Development of Mathematics, Statistics and Econometrics in Economics

It is essential that branches of science use methods to conduct research and develop theories. There is philosophy behind the method. The method allows for mathematical abstraction, which is at the root of science.

I do not know whether the issue of method is discussed in other sciences as much as in economics. However, I do know that it is discussed very intensively in economics.

This article aims to provide a condensed historical summary of economics' journey through mathematics, statistics and econometrics.

John Maynard Keynes (1883-1946) had made a revolution in economics. In England, Alfred Marshall’s (1842-1924) dominance and legacy in economics had an impact on Keynes. Under the influence of Knut Wicksell (1851-1926) , Keynes was destroying the tradition that was based on the Classical School, first with “A Treatise on Money (1930)” and then with “The General Theory of Employment, Interest and Money (1936) . The Great Depression that broke out in 1929 was a crisis of unprecedented severity. This crisis was creating Keynes .

Economics had become a discipline that included more mathematics and increased its scientific qualities with the Neoclassical School . The new breath brought by Keynes provided a conceptual plane that would help to include more mathematics in economics. Keynes took this concept from Richard Kahn (1905-1989) , who first used the multiplier coefficient, and adapted it to his own world. The concept analyzed how much public investment triggered how much employment. The analysis provided a structure suitable for mathematical measurements and econometric studies.

Two names that built work with mathematical equations on the plane created by Keynes were notable: David Champernowne (1912-2000) and John Hicks (1904-1989) . Then, Paul Samuelson (1915-2009) and Ragnar Frisch (1895-1973) made important works with dynamic business cycle models.

While Chawpernowne tried to express the Keynesian model in a mathematical dimension with three equations, Hicks created the IS-LM model . Although this model seemed to cover the crux of “The General Theory of Employment, Interest and Money”, it was criticized on the grounds that it neglected other very important aspects of the theory. The most important of these critics was Joan Robinson (1903-1983) . Robinson described the IS-LM model as a “bastardization” of the Keynesian model.

The dominant topic in the literature of the 1920s and 1930s was business cycles. The topic remained popular through 1929, but more mathematics was involved. Economics became a science that made increasing use of mathematics from the 1930s to the 1970s.

We see the use of mathematics in economics in explanations of theories and in the analysis of data that tests theories. 19th century theorists such as Karl Marx (1818-1883) , Johann Heinrich Thünen (1783-1850) and Antoine Augustin Cournot (1801-1877) used numerical values to explain theories. William Stanley Jevons (1835-1882) and Leon Walras (1834-1910) increased the use of mathematics to make economics more scientific. However, after the Keynesian revolution, the use of mathematics took on another dimension. The works of the past periods gave another momentum to this new period with the contributions of Keynes.

Statisticians, like theorists, also worked on empirical observations, that is, testing theories. In the late 19th century , Francis Galton (1822-1911) ,Karl Pearson (1857-1936) and Francis Ysidro Edgeworth (1845-1926) used correlation and regression analysis.

Lionel Robbins (1898-1984) wrote a book called “The Nature and Significance of Economic Science (1933)” in which he argued that economics is not the buying and selling of goods, unemployment or business cycles. Economics was concerned with a very specific aspect of behavior: choice. Economics was the allocation of limited resources among alternative uses. The theory of choice had to be adapted to solve different economic problems. Samuelson in his work “The Foundations of Economic Analysis (1947)” defended the same idea and applied the concept of optimization under constraints to consumers and firms.

There were those who felt that the increasing use of mathematics was not solving real-world problems. Robbins did not even consider it necessary to have knowledge beyond the knowledge that resources were limited in order to make an economic proposal. There were objections to the excessive use of mathematics in economics even before economics was characterized as autistic . But the use of mathematics had led to the development of the idea of a much-needed method of calculation: national income.

In the 1920s, there was no comprehensive national income accounting in any country. The first important attempt to this end was made in the USA in 1915 by Willford I. King (1880-1962) with “The Wealth and Income of the People of the United States” . King was a student of Irving Fisher (1867-1947) . In England, Arthur Lyon Bowley (1869-1957) conducted a study analyzing the topics of wages, employment, taxes, population, etc. However, by 1950, the formation of national income statistics in more than 100 countries had been achieved under the leadership of the United Nations.

Some of the terms and calculation methods used today within the framework of the concept of national income were developed in the 1930s and 1940s. Simon Kuznets (1901-1985) , who worked on national income statistics at the National Bureau of Economic Research (NBER) , examined national income from the perspective of production and income. Thus, he brought a two-way conceptual perspective to national income calculations. This two-way perspective used by macroeconomics books to explain the concept of national income has once been the subject of significant debate.

The term gross national product (GDP) was first used by Clark Warburton (1896-1979) in 1934. The term was defined as the total of final products. The definition refers to products that are sold to consumers and firms as a result of production processes and that do not enter the production process again for the production of other products. However, Warburton stated that usable resources would emerge by deducting depreciation, that is, wear and tear, from gross national product.

In England, Colin Clark (1905-1989) was trying to calculate both aggregate demand (consumption, investment and government spending) and the multiplier coefficient for England. Keynes’ “General Theory” published in 1936 provided support that emphasized the importance of Clark’s work. The process culminated in Clark’s “National Income and Outlay” in 1937. Later, Keynes published “How to Pay for the War” in 1940, using the data Clark had provided in 1937.

Hicks first used the C+I+G (consumption+investment+public expenditure) formula of economics in 1940. He formulated expenditures for all goods and services.

Economics, which included more mathematics, led to the formation of a sub-branch of science within itself: econometrics. In 1930, “The Econometric Society” was founded in Chicago by Charles Roos (1901-1958) , Irving Fisher and Ragnar Frisch. Frisch stated that mathematics alone was insufficient in economic analysis and that econometrics had a mission as a field where economic theory, statistics and mathematics came together. The Econometric Society began publishing Econometrica in 1933.

The Econometric Society was supported by businessman Alfred Cowles (1891-1984) . Cowles was the owner of an organization that made economic forecasts and in his 1933 article titled “Can Stock Market Forecasters Forecast” he tried to determine how successful stock market forecasters were. The result caused him to develop a very skeptical approach to success. He revealed that there was no significant difference in forecast success between professional forecasters and amateurs.

The first economist to conduct an econometric study for an entire economy was Jan Tinbergen (1903-1994) . He had a PhD in physics, but the title of his doctoral thesis was “Minimization Problems in Physics and Economics” . He worked in the central planning office of the Netherlands. As can be understood from the title of his doctoral thesis, it was not difficult to shift from physics to economics . He divided business cycles into two groups: impulses and propagation. He wrote a work called “Statistical Testing of Business Cycle Theories” under the sponsorship of the League of Nations. The work tested the content of Gottfried Haberler’s (1900-1997) 1936 work called “Prosperity and Depression” , which examined the theories of business cycles. Tinbergen stated that an economic model must contain a sufficient number of variables, the relationships between variables must be fully defined, and dynamics, that is, the time transitions between variables, must be revealed.

The Cowles Commission, founded by Cowles, and Jacob Marschak (1898-1977), who became the director of research at the head of this organization in 1943, made significant contributions to the development of econometrics. The work of the Cowles Commission, under Marschak's directorship, was directed towards the development of new methods that took into account the basic characteristics of economic theory and economic data rather than achieving concrete results. The basic principles of these methods were as follows:

1. Economic theory consists of a system of simultaneous equations. For example, the value of a commodity depends on the supply, demand, and price change processes created by the supply-demand imbalance of that commodity.

2. Most of the equations contain random conditions, because behavior is affected by shocks and factors that economic theory cannot deal with.

3. Most economic data consists of time series. Data from one period are affected by data from previous periods.

4. Most of the published data is aggregated, excluding individual elements. For example, national income, unemployment, etc.

New techniques began to be added to these approaches. One of the most important of the new techniques was presented by Trygve Haavelmo (1911-1999) . Haavelmo argued that no statistical data analysis method that did not include probability models would be meaningful. Until then, econometricians had seen probability models as a method that could only be used for games of chance. Haavelmo argued that no model in statistics that did not refer to stochastic (random) design would be meaningful. He thought that stochastic elements should enter models in economics, not as a measurement error, but as an element inherent in economic relations.

The techniques developed by the Cowles Commission were particularly advanced in the 1940s by Lawrence Klein (1920-2013), who developed tools for policy making. Klein's working models were similar to Marschak's. His approaches were used extensively in macroeconomic forecasting studies in the 1960s and 1970s.

There were times when econometrics’ efforts to integrate mathematics and statistics with economic theory were met with skepticism. Questions arose about how much value the work done by the Cowles Commission created. Because the belief that the models created and the empirical data were connected to economic theory were not formed to the extent that was intended. In fact, the work done by the Cowles Commission shifted to economic theory research in the 1940s. By the 1950s, there were those who expressed that econometrics’ efforts to create a synthetic economy of mathematics, statistics and economics, which was the ideal, had collapsed.

In 2000, a group of French students heavily criticized the economics education they were receiving. One of the main points of criticism was that the neoclassical teaching that dominated economics education was disconnected from reality. In this context, they stated that mathematics was used uncontrollably in economics and that economics created an imaginary world.

Mathematical measurements are very useful in social sciences to identify developments. However, I believe that it is necessary to understand that using mathematics to find solutions to problems and transforming mathematics from a tool to be used into an end distances economics from its social characteristics.