Wednesday, 28 April 2010

The pitfalls of mathematical economics

Manila Bulletin

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. The majority of these economists have been the top professors of the U.P. School of Economics, many of them actually occupying high positions in the various Administrations.

Unfortunately, however, the application of mathematical reasoning to economic problems – which at bottom are still predominantly human – led to a certain hubris which made some leading economists to avoid or even disdain moral considerations in looking for solutions to economic problems. Take the famous Edgeworth box diagram used in Welfare Economics. Without boring the nonspecialists in the intricacies of this geometric tool, it is often used by those who advocate completely free markets to demonstrate that the highest production from the available resources and the highest human satisfaction from limited consumer goods could be attained by allowing individuals to freely trade with one another. The starting point, however, could involve the rich controlling most of the resources and goods available. According to traditional welfare economics, the question of distribution of income and wealth is not to be decided in economics but in political science. Economists cannot make "value judgments" about what income or wealth distribution is just.

But somewhere along the way to actual policy implementation, the defenders of free market economics assumed that any government intervention is inefficient. Thus, the actual state of the very unequal distribution of income and wealth in most countries--including the United States--was unwittingly accepted as a given. Through the tools of mathematical economics, the free market advocates continued to argue that markets are self-correcting and automatically lead to highest levels of production and consumer satisfaction. In fact, it was also Samuelson who laid out the mathematics of stock price movements, an analysis that won for his student Mr. Robert Merton and Myron S. Scholes the Nobel Prize. These two designed formulas that Wall Street analysts use to trade options and other complicated securities known as derivatives. Well, everyone now knows that these "derivatives" were a major cause of the Great Recession in 2008 to 2009.

To avoid the pitfalls of mathematical economics, the practitioners of the science should also include in their assumptions that in the real world there are individuals who can be motivated by altruistic goals, i.e. that there are owners of business who can sacrifice profit in order to promote the welfare of their employees, protect their consumers from harmful products, or clean up the environment. They should also take account of the fact that there are necessary and efficient programs of intervention of the Government in promoting the welfare of the poorest of the poor who are left out by free market forces because they are either too hungry, too unhealthy, too unschooled, too unskilled, or too unhoused to be able to benefit from free market forces. Even if it means that the quantitative economists will have to reembrace the former profession of the political economists, despite their discomfort with "normative" statements, we need a new approach to studying the problems of poverty and unemployment. In this regard, with due respects to Paul Samuelson, I would like to recommend to the young economists today to consider as their role model another Nobel Laureate, Amartya Sen, currently a Professor of Economics at Harvard University, who is as steeped in mathematical economics as Samuelson, but also gives much importance to philosophy, anthropology, political science and sociology in his analysis of economic problems, especially in the developing countries of the world. For comments, my email address is

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