The Pitfalls of Mathematical Economics
Those who want to be professional economists in this day and age often require more mathematical skills than some engineers and natural scientists. Probably only physicists like the famous John Nash and electrical engineers need more sophisticated mathematics than economists. Although I stand to be corrected, civil and industrial engineers do not need to learn all the tools of difference equations or do not have to invert 200 by 200 Matrices as some economists are required to do in their study of business cycles or of the inter-dependences of hundreds of sectors within the economy. It is revealing that precisely, a physicist like John Nash (of "beautiful mind" fame) obtained his Nobel Prize in economics.
The pioneer in the "mathematization" of economics in the last century was the late Paul S. Samuelson who died last December 2009 at the age of 94. As reported by Michael Weinstein in The New York Times (December 14, 2009), quoting another Nobel laureate in economics, Robert Solow (who was one of the readers of my doctoral dissertation at Harvard): When economists "sit down with a piece of paper to calculate or analyze something, you would have to say that no one was more important in providing the tools they use and the ideas that they employ than Paul Samuelson."
Shortly after his death, an article appeared in the Financial Times authored by Stephanie Flanders entitled "Nobel laureate who turned economics from scattered thoughts to science dies." According to Flanders, Samuelson spent a large part of his career organizing scattered thoughts on economic theories since at least the time of Adam Smith in the 18th Century: "Welfare economics, the theories of consumption, capital accumulation, economic growth, finance and international trade all became subject to his rigorous 'picking and arranging'. It is difficult to name an important postwar debate in economics in which Samuelson did not play a role. He once boasted: 'My finger has been in every pie.' "
This work of systematization started with the doctoral dissertation at Harvard entitled The Foundations of Economic Analysis which he submitted in 1941 when he was only 19 years old. The dissertation contained only a few pages full of mathematical formulas. As Samuelson himself wrote: "To a person of analytical ability, perceptive enough to realise that mathematical equipment was a powerful sword in economics, the world of economics was his or her oyster in 1935. The terrain was strewn with beautiful theorems begging to be picked up and arranged in unified order." Through his pioneering work, economics began to comply with the definition of a "science", i.e. an organized body of demonstrated truths. Before this effort of systematic organization of theories, economics was known as political economy, a branch of philosophy. In fact, the first practitioners of economics such as Adam Smith, David Ricardo, and even Karl Marx were, strictly speaking, moral or social philosophers rather than economists in the present sense of the word.
There is no question that through the pioneering work of Samuelson, economics came closer to the empirical sciences such as physics and biology, by putting economic theories in quantifiable forms that could be subjected to empirical testing, especially through the tools of econometrics. As Weintein wrote in his article for The New York Times, "His early work, for example, presented a unified mathematical structure for predicting how businesses and households alike would respond to changes in economic forces, how changes in wage rates would affect employment, and how tax rate changes would affect tax collections." Indeed, a whole generation of Filipino economists have helped successive Governments at least from the time of President Marcos to use the tools of mathematical economics to determine the effects of varying monetary, fiscal and trade policies on prices, income and employment. …