Pablo Escrivá Sirera: The sterility of mathematical modelling in the social sciences. The case of Economics.
Pablo Escrivá Sirera- Can mathematical models explain social phenomena_It is well known that the most respected and prestigious branch of modern science, the natural sciences, speaks the language of mathematics. Thus, some social sciences have tried to acquire such respectability and rigor by means of mathematization; there is a general trend in the social sciences towards mathematical-abstract modelling. Economics represents the paradigmatic case of such tendency: a so-called science whose mainstream-orthodox approach tries to explain „economic phenomena“ mainly by means of mathematical models, such as rational choice theory and game theory equilibrium concepts, seeking to be „an ‚objective’ science in exactly the same sense as any of the physical sciences.“ The question here is if what has certainly worked in order to explain and predict natural phenomena –a mathematization so that formal deductions can lead to significant results and general laws, as in physics– can also work for social phenomena, that is if we can „naturalize“ the social sciences.
I will argue that such a pretension is absurd because a „naturalization“ of the social sciences is impossible. To be clear, I will not argue against the use of mathematics in economics in general –mathematics are very useful for measuring quantitative phenomena–, but I will criticize their misuse and fetishization, and question their usefulness and explanatory power. Green and Shapiro (1994) published a devastating analysis of the empirical theories and studies based on rational choice models derived from neoclassical economics. They showed that they require an absurd amount of meta-psychological devices and have problems with empirical testing – trying to prove the general theory becomes a priority over explaining the concrete reality–, and critically, the predictions and explanations they render are quite trivial and leave empirically crucial problems aside. And yet, opening a leading economic journal today means diving into a world of mathematical formulas. Even if mathematical models did explain social phenomena, which is very doubtful, it would not be necessary to use them for everything. Why, then, this obsession?
Many examples of theorization revolving around mathematical models in economics can be given. A classical one is the Hotelling model, which tries to explain the concentration of similar businesses around the same streets and of political parties around the same ideological spectrum by means of a highly idealized spatial analysis. But does the Hotelling model really explain something we did not already know? Probably not, since its application pertains only to the context of justification; this, like many other models, is an a posteriori rationalization of a social conduct that was already known. And in many cases, the use of devices with a high grade of mathematization renders worse results than the mere use of common sense would. As Smyth and Ash showed, social scientists employing abstract methods often make very bad predictions:
the forecasts produced on the basis of the most sophisticated economic theory for OECD since 1967 have produced less successful predictions than would have been arrived at by using the commonsense, i.e naive methods of forecasting rates of growth by taking the average rate of growth for the last ten years as a guide or rates of inflation by assuming that the next six months will resemble the last six months.
David Harvey tells another funny yet revealing story that illustrates the poor predictive power of economic experts using this kind of models. After the recent economic crisis the Queen of England visited the London School of Economics,
and asked the prestigious economists there how come they had not seen the crisis coming. Being a feudal monarch rather than an ordinary mortal, the economists felt impelled to answer. After six months of reflection the economic gurus of the British Academy submitted their conclusions. The gist was that many intelligent and dedicated economists had worked assiduously and hard on understanding the micro-processes. But everyone had somehow missed „systemic risk„. A year later, a former chief economist of the IMF said „we sort of know vaguely what systemic risk is and what factors might relate to it. But to argue that it is a well-developed science at this point is overstating the fact„. In a formal paper, the IMF described the study of systemic risk as „in its infancy„.
It’s not true, however, that no one predicted the financial crisis; as Mario Bunge shows, some economists, like Nouriel Roubini, did predict what was coming by using common sense instead of the dominant economic theory. Giving massive concessions of mortgage loans to people with dubious financial stability just so they could buy overpriced properties could lead to millions of clients not paying their due.
It seems clear that mathematization hasn’t helped a lot to improve the predictive power of economics. But it does helps to raise its scientific prestige, how rigorous is considered. Let’s have a look at the historical reasons for mathematization given by Roy Weintraub. He shows how economics was influenced by changes in mathematics, changes in what was meant by „rigor“ and „proof“. The discipline of mathematics suffered a profound crisis of foundations during the turn of the century, which led to a revision and reformulation of its own nature. While in the 19th century „mathematics required connected physical reasoning to be considered rigorous“, in the 20th century this was no longer the case. Instead, „rigorous“ meant derivable from a system of axioms in a formal manner. The Bourbaki school claimed that „mathematics [was] an autonomous abstract subject, with no need of any input from the real world“, glorifying pure formalism, beauty and elegance over applicability. David Hilbert defended that mathematics was a formal game without meaning, and that axiomatization was a path towards certainty and scientific discoveries. This change in the understanding of mathematics translated into economics, which by means of the „neoclassical synthesis“ became a „monolithic mathematical discipline“, losing the plurality it had before World War II. Weintraub concludes that „the king“ – namely, orthodox economics – is naked, since it has nothing to do with the real world and is purely self-referential, and points out that disillusion with Bourbaki has already happened in mathematics and the natural sciences, so sooner or later it will happen in economics as well.
However, it looks like this will happen later rather than sooner, since not even the 2008 financial crisis – with the shame it brought to economics – has instigated a change in the practices in any fundamental way: mathematical abstraction still dominates over empirical and historical investigation. As Michael Perelman notes,
although economists are legendary for applying their sophisticated techniques to the most arcane of subjects, those economists who are involved in making important policy decisions rarely make use of anything but the most elementary economic tools. Consider the testimony of Herbert Stein, who was the chief economic advisor to the Nixon Administration. According to Stein, „It may seem a shocking thing to say, but most of the economics that is usable for advising on public policy is at about the level of the introductory undergraduate course.
Peter Gowan despises orthodox economic methodology, assuring that
in exploring this Dollar-Wall Street Regime we need no algebra or geometry and almost no arithmetic or even statistics. The basic relationships and concepts can be understood without the slightest familiarity with neo-classical economics. Indeed, for understanding international monetary and financial relations, lack of familiarity with the beauties and ingenuities of neo-classical economics is a positive advantage.
So again, why is there this fixation on mathematization? Surely, the formulation of the theories in rigorous mathematical terms gives orthodox economics a brilliant scientific appearance; however, these theories aren’t able to explain real economic systems and predict their actual behavior. Among other reasons, this is because they systematically ignore important factors, such as rating agencies, unions, or the culture and history of each part of the world. The perfectly competitive free market is like a unicorn, a mythological entity, as it is dismissed by the sheer existence of things like unions, cooperatives, state companies, social security services, sovereign states and interventionist governments, laws and regulations. Yet all the ingenuity of economists is spent in formalizing and embellishing fantasmatic theories and models which assume the existence of such a free market.
Akin to other social sciences, such as psychology or sociology, economics is competing directly with popular, common sense knowledge, and therefore it tends to shelter itself under the umbrella of abstract theorization. Thomas Piketty notes that,
for far too long economists have sought to define themselves in terms of their supposedly scientific methods. In fact, those methods rely on an immoderate use of mathematical models, which are frequently no more than an excuse for occupying the terrain and masking the vacuity of the content.
He argues that mathematization is a quick way of acquiring the appearance of rigorous scientificity, while removing the burden of having to answer the complex questions that the real world poses. To put it in Leontief’s terms, „uncritical enthusiasm for mathematical formulation tends often to conceal the ephemeral substantive content of the argument behind the formidable front of algebraic signs.“ Interestingly, a discipline like history, which does not compete as readily with popular knowledge, has not taken the path of idealization; instead, it has recognized its own role and limitations, expanding on everyday knowledge quite successfully, and with a low degree of formalization.
Another reason for this obsession with mathematization may be ideological; indeed, with mathematical jargon spreading all over the discipline, economics becomes a matter of „experts“, that is people who have studied microeconomics, econometrics and the like. Studying these disciplines becomes a sort of initiation rite necessary to talk about the economy at all, a rite that the vast majority of people is not willing to endure, and rightly so. Hence, the possibility of understanding what happens is denied to the public: the average citizen cannot have and informed opinion about the economy, and now the „experts“ will be able to pass what ultimately are political decisions as corollaries of an objective science which only they can understand. We enter, therefore, the realm of technocracy and oligarchy, and a dangerous form of elitism that threatens democracy. Michel De Vroey shows that the change in economics from classical to neoclassical theory was nothing like a progress towards more scientificity, but that it had a highly important political component. For example, it was a means to undermine the radical conclusions to which Ricardian economic theory, the labor theory of value later taken up by Marx in order to analyze exploitation, could lead. In the end, „what was socially dangerous could not possibly be true.“
Economics situates itself in front of a quagmire: if it wants to „elevate„ its scientificity by means of mathematization, it has to abstract away from social phenomena thus simplifying them enormously, at the high price of losing the social phenomena as such and end up dealing only with an idealization that has little or nothing to do with them. Indeed, the mathematical-economic models which are in use, like the Hotelling model, are unrealistic for various reasons: they present the phenomena they seek to explain in a very simplified and idealized way, including unreal assumptions, e.g. postulating there is only one spatial dimension, a perfect market, or a totally rational individual; also, they are incomplete, since they disregard variables that are causally important. It is very problematic to apply rational choice theory to analyze, explain and predict the behavior of real human beings. As John Elster points out,
How can one impute to real flesh and blood individuals the capacity to make in real time the calculations that occupy many pages of mathematical appendixes in the leading journals, and that can be acquired only through years of professional training?
We do not live in a world of fully rational agents with perfect information and complete markets. Also, the rational choice theory in which economics is based has mayor flaws; for example, its basic notion of the individual with preferences is very restrictive. As Elster indicates, some facts pertaining to the family environment refute the idea that self-interest rules the world; a parent does not change his baby’s diaper because he „prefers“ to do that over eating ice-cream or going to the cinema, but he or she would still consider the former a priority. But, with all of these doubts in mind, if economics does not mathematize, it stops to be considered a serious and rigorous science. What, then, are the solutions to this situation?
To me, it seems like the only solution is lowering the expectations of economic theory, changing again what is considered to be „rigorous“ and „scientific“. The logical positivists at the Vienna Circle which, as Bruce Caldwell says, „dominated not only the philosophy of science, but also the methodologies of most of the natural and social sciences“ tried to establish a criterion to distinguish scientific statements from metaphysical and pseudo-scientific ones, pretending to have found such demarcation in verifiability. But that decision carried with it some problems: it was too strict, since it rejected as non-scientific all affirmative universal statements – which indeed cannot be verified, yet they are crucial to science, since general laws are expressed in this way. Problems which the theories of Karl Popper came to resolve: the new criterion was falsifiability. In Popper’s view, the honest scientist should test his own hypothesis in the strictest of ways, with the explicit purpose of showing they are false. This approach is what he called critical methodology. However, this theory was prescriptive, rather than descriptive; it told how proper science should be done, not how scientist actually do it. Popper had an enormous influence among natural and social scientists – Friedman himself was an admirer –, and his methodology was the paradigm one had to imitate in order to obtain scientific rigor.
This methodology, however, had some problems itself: it was too radical, and it could not be applied to all scientific disciplines. It rejected the importance of the context of discovery (due to the problem of induction) and it was mainly inspired by physics, attributing all the importance to the context of justification:
The question, „How did you first find your theory?“ relates, as it were, to an entirely private matter, as opposed to the question, ‘How did you test your theory?’ which alone is scientifically relevant.
However, for some disciplines of the natural sciences, such as geology, paleontology and evolutionary biology, the context of discovery is crucial, so the Popperian deductive test of hypothesis is just not a methodology those disciplines can use, not only because it’s too demanding, but because it’s inadequate. The fact that they do not use the Popperian method doesn‘t stop us from thinking that they are still reliable and successful sciences. This means there is not just one transparent, univocal and definitive method of science, as Popper thought, but that there are different methods for different disciplines. If even in some natural sciences the context of justification is at the same level of the context of discovery – as it happens with the examples above –, then natural sciences like physics, which are more linked to the context of justification, cease to be a role model for all scientific practices.
Popper practiced an imperialism of physics, imposing a methodology of science taken from a particular field, to all sciences, despising well consolidated scientific practices that did not fit to his proposed methodology. This is a trap into which many economists have followed him. Some critics have said that economics has an „envy of physics“, and indeed this seems to be the case. However, this approach shows two errors: (1) the pretension to imitate physics, derived from (2) the injustice of establishing a methodology taken from physics as the only possible scientific one. It’s true that physics, compared to economics, has much more empirical success and predictive power; but this is not a reason for the latter to be envious of the former. We simply cannot expect the same kind of results in such different disciplines.
Therefore, economics should not try to imitate the natural sciences. Instead, it should assume its position as a social science, expecting less from explanations, and abandoning the mathematical fetish. Certain objects of inquiry are not so prone to be mathematized. Social phenomena are among these objects, maybe the most paradigmatic in their resistance to abstraction. In effect, the enormous complexity – the multiplicity of factors that needs to be taken into account when it comes to studying the social reality – make of this object a tough nut to crack for those who pretend to translate it to mathematical formulae.
At the same time, the interconnection of all the social phenomena makes it difficult to separate the disciplines that study society, the social sciences. Indeed, at this point few can really believe that it’s possible to separate economics from political science sharply, or that both can be independent from history, psychology or sociology, or that all these disciplines are independent among themselves. In fact, the economics that really deals with empirical problems is very similar to conventional history. All such disciplines are complexly intertwined, because they all study the same object, from different perspectives. Thus, economics should also stop pretending to be a separate, autonomous science. It should engage in a fruitful exchange with other social sciences. Mathematics should continue to be used to construct models and theories for economics, but only if it’s used as a tool rather than as and end in itself. The late Bernard Maris proposed and interesting alternative: economists could finally admit that they are playing an empty game of logic and math, just for the sake of it – enjoying their own futility. Or they could recognize that the only possible economics is history, returning to classic questions, like „what is wealth and how should it be distributed?“
Charles University in Prague, Winter Semester 2014/15
 Milton Friedman: „The Methodology of Positive Economics“. In: Essays in Positive Economics. Chicago: Univ. of Chicago Press, 1966, p 4. In this famous article Friedman states that economy is a „positive science“ whose main goal is to „yield valid and meaningful… predictions“, and embraces some short of radical instrumentalism (he assures that „in general, the more significant the theory, the more unrealistic the assumptions… To be important, therefore, a hypothesis must be descriptively false in its assumptions“). This has merited a lot of criticism. First, the goal of economy in particular and of science in general is not thought anymore to be mere prediction, but explanation, as even positivist philosophers admit. That itself renders the instrumentalist approach inappropriate and anachronic (Bruce Caldwell: „A critique of Friedman’s methodological instrumentalism.“ In: Southern Economic Journal. Vol. 47, No. 2. 1980. pp. 488-497). Second, there is an ambiguity in the use of the term „assumption“. As Musgrave points out, it is possible to differentiate three types of assumptions: (1) Neglibility assumptions, which determine certain factors as being irrelevant for the phenomena to be explained. (2) Domain assumptions, which establish that the theory is only true as long as the assumption holds. (3) Heuristic assumptions, which are conterfactual models. He claims that Friedman doesn’t distinguish these three kind of assumptions, and shows that the thesis cited above, namely that „the more significant the theory, the more unrealistic the assumptions“ is not true for any of them (Alan Musgrave: „Unreal assumptions in economic theory.“ In: Kyklos. Vol. 34. 1981 Fasc. 3, pp. 377-387). Third, the claim that there can be a pure positive economic science, away from all value considerations (a purely descriptive, entirely non-normative science) is illusory.
 Physical laws express a relation between metrical concepts with the help of a mathematical apparatus.
 Donald Green and Ian Shapiro: Pathologies of Rational Choice. New Haven: Yale University Press, 1994.
 See e.g. Julian Reiss: Philosophy of economics. London: Routledge, 2013, Ch. 7.
 D.J. Smyth and J.C.K. Ash: „Forecasting Gross National Product, the Rate of Inflation and the Balance of Trade: the O.E.C.D. Performance“, In: The Economic Journal, 85, 1975: pp. 361-4. Cited in: Alasdair MacIntyre: After Virtue. Notre Dame: University of Notre Dame Press,1984, p. 89.
 David Harvey: The Enigma of Capital and the Crisis this Time. http://www.davidharvey.com http://davidharvey.org/2010/08/the-enigma-of-capital-and-the-crisis-this-time/ (Visited last on 05/11/2015).
 Mario Bunge: Economía y filosofía. Buenos Aires: Laetoli, 2015.
 Roy Weintraub: How Economics Became a Mathematical Science. Durham: Duke University Press, 2002, p.17. He shows that today the notion of rigor is related to „abstract reasoning chains of formal mathematics“, while provi- ding „informal reasoning chains“ simply means to be non-rigorous. So rigor, for economics, does not require empi- rical evidence or connection with real world anymore: „One could have „a mathematical model of a phenomenon without having a physical model of the phenomenon, and still provide ‘rigor’ and ‘truth’“. Paul Davidson: „Is ‘mathematical science’ an oxymoron when used to describe economics?“ In: Journal of Post Keynesian Economics. Vol. 25, No. 4 2003, pp. 527-545).
 Paul Davidson: „Is ‘mathematical science’ an oxymoron when used to describe economics?“, p. 536.
 Pauld Davidson: „Is ‚mathematical science‘ an oxymoron when used to describe economics?“, p. 532.
 Through a very influential paper (Gerald Debreu and Kenneth Arrow: „Existence of an Equilibrium for a Competitive Economy“. In: Econometrica. Vol. 22. No. 3. 1954, pp. 265-290), which was influenced by the Bourbaki school. Weintraub shows how this paper (which was only published due to the „reputation of the authors“) set the rules of the economics game since then: an axiomatization of Walrasian General Equilibrium model. He also shows that this predominance of neo-Walrasian theory (which was equivalent to good economic theory) „liberated economics from its dependance on real-world analogies“. Now, „theories that are readily recognizable as descriptions of reality are not necessarily important“ (Paul Davidson: „Is ‘mathematical science’ an oxymoron when used to describe economics?“, p. 537).
 Paul Davidson: „Is ‚mathematical science‘ an oxymoron when used to describe economics?“, p. 541.
 Michael Perelman: The End of Economics. London: Routledge, 1996, p. 22.
 Peter Gowan: Global Gamble. New York: Verso, 1999, p. 5.
 Joseph Stiglitz likes to tell an anecdote that shows the absurdities into which historical ignorance can lead some economists: The IMF teams that help intervening in economic crisis work with a series of computer programs designed for each country, which they apply without much contextual complications. On one occasion, a team of IMF officials who were preparing the travel to some African country that had requested their help made a mistake: to analyze the situation of the country X, they had loaded the hard drive that contained the country Y. Trough their stay in the country X, they worked with the data gathered for the country Y without noticing their error.
 Thomas Piketty: Capital in the Twenty-First century. Cambridge: Harvard University Press, 2014, p. 574.
 Wassily Leontief: Essays in Economics. New York: M. E. Sharpe, p. 25.
 Citing Piketty is a good idea here: „To be sure, it would be a mistake to underestimate the importance of the intuitive knowledge that everyone acquires about contemporary wealth and income levels, even in the absence of any theoretical framework or statistical analysis… Indeed, the distribution of wealth is too important an issue to be left to economists, sociologists, historians, and philosophers. It is of interest to everyone, and that is a good thing… Democracy will never be supplanted by a republic of experts— and that is a very good thing. Expert analysis will never put an end to the violent political conflict that in equality inevitably instigates“. Thomas Piketty: Capital in the Twenty-First century, p. 2.
 De Vroey concludes his article very eloquently: „We face here a clear example of a contradiction between a theoretical framework leading to radical conclusions and the power structure within society, in which the bourgeoisie had become the dominant class. The stumbling block or anomaly within the classical paradigm lay in its political consequences. Therefore, it was necessary both to discard the disharmonious elements of the Ricardian approach and to propose a justification for profit. […] This was exactly the function played by the neoclassical scientific revolution. The new paradigm was especially attractive because it looked as scientific as the natural sciences theories, while it eluded the dangerous topics of class interests and transformation of the system“. Michel De Vroey: „The transition from Classical to Neoclassical Economics: A Scientific Revolution“. In: Journal of Economic Issues, Vol. 9, No. 3. 1975, pp. 415-439.
Indeed, economics has never been a politically neutral science; as Marx wrote, „in the domain of political economy, free scientific inquiry does not merely meet the same enemies as in all other domains. The peculiar nature of the material it deals with summons into the fray on the opposing side the most violent, sordid and malignant passions of the human breast, the Furies of private interest“. Karl Marx: Capital. A critique of political economy. London: Penguin, 1982, p. 92.
 Bruce Caldwell: „Positivist Philosophy of Science and the Methodology of Economics“. In: Journal of Economic Issues. Vol. XIV. No. 1. 1980 pp. 54-76, p. 53.
 Karl Popper: The Poverty of Historicism. London: The Beacon Press, 1957, §29.
 As Marx also famously pointed out in the preface of Capital, his major work, „in the analysis of economic forms neither microscopes nor chemical reagents are of assistance… The physicist either observes natural processes where they occur I their most significant form, and are least affected by disturbing influences, or, wherever possible, he makes experiments under conditions which ensure that the process will occur in its pure state“ (ibid, p. 90), and that is not possible when studying the economy, or the social phenomena in general.
 One example is behavioral economics, which combines economics with empirical psychology, and turns out to be much more realistic than the orthodox approach.
 Bernard Maris: Lettre ouverte aux gourous de l’économie qui nous prennent pour des imbéciles. Paris: Albin Michel, 1999.