The Overmathematicization of Economics: Lessons for Business Disciplines.
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| Title: | The Overmathematicization of Economics: Lessons for Business Disciplines. |
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| Language: | English |
| Authors: | Quddus, Munir, Rashid, Salim |
| Source: | Journal of Education for Business. May-Jun 1993 68(5):288-292. |
| Peer Reviewed: | Y |
| Page Count: | 5 |
| Publication Date: | 1993 |
| Document Type: | Opinion Papers Journal Articles |
| Descriptors: | Course Selection (Students), Economics, Economics Education, Higher Education, Mathematics, Research Methodology |
| ISSN: | 0883-2323 |
| Abstract: | Opposition to excessive use of mathematical techniques in economics is growing. Math dominance reduces the diversity of traditions in economics. When used appropriately, it is a useful, efficient research tool, but it should be balanced with other methodologies. (SK) |
| Entry Date: | 1993 |
| Accession Number: | EJ463538 |
| Database: | ERIC |
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| FullText | Text: Availability: 1 Value: <anid>AN9306170210;JEB01MAY.93;1997Dec18.11:53;v2.3</anid> <title id="AN9306170210-1">THE OVERMATHEMATICIZATION OF ECONOMICS: LESSONS FOR BUSINESS DISCIPLINES </title> <p> <bold> ABSTRACT. </bold> The literature critical of excessive quantification in economics may hold lessons for the related business disciplines that, in the past, have often been influenced by the intellectual legacy of economics. There is concern that the economics profession is losing good students from liberal arts programs and that there is increasing polarization within the profession. In the long run, this will undermine the effectiveness of the discipline in influencing public policy. Are there similar trends in the related business disciplines? Can the experience of economics with mathematical tools be a precursor to similar trends in finance, management, marketing, and the decision sciences? In this article, we discuss the growing literature that is critical of the current dominant status of mathematics in economics. The lessons learned from the crisis in economics may result in avoidance of repetition of these errors in other business disciplines. </p> <p>Academic economics has rapidly become the most mathematicized of all the social sciences and business disciplines.(<reflink idref="bib1" id="ref1">n1</reflink>) The spectacular growth of mathematical methods in economics has spawned a growing literature that is opposed to the domination by mathematics of what is essentially a social science. The hostility to the use of mathematical methods has a long tradition in the history of economic thought.(<reflink idref="bib2" id="ref2">n2</reflink>) However, the present opposition seems to be gaining momentum. In this article, we present concerns expressed by important leaders and contributors to contemporary mathematical economics(<reflink idref="bib3" id="ref3">n3</reflink>) We believe that these trends in academic economics may very well be the precursors to similar trends in related business disciplines. The mathematics used in finance, management, marketing, and decision sciences, though still lagging behind the mathematics used in economics, seems to be catching up. Therefore, our discussion has significance for members of the other business disciplines and the social sciences who are interested in methodological questions.(<reflink idref="bib4" id="ref4">n4</reflink>) </p> <hd id="AN9306170210-2"> Why Employ Mathematics? </hd> <p>Since the beginning of political economy, writers have attempted to use mathematics to analyze economic topics. Up until the 1870s, these attempts were scattered and largely unsuccessful. A group of authors now known as the "marginalists" successfully started the process of mathematicizing economics in the later decades of the 19th century. In the 20th century, especially in the post-World War II decades, mathematical tools of relative complexity came to be routinely used in economics. Today, economics has the distinction of being the most mathematicized discipline among all social sciences and business fields. In the present and past literature, there are various reasons given to justify the employment of mathematics. We begin with a discussion of some of these reasons along with the corresponding specific criticisms. A more detailed discussion of these critical views will follow. </p> <p>1. Economic variables such as money supply, output, costs, revenue, and income are naturally quantifiable. Hence the use of mathematics will enhance the efficiency of the economic analysis. </p> <p>Criticism: This is only partially true. Many other economic variables such as utility, want, and satisfaction are not quantifiable. Another problem with quantifying economic variables is that these are usually not "internally homogeneous, " unlike variables in physics or engineering (distance, weight), which are. </p> <p>2. Mathematics is simply another language. Furthermore, it is the language of the sciences and has the advantage that it imposes rigor and logical discipline on the analysis. </p> <p>Criticism: Critics have pointed out that the claim that mathematics is simply another language is somewhat exaggerated. As Boulding pointed out, it is not possible to express "I love you" in mathematics. Second, there are numerous examples in the literature of confused analysis wrapped in mathematical symbolism by authors who have used mathematics as a smokescreen to hide their lack of clarity and understanding of the topic. Thus, the use of mathematics does not preclude and in fact may encourage a sense of "false professionalization" of the discipline.(<reflink idref="bib5" id="ref5">n5</reflink>) </p> <p>3. When the analysis is complex, mathematics can be more efficient than plain English. Because there is no dearth of complex problems in the real world, mathematics is ideally suited for real-world analysis. </p> <p>Criticism: This point is well taken. Critics, however, point out that sometimes it is sensible to separate the research from "publication" or even "pedagogy." In research, any tool that helps must be employed. However, when presenting the research findings or teaching these findings, we must be sensitive to the audience. To understand basic principles of economics, calculus may be used, but it is neither necessary nor sufficient. Second, no matter how sophisticated the mathematics is, it cannot capture all the complexity of the real world. As a result, quantification is often a false prophet, disappointing us after making excessive promises. This is especially true for the economic model building and forecasting industry. Despite immense labor, models involving hundreds of equations, and the latest in computer technology, the industry's record in predicting future movements in the economy has been woefully inadequate. As a result, quantification can be downright misleading for policymakers and business leaders who would make decisions based on forecasts from these mathematical models. </p> <hd id="AN9306170210-3"> The Opposition to Mathematical Methods </hd> <p>In a recent survey of the economics profession, Grubel and Boland (1986) found that it is mostly the distinguished members of the profession--the Nobel laureates, the AEA presidents, and those in Who's Who in Economics biographies--who are most vocal in expressing alarm at the excessive use of mathematical methods in economics today. In this section we present a brief sample of some of the critical views that we have collected. We present these in the form of original quotes so that the reader may get a flavor of the depth of these concerns. Kenneth Boulding, an early and vigorous proponent of the view that mathematical techniques are overused and frequently abused in academic economics, recently criticized the lack of appreciation on the part of mathematical economists for the "qualitative" dimensions of the economic variables. </p> <p>Quantification leads to something that might be described as "reducingism," that is, reducing complex structures and sets to single numbers. There is a certain value in this. The reality behind a single figure for the GNP, for instance, is a set of perhaps 100 million prices and quantities. The reality behind a population figure is a vast variety of human beings of different shapes, sizes, ages, skills and capacities. These reductions are not meaningless, but their meaning has to be interpreted. The numbers are evidence, not truth. Two countries can have the same GNP for the same population and be enormously different in their structure and proportion. Boulding, 1985, p. 14) </p> <p>One of the most perceptive commentators of mathematical methods in economics is Nicholas Georgescu-Roegen, a philosopher of sciences who has been credited with profound contributions to the discipline. Georgescu-Roegen is keenly aware of the many limitations of the mathematical methods. Pointing to the many unresolved issues regarding the measurability of economic variables, he wrote: </p> <p>. . . we [mathematical economists] gradually came to realize that measurability, whether cardinal or ordinal, requires very stringent conditions . . . that neither wants nor expectations fulfill the conditions of measurability. (Georgescu-Roegen, 1966, pp. 119-120) </p> <p>He faults mathematical economists for getting carried away with their mathematics and for putting economics in a secondary position. Using a quote from Knut Wicksell, he wrote: </p> <p>From whatever angle we may look at arithmomorphic [mathematical] models, we see that their role is "to facilitate the argument, clarify the results, and to guard against possible faults of reasoning--that is all. " . . . Unfortunately, we are apt, it seems, to be fascinated by the merits of arithmomorphic models to the point of thinking only of the scalpel and forgetting the patient. (Georgescu-Roegen, 1966, p. 124) </p> <p>According to Georgescu-Roegen, there is an element in mathematics that encourages elegance in theory and model building at the cost of realism and relevance, thus corrupting the incentive structure for academic researchers.(<reflink idref="bib7" id="ref6">n7</reflink>) He tells us: </p> <p>there are endeavors that now pass for the most desirable kind of economic contributions although they are just plain mathematical exercises, not only without any economic substance but also without mathematical value. (Georgescu-Roegen, 1979, p. 317) </p> <p>Maurice Allais, who received the Nobel Prize in Economics in 1988, has been both a sensible user and outspoken critic of the many instances of the pointless employment of mathematical methods in economics. Recently he emphasized the proper role of mathematics: </p> <p>While mathematics is an instrument whose mastery is extremely precious, it is, and can only be, an instrument. One cannot be good physicist or economist simply beause one has some ability in mathematics. (Allais, 1989, p. 13) </p> <p>A danger with the unrestrained use of mathematics in a social science or business discipline concerned with problems that are often nonquantifiable is that the discipline-specific research program may be compromised by incentives to mathematize. In academic economics today, this danger has become a reality. Decrying the pervasive influence of mathematical methods in economics and the detrimental impact this has had on its research program, Allais wrote: </p> <p>Indeed a large part of contemporary theoretical literature has progressively come under the control of pure mathematicians who are more concerned with mathematical theorems than with analysis of the real world. A new scholastic totalitarianism has arisen based on abstract and apriorist conceptions, detached from reality; this kind of "mathematical charlatanry" had already been denounced by Keynes in his Treatise on Probability. (Allais, 1989, p. 13). </p> <p>For almost fifty years contemporary economic literature had developed too often in a totally erroneous direction with the construction of completely artificial mathematical models detached from reality; and too often it is dominated more and more by a mathematical formalism which fundamentally represents an immense regression. (Allais, 1989, p. 13) </p> <p>It cannot be repeated too often: for the economist, as for the physicist, the essential objective is not to use mathematics for its own sake, but as a means of exploring and analyzing concrete reality, and consequently never to dissociate a theory from its application. (Allais, 1989, p. 13) </p> <p>Another Nobel laureate in economics, James Buchanan, has pointed to the very real but usually ignored costs of mathematicizing economics. The time spent in mastering the minimum mathematical skills necessary to pursue a career m academic economics has increased dramatically. This time is not without substantial costs. It could have been spent in gaining knowledge of the institutions crucial for analysis or improving our understanding of basic economic principles. Thus our top graduate programs, which are invariably highly mathematical, may be producing mathematically sophisticated graduates who are not competent economists. Buchanan wrote: </p> <p>I do deplore the waste that such [learning mathematics] investment of human capital reflects. The intellectual achievement comes with a major resource cost, and, as with any such commitment, the opportunity cost is measured in benefits that might be expected from the alternative that is sacrificed. In modern economics that which is sacrificed is an understanding of the principles of the market process and of the relationship of this process to the institutional setting within which persons choose. (Buchanan, 1985, p. 15) </p> <p>A pioneer in modern quantitative economics, Wassily Leontif, has been critical of the trends in the mathematicization of economics, especially because these gains in our technical virtuosity have not produced a corresponding improvement in our understanding of the economy. He explained why much of the complicated mathematics now employed in economics has contributed so little to our knowledge of the structure of the real economy: </p> <p>Not having been subjected from the outset to the harsh discipline of systematic fact-finding, traditionally imposed on and accepted by their colleagues in the natural and historical sciences, economists developed a nearly irresistible predilection for deductive reasoning. As a matter of fact many, many entered the field after specializing in pure or applied mathematics. Page after page of professional economics journals are filled with mathematical formulas leading the reader from sets of more or less plausible but entirely arbitrary assumptions to precisely stated but irrelevant theoretical conclusions. (Leontief, 1982, p. 104) </p> <p>Year after year economic theorists continue to produce scores of mathematical models and to explore in great detail their formal properties; and the econometricians fit algebraic functions of all possible shapes to essentially the same set of data without being able to advance, in any perceptible way, a systematic understanding of the structure and the operations of a real economic system. (Leontif, 1982, p. 107) </p> <p>Recently William Baumol, an important figure in mathematical economics, joined this ever-louder chorus of mathematically oriented economists who have voiced the opinion that the discipline may very well have become overmathematicized. In his article "Towards a New Economics: The Future Lies Ahead," he wrote:(<reflink idref="bib8" id="ref7">n8</reflink>) </p> <p>As one of those who worked with some determination to change this state of affairs and to introduce some grounding in mathematics as a standard part of postgraduate curriculum in several universities, it may be pardonable for me to suggest that things may have gone a bit far in the opposite direction. </p> <p>. . . there are at least two grounds on which such a state of affairs is to be deplored--its preclusion of other promising lines of attack, and its consequences for those students whose talents are for approaches other than the mathematical (Baumol, 1991, p. 2) </p> <p>Michio Morishima, a respected mathematical economist, has gone further than most in his criticism by also suggesting a constructive solution for the problem. The mathematical economists who lost contact with the ground must learn to incorporate both history and institutional knowledge in their analysis: </p> <p>The reason for present-day economics having lapsed into the wretched state of affairs we have noted above is the fact that so deep and extensive has been the mathematicization of economics since 1940 that it has lost all sense of balance, becoming divorced from knowledge of economic systems and economic history. There is only one medicine which will cure this malaise, and that is for the theorists to make a serious effort in the direction of the institutionalization of economics, in the sense of slowing the speed of all development towards mathematicization and developing economic theory in accordance with knowledge of economic organizations, industrial structure and economic history. (Morishima, 1984, p. 70) </p> <p>Toward the end of his illustrious career, Sir John Hicks, one of the greatest twentieth century economic theorists and a pioneer in the appropriate use of mathematical methods in economics, made the following comment on the writings of mathematical economists: </p> <p>I do feel that most of this stuff that I pick up and see in the journals seems to have very little relevance to the sort of practical problems that really bother people.... I mean, what have these mathematical theories got to say about whether Britain should go into the EMS? Nothing! That is the sort of question about which economists should have something to say.... A lot of these mathematical models, including some of my own, are really terribly much in the air. They lost their feet off the ground. (quoted in Klamer, 1989, p. 180) </p> <p>In conclusion, we quote from Gerard Debreu, a Nobel economist widely considered to be one of the father figures in modern mathematical economics. In his position as the president of the American Economic Association, he noted the increasing strain the rapid mathematicization has placed on general membership in the economic profession: </p> <p>Our profession may take pride in its exceptional intellectual diversity.... Yet that diversity is strained by the increasing impenetrability to the overwhelming majority of our Association of the work done by its most mathematical members. The extent of (that) mathematization has given rise to discordant assessments of its effects and to attempts to change its heading. (Debreu, 1991, p. 6) </p> <hd id="AN9306170210-4"> Lessons From the Methodological Crisis in Economics </hd> <p>These lessons from the literature discussed above may be summarized as follows: </p> <olist> <item> Mathematics is an important research tool and should be employed, wherever useful, in research and analysis. </item> <item> Not all areas and topics are quantifiable. Therefore, research topics that depend on nonmathematical methodologies should be given appropriate coverage and respect. </item> <item> There are research methodologies besides the mathematical. The foundations of a discipline should be based on all of these diverse methodologies, instead of on a single one. Diversity in methodology is a source of strength. This diversity must be protected and encouraged. No single methodology or school should be allowed to stifle the others. </item> <item> The "research" or "teaching" and "writing" activities sometimes need to be separated. The great Cambridge economist Alfred Marshall wrote to a friend that he often "burned" his mathematical analysis after he had derived the results and successfully translated these into plain English. </item> <item> The powers that be, in an academic profession--the school deans, department and dissertation committee chairs, the journal editors, the Nobel Prize winners, and the Association presidents--must be actively involved in methodological debates in their respective disciplines. Once established, trends are difficult to reverse as they take on a life of their own. From the beginning a balance must always be maintained. </item> <item> The best graduate schools should hire qualified faculty whose strengths and research agenda are other than mathematical. They should admit good students whose aptitude is in nonmathematical methodologies. Similarly, the best journals should reserve space and encourage writing that is analytical, yet descriptive. </item> <item> New journals and authors should devote themselves to the task of "translation" of mathematical publications and their research findings into plain English. This is important to prevent polarization within the discipline. </item> </olist> <hd id="AN9306170210-5"> Concluding Remarks </hd> <p>Despite the dominant position occupied by mathematics in modern academic economics, the opposition to the excessive use of mathematical techniques presently appears to be gaining momentum. Participating in the growing chorus of critical voices are some illustrious names in economics, many of whom also are accomplished mathematical economists. To the extent that developments in economics are sometimes precursors to similar trends in the other business disciplines, there may be important methodological lessons for academics in these disciplines. Perhaps the dissent in economics can help them avoid some of the mistakes in their own discipline. </p> <p>The message from this literature may sound paradoxical at first. How can authors who have employed mathematics in their own work, in fairness, oppose its use by others? The paradox is understandable when we are careful to read between the lines of these cautionary remarks. We are opposed to the pointless use of mathematics, not its useful application. We are critical of the abuse of mathematics in economic analysis, not its judicious use, and are opposed to the dominance of mathematics in economics, not its useful service. Our concern is that the hegemonic position of mathematical tradition is reducing the diversity of traditions in economics, not contributing to it. We are resisting the mathematics that gives monopoly to a few, not the mathematics that is usefully shared by all members of the profession. These distinctions are subtle and yet important. </p> <p>Mathematics is a useful and efficient research instrument ideally suited to many topics in economics and business. However, there are limitations to its usefulness. There are explicit costs involved in learning and using mathematics. Its unwise use may do more harm than good. Any discipline that encourages the use of mathematics must be vigilant in guarding its own traditions and research agenda. Unrestrained use of mathematics can overwhelm the host discipline. Let the academic and researcher in business fields beware of the pitfalls of quantification. Let them employ mathematics judiciously, balanced with the use of other methodologies. These are some of the lessons that academic business disciplines should learn from the 20th century's experience of economics with quantification. </p> <ref id="AN9306170210-6"> <title>NOTES</title> <blist> <bibl id="bib1" idref="ref1" type="bt">(n1.)</bibl> <bibtext>The mathematics used in economics is not only sophisticated but also pervasive. No branch in the field, theoretical or applied, is left untouched by this seemingly insatiable urge to quantify. </bibtext> </blist> <blist> <bibl id="bib2" idref="ref2" type="bt">(n2.)</bibl> <bibtext>For a study of this tradition, see Mirowski (1991) and our paper (Quddus &amp; Rashid, 1991). </bibtext> </blist> <blist> <bibl id="bib3" idref="ref3" type="bt">(n3.)</bibl> <bibtext>This seems to be an appropriate benchmark for determining if the present use is excessive. Admittedly, our sampling of the literature is somewhat biased in that we highlight only those authors and views that are opposed to unrestrained use of mathematics. However, given the fact that all of these authors belong to the mathematical tradition in economics, their comments are an important barometer of the dissent within the profession. </bibtext> </blist> <blist> <bibl id="bib4" idref="ref4" type="bt">(n4.)</bibl> <bibtext>When we talk about the use of mathematics in economics, we refer to mathematics in the research, writing, and teaching of economics. The concern, however, is greatest with the writing and the teaching. </bibtext> </blist> <blist> <bibl id="bib5" idref="ref5" type="bt">(n5.)</bibl> <bibtext>For similar sentiments expressed with regard to the field of marketing, see the article by Bennet R. Rudolph (1989). He laments that in an effort to "professionalize" marketing, the academics are resorting to "the quantification of everything possible, including many things which are, in fact, not quantifiable" (p. 20). </bibtext> </blist> <blist> <bibl id="bib6" type="bt">(n6.)</bibl> <bibtext>In this section, we draw heavily from our more detailed paper, "Resistance to Mathematical Methods in Economics--Past and Present." For a copy of this paper, the interested reader is encouraged to write to us at the Department of Economics, University of Illinois, P.O. Box 34, 1206 S. 6th St., Champaign, Urbana, Illinois. </bibtext> </blist> <blist> <bibl id="bib7" idref="ref6" type="bt">(n7.)</bibl> <bibtext>According to Georgescu-Roegen (1979) and more recently Mirowski (1991), the infatuation of early neoclassical economists with the metaphor of mechanics is the source of this problem. Economics was shunted permanently into the wrong direction by the desire of a few economists of that time to emulate the natural sciences and gain the stature of physics and more precisely the science of mechanics. However, in their enthusiasm and haste they made fundamental errors in using the mathematics they borrowed. To this day, academic economics remains hostage to this mathematics. </bibtext> </blist> <blist> <bibl id="bib8" idref="ref7" type="bt">(n8.)</bibl> <bibtext>This special anniversary issue of one of the oldest and most respected journals in economics was devoted to predicting where economics was headed over the next 100 years. </bibtext> </blist> </ref> <p>REFERENCES </p> <p>Allais, M. (1989). My life philosophy. The American Economist, Fall, 3-17. </p> <p>Baumol, W. (1991). Towards a newer economics: The future lies ahead! Economic Journal, 101(<reflink idref="bib404" id="ref8">404</reflink>), 1-8. </p> <p>Boulding, K. (1948). Samuelson's foundations: The role of mathematics in economics. Journal of Political Economy, 56(<reflink idref="bib3" id="ref9">3</reflink>), 187-209. </p> <p>Boulding, K. (1985). What went wrong with economics? The John R. Commons Award Lecture, ODE, December 29. Boulder, CO: IBS. </p> <p>Buchanan, J. (1985). Liberty, market and state. New York: New York University. </p> <p>Debreu, G. (1991). The mathematization of economic theory. American Economic Review, March 1991, 81(<reflink idref="bib1" id="ref10">1</reflink>), 1-7. </p> <p>Georgescu-Roegen, N. (1979). Methods in economic science. Journal of Economic Issues, 13(June), 317-328. </p> <p>Georgescu-Roegen, N. (1966). Analytical economics: Issues and problems. Cambridge, MA: Harvard University. </p> <p>Grubel, H., &amp; Boland, L. (1986). On the efficient use of mathematics in economics. Kyklos, 39, 419-442. </p> <p>Klamer, A. (1989). An accountant among economists: Conversations with Sir John R. Hicks. The Journal of Economic Perspectives, 3(<reflink idref="bib4" id="ref11">4</reflink>), 167-180. </p> <p>Leontief, W. (1982). Letter: Academic economics. Science, 217, 104 107. </p> <p>Mirowski, P.(1991). The when, the how, and the why of mathematical expression in the history of economic analysis. Journal of Economic Perspectives, 5(<reflink idref="bib1" id="ref12">1</reflink>), 145-157. </p> <p>Morishima, M. (1984). The good and bad uses of mathematics. In P. Wiles and G. Routh (Eds.), Economics in disarray. Oxford, England: Blackwell. </p> <p>Quddus, M., &amp; Rashid, S. (1991). The resistance to mathematical methods in economics--Past and present. University of Southern Indiana, Faculty Working Paper 7-1991. </p> <p>Rudolph, B. (1989, July 17). Let's not go overboard with the "professionalizing" of marketing. Marketing News, 23, pp. 4, 20. </p> <aug> <p>By MUNIR QUDDUS, University of Southern Indiana Evansville, Indiana and SALIM RASHID, University of Illinois Urbana, Illinois </p> </aug> <nolink nlid="nl1" bibid="bib404" firstref="ref8"></nolink> |
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