The Econometricians

Gauss, Galton, Pearson, Fisher, Hotelling, Cowles, Frisch and Haavelmo

Colin Read

• Editorial: Palgrave Macmillan
• Año: 2016
• ISBN:
  9781137341372
• Categoría: Negocios y empresa
• Categoría: Finanzas

This is the seventh book in a series of discussions about the great minds in the history and theory of finance. While the series addresses the contributions of scholars in our understanding of financial decisions and markets, this seventh book describes how econometrics developed and how its underlying assumptions created the underpinning of much of modern financial theory. The author shows that the theorists of econometrics were a mix of mathematicians and cosmologists, entrepreneurs, economists and financial scholars. The author demonstrates that by laying down the foundation of empirical analysis, they also forever determined the way in which we think about financial returns and the vocabulary we employ to describe them. Through this volume, the reader can discover the life stories, inspirations, and theories of Carl Friedrich Gauss, Francis Galton, Karl Pearson, Ronald Aylmer Fisher, Harold Hotelling, Alfred Cowles III, Ragnar Frisch, and Trygve Haavelmo, specifically. We learn how each theorist made an intellectual leap simply by thinking about a conventional problem in an unconventional way.

Part 1
Mathematicians and Astronomers

We begin with the struggle of some great mathematicians who wrestled first with an understanding of problems that concerned their gambling patrons, and then with ways their understanding of probability could be used to better predict the movement of the planets.

These explorations over the seventeenth and eighteenth centuries eventually allowed a very young nineteenth-century theorist to translate the insights of those who came earlier with a discovery that revolutionized almost every aspect of science, including finance and statistics. Perhaps what is most surprising, though, is that the genius of Carl Friedrich came from the most humble of beginnings.

© The Author(s) 2016

Colin ReadThe EconometriciansGreat Minds in Finance10.1057/978-1-137-34137-2_1

Begin Abstract

1. The Early Life of Carl Friedrich Gauss

Colin Read¹

(1)

Professor of Economics and Finance former Dean of the School of Business and Economics, The State University of New York at Plattsburgh (SUNY), Plattsburgh, USA

End Abstract

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.

The circle of academics was an extremely small one before the twentieth century. There was no public education, and hence little opportunity for higher education, except for the noble and elite. Nor was science so technical then that it commanded extensive knowledge, or large teams devoted to research. Indeed, intellectual discovery was a luxury supported by family wealth and royal courts which might sponsor one or two such men of ideas.

These prodigies were viewed more as intellectual athletes and mystics. They would be pitted against each other to demonstrate their intellectual cunning and lend pride to their patrons. These were not the circles in which a humble boy of modest means and upbringing could find himself.

Carl Friedrich Gauss was an exception. He also became one of the most exceptional mathematicians of all time, who is spoken in the same breath only with Euclid and Newton .

Gauss came from a family of farmers and laborers. His great-great-grandfather, Hans Gauss (c.1600–?), was born in Hanover, Germany, and had found his way to Wendeburg, a small farming village in the neighboring district of Peine of Germany’s Lower Saxony region. He had a family of small size in this era: a wife, two sons and four daughters. At first, his family and progeny remained close to home.

His son Henrich Gauss (1 December 1648–25 October 1726) was born in Wendeburg. He married three times. The first marriage resulted in a dowry of a farm that had belonged to his first wife, Anna Grove, a widow, in nearby Volkenrode, less than six kilometers to the southeast of Wendeburg (Fig. 1.1).

Fig. 1.1

The ancestry of Carl Friedrich Gauss

Henrich had a dozen children, four from each marriage, and was left a widower from each of his first two marriages. His last marriage resulted in a son Jurgen.

Jurgen Gauss (or Goos) (3 November 1712–5 July 1774) was born in Volkenrode and grew up tending the farm. However, as one of the last of a dozen children, there would be no room for him on the farm once he became an adult. Instead, he moved to the large German city of Braunschweig, or Brunswiek in Low German, Brunswick in English, at the extreme southern port of the Oker River as it makes its way toward the North Sea. At the time, Brunswick was a major economic and cultural center for Germany. It was also a center for education.

Jurgen Gauss arrived in Brunswick late in the decade of the 1730s, with a new bride, Katharine Magdalene Eggling (5 March 1713–3 April 1774), the daughter of Hans Heinrich Eggling (1667–25 December 1714) and Cathrine Heuer. Soon upon his acceptance as a resident of Brunswick, he took his first job off of the farm, on 23 January 1739. His adopted city first employed him as a day laborer, then as a clay mason and a butcher. Each of the latter occupations entitled Jurgen membership to guilds, and all would provide him with employment through the four seasons. The family enjoyed a level of urban economic comfort not readily afforded to the youngest child in a farming family.

Jurgen Gauss and Katharine soon secured a small and narrow house for his family, at 10 Ritterbrunnen. They lived in that home for 14 years, and raised four children there, including an eldest son, Gebhard Dietrich Gauss (13 February 1744–14 April 1808). The family then moved to a larger home at 30 Wilhelmstrasse, where Jurgen would die of tuberculosis on 5 July 1774, just three months and two days after the death of his wife from a prolonged fever.

By the time his father died, the second child and the eldest son, Gebhard, had worked and learned the family trades. Upon his parents’ death, Gebhard used a dowry from his first wife, Dorothea Emerenzia Warnecke, and a loan from the town’s mayor Wilmerding, to buy out the shares of his family home from his brothers Johanne Franz Heinrich and Peter Heinrich. By the age of 30, Gebhard was able to provide a home and a secure but not affluent living for his own family.

Gebhard’s first wife did not long enjoy the house, though. She died on 5 September 1775 of tuberculosis as had her father-in-law, but not before giving birth to a boy. Johann Georg Heinrich was born on 14 January 1769.

Seven months after Dorothea Warnecke died, Gebhard married Dorothea Benze, the daughter of a stonemason, Christophe Benze (2 March 1717–1 September 1748). Dorothea’s father died prematurely as well, from pulmonary respiratory illness associated with his profession as a stonemason. He also left a son, Johann Friedrich. Both of Christophe Benze’s children were thoughtful and intelligent, but neither enjoyed the luxury of formal schooling.

Dorothea was illiterate, but she was a kind and nurturing woman by nature. She worked as a maid before she married Gebhard. While Gebhard was also uneducated, he nonetheless managed to be appointed the city’s master of waterworks as he was an experienced stonemason and was reasonably good with sums.

In contrast to his wife’s gentle nature, Gebhard was quite domineering as a father, and was considered rather somewhat uncouth. Yet, he provided reasonably well for his family.

The Arrival of Carl Gauss

Gebhard and his second wife had a son just over a year after their marriage, on 25 April 1776. Carl Friedrich was born in the family home in Brunswick on 30 April 1777, on the Wednesday eight days before the Ascension. He was an only child of the second marriage, but was a half brother to Gebhard’s eldest son Johann.

When a young Carl once quizzed his mother about his birthdate, she could not recall the exact date. Later in life, Carl was able to calculate it based on his mother’s recollection of his birth before the Ascension. At a young age, he used this small family mystery as an opportunity to develop a formula for the day Easter arose for any given year. It did not take long for his family to discover that the young Gauss was a mathematical prodigy.

Carl had great affection for his mother, and for her brother, his uncle Johann Friedrich, but had a somewhat awkward relationship with his half brother. Indeed, he did not know his brother Johann Georg very well. More than eight years his senior, Johann struck out on his own as a day laborer before Carl’s tenth birthday. Johann returned home some years later, but an eye injury made him only of limited help to his father. Instead, Johann enlisted in the army for almost a decade, and returned to his family home to take over his father’s trade once his father died on 14 April 1808.

While Carl Friedrich grew up with a harsh and domineering father, he enjoyed the better nature of his kind and devoted mother. In turn, he doted on his mother all his life, until Dorothea’s death at the remarkably advanced age of 97, even through her infirmities and her affliction with blindness in her last four years.

Carl harbored fond and vivid memories of his childhood. One of his earliest memories was falling into the river and being saved at a very young age. This terrifying memory did not taint his recollections otherwise, though.

He also recalled that he taught himself to read by asking his family members how to pronounce letters on the page. His ability to manipulate numbers became a favorite parlor trick among family friends. When his father would pay his bricklaying workers, a three-year-old Carl once impudently but accurately corrected his father’s calculations. While access to school was out of the question for many children in his neighborhood, his intellectual precociousness compelled his family to consider his education.

In 1784, when young Carl was seven years of age, his father agreed to let him enter nearby St. Katharine’s Volksschule, a people’s school for the more motivated of the children of non-prosperous families. The school, which adjoined St. Katharine’s Church, had a teacher named J.G. Buttner who oversaw a dark and dank classroom of 200 children.

Young Gauss endured two years among those 200 classmates, but managed to stand out nonetheless. When the teacher gave his students an assignment he felt would keep them occupied for hours, Gauss almost immediately announced the solution. The teacher felt it impossible that Gauss could have so quickly added all the numbers from 1 to 100. Yet, an eight-year-old Gauss reasoned his way to a solution.

Gauss had noticed that the first and last number in the sequence, 1 and 100, added to 101. So did the second and the second to last, 2 and 99, and, indeed, so do all 50 such pairs. Gauss proclaimed that 50 pairs which each add each to 101 must then total 5050. While he may not have been praised for his brilliance, he was at least spared the whip that often accompanied the incorrect answers from lesser classmates.

Headmaster Buttner quickl...

Índice

• Cover
• Frontmatter
• 1. Mathematicians and Astronomers
• 2. From Least Squares to Eugenics
• 3. The Formation of Modern Statistics
• 4. The Birth of a Commission and Econometrics
• 5. What We Have Learned
• Backmatter