The excessive use of mathematics in economics has long been discussed by professional economists. The topic has now reached the general public when recently John Robson and Stephen Gordon debated the topic in the National Post, one of Canada’s two national newspapers.[i]
According to Robson “Mathematical technique has severe limits, including that you cannot model the economy. There are too many variables, whose interactions are too uncertain and whose feedbacks are too complex. In short, it is transcomputable. (sic)”
Gordon argues “Robson’s assessment of the complexities involved in economic analysis is depressingly accurate, but these complexities strengthen, rather than weaken, the case for using models and mathematics as tools for understanding economics.”
Both authors are right and the real issue is whether the use of mathematics in economics is at an optimal level. Larry Boland and I published a peer reviewed article on this subject in 1986.[ii] In it we documented a rapid growth in mathematical economics in publications and teaching, which we considered to be an important problem since it attracted increasing amounts of resources away from research and university teaching needed for students‘understanding of the real world, the design of government policies and political agendas.
The failure of mathematical economists to provide students with this understanding of the real world is due to the fact that most of them are poorly prepared to do so. Many come to economics trained in mathematics and took few if any courses in which they would have learned about economic institutions, real world practices and history.
A second problem arises from the fact that some mathematical economists believe that their abstract reasoning has important policy implications, which often are reported uncritically by media that like the findings for political and ideological reasons. In fact, mathematical models never result in valid policy implications since they use many simplifying assumptions, which logically pre-determine the conclusions and often can be changed at will.
However, mathematical modelling also brings some benefits to the profession and the world claimed by Gordon. It has brought rigor to the formulation of some fundamental ideas in economics, such as the way in which Adam Smith’s “invisible hand” guided by competition leads to a welfare maximizing allocation of resources.[iii] It also is fundamental to the design of computer models that are used with limited success for economic forecasting and the study of the effects of government policies.
Assuming that mathematical modelling produces some useful results and that it is achieved by diverting resources away from more traditional approaches to economic analysis, the question becomes how many resources should be devoted to each of the two disciplines.
Our 1986 study argues that the optimum level has been exceeded because economists specializing in mathematic modelling have formed a cartel. They have much more time than economists analyzing the real world to devote to the promoting and praising their work among the public. They scheme and take over hiring and tenure decisions in economic departments. They become editors of journals and find referees sympathetic to studies heavy on mathematical modelling. The resultant publications lead to tenure and ever more of their friends in university positions. They also are very influential in the committee that chooses winners of the Nobel Prize in Economics awarded annually by the Swedish Central Bank.[iv]
Nobel laureate George Stigler has argued that competition among universities and the success of their economics graduates in finding jobs in the real world limits the ability of mathematical economists to create such a cartel and that at any time the use of mathematical economics is at the optimum level.
Surveys of economists undertaken for our 1986 study showed that most disagree with Stigler and that research and teaching mathematical models has been much above optimal. It would be interesting to know what Gordon and other economists think about this issue in 2016.
[i] The articles are found at http://news.nationalpost.com/full-comment/john-robson-you-cant-compute-your-way-to-a-better-economy and
http://news.nationalpost.com/full-comment/stephen-gordon-the-case-for-mathematical-models-in-economics. The references show the titles of the articles, which in turn summarize the views expressed by the two authors.
[ii] Herbert G. Grubel and Lawrence A. Boland, “On the Efficient Use of Mathematics in Economics: Some Theory, Facts and Results of an Opinion Survey”, Kyklos, August 2986, found at http://onlinelibrary.wiley.com/doi/10.1111/j.1467-6435.1986.tb00779.x/abstract
[iii] This work has been done by Nobel laureates Kenneth Arrow and Gerard Debreu. In 1988 I presented a seminar on trade in services at a research institute in New Dehli, India, which demonstrated to me the misuse and misunderstanding that can arise from a faulty interpretation of mathematical modelling. During the discussion a young economist with a PhD from the Massachusetts Institute of Technology challenged me with the proposition that the mathematical model by Arrow and Debreu had proven that capitalism did not work since some of the assumptions they made in their analysis did not hold in the real world. Fortunately, the discussion of this issue ended after the director of the institute reminded his colleague that the theme of the seminar was trade in services, not the merit of capitalism versus socialism.
[iv] In the 1970s Peter Lloyd and I published a number of papers and the book “Intra-Industry Trade: Theory and Measurement of Trade in Differentiated Products” (MacMillan, 1976), which contain very nearly the same models and conclusions reached by Paul Krugman in his papers on the subject. Krugman received the Nobel Prize in 2008 for his work, all of which was published several years after the appearance of the Grubel and Lloyd studies. While we used words and diagrams to develop our theories, Krugman used mathematical models to explain his. However, we are pleased to know that the Nobel committee acknowledged our work as having been the most important inspiration for Krugman who used the empirical evidence we had provided.