Econometrics Beat: Dave Giles' Blog

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!

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 4^th 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 5^th 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?

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

-and-

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

-and-

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."

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.......

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?"

Enjoy!

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.

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 (y_i, x_i') and the next ‘n’ of them would be of the form (-y_i , -x_i'). 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.....

Wednesday, September 25, 2013

Blogging About Your Research

Hat-tip to Arthur Charpentier for this link: "28 Reasons Why You Should Blog About Your Research".