The Econometricians

There is perhaps no discipline that is so intrinsically tied to data than the study of finance. Every financial theory is formulated not for some esoteric purpose, but rather to better understand future occurrences based on past information. This world of financial data is so broad that it makes little sense unless it can be simplified and represented by a few familiar measures. Our models then incorporate these measures to predict movements in financial variables. This problem is not unlike the challenge of those who gazed at the planets and stars and tried to predict their motion. One such mathematical explorer enjoyed more success in challenging predictions than any other. His surprisingly humble upbringing almost defies his incredible insights and contributions to dozens of sciences since, finance included.

GaussGauss, Carl Friedrich loved numbers. When he imagined geometric concepts and from them developed what we would now call abstract algebra, he came to shapes from the perspective that these new approaches would help him better understand the nature of numbers. Ever since his elementary school experience in which he successfully solved a problem for his teacher based on the application of a numerical series, Gauss had numbers, integers and shapes racing in his head. While he was already publishing academic papers of high quality at the age of 18, Gauss had been interested in arithmetic and geometric meanGeometric means for 4 years by then, and, by 17, had explored the representation of average values through power series, and the method of least squaresLeast squares. Gauss developed these concepts from a position of great practicality. He used numbers, and especially their patterns, to better understand practical problems. His choice of study at the University of Göttingen was an ideal match for this intellectual curiosity.

With what he later considered as his most profound intellectual contribution, the 17-sided regular polygonRegular Polygon solution, at hand, GaussGauss, Carl Friedrich began his most practical explorations in support of a profession that would earn his family a reliable income. In 1800, the Italian astronomer Giuseppe Piazzi (16 July 1746–22 July 1826), a mathematician by training, had been appointed to catalog celestial bodies in a compilation called the Palermo Catalogue of Stars. On the first day of 1801, he claimed he discovered a new planet, the Ceres, in between Mars and Jupiter in what we now know as the asteroid belt.

At first, GaussGauss, Carl Friedrich considered his work on the method of least squaresLeast squares to be relatively inconsequential and obvious. He developed his method as a practical solution to problems of observational error in astronomy and geodesy so that he may streamline his calculations and better earn a living for himself and his family. To him, they were a means to a larger end. As a consequence, he did not see any pressing need to quickly publish his technique. Instead, he worked only slowly toward the publication of his collection of algebraic results, his method of least squares included, until 1809.

If GaussGauss, Carl Friedrich lacked pedigree, Francis Sacheverel GaltonGalton, Francis certainly did not.

LambertLambert, Johann Adolphe Jacques QueteletQuetelet, Lambert Adolphe (22 February 1796–17 February 1874) was a contemporary of GaussGauss, Carl Friedrich who also directed an observatory, in Brussels, Belgium, 300 miles to the west of Göttingen. BornBorn, Max in Ghent, then part of Napoleon’s French Republic, to a city agent, François-Augustin-Jacques-Henri Quetelet, and Anne Françoise Vandervelde, Adolphe lost his father when he was only seven years old. He channeled that loss into his studies.

GaltonGalton, Francis remained preoccupied by his work and by his need to ensure he remained at the center of intellectual thought, however controversial, within the London social scientific circles at the time. He spent little time at home, and he and Louisa failed to have children together.

One might contrast the life of GaussGauss, Carl Friedrich with that of GaltonGalton, Francis. Gauss’ humble beginnings might suggest he had everything to prove. Yet, over his lifetime, and despite his place as perhaps one of the three most accomplished mathematicians of all time, he took far too little time documenting and publishing his contributions. His brilliance was understated in his own lifetime.

Almost immediately after he began, KarlPearson, Karl gave up the practice of law. Yet, the pressures for him to succeed were almost unrelenting. To free him from the forces of familial conformation, he joined the intellectual circles of London. He lectured locally at the intellectual clubs in Soho, including the Men and Women’s Club. While he considered himself a man of numbers, others increasingly viewed him as a man of words.

Carl Friedrich GaussGauss, Carl Friedrich was a most unusual polymath. Considered one of the greatest mathematical minds in history, it is possible that there could have been born a dozen like him who went unnoticed throughout life. Gauss grew out of the humblest of beginnings, demonstrated fantastic resilience and rose to great accomplishments, but were it not the help of a benefactor who saw something in young Gauss that no one else could see, we might have never benefited from his brilliance. Gauss also rose out of an era in which only the well-to-do could spend a lifetime studying the most esoteric of subjects. Indeed, by some calculations, he never published the majority of his ideas. He was busy maintaining a livelihood for his family at a time when publication was both financially expensive and time consuming.

Ronald FisherFisher, Ronald is remembered as the father of modern statistics. Ironically, Fisher endured much of his life in the unfortunate shadow of Pearson.

By the time Fisher began to mature as a scholar, theories of evolution and eugenics were already spawning a nascent literature in statistics. CharlesDarwin, Charles Darwin had argued that the natural variations of human qualities are adaptive and evolve over time, while his cousin, Francis Galton,Galton, Francis had shown that variations are inherited. Pearson had concluded that such subtleties could not be observed. But, Fisher subsequently produced a paper that showed that such correlations could be observed, and, in doing so, also established the field of biometric genetics. At the same time, he introduced into the statistical vocabulary the term varianceVariance, and produced the methodology analysis of variance. Clearly, Fisher’s observations were astute and his contribution profound. But he did so at odds with the then established monarch of modern statistics, KarlPearson, Karl Pearson.

While Pearson had spent a lifetime formulating statistics for such individual predictors as a distribution’s meanMean and varianceVariance, and Fisher helped improve Pearson’s statistics, Fisher also offered a new and groundbreaking insight into the overall power of statistical models. While at Rothamsted, Fisher also refined a geometric interpretation of statistical measures that dated back to GaussGauss, Carl Friedrich, and integrated most of the statistical measures we employ today.

There are but a few scholars in any discipline who are simultaneously claimed by multiple disciplines as their own. The Great Mind John von Neumannvon Neumann, John is one such scholar. The major award in computer science is a tribute to his leadership and scholarship in the development of computers and their programming. Physicists remember him for his contributions, and the Manhattan Project relied on his expertise in chemical engineering. He was a disciple of David HilbertHilbert, David and an extraordinary mathematicians, and he was perhaps the most significant father of game theory that added so much to so many disciplines. Finally, he is recognized as one of the cleverest economists who also made significant contributions to finance theory. Ronald FisherFisher, Ronald shares with von Neumann this unique characteristic of recognition by scholars from many disciplines.

While the names GaussGauss, Carl Friedrich, GaltonGalton, Francis and Fisher may not be well known to finance students of statistics, the name HotellingHotelling, Harold often elicits at least some acknowledgment. This is perhaps because he helped establish statistics, economics and econometrics from a distinctly American perspective. Fisher was experiencing resistance in England over his theories that defied the powers that be in Britain’s statistical community. America was more receptive. Its embracement of Fisherian statistics caused the center of massCenter of mass of the statistics world to migrate across the ocean. The primary proponent was an American mathematician and economist whose ancestors made the same migration as founders of America’s first colonies.

While at Stanford, HotellingHotelling, Harold began teaching in both the areas of mathematics and the burgeoning new theory of statistics. One can see from the names of the courses he taught that he was developing his statistical insights through his pedagogy. His first offering was in the theory of probability and in statistical inference, and by 1926–27, he was also teaching differential geometry and topology. His expertise in this emerging discipline of statistics led to his appointment as an Associate Professor of Mathematics at Stanford by 1927. Clearly, he had made a great impression at a relatively young age of 31 and at one of the best schools in the West.

Beyond his efforts to establish statistics as a rigorous study and as a tool for modern finance, perhaps HotellingHotelling, Harold’s most lasting legacy was in further developing a notion first formulated by Carl GaussGauss, Carl Friedrich, the method of maximum likelihood.

There are a few scholars who are claimed by multiple disciplines. Fisher and von Neumannvon Neumann, John were two striking examples. The same rare ability to span multiple disciplines was demonstrated by Harold HotellingHotelling, Harold. He began as a theoretical mathematician who soon found application in economics and in statistics. His location theory and his theory of exhaustible resources are still taught in economics. And, he represented the establishment of statistics as a discipline that now stands on its own, but spawned from the unique combination of theoretical mathematics and practical research methodological studies.

Some Great Minds make their mark through shear brilliance. Others make a historically significant contribution not by solving a seemingly intractable problem, but by recognizing, perhaps from a unique vantage point, that a problem exists, or by offering, from their access to unique resources, a pathway to solve the problem. Alfred CowlesCowles, Alfred III III was a great mind because of his unique ability to motivate others. He also brought to the problem an infectious entrepreneurial spirit, and access to financial resources almost never found among modern academics.

CowlesCowles, Alfred III remained in Colorado Springs for two decades. He had survived the stock market turmoil of the late 1920s relatively unscathed financially, and had simultaneously decided to withdraw from both the financial markets and urban congestion before the crash of 1929. He was firmly entrenched in the dry mountain air of Colorado Springs.

With his interest in statistics stimulated and the time afforded with a life of semi-retirement, CowlesCowles, Alfred III became interested in applying statistical principles to a finance discipline for which he had developed a professional suspicion that it lacked scientific rigor. He had become growingly suspicious of the spurious advice offered by many financial advisors over the Roaring Twenties, especially in the wake of the Great Crash of 1929, and he had schooled himself on the mathematics of least squaresLeast squares and statistics that could act as the basis for the treatment of finance as a science rather than an art. His first project in finance was to determine the effectiveness and correlation of the advice from 24 market newsletters and stock market performance.

While Alfred CowlesCowles, Alfred III III was not college-trained in finance and economics, he nonetheless attained some of the highest accolades of his field. He was a Fellow of the American Association for Advancement of Science, and a Fellow and Treasurer of the Econometric Society. He also was the principal author of the Cowles Monograph Common Stock Indexes, and contributed to Econometrica and the Journal of American Statistical Association. Some of his publications include Can Stock Market Forecasters Forecast?, a paper read before a joint meeting of the Econometric Society and the American Statistical Association, Cincinnati, Ohio, 31 December 1932. This article was subsequently reprinted in Econometrica.1

While CowlesCowles, Alfred III and his scholarship were distinctly American, two of the greatest influences on the Cowles Commission were distinctly Norwegian. This tradition began with Ragnar FrischFrisch, Ragnar.

By the time FrischFrisch, Ragnar began to lead the development of the new field of econometrics, Ronald FisherFisher, Ronald’s Handbook had been well reviewed by Harold HotellingHotelling, Harold, and statistics groups were beginning to sprout across the USA, especially at the major land-grant universities that contained in their mission the need to perform research in support of agriculture. With a fresh PhD in hand by 1926, Frisch was about to join that fray among other founders of econometrics. In 1927 he was offered a Rockefeller Foundation scholarship to travel to the USA. One of his first collaborations came when he arrived at Yale University in New Haven, Connecticut, to work with the great mind Irving FisherFisher, Irving, just as CowlesCowles, Alfred III was encouraging Fisher to bring to fruition the vision of an Econometric Society.

The rousing editorial of Joseph SchumpeterSchumpeter, Joseph was not the only immortal contribution to the first edition of Econometrica. Also in the volume was a paper by Ragnar FrischFrisch, Ragnar and his agricultural economist colleague F.W. WaughWaugh, Frederick that both postulated and solved a problem that is both somewhat unique and ubiquitous in financial and economic data.

With this lofty beginning, and the combination of FrischFrisch, Ragnar’s vision and tenacity and CowlesCowles, Alfred III’ funding, came to be both a new scholarly society and perhaps the greatest research commission ever created in the social sciences.

In the 1800s, aside from a few centers of government and company towns, much of Norway remained rural. One such community, Gol, in the county of Buskerud, is a farming and forestry community about an hour’s drive northwest of Oslo. There, a family named Olsen was headed by Halvor (1853–?) and his wife Ingeborg (1857–), formerly Eikro.

In 1947, HaavelmoHaavelmo, Trygve returned to Norway to take up a position alongside FrischFrisch, Ragnar at the University of Oslo. He spent the balance of his career teaching at Oslo, with Frisch as his colleague.

FrischFrisch, Ragnar had described implications of the statistical problems unique to econometrics and finance in his paper published in the Nordic Statistical Journal in his 1929 “Correlation and Scatter in Statistical Variables” and also in his 1934 book Statistical Confluence Analysis by Means of Complete Regression Systems.1 This work was influential on HaavelmoHaavelmo, Trygve, who followed up Frisch’ work with his Econometrica paper “The Statistical Implications of a System of Simultaneous Equations.”2 The Haavelmo paper, at only a dozen pages long, set the agenda for the CowlesCowles, Alfred III Commission over the next decade and econometrics ever since.

HaavelmoHaavelmo, Trygve explained the reason why our world of financial econometrics may be more complicated than some would like to believe. While he offered clarity in the reasons why simultaneitySimultaneity of equations and the probabilistic nature of observations must be further considered, members of the CowlesCowles, Alfred III Commission were only partially successful in their completion of Haavelmo’s agenda. It would take decades to fully digest Haavelmo’s observation, and to develop methods such as Monte Carlo simulations, non-parametric testing tools and tests of causality. However, eventually, the discipline made headway.

Quantitative methods underpin modern financial analysis. These methods combine mathematical techniques developed by Great Minds documented in the series volume Rise of the Quants and the statistical techniques developed by the Great Minds described here.