In a must read book, �The Three Cultures� , the author, Jerome Kagan, writes on the drawback of model used in economics. Whilst much has been written on the subject, what is interesting here are the rich inputs from a number of disciplines. prefix = o ns = "urn:schemas-microsoft-com:office:office" /

�Economists and psychologists are the most intellectually ambitious social scientists because both strive to explain broad areas of human variation. However, the two disciplines have divergent explanatory goals. Psychologists probe the joint effects of personal experience and biology on individual achievement, personality, and mental illness. Economists study the influence of institutions, technology, populations, and natural and human resources on aggregated indexes of wealth and productivity that are presumably correlated with the material comforts and health of the largest number. However, economists enjoy greater respect from governments and the public because they have the advantage of the consensual metric of money, which permits them to make reasonable predictions of the relations between the prices of goods and the balance between supply and demand. In addition, their reliance on mathematical models, which is not well understood by the public or their clients, has the advantage of persuading audiences that their conclusions have the certainty associated with equally obscure equations in physics. The authority of a physician's prescription is enhanced when written in Latin.

Simon Kuznets

It is important, however, to differentiate between finding a mathematical description for a rich corpus of data and positing formal models based on a priori assumptions that either have not been validated, or are inconsistent with the evidence. The former strategy is the admirable goal of all scientists. Kepler, Newton, and Planck invented powerful equations that described reliable observations that could not be explained with the theories of the time. The Nobel economist Simon Kuznets, who also fit mathematical propositions to rich corpora of data, was suspicious of the validity of formal models. However, the economists who advocate formal models based on the debatable premise that individuals always try to maximize their economic self-interest by making rational decisions uninfluenced by the actions or economic position of others resemble string theorists because both models contain variables that either have not been measured or, at the moment, are not even measurable.

Philip Mirowski

Philip Mirowski, an economic historian, has argued that the invention of the computer and the prolonged Cold War motivated some twentieth-century economists to replace their traditional interest in the optimal allocation of scarce resources with the processing of information between competitors in a game-like setting. American generals hungered for a rational solution to the worrisome problem of a possible Soviet first strike and the Pentagon poured money into research that utilized models of games simulating the relation between the two superpowers. The economists were not troubled by the fact that the study of game-like situations in which one hypothetical agent processed information about another hypothetical agent was analogous to substituting the sixty minutes of Super Bowl play with a printout of the thoughts of the two coaches.

Humans inherited the combination of an ability to recognize a number of alternative action to cope with a challenge and an inability to tolerate the uncertainty this awareness generates. So we insist there must be some ideology somewhere that rationalizes the best action and dilutes this uncomfortable state. A belief in gods or astrologers had been effective in the past. Economic theorists who rely on the formal models of game theories played this role for the generals, and continue to do so for corporate executives and portfolio managers, even though history, laboratory evidence, and personal experience affirm the presence of non rational elements in all human decisions. Hence, it is reasonable to ask why so many economists refuse to accommodate to this truth. Their resistance reminds me of patients with obsessive-compulsive disorder who cannot tolerate "not knowing" whether a storm will happen tomorrow.

Higgs Boson

The economists who are troubled by this critique retreat occasionally and declare that a formal model does not have to represent what is actually happening in the economy and all the concepts do not have to be measured accurately. As long as the model appears to explain an economic fact, or predict a phenomenon better than chance, these economists are willing to defend its utility. However, physicists would be dissatisfied with this argument. The equations of quantum theory contain a mathematical concept, called the Higgs boson, that predicts experimental phenomena very well. Nonetheless, physicists persuaded European governments to spend more than 8 billion dollars to build the Hadron Collider so they could determine whether this hypothetical concept did indeed "exist" in nature. Natural scientists care deeply about the realistic nature of their models and economists should also care. Perhaps they should be reminded that Ptolemy's model for the cosmos did as well as Newton's in predicting many heavenly events, but this second-century model assumed that the sun revolved around the Earth. The economists who invent formal models mimic the physicists' mathematical forms, but they fail to honor the more important demand that the models accommodate to the known facts.

Although the formal mathematical models make economists appear similar to physicists, a mathematical equation purporting to describe a set of facts does not explain how or why the events occurred. Recall that the equation stating that the distance an object will fall is one-half the product of the force of gravity and the square of the time falling fails to explain the nature of the gravitational force. Second, the physicist's equations do not specify the context or the exact nature of the outcome. The Newtonian equation f= ma (force equals the product of mass and acceleration) does not specify the masses or the objects the resulting force acts upon. The observed phenomena are different for a fist striking a table, a hammer hitting a glass, and a knife plunged into a body. A model with only three variables - the education of each parent and the family income - provides a good prediction of the future educational level, vocation, and income of the children in the family, but it does not explain why this is so. It does not tell us the relative importance of the parents' behaviors, the children's identification with their class, the quality of schools attended, or the values of peers in the neighborhood.

Many economists want to eliminate each person's psychology and his or her cognitive constructions of the concepts in their equations. Hence, they treat concepts like the expected utility of a preference in an objective mode, even though the subjective and objective indexes of this concept are not the same. The utility of food and clothing, which are necessary for life, differs from the utility of a cherry-paneled study that satisfies a desire for higher status. Remember, the elements in these models are symbols, not feelings. There are no conflicts, guilts, or lapses of consciousness in these models. For example, the models ignore the possibility that some individuals might feel that they are not entitled to an ascent in status because of their personal history or ethnicity. Some who grew up poor developed a strong anger at the rich and, therefore, becoming wealthy implied that one had become a member of the hated group. Still others restrain efforts to rise from a disadvantaged position because they do not want to be disloyal to the values of family and friends. These conflicts, which can block a persistent effort to make a great deal of money or ascend in status, are missing from the economists' models.

Readers unfamiliar with the writings of neoclassical economists may be surprised to learn that some regard the decision to have a child as no different from the decision to purchase a pet dog because both are acts of consumption motivated by the anticipation of future happiness. However, most mothers decide to have a child because they regard the experience as one of the obligations of being a woman, but that is not why one buys a dog. One economist estimated that a middle-income American family with two children will spend more than $300,000 over the first eighteen years of their lives. A couple who had invested that money at 5 percent for thirty-five years would have accumulated more than one-and-a-half million dollars. An economist who thought it was rational to compare the feeling of well-being generated by raising children with the feeling accompanying reflection on a large savings account should be asked if he prefers dinner or watching a foreign movie. The mass of a pile of ten quarters is a physical property whose value can be placed on a ratio scale. But the monetary value of the pile of coins is a symbolic property that has different utilities for different people. A pound of lead shot and a pound of feathers enclosed in identical cardboard boxes have exactly the same masses, but humans perceive the box of lead as heavier because of the different distributions of the weights of the two substances.

Robert Lucas

Economists also rely on concepts whose meaning varies with the source of evidence. For example, the estimate of national income depends on whether consumer spending, tax statements, or the appreciation of houses, jewelry, and paintings is included in the index. Further, economists regard the way an income was earned as unimportant, whether the salary of a bank clerk, the fees of a surgeon, or the royalties paid to an actress in a pornographic film. They seem to ignore the fact that there are many ways to arrive at the same value. The number �4� can be the result of 2+2, 3+1, 2x2 5-1, and the cube root of 64. Thus, Robert Lucas's insistence that all economic theory should be mathematical in form is unusual among most biologists. Few biochemists or ecologists would make a similar declaration. All cognitive psychologists do not argue that computer programs simulating cognitive processes are the only legitimate bases for theory construction, even though some believe that the computer is still the best metaphor for mind. To rephrase Shakespeare, it appears that Robert Lucas doth protest too much.

Many important discoveries in the natural sciences were unexpected empirical observations described with semantic or schematic forms, rather than formal models. Darwin's evolutionary hypotheses, recognition of the helical structure of DNA, and the realization that some viruses, called retroviruses, can go from RNA to DNA are examples. None is described primarily with formal models whose abstract concepts aggregate diverse phenomena. The economists' premise that mathematical tools invented to describe inanimate matter, or to explain a paradox in formal mathematics, should be applicable to economic decisions made under conditions created by history is just that - a premise based on faith, rather than on a persuasive argument or empirical evidence.

Paul Samuelson

Paul Samuelson advocated mathematical forms in his early, influential monograph on economic analysis because he had been influenced by an older Harvard physicist studying thermodynamics. The young Samuelson assumed that the success of mathematical formulations in explaining changes in physical energies should be equally powerful in accounting for economic decisions. He ignored the fact, noted earlier, that the physical concepts have fixed definitions that do not change with locale or time, whereas human preferences and expectations change over the course of a life and vary with historical era, culture, gender, ethnicity, and class. That is why a respected minority of economists, following John Maynard Keynes's position almost a century ago, is not as confident in the utility of mathematical models as Samuelson or Lucas. Partha Dasgupta, who teaches economics at Keynes's alma mater, Cambridge University, emphasized psychological concepts, such as trust, cooperation, and the values of a community, not formal models, in his primer on economics.

One reason for the increased popularity of mathematical descriptions of economic data after World War II was the decision by many twentieth-century governments to collect a great deal of statistical information on their nations and their economies. The availability of large corpora of data motivated mathematically talented scholars to invent equations that might account for the plethora of numbers, and by the 1970s economists began to favor formal models that rested on the canonical trio of greed, rationality, and equilibrium.

Noam Chomsky

It is worth noting that Chomsky's formal syntactic model for linguistics, artificial intelligence models for reasoning, and mathematical models of brain functioning, which also made strong a priori assumption, were written at about the same time because the introduction of computers allowed scholars who favored formal theories to simulate some of their phenomena. Unfortunately they, too, eventually had to acknowledge that their formal models did not fit the phenomena as well as they had hoped because they ignored metaphorical meanings and emotions.

A number of economists, especially Europeans, have challenged the dominance of the formalists. Some, persuaded by the arguments of Kahneman and Tversky, questioned the usefulness of the predictions or explanations that were based on abstract models resting on questionable assumptions about the rationality of human choice that ignored the detailed features of the economy they were modeling or the local contexts in which agents made decisions. Jerry Fodor offered a particularly pessimistic evaluation when he wrote that our attempt to explain human cognitive processes with formal or computational models was "no farther advanced than we were in the darkest days of behaviorism.�

Economists who study communication networks among investors, managers, and consumers provide an example of the unfortunate consequences of simplifying conditions that distort reality so that formal mathematical model can be used. Economists who apply the most popular models for communication networks assume that the links between any two people are always of the same strength, and only one link can exist between any two individuals. Both assumptions violate what is known to be true. The strength of a twenty-year friendship between an investor and a portfolio manager who is his brother, compared with one between a new investor and the same manager who is a stranger, is not only stronger but, in addition, is composed of two different kinds of links: the roles of investor and sibling.

Wasily Leontief

Wasily Leontief, another Nobel laureate in economics, wrote more than twenty-five years ago that American departments of economics, which prefer to hire faculty with mathematical talents, resemble the Marine sergeants who maintain discipline on Parris Island. The Harvard economist Greg Mankiw told an interviewer that it was difficult to justify the millions of tax dollars spent on economic research utilizing mathematical models that were not leading to substantial progress. This sentiment is shared: "Too large a proportion of recent mathematical economics are mere concoctions as imprecise as the initial assumptions they rest on, which allow the authors to lose sight of the complexities and interdependencies of the real world in a maze of pretensions and unhelpful symbols. The price exacted by the clarity of the models is a loss of fidelity to the actual events."