Thursday, March 3, 2011

The Origin of Our Species


"Nescire autem quid ante quam natus sis acciderit, id est semper esse puerum. Quid enim est aetas hominis, nisi ea memoria rerum veterum cum superiorum aetate contexitur?" (Marcus Tullius Cicero, 46 B.C.)
For those of you whose Latin is a little rusty (or maybe you missed the benefits of a classical education), this translates to:
"Not to know what happened before you were born is to be a child forever. For what is the time of a man, except it be interwoven with that memory of ancient things of a superior age?"
In other words, it's worth knowing where you came from - and this includes econometricians!

The Econometric Society was founded following a meeting of  a group of eminent empirically-oriented economists at the Statler Hotel in Cleveland, OH, on 29 December 1930. The names of the members of that founding group can be found in the various histories of the Society, such as those written by Christ (1983), Bjerkholt (1995), and Gordon (1997). More general treatments of the birth and development of Econometrics as a discipline in its own right are provided by Morgan (1990), and other authors.

Economists and statisticians from the Scandinavian countries played a major role in the emergence of Econometrics. Some of their names are very well known, including the Nobel laureates Ragnar Frisch and Trygve Haavelmo, both from Norway. Less widely known is the Danish economist and statistician, Edvard Mackeprang, whose doctoral thesis (Mackeprang, 1906) translates to Price Theories. Kærgaard (1984) provides a fascinating account of this early Danish influence on our profession.

The very word, "Econometrics", was coined by Frisch in 1926:
"Intermédiaire entre les mathématiques, la statistique et l'économie politique, nous trouvons une discipline nouvelle que ion peut, faute de mieux, designer sous le nom de l'économetrie. L'économetrie se pose le but de soumettre les lois abstraites de l'économie politique thoérique ou l'économie  «pure» à une vérification expérimentale et numériques, et ainsi de constituer, autant que cela est possible, l'économie pure en une science dans le sens restreint de ce mot." (Frisch 1926, p.1.)
In English translation:
"Intermediate between mathematics, statistics, and economics, we find a new discipline which for lack of a better name, may be called econometrics. Econometrics has as its aim to subject abstract laws of theoretical political economy or 'pure' economics to experimental and numerical verification, and thus to turn pure economics, as far as possible, into a science in the strict sense of the word."
Indeed, the first paragraph of the Constitution of the Econometric Society captures the spirit of Frisch's own definition, stating that the object of the Society should be to:

"... promote studies that aim at a unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems and that are penetrated by constructive and rigorous thinking similar to that which has come to dominate in the natural sciences. Any activity which promises ultimately to further such unification of theoretical and factual studies in economics shall be within the sphere of interest of the Society."

Ragnar Frisch was the first Editor-in-Chief of the prestigious journal, Econometrica (1933 - 1954), and in that role he had a significant influence on the early development of our professsion. It was fitting that in 1969 he shared, with Jan Tinbergen, the very first award of The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. The citation was:

"for having developed and applied dynamic models for the analysis of economic processes".
Since that date, numerous econometricians have been among those who have received The Nobel Prize in Economics, as it is loosely called.

Certainly, it's interesting to look back at the development of the Econometric Society, as being representative of the econometrics profession. However, as has been amply discussed by Morgan (1990) and others, there was considerable international activity of what we would now call an econometric nature prior to 1930. So, this raises the question: "Can we date the birth of econometrics?" Let's see what we can do!

In a rather cute piece of empirics, Intriligator (1978, pp.134-136) fits an exponential growth curve to membership data for the American Economic Association over the period 1950 to 1973. He then backcasts the OLS regression and determines that the first economist in the U.S.A. can be dated to 1777, a date that he finds to be quite reasonable, being just two years after the publication of Adam Smith's Wealth of Nations. Just give it 2 years to cross the Atlantic, and "Bingo"!

Before applying this basic idea to data relating more to econometricians, rather than economists at large, I first checked the robustness of Intriligator's result by using an extended sample of annual data (1893 to 2009) and a more flexible functional form for the growth regression. Specifically, I estimated the following logistic function by non-linear least squares:

yt = α / [1 + exp (β + γ t) ]νt  ,       

where yt is the number of members of the American Economic Association at time t, and  νt  is a log-normally distributed random error term. In order to identify the three parameters of this model, I set α = 22,205 (the maximum value of y in the sample, occurring in 1993), because the interpretation of this parameter is that it is the "upper bound" that the function approaches as t increases. The data that I used can be found on the Data page of this blog; and the EViews (Quantitative Micro Systems, 2010) workfile that includes all of the estimation details and results is provided on the accompanying Code page.

To estimate the model, I took a logarithmic transformation:

ln ( yt / 22205) = -ln [1 + exp (β + γ t) ] + εt   ,

where  εt = ln (νt ) is normally distributed. This yielded  parameter estimates (and HAC standard errors) of 105.843 (4.974) and -0.054 (0.003) for β and γ respectively, with R2 = 0.962. The fitted regression model is depicted in Figure 1.


Then, when we backcast the regression to locate the date when y = 1, we find (Figure 2) that this occurs in 1777, so Intriligator's result is remarkably robust!




[As an aside, I should remark that my son, Matt, observed that while this exercise enables us to date the first economist in the U.S., it does not provide us with that person's name. My only defense is that this is an example of inferential, not descriptive, econometrics, but I am not going to let this slow me down in what follows - trust me!]

Emboldened by the obvious success of this exercise, I then proceeded to apply the associated methodology to data relating to econometricians. These data are annual (end-of-year) numbers for non-institutional members of the Econometric Society, as reported in various Reports of the Secretary of that Society, between 1977 and 2009. The latter date corresponds to the latest available data-point, and the former date corresponds to the end of a somewhat turbulent period for both the membership and finances of the Econometric Society. Again, the data can be found on the Data page of this blog; and the EViews workfile is provided on the accompanying Code  page so that you can verify what follows.

Application of the ADF and KPSS tests indicates that the data are trend-stationary. More specifically, the ADF statistic is -3.783 (p = 0.030), and the KPSS statistic is 0.082 (p > 0.10). I set α = 5,852 (the maximum reported membership in our sample, in 2007). 

Estimating the logistic growth model by non-linear least squares resulted in residuals that were clearly autocorrelated, so the model was re-estimated with an allowance for AR(1) errors, with autoregressive parameter, ρ. The following results were then obtained. The estimated parameters (and HAC standard errors) were 156.675 (29.124),  -0.079 (0.015) and 0.491 (0.228) for β, γ and ρ, respectively, and R2 = 0.900. The fitted logistic regression model appears in Figure 3.


The estimated regression model was used to backcast the number of econometricians. The calculation of the backcasts took account of both the log-normality of the errors in the basic model, and the negative skewness (-0.238) of the residuals. The exponentiated backcasts from the fitted log-linear model were multiplied by a factor of  Σt (exp (et ) /  T, where et is the residual at time t, and T  is the sample size, to reduce the forecast bias (see Cowpertwaite and Metcalfe, 2009, p.117). This backcasting yielded predicted values for y increasing from  1.047 in 1873 to 1.437 in 1877. From 1878 onwards the predicted number of econometricians, rounded to the nearest integer, was two or more. So, effectively, y = 1 during the period 1873 to 1877. (See Figure 4.)


Amazingly, the dates 1873 to 1877 are just dripping with significance! Yes, I know that this is a somewhat non-technical expression, but I am sure I can be forgiven in view of the enormity of these results. Just consider the following revealing historical facts.

Francis Galton, half-cousin of Charles Darwin, was considered to be one of the first (if not the first) social scientists. He had diverse interests - he was what we call a "polymath". Among many other things he was an explorer and geographer (the latter implying that he probably owned lots of different coloured pencils). He produced the first popular weather maps, and wrote various papers and three books on the science of fingerprints.


More to the point, Galton also made many major contributions to the development of statistics. By way of example, he developed the concept of the standard deviation in the late 1860's.  He was a pioneer in the use of questionnaires as a means of gathering data. In 1873 (note the date carefully), Galton invented the Quincunx, which can be used to illustrate (among other things) the Lindeberg-Lévy central limit theorem. I'll leave you to find out more about this intriguing device by playing with Daryl Nester's Java applet and by reading Stephen Sigler's description. Then, on the evening of Friday 9 February 1877, Galton delivered a seminal address entitled, Typical Laws of Heredity, to the Royal Institution. It was in this paper that Galton introduced the concept of regression to the mean. His paper (Galton, 1877) was published in the premier journal, Nature, on 5 April of that year. Regression analysis - the backbone of econometrics - can be dated from 1877.


So, the period 1873 to 1877 that was cunningly unearthed by my econometric analysis is especially revealing. Moreover, in this instance not only are we able to pinpoint the date of the birth of econometrics, but we can put a name and face to that first bold econometrician!

Acknowledgement
I am most grateful to Marcus Tullius Cicero for suggesting this line of research.

Postscript
Regrettably, there was a somewhat less tasteful side to some of the interests and research of Galton and many other influential statisticians, including Karl Pearson and Ronald Fisher, during the "Age of Statistical Enlightenment" (Stigler, 2010). They immersed themselves deeply in the study of Eugenics, and indeed the word itself was proposed by Galton (1883).


References

Bjerkholt, O. (1995). Ragnar Frisch and the foundation of the Econometric Society and Econometrica. Document 95/9, Research Department, Statistics Norway.

Christ, C. F. (1983). The founding of the Econometric Society and Econometrica. Econometrica, 51, 3-6. 

Cowpertwait, P. S. P. and A. V. Metcalfe (2009). Introductory Time Series With R. Springer, New York.
Frisch, R. (1926). Sur un probleme d'economie pure. Norsk Matematisk Forenings Skrifter, Series I, No. 16, 1-40.

Galton, F. (1874). On a proposed statistical scale. Nature, 9. 342-343.

Galton, F. (1875). Statistics by intercomparison with remarks on the Law of Frequency of Error. Philosophical Magazine, 49, 33-46.

Galton, F. (1877). Typical laws of heredity. Nature, 15, 492-495, 512-514, 532-533.

Galton, F. (1883). Inquiries into Human Faculty and its Development. Macmillan, London.

Gordon, R. J. (1997). What is the Econometric Society? History, organization, and basic procedures. Econometrica, 65, 1443-1451. (Revised version available on the Econometric Society website at http://www.econometricsociety.org/society.asp.)

Intriligator, M. D. (1978). Econometric Models, Techniques, and Applications. Prentice-Hall, Englewood Cliffs, NJ.

Kærgaard, N. (1984). The earliest history of econometrics: Some neglected Danish contributions. History of Political Economy, 16, 437-444.

Mackeprang, E. P. (1906). Pristeorier. Copenhagen.

Morgan, M. S. (1990). The History of Econometric Ideas. Cambridge University Press, Cambridge.

Quantitative Micro Software (2010). EViews 7.1. Irvine, CA: Quantitative Micro Software.

Stigler, S. M. (2010). Dalton, Galton and the statistical enlightenment. Journal of the Royal Statistical Society, A, 173, 469-482.







© 2011, David E. Giles

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