class in machine learning'."
Interestingly, my son (a computer science grad.) "audited" my classes on Bayesian econometrics when he was taking machine learning courses. He assured me that this was worthwhile - and I think he meant it! Apparently there's the potential for synergies in both directions.

© 2013, David E. Giles

Wednesday, December 4, 2013

The International Association for Applied Econometrics

Here's an organisation that deserves promoting - The International Association for Applied Econometrics. What more can I say?

Well, I had better add something!

"The aim of the Association is to advance the education of the public in the subject of econometrics and its applications to a variety of fields in economics, in particular, but not exclusively, by advancing and supporting research in that field, and disseminating the results of such useful research to the public."

There next Annual Conference will be held in London, U.K., in June 2014, and the line-up of keynote speakers is impressive. Submissions of papers are due by 1 February 2014, and there is a nice prize for the best paper presented by a graduate student.

© 2013, David E. Giles

Friday, November 29, 2013

Do You Have a Tattoo?

Significance Magazine  is a joint publication of the Royal Statistical Society and the American Statistical Association. The "News" section of the latest issue (which can be read by subscribers) contains an item titled, "More Than Skin Deep". It's about a mathematics teacher who has an interesting tattoo:

In case you need an interpretation, it reads:  
The item concludes:
"It attracts attention. Often on a beach someone will say something like 'You're either a math teacher or in a really, really odd motorcycle gang.'
Why should statisticians lag behind? A bottle of champagne to the first reader who can show a permanent tattoo of Bayes' theorem - preferably on a part of the anatomy that we can decently reproduce."
Needless to say, this got me thinking! Are there any Econometrics tattoos out there that I should be aware of?

© 2013, David E. Giles

Lawrence R. Klein Memorial Prize

Nobel Laureate Lawrence R. Klein passed away in October of this year in Philadelphia. (See here.) 

Empirical Economics has established a prize in his honour given for the best empirical paper published in the last two years in the journal. An upcoming issue of Empirical Economics will include an obituary written by Badi Baltagi.

© 2013, David E. Giles

Monday, November 25, 2013

A Bayesian View of P-Values

"I have always considered the arguments for the use of P (p-value) absurd. They amount to saying that a hypothesis that may or may not be true is rejected because a greater departure from the trial was improbable: that is, that it has not rejected something that has not happened'"
H. Jeffreys, 1980. Some general points in probability theory. In A Zellner (ed.), Bayesian Analysis in Probability and Statistics. North-Holland, Amsterdam, p. 453.

© 2013, David E. Giles

Thursday, November 21, 2013

Forecasting from a Regression Model

There are several reasons why we estimate regression models, one of them being to generate forecasts of the dependent variable. I'm certainly not saying that this is the most important or the most interesting use of such models. Personally, I don't think this is the case.

So, why is this post about forecasting? Well, a few comments and questions that I've had from readers of this blog suggest to me that not all students of econometrics are completely clear about certain issues when it comes to using regression models for forecasting.

Let's see if we can clarify some terms that are used in this context, and in the process clear up any misunderstandings.

Wednesday, November 20, 2013

Data, Data, Everywhere.....

Data - the life-blood of econometrics - we can't live without them.!

So, thank goodness for the recent re-vamp of the the FED's FRED data site. And also the recent additions to the Quandl site.

© 2013, David E. Giles

Saturday, November 16, 2013

How Science (Econometrics?) is Really Done

If you tweet, you may be familiar with #OverlyHonestMethods. If not, this link to Popular Science will set you on the right track. As it says: "In 140 characters or less, the info that didn't get through peer review."

Here are some beauties that may strike an accord with certain applied econometricians:
  • "Our results were non-significant at p > 0.05, but they're humdingers at p > 0.1"
  • "Experiment was repeated until we had three statistically significant similar results and could discard the outliers"
  • "We decided to use Technique Y because it's new and sexy, plus hot and cool. And because we could."
  • "I can't send you the original data because I don't remember what my excel file names mean anymore."
  • "Non-linear regression analysis was performed in Graph Pad Prism because SPSS is a nightmare."
  • "We made a thorough comparison of all post-hoc tests while our statistician wasn't looking."
  • "Our paper lacks post-2010 references as it's taken the co-authors that long to agree on where to submit the final draft."
  • "If you pay close attention to our degrees-of-freedom you will realize we have no idea what test we actually ran."
  • "Additional variables were not considered because everyone involved is tired of working on this paper."
  • "We used jargon instead of plain English to prove that a decade of grad school and postdoc made us smart."

Oh yes!!!!

© 2013, David E. Giles

A Talk With Lars Peter Hansen

Now that some of the commotion and excitement over this year's Economics Nobel Prize has died down a little, an informal chat with co-winner Lars Peter Hansen is definitely in order.

So, a hat-tip to Mark Thoma for alerting me to this interview of Hansen by Jeff Sommer in the New York Times, today. Jeff manages to get a comment about efficient markets from his interviewee.

And here's a comment that all students of econometrics should take to heart:

"The thing to remember about models is they’re always approximations and they will always turn out to be wrong at some point. When someone says all the models that economists use are wrong, well, in a sense that’s true. But you need to ask, are the models wrong in ways that are central to the questions, or are they wrong in ways that aren’t so central?
And so part of the task of statistical analysis is to look at models and try to figure out what the gaps are so that people will build better models in the future."

© 2013, David E. Giles

Monday, November 11, 2013

Calling All Forecasters!

The 34th International Symposium on Forecasting will be held in Rotterdam between 29 June and 2 July, 2014. Full details can be found here

I participated in the 2010 Symposium, in San Diego. It was a great meeting, very well run, and with a fabulous program. Definitely recommended!

© 2013, David E. Giles

Sunday, November 10, 2013

Free EViews Tutorials

Free Eviews tutorials - but not from me, I'm afraid!

"Free" is good, and you should keep in mind that free introductory tutorials are indeed available from the distributors of the EViews package. You can find the details here.

You can even download all of the associated Powerpoint presentations, and data files, in a zip file. Nice!

© 2013, David E. Giles

Friday, November 8, 2013

The Econometric Game, 2014

Doesn't time fly. We must be having fun! It's time to start thinking about The Econometric Game once again - this time, the 2014 edition.

April  15 to 17 2014 are the dates to keep in mind, and once again Amsterdam will be the place to be. Apparently entries are rolling in!

More on this in due course.

© 2013, David E. Giles

The Stock Market Crash - VECM's & Structural Breaks

A few weeks ago, Roger Farmer kindly drew my attention to a recent paper of his - "The Stock Market Crash Really Did Cause the Great Recession" (here). To whet your appetites, here's the abstract:
"This note shows that a big stock market crash, in the absence of central bank intervention, will be followed by a major recession one to four quarters later. I establish this fact by studying the forecasting ability of three models of the unemployment rate. I show that the connection between changes in the stock market and changes in the unemployment rate has remained structurally stable for seventy years. My findings demonstrate that the stock market contains significant information about future unemployment."

Sunday, November 3, 2013

Specification Testing for Panel Data Models

Recently, I received a query from Rolf Lyneborg Lund who asked for references to material on specification testing in the context of panel data models. After I responded to Rolf. it occurred to me that these references might also be of interest to others.

Going beyond the standard Hausman test for random versus fixed effects, here are some general references that may be helpful:
  • Baltagi, B. H., 1998. Panel data methods. In A. Ullah and D. E. A. Giles (eds.), Handbook of Applied Economic Statistics, Marcel Dekker, New York.
  • Baltagi, B. H., 1999. Specification tests in panel data models using artificial regressions. Annales d'Économie et des Statistiques, 55-56, 277-298.
  • Lee, Y-J., 2005. Specification testing for functional forms in dynamic panel data models.
  • Metcalf, G. E., 1996. Specification testing in panel data with instrumental variables. Journal of Econometrics, 71, 291-307.
  • Park, H. M., 2011. Practical guides to panel data modeling: A step by step analysis using stata. Public Management and Policy Analysis Program, Graduate School of International Relations, International University of Japan.
In addition, there's quite an extensive literature on testing for unit roots and cointegration in panel data models. I won't attempt to summarize this literature here, but a useful, recent, summary is provided by:
  • Chen, M-Y., 2013. Panel unit root and cointegration tests. Mimeo., Department of Finance, National Chung Hsing University.

© 2013, David E. Giles

Friday, November 1, 2013

Some Weekend Reading

Just what you need - some more interesting reading!
  • Al-Sadoon, M. M., 2013. Geometric and long run aspects of Granger causality. Mimeo., Universitat Pompeu Fabra. (Forthcoming in Journal of Econometrics.)
  • Barnett, W. A. and I. Kalondo-Kanyama, 2013. Time-varying parameter in the almost ideal demand system and the Rotterdam model: Will the best specification please stand up? Working Paper 335, Econometric Research Southern Africa.
  • Delgado, M. S. and C. F. Parmenter, 2013, Embarrassingly easy embarrassingly parallel processing in R. Journal of Applied Econometrics, early view, DOI: 10.1002/jae.2362 .
  • Doko Tchatoka, H., 2013. On bootstrap validity for specification tests with weak instruments. Discussion Paper 2013-05, School of Economics and Finance, University of Tasmania.
  • Fisher, L. A., H-S. Huh, and A. R. Pagan , 2013, Econometric issues when modelling with a mixture of I(1) and I(0) variables. NCER Working Paper Series, Working Paper #97.
  • Pesaran, H. H. and Y. Shin, 1998. Generalized impulse response analysis in linear multivariate models. Economics Letters, 58, 17-29.
  • Warr, R. L. and R. A. Erich, 2013. Should the interquartile range divided by the standard deviation be used to assess normality? American Statistician, online, 
    10.1080/00031305.2013.847385 .
  • Zhang, X. and X. Shao, 2013, On a general class of long run variance estimators. Economics Letters, 120, 437-441.

© 2013, David E. Giles

Tuesday, October 29, 2013

swirl: Learning Statistics & R

Most of us would acknowledge that getting up to speed with R involves a pretty steep learning curve - but it's worth every drop of sweat we shed in the process!

If you're learning basic statistics/econometrics, and learning R at the same time, then the challenge is two-fold. So, anything that will make this feasible (easy?) for students and instructors alike deserves to be taken very seriously.

Enter swirl - "statistics with interactive R learning" - developed at the Department of Biostatistics, Johns Hopkins University.  It's dead easy to download and install swirl - it just takes a few moments, and you're underway.

There are simple, interactive, lessons that introduce you to the essential concepts, and you have the option to watch related videos. If you need to take a break part way through a lesson then you can save what you've completed, and pick up from that point at a later time.

My guess is that students will find swirl appealing and very helpful.

© 2013, David E. Giles

Sunday, October 27, 2013

The Joys of Publishing!

I owe a VERY BIG hat-tip to Arthur Charpentier (he of the Freakonometrics blog) for alerting me to this one!

Getting your work published can pose interesting challenges at the best of times. But what about at the worst of times? 

Rick Trebino, of the School of Physics at Georgia Tech., tells us "How to Publish a Scientific Comment in 1 2 3 Easy Steps". I just love it!

Here's how Rick's story begins:

The Future of Statistical Sciences Workshop

No doubt you know, already, that 2013 has been the International Year of Statistics. To that end, there's been a veritable smorgasbord of activities and events promoting the discipline, and the contributions of statisticians far and wide.

The capstone event for Statistics2013 is "The Future of Statistical Sciences Workshop", to be held in London (England) on 11 and 12 November.

This workshop
"...will showcase the breadth and importance of statistics and highlight the extraordinary opportunities for statistical research in the coming decade.
This invitation-only workshop will be an opportunity for presenters, all statisticians and organizers to think about where statistics should go as a discipline and the lessons learned in the past that will guide us into the future. During this unique event, statistical scientists and scientists from other disciplines will interact and chart a shared vision for the future."
There are some great speakers lined up for this two-day event, and although the workshop is invitation-only, you can register now for the associated webinar.

And don't forget The Unconference on the Future of Statistics!
© 2013, David E. Giles

Saturday, October 26, 2013

Segmented Regression - Some (Relatively) Early References

In response to a recent post of mine on "segmented regression", an anonymous reader asked if I knew when such regressions first appeared in the literature. I'm not sure of the very first reference, but there was certainly an active literature on this by the mid 1960's.

One good reference is V. E. McGee and W. T. Carleton (1970), "Piecewise Regression", Journal of the American Statistical Association, 65, 1109-1124. Those authors cite the following other material, which includes several earlier papers on this topic:

Hopefully, this is helpful.

© 2013, David E. Giles

Friday, October 25, 2013

Chris Sims on Bayesianism

I just love this piece by Chris Sims: "Bayesian Methods in Applied Econometrics, or, Why Econometrics Should Always and Everywhere Be Bayesian", from 2007.

In addition to the solid content, there are some great take-away snippets, such as:

  • "Bayesian inference is hard in the sense that thinking is hard."
  • "(People) want to characterize uncertainty about parameter values, given the sample that has actually been observed."
  • "Good frequentist practice has a Bayesian interpretation."

  • And Sims' conclusion: "Lose your inhibitions: Put probabilities on parameters without embarrassment."

    I can live with that!

    © 2013, David E. Giles

    Tuesday, October 22, 2013

    Solution to the Segmented Regression Problem

    Here's my solution to the "segmented regression" problem that I posed yesterday. Thanks for the comments and suggestions!

    You'll recall that what we wanted to do was to end up with a fitted least squares "line" looking like this:

    In particular, the "kink" in the line is at a pre-determined point - in this example when x = 30.

    Here's how we can achieve this:

    Money 101: Top Resources for Finance Majors

    Abigail Moore, the Content Creator at OnlineFinanceDegree.org, emailed me today:

    "I'm writing with the exciting news that our latest article, "Money 101: Top Resources for Finance Majors," has been published, and Econometrics Beat: Dave Giles' Blog is cited on it.
    Finance is an engaging and highly competitive professional field to get into. For those studying finance, the internet can offer a wealth of resources. That said, it can be hard to sift through and find the best. We hope this feature will help finance students find information about financial organizations, current economic news, financial modeling software and techniques, and the finance industry as a whole. Your site is a valuable addition to this resource.
    We're hoping to share this article with as many finance students and professionals as possible and will be contacting our readers and followers. If you're able to post this on your website or share the article anywhere else you can think of too, I'd really appreciate it." 
    No problem, Abigail - happy to oblige. You'll find this blog listed as site #8.

    © 2013, David E. Giles

    Monday, October 21, 2013

    Lawrence R. Klein, 1920-2013

    One of the great figures of econometrics passed away yesterday. Lawrence Klein was the father of whole-economy macroeconometric modelling, and his massive contributions to this field earned him the Nobel Prize in 1980.

    Klein created some of the earliest simultaneous equations models of the U.S. economy (e.g., see here), and he was the driving force behind countless such models for other economies around the world. Among other things, Klein was responsible for the foundation of Project LINKin 1968. This ambitious endeavour now brings together econometric models for 78 countries to provide a "world econometric model".

    Lawrence Klein shaped econometric modelling, and his passing marks the end of an amazing era.

    Businessweek's obituary for Lawrence Klein can be found here.

    © 2013, David E. Giles

    A "Segmented" Regression Problem

    Here's a little exercise for the students among you.

    Suppose that we want to fit a least squares regression model that allows for a "break" in the underlying relationship at a particular sample value for the regressor(s). In addition, we want to make sure that the fitted model passes through that sample value.

    In other words, we want to end up with a fitted model that gives a result such as this:

    Here, the two segments of the regression line "join" when X=30. What's a simple way to achieve this?

    © 2013, David E. Giles

    Monday, October 14, 2013

    Economics Nobel Prize, 2013

    The waiting is over - the 2013 Nobel in Economics was announced this morning! Most deservedly, it has been awarded to Eugene F. Fama (U. Chicago), Lars Peter Hansen (U. Chicago), and Robert J. Shiller (Yale U.). The citation says: "For their empirical analysis of asset prices". 

    For more details, see here.

    It's really  nice to see the recognition of empirical research.

    And let's not forget that Hansen gave us GMM estimation; and do you recall Shiller distributed lag models?

    © 2013, David E. Giles

    Saturday, October 12, 2013

    Project-Based Learning of Modern Econometrics

    The U.K.  Economics Network is supported by, and housed at, the University of Bristol. It provides a wealth of resources for those teaching Economics.  These resources include material produced by various funded projects, including one by Steve Cook (Swansea University). His project (in 2010-11) was titled, "Project-Based Learning of Modern Econometrics. Here's Steve's overview:

    Friday, October 11, 2013

    Do Better Economic Models Lead to Better Forecasting?

    Earlier this month I had a post drawing attention to a short video by David Hendry. Here's another one - this time titled, "Do Better Economic Models Lead to Better Forecasting?

    © 2013, David E. Giles

    Thursday, October 10, 2013

    Seven Deadly Sins

    Xiao-Li Meng has an interesting piece in the September 2013 issue of the IMS Bulletin. (IMS = Institute of Mathematical Statistics). You'll find it on page 4, and it's titled "Rejection Pursuit".

    In short, it's about the author's repeated efforts, as a young researcher, to get a particular paper published. The story has a happy ending, and Xiao-Li leaves us with a list of "Seven Deadly Sins of Research Papers, and Seven Virtues to Cultivate":

    This looks like excellent advice, regardless of your discipline.

    And yes, the article does have an econometric connection. If you read the article and you're interested in non-stationary time-series, you'll probably see the connection coming before the author mentions it!

    © 2013, David E. Giles

    Beyond MSE - "Optimal" Linear Regression Estimation

    In a recent post I discussed the fact that there is no linear minimum MSE estimator for the coefficients of a linear regression model. Specifically, if you try to find one, you end up with an "estimator" that is non-operational, because it is itself a function of the unknown parameters of the model. It's note really an estimator at all, because it can't be computed.

    However, by changing the objective of the exercise slightly, a computable "optimal estimator" can be obtained. Let's take a look at this.

    Wednesday, October 9, 2013

    Blogs on Resources for Economists

    Nice to see that we're now listed on the list of Economics blogs on Resources for Economists.


    © 2013, David E. Giles

    Tuesday, October 8, 2013

    So Much Good Reading........

    Here are my latest reading suggestions:
    • Choi, I., 2013. Panel Cointegration. Working Paper, Department of Economics, Sogang University, Korea.
    • Davidson, R. and J. G. MacKinnon, 2013. Bootstrap tests for overdentification in linear regression models. Economics Department Working Paper No. 1318, Queen's University.
    • Deng, A., 2013. Understanding spurious regression in financial econometrics. Journal of Financial Econometrics, in press.
    • Feng, C., H. Wang, Y. Han, and Y. Xia, 2013. The mean value theorem and Taylor's expansion in statistics. The American Statistician, in press.
    • Kiviet, J. F. and G. D. A. Phillips, 2013. Improved variance estimation of maximum likelihood estimation in stable first-order dynamic regression models. EGC Report No. 2012/06, Division of Economics, Nanyang Technical University.
    • Lanne, M., M. Meitz, and P. Saikkonen, 2013. Testing for linear and nonlinear predicatability of stock returns. Journal of Financial Econometrics, 11, 682-705.

    © 2013, David E. Giles

    The History of Statistics in the Classrom

    You've probably gathered already that I like to incorporate material relating to the history of econometrics, and the history of statistics, into my classroom material. I've always found that it adds perspective, and knowing something about the characters who've contributed to the development of the discipline brings the material to life.

    A few years ago, Herbert David presented a paper at the Joint Statistical Meetings, titled "The History of Statistics in the Classroom". It discusses three big players - Laplace, Gauss, and Fisher. You can download a copy of the paper here.

    © 2013, David E. Giles

    Monday, October 7, 2013

    A Second Lesson in Econometrics

    In an earlier post (here) I discussed John Siegfried's short piece titled "A First Lesson in Econometrics".

    A reader of this blog "veli y" has drawn my attention to a very important follow-up piece by Damien Eldridge, of La Trobe University in Australia. His paper, "A Comment on Siegfried's First L"esson in Econometrics can be seen here

    Thanks for the tip!

    © 2013, David E. Giles

    Society for Economic Measurement

    Hat-Tip to Michael Belongia for drawing my attention to the Society for Economic Measurement.

    Initiated by William Barnett, the Society will be holding its first conference next (Northern) summer.

    Definitely worth checking out!

    © 2013, David E. Giles

    A Regression "Estimator" that Minimizes MSE

    Let's talk about estimating the coefficients in a linear multiple regression model. We know from the Gauss-Markhov Theorem that, within the class of linear and unbiased estimators, the OLS estimator is most efficient. Because it is unbiased, it therefore has the smallest possible Mean Squared Error (MSE), within the linear and unbiased class of estimators.

    However, there are many linear estimators which, although biased, have a smaller MSE than the OLS estimator. You might then think of asking: “Why don’t I try and find the linear estimator that has the smallest possible MSE?”

    Sunday, October 6, 2013

    Contemporary Econometrics in Economic Education Research

    Under the auspices of the Council for Economic Education, and the American Economic Association, William Becker has developed of An Online Handbook for the Use of Contemporary Econometrics in Economic Education. Details can be found here.

    While some might find the choice of topics (to date) to be somewhat idiosyncratic, it's still a very nice resource.

    © 2013, David E. Giles

    Saturday, October 5, 2013

    The History of Statistical Terms

    Do you ever wonder where those expressions that we use in econometrics come from? You know - terms such as "regression", "autocorrelation", and so on.

    Most of them are, of course, borrowed from mathematical statistics. But when were they first used, and who first coined these names?

    Friday, October 4, 2013

    Peter Kennedy on "Getting the Wrong Sign"

    The late Peter Kennedy spent most of his career in the Department of Economics at Simon Fraser University. He was a well-liked "just across the water" academic neighbour of mine.

    Peter was an excellent and passionate teacher. He was adept at explaining econometrics to reluctant listeners! Several years ago, he gave a seminar in our department titled, "Oh No! I Got the Wrong Sign! What Should I Do?"

    The paper was later published in The Journal of Economic Education, 2005, 36(1), 77-92.

    If you haven't seen it before, I'm sure you'll enjoy it.

    © 2013, David E. Giles

    The Unconference

    Another item from the September issue of the International Year of Statistics Newsletter:
    'Nearly two weeks before the Future of the Statistical Sciences Workshop*, the Unconference on the Future of Statistics will be staged. Organized by two of the authors of the Simply Statistics blog, the Unconference will be a virtual event hosted on Google Hangouts. 
    “It is a great time to be a statistician and discussing the future of our discipline is of utmost importance to us,” say Roger Peng and Jeff Leek, Unconference organizers, referring to the Future of the Statistical Sciences Workshop. “In fact, we liked the idea so much we decided to get in the game ourselves. We are super excited to announce the first ever ‘Unconference’ hosted by Simply Statistics. Our goal is to compliment and continue the discussion inspired by the Statistics 2013 Workshop.” 
    The Unconference, which will focus on the future of statistics from the perspective of junior statisticians, will be held October 30 from noon to 1 p.m. EST on Google Hangouts and simultaneously live-streamed on YouTube
    The event will feature several of the most exciting and innovative statistical thinkers discussing their views on the future of the field, especially those issues that affect junior statisticians the most: education, new methods, software development, collaborations with natural sciences/social sciences, and the relationship between statistics and industry. 
    You can sign up for the Unconference here. During the lead-up to the conference, organizers ask that you submit your thoughts on the future of statistics via Twitter using the hashtag #futureofstats. They will compile all comments and make these available along with the talks.' 
    * The Future of Statistical Sciences Workshop is a capstone event for the International Year of Statistics, which will take place in London, England in November of this year. There'll be more on this in a post closer to that date.

    © 2013, David E. Giles

    Thursday, October 3, 2013

    Something to Tweet About

    From the September issue of the International Year of Statistics Newsletter:
    "The Fields Institute for Research in Mathematical Sciences at the University of Toronto is sponsoring a Twitter contest called “The Normal Curve”. The contest is being held in recognition of the Institute’s 20th anniversary and the International Year of Statistics. In this unique contest, the Institute poses this question to the world: “What would the world be like if the normal curve was not discovered?” To enter, tweet your answer to the question using the hashtag #WithoutTheCurve for a chance to win one of three autographed copies of Jeffrey Rosenthal’s bestselling book, Struck by Lightning. Submissions for The Normal Curve contest will be accepted beginning September 25 at 12:01a.m. EST. To be eligible for the contest, submissions must be submitted by Twitter, tagged as #WithoutTheCurve and address the contest question. The entry deadline is 11:59 p.m. EST October 15. The top entries selected by volunteers at the Fields Institute’s MathEd forum will be entered into a pool for the drawing the prizes. Winners will be randomly selected for the three prizes. Winners will be announced by the end of October. The contest is open to users internationally. Submissions not in English may be translated using Google Translate if there is no one on the judging panel who can translate the tweet."
    Time to start tweeting!

    © 2013, David E. Giles

    The 5th Lindau Meeting on Economic Sciences

    The Lindau Nobel Laureate Meetings have been held since 1951. They bring together Nobel Laureates and a group of hand-picked young researchers from around the world in Lindau, Germany.

    The 4th such meeting for Economic Sciences was held in 2011, and involved 17 Economics Nobel laureates and more than 350 young economists from 65 countries.

    The 5th Lindau Meeting on Economic Sciences will be held in August 2014:
    "The 5th Lindau Meeting on Economic Sciences will provide an open exchange of economic expertise and inspire cross-cultural and inter-generational encounters among economists from all over the world. The world economic and financial crisis will surely be a central theme between the laureates and the young participants, but most likely the global central banking system or the challenges to the international free trade will also be main topics."
    Perhaps you know someone who deserves to be nominated to participate in this Meeting?

    © 2013, David E. Giles

    Wednesday, October 2, 2013

    The True Title of Bayes's Essay

    As someone whose Ph.D. dissertation was in the area of Bayesian Econometrics, I was fascinated to read this recent paper by Stephen Stigler: "The True Title of Bayes's Essay". It appeared this month in Statistical Science, 2013, vol. 28(3), 283-288.

    The abstract of the paper is succinct, but very clear:
    "New evidence is presented that Richard Price gave Thomas Bayes's famous essay a very different title from the commonly reported one. It is argued that this implies Price almost surely and Bayes not improbably embarked upon this work seeking a defensive tool to combat David Hume on an issue in theology."
    So, it wasn't just intended to provide a painful experience for those being introduced to probability theory for the first time, after all!

    October Means Nobel Prizes

    Yes, it's almost that time of year again!  The recipient(s) of the 2013 Nobel Prize in Economic Sciences (abbreviated title) will be announced in less than two weeks' time - Monday 14 October, to be precise.

    Thomson Reuters have made their predictions for the likely recipients in each field, including Economics.

    I particularly like one of their three potential "winning teams":

    "Sir David F. Hendry
    Professor of Economics
    University of Oxford
    Oxford, England, UK


    M. Hashem Pesaran
    John Elliot Distinguished Chair in Economics & Professor of Economics, and Emeritus Professor of Economics & Fellow of Trinity College, Cambridge
    University of Southern California, Los Angeles, CA, USA 
    and University of Cambridge, Cambridge, England, UK


    Peter C.B. Phillips
    Sterling Professor of Economics and Professor of Statistics
    Yale University
    New Haven, CT, USA

    For their contributions to economic time-series, including modeling, testing and forecasting."

    © 2013, David E. Giles

    In What Sense is the "Adjusted" R-Squared Unbiased?

    In a post yesterday, I showed that the usual coefficient of determination (R2) is an upward -biased estimator of the "population R2", in the following sense. If there is really no linear relationship between y and the (non-constant) regressors in a linear multiple regression model, then E[R2] > 0. However, both E[R2] and Var.[R2] → 0 as n → ∞. So, R2 is a consistent estimator of the (zero-valued) population R2.

    At the end of that post I posed the following questions:
    "You might ask yourself, what emerges if we go through a similar analysis using the "adjusted" coefficient of determination? Is the "adjusted R2" more or less biased than R2 itself, when there is actually no linear relationship between y and the columns of X?"
    Here's the answer.......

    Tuesday, October 1, 2013

    Can Economists Forecast Crashes?

    Without a doubt, Professor Sir David Hendry (University of Oxford) is one of the giants of econometrics. He's a wonderful speaker and champion of our profession, as you can see in this video, titled "Can Economists Forecast Crashes?"


    © 2013, David E. Giles

    More on the Distribution of R-Squared

    Some time ago, I had a post that discussed the fact that the usual coefficient of determination (R2) for a linear regression model is a sample statistic, and as such it has its own sampling distribution. Some of the characteristics of that sampling distribution were discussed in that earlier post.

    You probably know already that we can manipulate the formula for calculating R2, to show that it can be expressed as a simple function of the usual F-statistic that we use to test if all of the slope coefficients in the regression model are zero. This being the case, there are some interesting things that we can say about the behaviour of R2, as a random variable, when the null hypothesis associated with that F-test is in fact true.

    Let's explore this a little.

    Monday, September 30, 2013

    Solution to the Regression Trick

    In a post earlier this month, I posed the following problem:

    A researcher wishes to estimate the regression of y on X by OLS, but does not wish to include an intercept term in the model. Unfortunately, the only econometrics package available is one that "automatically" includes the intercept term. A colleague suggests that the following approach may be used to ‘trick’ the computer package into giving the desired result – namely a regression fitted through the origin: 
    Enter each data point twice, once with the desired signs for the data, and then with the opposite signs. That is, the sample would involve ‘2n’ observations – the first ‘n’ of them would be of the form (yi, xi') and the next ‘n’ of them would be of the form (-yi , -xi'). Then fit the model (with the intercept) using all ‘2n’ observations, and the estimated slope coefficients will be the same as if the model had been fitted with just the first ‘n’ observations but no intercept.” 
    Is your colleague's suggestion going to work?

    The answer is.....

    Friday, September 27, 2013

    More Interesting Papers to Read

    Here's my latest list of suggested reading:

    • Bayer, C. and C. Hanck, 2012. Combining non-cointegration tests. Journal of Time Series AnalysisDOI: 10.1111/j.1467-9892.2012.814.x 
    • Cipollina, M., L. De Benedictis, L. Salvatici, and C. Vicarelli, 2013.  A note on dummies for policies in gravity models: A Monte Carlo experiment. Working Paper no. 180, Dipartimento di Economia, Università degli studi Roma Tre.
    • Fair, R. C., 2013. Reflections on macroeconometric modelling. Cowles Foundation Discussion Paper No. 1908, Yale University.
    • Kourouklis, S., 2012. A new estimator of the variance based on minimizing mean squared error. The American Statistician, 66, 234-236.
    • Kulish, M. and A. R. Pagan, 2013. Issues in estimating new-Keynesian Phillips curves in the presence of unknown structural change. Research Discussion Paper, RDP 2012-11, Reserve Bank of Australia.
    • Little, R. J., 2013. In praise of simplicity, not mathematistry! Ten simple powerful ideas for the statistical scientist. Journal of the American Statistical Association, 108, 359-369.
    • Zhang, L., X. Xu, and G. Chen, 2012. The exact likelihood ratio test for equality of two normal populations. The American Statistician, 66, 180-184.

    © 2013, David E. Giles