## Formal mathematical modeling in economics — a dead-end

from **Lars Syll**

Using formal mathematical modeling, mainstream economists sure can guarantee that the conclusions hold given the assumptions. However, the validity we get in abstract model worlds does not warrantly transfer to real world economies. Validity may be good, but it isn’t enough. From a realist perspective both relevance and soundness are *sine qua non*.

In their search for validity, rigour and precision, mainstream macro modellers of various ilks construct microfounded DSGE models that standardly assume rational expectations, Walrasian market clearing, unique equilibria, time invariance, linear separability and homogeneity of both inputs/outputs and technology, infinitely lived intertemporally optimizing representative household/ consumer/producer agents with homothetic and identical preferences, etc., etc. At the same time the models standardly ignore complexity, diversity, uncertainty, coordination problems, non-market clearing prices, real aggregation problems, emergence, expectations formation, etc., etc.

Behavioural and experimental economics — not to speak of psychology — show beyond any doubts that “deep parameters” — peoples’ preferences, choices and forecasts — are regularly influenced by those of other participants in the economy. And how about the homogeneity assumption? And if all actors are the same – why and with whom do they transact? And why does economics have to be exclusively teleological (concerned with intentional states of individuals)? Where are the arguments for that ontological reductionism? And what about collective intentionality and constitutive background rules?

These are all justified questions – so, in what way can one maintain that these models give workable microfoundations for macroeconomics? Science philosopher Nancy Cartwright gives a good hint at how to answer that question:

Our assessment of the probability of effectiveness is only as secure as the weakest link in our reasoning to arrive at that probability. We may have to ignore some issues to make heroic assumptions about them. But that should dramatically weaken our degree of confidence in our final assessment. Rigor isn’t contagious from link to link. If you want a relatively secure conclusion coming out, you’d better be careful that each premise is secure going on.

On a deep level one could argue that the one-eyed focus on validity makes mainstream economics irrelevant, since its insistence on deductive-axiomatic foundations doesn’t earnestly consider the fact that its formal logical reasoning, inferences and arguments show an amazingly weak relationship to their everyday real world equivalents. Although the formal logic focus may deepen our insights into the notion of validity, the rigour and precision has a devastatingly important trade-off: the higher the level of rigour and precision, the smaller is the range of real world application. So the more mainstream economists insist on formal logic validity, the less they have to say about the real world.

I am uneasy about the tone that Lars Syll talks about mathematics. Real question is not mathematics. The trouble with the mainstream economics is that it is a system of misguided problem setting, irrelevant assumptions, and implausible choice of analytical tools. Syll is not hitting the right target.

Syll thinks that economy is an entity full of “complexity, diversity, uncertainty, and emergence”. We must be concerned with “coordination problems, non-market clearing prices, real aggregation problems, expectations formation.” (I have removed “emergence” in the first group from the second group.) I agree with him. What have we to do then? The most crucial and urgent problem for us is to construct a new theory that replace neoclassical economics. To take account of complexity, diversity, uncertainty, and emergence, we need mathematical thinking. Or, at least, we need that sense of analysis of physicists who work on complex systems. They do not refuse mathematics. Of course, the traditional mathematics such as calculus does not help us much. They search a suitable mathematical model with which to explain the phenomenon we are concerned. In many cases, we have to construct a new mathematics.

To analyze “coordination problems” and “non-market clearing prices”, we need mathematics too. For example, in the modern economy (at least after 1900), it is not the prices which regulate the network of productions. The economy is a huge network of quantity adjustment run by firms (or more appropriately by those managers in the production and vending sites). To know the total behavior of this network, it is necessary to appeal to mathematics and to computer simulations. It is possible that mathematics is not sufficient to clarify the phenomena. Physicists often use physical way of reasoning. It is often something beyond mathematics. Even though, in many cases (if they are successful), they succeed in finding an essential core of what is happening behind the apparent phenomenon. In economics too, we need these efforts. Bavardage ne fait pas avancer les sciences.

In engineering math modeling is very useful: given material and workload we can calculate a shaft and for safety reasons we add a safety margin according standards and laws.

In economics I’m still a heavy user of math modeling. I use utility functions and all the micro-macro models, LP, DP, Control Theory…you name it, only to get a feeling in which direction a decision might lead.

And definitely not to calculate results for use as in mechanical engineering. Or worse, to form and fill with all the requirements a model has to fulfill, a regulatory institution to assure that a real world economic outcome fit the results of economic models. Dictate very narrowly what’s allowed and what’s forbidden, enforce it by a huge body of regulatory law and sell it as absolutely necessary for a ‘liberal economy’. Now you got the desired ideology – of course with room for further improvements.

This is all interesting but it misses the point of the science of economics. Assuming, perhaps wrongly that economists want to be scientists. Science attempts to allow the subject of its study to be seen, to shine through, if you will in the languages (including mathematics) the scientists choose to use. Scientists try to get out of the way so that what is observed is seen as fully as possible. With as few add ons from the social scientists as possible. If mathematics, logic, simulations, and formal theory aid this effort, their use is justified. So, the questions are these, how do mathematics, logic, etc. distort observations and how are the decisions made about how and when to use these tools. Since science is a human activity it must be expressed in some language. And since all languages distort experience, scientists must be doubly careful in their choice and use of language. For example, we know from experience that mathematics is useful for the study of physical objects like plants, animals, stars, etc. But less useful and highly distorting for the study of human collective life. Yet even here mathematics can find useful application, if the scientist in prudent in choosing how to use it. Long story short, Lars is correct about the dangers of applying mathematics and formal logic to economic questions. In fact, the study of economics could proceed successfully without mathematics or formal logic at all. For once and all we need to recognize that mathematics, formal logic, etc. are merely tools people invent in their efforts to study and understand the events around them. They don’t define science any more than a laboratory or social survey.