Economic History

On the mathematization of Economics in the 21st Century.

The origins:

The origins of mathematization of economics apparently is a contested issue even for economists. The genesis of this phenomenon may change depending on the measure used for establishing when historically math joined economics. However, and regardless of the precise historical development of such relationship, what seems to be useful to note are Wassaly Leontief’s and Gerard Debreu’s main conclusions: mathematics have allowed economics to progress as a science; and, economics have the same all-social-science epistemological boundaries given the nature of its object of study –society. The former conclusion seems to be robust and uncontested; whereas the latter conclusion can be questioned given the rise of “Big data”. This essay contributes to the mentioned author’s conclusions by pointing out that the rise of “Big data” may make applied statistics a more suitable data science than either calculus or matrix algebra in a vacuum. This essay starts by summarizing the accounts provided by Gerard Debreu and Wassaly Leontief regarding the mathematization of economics. Then the essay takes Cukier & Mayer-Schoenberger’s essay about the Rise of Big data to complement both Leontief’s and Debreu’s main concerns. The main conclusion is that Economics may benefits wider from the digitization of the society than from the mathematization of its core concepts.

First, Gerard Debreu (1991) introduces an account of events that relates the origins of interdisciplinary in economics. Debreu states that the stimulus for the mathematization of economics derives from an ideal –not feasible- emulation of physics. Starting by 1933 with the launch of the Journals Econometric and the Review of Economics Studies, Debreu places such year as the beginning of a fruitful interdisciplinary relation between mathematics and economics. Debreu also looks historically into other possible measures for determining the integration of both fields, such as the rise of Game Theory in 1944, the growing use of mathematical expressions in refereed publications, and even, the increasing number of the Econometric Society fellows as faculty members of Departments of Economics (Debreu, 1991).

For Gerard Debreu (1991), though, there exists a limit to the economics’ ideal pursuit of physics scientific formalization. Such a limitation is given by both the possibilities of performing experiments, and the use of mathematical deductive reasoning itself. In regards to the former Debreu states that “being denied a sufficiently secure experimental base, economic theory has to adhere to the rules of logical discourse and must renounce the facility of internal consistency” (Debreu, 1991. Page 2). Meaning there is no other way than logic in which economists can inquire their object of study. As well as in any other social science, the limits set by epistemology apply to economics. Nonetheless, it is this use of mathematical logic which has given economics the chance to scientifically progress through a constant dialogue with previous proposed ideas and theories. In Debreu’s words, “the great logical solidity of more recent analysis has contributed to the rapid contemporary construction of economic theory. It has enable researches to build on the work of their predecessors and to accelerate the cumulative process in which they are participating” (Debreu, 1991. Page 3). Such a dialogue plays a key role in the structure of scientific revolutions and scientific progress (Kuhn, 1962).

A Second View:

The second interpretation about the mathematization of economics is introduced by Wassaly Leontieff (1954). In his account Leontieff sort out the contributions mathematics have done to some working concepts in economics. Working concepts such as the idea of maximizing behavior, theory of games and interdependent choices, dynamics approaches for analyzing repeated economic phenomena among others have benefited from the use of calculus, statistics and matrix algebra (Leontieff, 1954). For Leontieff, the same way as for Debreu, the boundaries of epistemology limit the possibilities of assessing social-economic reality. The eternal dichotomy between subjectivism and objectivism is introduced by Leontieff as a struggle between theorists and empiricists (Leontieff, 1954). The tension between inductive reasoning and deductive reasoning does not scape to economics.

For both authors the use of mathematics in economics has meant the vehicle for advancing the field. Mathematics as a shared and precise language has allowed economist to compare ideas, refine concepts, and -in general- to speak to each other in order to build upon predecessor’s work. To mention that economics has been able to build and progress upon previous works sounds odd; however, it is a key consideration if taken in the context of other social sciences which barely speak even within themselves.

Likewise, both authors point out the boundaries for understanding cogently economic phenomena. For both of them, the economic “laboratory” is not as feasible to build and use as it is for physics. Therefore, economics will always have the limitations for really knowing the parameters of the measures it inquires about. However, such a limitation may be getting to an end with the rise of “Big data”. Here is where “The rise of big data”

Photographer: Catherine De Las Salas

Photographer: Catherine De Las Salas

comes into place (Cukier & Mayer-Schoenberger 2013). Cukier & Mayer-Schoenberger’s essay aims at unfolding the potential use of information generated by the growing trend in the consumption of internet. They propose a twofold argument: the rise of an endless possibility of new sources of information and, therefore, a paradigm shift in research –possibly for social sciences. They do articulate such argument by relating four pillars. First, the authors point out the evidence of the latest technological revolution; second, they show a bit of evidence of a growing data collection practice that they call “Datification”; third, the authors stress the convenience of getting massive data at a fraction of the current cost, which basically means overcoming the cost barriers for “approaching the N=ALL”; and fourth, Cukier and Mayer-Schoenberger remark the usefulness of working with correlations instead of just causations.

In spite of the Cukier and Mayer-Schoenberger’s implicit assumption that research methods may be under a paradigm shift, it really deserves more of both attention and solid evidence. The authors claim that “All those digital bits that have been gathered can now be harnessed in novel ways to serve new purposes and unlock new forms of value. But this requires a new way of thinking and will challenge institutions and identities”. Evidently, the author’s use of new-proposed-terms such as “datification” is strong evidence of an emergency, or at least, an improvement of what maybe an obsolete set of methodological tools. Thus, if a brand-new field is emerging and a paradigm is being shifted from the current use of statistics toward the innovative interpretation of Big Data, then, we are indeed in front of an unprecedented turn in social sciences research, and particularly in Economics research. In the context of Big Data, apparently, economics may benefit wider from the digitization of the society than from the mathematization of its concepts. In other words, it is reasonable to expect that “Big data” will yield enough material for a better, more data grounded economic theory, and a larger information dataset used with the purpose of interpreting socio-economic reality.

References:

Debreu, G. (1991). The mathematization of economic theory. The American Economic Review. Vol. 81. No. 1.

Leontief, W. (1954). The twenty-seventh Josiah Willard Gibbs lecture, delivered at Baltimore Maryland. December, 1953.

Kuhn, T. (1962). The Structure of the scientific revolutions. University of Chicago Press.

Kenneth N. Cukier and Viktor Mayer-Schoenberger (2013). “The rise of big data”. Foreign Affairs.

1 reply »

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