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."

© 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.......

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!

© 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.

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.....

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 Analysis, DOI: 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

Blogging About Your Research

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

© 2013, David E. Giles

New Working Paper

Yanan Li (a former graduate student) and I have just released a new Working Paper. It's titled, "Modelling Volatility Spillover Effects Between Developed Stock Markets and Developing Asian Stock Markets".

If you're interested, you can download a copy of the paper from here.

ver Effects Between Developed Stock Markets and Asian Emerging Stock Marketsodelling Volatility Spillover Effects Between Developed Stock Markets and Asian Emerging Stock Markets

© 2013, David E. Giles

Roger Farmer on the Natural Rate Hypothesis and the Phillips Curve

Following yesterday's post about the Phillips Curve, Roger Farmer kindly emailed me and drew my attention to some of his related work.

One of his articles appeared recently in the Bank of England's Quarterly Bulletin - see here. It's titled, "The Natural Rate Hypothesis: An Idea Past its Sell-By Date". The "quick summary" is as follows:

• "Central banks throughout the world predict inflation with New Keynesian models where, after a shock, the unemployment rate returns to its so-called ‘natural rate’. That assumption is called the Natural Rate Hypothesis (NRH).

• This paper reviews a body of work, published over the past decade, in which I argue that the NRH does not hold in the data and provide an alternative paradigm that explains why it does not hold.

• I replace the NRH with the assumption that the animal spirits of investors are a fundamental of the economy that can be modelled by a ‘belief function’. I show how to operationalise that idea by constructing an empirical model that outperforms the New Keynesian Phillips Curve."

On p.246 of his article, Roger has a very nice illustrated summary of the estimation of the first Phillips Curve.