Econometricians' Debt to Alan Turing

The other day, Carol and I went with friends to see the movie, The Imitation Game. I definitely recommend it.

I was previously aware of many of Alan Turing's contributions, especially in relation to the Turing Machine, cryptography, computing, and artificial intelligence. However, I hadn't realized the extent of Turing's use of, and contributions to, a range of important statistical tools. Some of these tools have a direct bearing on Econometrics.

For example:

• (HT to Lief Bluck for this one.) In 1935, at the tender age of 22, Turing was appointed a Fellow at King's College, Cambridge, on the basis of his 1934 (undergraduate) thesis in which he proved the Central Limit Theorem. More specifically, he derived a proof of what we now call the Lindeberg-Lévy Central Limit Theorem.  He was not aware of Lindeberg's earlier work (1920-1922) on this problem. Lindeberg, in turn, was unaware of Lyapunov's earlier results. (Hint: there was no internet back then!). How many times has your econometrics instructor waved her/his arms and muttered ".......as a result of the central limit theorem....."?
• In 1939, Turing developed what Wald and his collaborators would later call "sequential analysis". Yes, that's Abraham Wald who's associated with the Wald tests that you use all of the time.Turing's wartime work on this subject remained classified until the 1980's. Wald's work became well-established in the literature by the late 1940's, and was included in the statistics courses that I took as a student in the 1960's. Did I mention that Wald's wartime associates included some familiar names from economics? Namely, Trygve Haavelmo, Harold Hotelling, Jacob Marschak, Milton Friedman, W. Allen Wallis, and Kenneth Arrow.
• The mathematician/statistician I. J. ("Jack") Good was a member of Turing's team at Bletchley Park that cracked the Enigma code. Good was hugely influential in the development of modern Bayesian methods, many of which have found their way into econometrics. He described the use of Bayesian inference in the Enigma project in his "conversation" with Banks (1996). (This work also gave us the Good-Turing estimator - e.g., see Good, 1953.)
• Turing (1948) devised the LU ("Lower and Upper") Decomposition that is widely used for matrix inversion and for solving systems of linear equations. Just think how many times you invert matrices when you're doing your econometrics, and how important it is that the calculations are both fast and accurate!

Added, 20 February, 2015: I have recently become aware of Good (1979)

References

Banks, D. L., 1996. A conversation with I. J. Good. Statistical Science, 11, 1-19.

Good, I. J., 1953.The population frequencies of species and the estimation of population parameters. Biometrika, 40, 237-264.

Good, I. J., 1979. A. M. Turing's statistical work in World War II. Biometrika, 66, 393-396.

Turing, A. M., 1948. Rounding-off errors in matrix processes. Quarterly Journal of Mechanics and Applied Mathematics, 1, 287-308.

© 2014, David E. Giles

Multivariate Medians

I'll bet that in the very first "descriptive statistics" course you ever took, you learned about measures of "central tendency" for samples or populations, and these measures included the median. You no doubt learned that one useful feature of the median is that, unlike the (arithmetic, geometric, harmonic) mean, it is relatively "robust" to outliers in the data.

(You probably weren't told that J. M. Keynes provided the first modern treatment of the relationship between the median and the minimization of the sum of absolute deviations. See Keynes (1911) - this paper was based on his thesis work of 1907 and 1908. See this earlier post for more details.)

At some later stage you would have encountered the arithmetic mean again, in the context of multivariate data. Think of the mean vector, for instance.

However, unless you took a stats. course in Multivariate Analysis, most of you probably didn't get to meet the median in a multivariate setting. Did you ever wonder why not?

One reason may have been that while the concept of the mean generalizes very simply from the scalar case to the multivariate case, the same is not true for the humble median. Indeed, there isn't even a single, universally accepted definition of the median for a set of multivariate data!

Let's take a closer look at this.

Econometrics in the Post-Cowles Era

My thanks to Olav Bjerkholt for alerting me to a special edition of the open access journal, Oekonomia, devoted to the History of Econometrics. Olav recently guest-edited this issue, and here's part of what he has to say in the Editor's Foreword:

"Up to World War II there were competing ideas, approaches, and multiple techniques in econometrics but no ruling paradigm. Probability considerations played a very minor role in econometric work due to an unfounded but widely accepted view that economic time series were not amenable to such analysis. The formalization of econometrics undertaken at Cowles Commission in Chicago in the late 1940s inspired by the Probability Approach of Trygve Haavelmo, and often referred to as the CC-Haavelmo paradigm, placed the whole problem of determining economic relationships firmly within a probabilistic framework and made most traditional techniques redundant. A key assumption in this paradigm as it was conceived is that models to be estimated have been fixed with certainty by a priori formulated theories alone, it can thus be labeled as “theory-oriented”. It exerted a strong influence in the ensuing years, not least as consolidated standard econometrics propagated by textbooks. The history of econometrics, as written in the 1980s and 1990s, covered mainly the period up to and including the Cowles Commission econometric achievements.

Haavelmo made a remark at the beginning of his influential monograph that econometric research aimed at connecting economic theory and actual measurements, using appropriate tools as a bridge pier, “[b]ut the bridge itself was never completely built.” From around 1960 there arose increasingly discontents of different kinds with the CC-Haavelmo paradigm, not least because of the key assumption mentioned above. The bridge needed mending but the ideas of how to do it went in different directions and led eventually to developments of new paradigms and new directions of econometric analysis. This issue comprises four articles illuminating developments in econometrics in the post-Cowles era."

These four articles are:

• Marc Nerlove,  “Individual Heterogeneity and State Dependence: From George Biddell Airy to James Joseph Heckman”.
• Duo Qin, “Inextricability of Confluence and Autonomy in Econometrics”.
• Aris Spanos, “Reflections on the LSE Tradition in Econometrics: a Student’s Perspective”.
• Nalan Basturk, Cem Cakmakli, S. Pinar Ceyhan, and Herman van Dijk, “Historical Developments in Bayesian Econometrics after Cowles Foundation Monographs 10, 14”.

Coincidentally, the last of these papers was the topic of another post of mine last month, before I was aware of this special journal issue. I'm looking forward to reading the other three contributions. If they're even half as good as the one by Basturk et al., I'm in for a treat!

© 2014, David E. Giles

The Demise of a "Great Ratio"

Once upon a time there was a rule of thumb that there were 20 sheep in New Zealand for every person living there. Yep, I kid you not. The old adage used to be "3 million people; 60 million sheep".

I liked to think of this as another important "Great Ratio". You know - in the spirit of the famous "Great Ratios" suggested by Klein and Kosubod (1961) in the context of economic growth, and subsequently analysed and augmented by a variety of authors. The latter include Simon (1990), Harvey et al. (2003), Attfield and Temple (2010), and others.

After all, it's said that (at least in the post-WWII era) the economies of both Australia and New Zealand "rode on the sheep's back". If that's the case, then the New Zealand Sheep Ratio (NZSR) may hold important clues for economic growth in that country.

My interest in this matter right now comes from reading an alarming press release from Statistics New Zealand, a few days ago. The latest release of the Agricultural Production Statistics for N.Z. revealed that the (provisional) figure for the number of sheep was (only!) 26.9 million at the end of June 2014 - down 4% from 2013.

I was shocked, to say the least! Worse was to come. The 2014 figure puts the number of sheep in N.Z. at the lowest level since 1943! 

I'm sure you can understand my concern. We'd better take a closer look at this, and what it all means for the NZSR:

End-of-Semester Econometrics Examination

My introductory graduate econometrics class has just finished up. The students sat the final examination yesterday. They did really well!

If you'd like to try your hand, you can find the exam. here.

(Added later: A rough solution is available here.) 

© 2014, David E. Giles

The Rotterdam Model

Ken Clements (U. Western Australia) has sent me a copy of his paper, co-authored with Grace Gao this month, "The Rotterdam Demand Model Half a Century On". 

How appropriate it is to see this important landmark in econometrics honoured in this way. And how fitting that this paper is written by two Australian econometricians, given the enormous contributions to empirical demand analysis that have come from that group of researchers - including Ken and his many students - over the years. (But more on this another time.)

Any student who wants to see applied econometrics at its best can do no better than look at the rich empirical literature on consumer demand. That literature will take you beyond the "toy" models that you meet in your micro. courses, to really serious ones: the Linear Expenditure System, the Rotterdam Model, the Almost Ideal Demand System, and others. Where better to see the marriage of sound economic modelling, interesting data, and innovative statistical methods? In short - "econometrics".

Back to Ken and Grace's paper, though. Here's the abstract:

When Did You Last Check Your Code?

Chris Blattman (Columbua U.) has a blog directed towards international development, economics, politics, and policy.

In a post yesterday, Chris asks: "What happens when a very good political science journal checks the statistical code of its submissions?"

The answer is not pretty!

His post relates to the practice of the Quarterly Journal of Political Science to subject empirical papers to in-house replication. This involves running the code provided by authors. He cites a batch of 24 such papers in which only 4 were found to be error-free.

Have you checked you own code recently?

© 2014, David E. Giles

"The Error Term in the History of Time Series Econometrics"

While we're on the subject of the history of econometrics ......... blog-reader Mark Leeds kindly drew my attention to this interesting paper published by Duo Qin and Christopher Gilbert in Econometric Theory in 2001.

I don't recall reading this paper before - my loss.

Mark supplied me with a pre-publication version of the paper, which you can download here if you don't have access to Econometric Theory.

Here's the abstract:

"We argue that many methodological confusions in time-series econometrics may be seen as arising out of ambivalence or confusion about the error terms. Relationships between macroeconomic time series are inexact and, inevitably, the early econometricians found that any estimated relationship would only fit with errors. Slutsky interpreted these errors as shocks that constitute the motive force behind business cycles. Frisch tried to dissect further the errors into two parts: stimuli, which are analogous to shocks, and nuisance aberrations. However, he failed to provide a statistical framework to make this distinction operational. Haavelmo, and subsequent researchers at the Cowles Commission, saw errors in equations as providing the statistical foundations for econometric models, and required that they conform to a priori distributional assumptions specified in structural models of the general equilibrium type, later known as simultaneous-equations models (SEM). Since theoretical models were at that time mostly static, the structural modelling strategy relegated the dynamics in time-series data frequently to nuisance, atheoretical complications. Revival of the shock interpretation in theoretical models came about through the rational expectations movement and development of the VAR (Vector AutoRegression) modelling approach. The so-called LSE (London School of Economics) dynamic specification approach decomposes the dynamics of modelled variable into three parts: short-run shocks, disequilibrium shocks and innovative residuals, with only the first two of these sustaining an economic interpretation."

© 2014, David E. Giles

More on the History of Econometrics From Olav Bjerkholt

If you look back at the various posts on this blog in the category of History of Econometrics, you'll find that I've often mentioned papers written by Olav Bjerkholt, of the University of Oslo.

Olav has drawn my attention to two more recent papers of his. They're titled, "Econometric Society 1930: How it Got Founded", and "Glimpses of Henry Schultz in Mussolini's Italy 1934". The second of these is co-authored with Daniela Parisi.

Here's the abstract from the first paper:

"The Econometric Society was founded at an “organization meeting” in December 1930. The invitations had been issued by Irving Fisher, Ragnar Frisch and, Charles F. Roos. In June the same year they had sent a form letter to a list of 31 scholars to solicit advice about establishing an international association “to help in gradually converting economics into a genuine and recognized science.” The responses of these scholars from ten different countries are set out at some length in the paper. Rather than persevering in building a constituency of adherents on which a society could be founded the three initiators decided to rush ahead and sent out invitations to an organization meeting to found the Econometric Society at short notice. The paper discusses possible reasons for the change of pace, indicating that Schumpeter had a decisive role, and gives an account of the deliberations of the organization meeting founding the Econometric Society."

The second paper covers material that I was previously quite unaware of. Here's the abstract:

"Professor of Economics at the University of Chicago, Henry Schultz, spent a sabbatical year in Europe in 1933/34 working on his forthcoming monograph The Theory and Measurement of Demand (Schultz 1938). During the year he found time to travel in 6-7 countries meeting economists and other scholars. The article describes and comments his seven weeks long visit to Italy in March-April 1934. The glimpses of Henry Schultz in Italy are provided by Schultz’s own brief diary notes during that visit. Henry Schultz was a prominent member of the Econometric Society and had been present at the organization meeting of the Society in 1930. In Italy he met with practically all the leading econometricians in Italy. Schultz was particularly interested in the stand taken by Italian economists on Mussolini’s Corporate State and also in the situation of Jews under fascism. Schultz followed a tourist trail in Italy visiting also Roman and Etruscan remains and a number of places of Christian worship."

My thanks to Olav for alerting me to these two fascinating papers.

© 2014, David E. Giles

New Features in EViews 9 (Beta)

When you get a chance to check out the "beta" release of EViews 9 (which current users can download from here), you'll find lots of new features.

Many of these relate to the Eviews interface, data handling, and graphs and tables. And then (of course) there are lots of new Econometrics goodies! To summarize them, under the headings used in the documentation:

Computation
• Automatic ARIMA forecasting of a series
• Forecast evaluation and combination testing
• Forecast averaging
• VAR Forecasting

Estimation
• Autoregressive Distributed Lag regression (ARDL) with automatic lag selection
• ML and GLS ARMA estimation
• ARFIMA models
• Pooled mean group estimation of panel data ARDL models
• Threshold regression
• New optimization engine

Testing and Diagnostics
• Unit root tests with a structural break
• Cross-section Dependence Tests
• Panel Effects Tests

I just had to highlight ARDL models. My earlier posts on these models (here and here) attracted a lot of readers, and many questions and comments.

I've been promising a follow-up post on this topic for some time. You can guess why I've been holding off, and what one of my upcoming posts will be about!

© 2014, David E. Giles

Two Non-Problems!

I just love Dick Startz's "byline" on the EViews 9 Beta Forum: 

"Non-normality and collinearity are NOT problems!"

Why do I like it so much? Regarding "normality", see here, and here. As for "collinearity": see here, here, here, and  here

© 2014, David E. Giles

EViews 9 - Beta Version

If you're an EViews user then you'll be delighted to learn that the beta version of the new EViews 9 was released this morning.

Provided that you have EViews 8.1 on your machine, you can download the beta version of this latest release from http://register1.eviews.com/beta/.

Here's what you'll see:

There are no delays - just make sure that you know if you need the 32-bit or 64-bit version.

I've had the opportunity to play around with the alpha version of EViews 9 over the past few weeks (thanks, Gareth!), and I can assure you that there are lots of really nice goodies in store for you.

I'll be devoting a few posts to some of the new features over the next short while, so stay tuned.

© 2014, David E. Giles

Marc Bellemare on Social Media

Marc Bellemare has been catching my attention recently. On Saturday I had a post that mentioned his talk on "How to Publish Academic Papers". I know that a lot of you have followed this up already.

Today, I just have to mention another of his talks, given last Friday, titled "Social Media for (Academic) Economists". Check out his blog post about the talk, and then look at this slides that are linked there.

Yep, I agree with pretty much everything he has to say. And nope, we're not related!

© 2014, David E. Giles

"Mastering 'Metrics"

Mastering 'Metrics: The Path from Cause to Effect, by Joshua Angrist and Jörn-Steffen Pischke, is to be published by Princeton University Press later this month. This new book from the authors of Mostly Harmless Econometrics: An Empiricist's Companion is bound to be well received by students and researchers involved in applied empirical economics. My guess is that the biggest accolades will come from those whose interest is in empirical microeconomics.

You can download and preview the Introduction and Chapter 1.

Apparently the book focuses on:

"The five most valuable econometric methods, or what the authors call the Furious Five - random assignment, regression, instrumental variables, regression discontinuity designs, and differences in differences."

If this sounds interesting to you, then make sure that you take a look at Peter Dizikes' recent post, "How to Conduct Social Science Research", on the World Economic Forum website.

© 2014, David E. Giles

Advice on Publishing

I've put in a lot of time over the years as an Editor, Associate Editor, or Editorial Board member, for a number of economics and statistics journals, ranging from Journal of Econometrics and Econometric Theory, to Journal of International Trade & Economic Development.  I've also refereed more papers than care to think about. 

Students, rightly, are eager to get the scoop on how to get their work published in good journals. They often talk to me about this. My suggestion would be to read, and follow the advice given by Marc Bellemare in his talk, "How to Publish Academic Papers". 

Just do it!

(HT to David Stern for unwittingly making me aware of Marc's talk,)



© 2014, David E. Giles

More on Prediction From Log-Linear Regressions

My therapy sessions are actually going quite well. I'm down to just one meeting with Jane a week, now. Yes, there are still far too many log-linear regressions being bandied around, but I'm learning to cope with it!

Last year, in an attempt to be helpful to those poor souls I had a post about forecasting from models with a log-transformed dependent variable. I felt decidedly better after that, so I thought I follow up with another good deed.

Let's see if it helps some more:

Statistical Controls Are Great - Except When They're Not!

A blog post today, titled, How Race Discrimination in Law Enforcement Actually Works", caught my eye. Seemed like an important topic. The post, by Ezra Klein, appeared on Vox.

I'm not going to discuss it in any detail, but I think that some readers of this blog will enjoy reading it. Here are a few selected passages, to whet your collective appetite:

"You see it all the time in studies. "We controlled for..." And then the list starts. The longer the better." (Oh boy, can I associate with that. Think of all of those seminars you've sat through.......)

"The problem with controls is that it's often hard to tell the difference between a variable that's obscuring the thing you're studying and a variable that is the thing you're studying."

"The papers brag about their controls. They dismiss past research because it had too few controls." (How many seminars was that?)

"Statistical Controls Are Great - Except When They're Not!"

© 2014, David E. Giles

Here's Your Reading List!

As we count the year down, there's always time for more reading!

• Birg, L. and A. Goeddeke, 2014. Christmas economics - A sleigh ride. Discussion Paper No. 220, CEGE, University of Gottingen.
• Geraci, A., D. Fabbri, and C. Monfardini, 2014. Testing exogeneity of multinomial regressors in count data models: Does two stage residual inclusion work? Working Paper 14/03, Health, Econometrics and Data Group, University of York.
• Li, Y. and D. E. Giles, 2014. Modelling volatility spillover effects between developed stock markets and Asian emerging stock markets. International Journal of Finance and Economics, in press.
• Ma, J. and M. Wohar, 2014. Expected returns and expected dividend growth: Time to rethink an established literature. Applied Economics, 46, 2462-2476. 
• Qin, D., 2014. Resurgence of instrument variable estimation and fallacy of endogeneity. Economics Discussion Papers No. 2014-42, Kiel Institute for the World Economy. 
• Romano, J. P. and M. Wolf, 2014. Resurrecting weighted least squares. Working Paper No. 172, Department of Economics, University of Zurich.
• Tchatoka, F.D., 2014. Specification tests with weak and invalid instruments. Working Paper No. 2014-05, School of Economics, University of Adelaide.

© 2014, David E. Giles