## Economic modeling — a constructive critique

31 Dec, 2022 at 11:29 | Posted in Economics | 5 CommentsIf we have independent reasons to believe that the phenomena under investigation are mechanical in Mill’s sense, well and good: mathematical modeling will prove an apt mode of representation … But if we have independent reasons to believe that there is more going on in the phenomena under investigation than a mathematical model can suggest – that is, that the phenomena in question are not in fact mechanical in the required sense – then mathematical modeling will prove misleading … Moreover, as will be discussed, the empirical assessment of such models using econometric methods will not be sufficient to reveal that mismatch.

These problems cannot themselves be addressed through reforms to mathematical methods. That would simply be to produce a more refined version of the wrong tool for the job, like sharpening one’s knife when what is needed is a spoon. Rather than striving to improve the quality of mathematical models given the assumption that the subject matter under investigation is mechanical in Mill’s sense and therefore susceptible of mathematical analysis, we need to ask a prior question, which is whether there is sufficient reason to feel confident that the subject matter under investigation is mechanical in the first place. That means scrutinizing the subject matter in the first instance in non-mathematical ways … We as scientists must remain sensitive to information about the phenomena in which we are interested that lies outside our models’ conceptual maps. In the case of economics, what this requires is a new field dedicated to qualitative empirical methods that would play a similar role to that played by econometrics in the matter of quantitative empirical methods.

Highly recommended reading!

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.

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 doubt 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?

The rigour and precision in formal logic focus has a devastatingly important trade-off: the higher the level of rigour and precision, the smaller 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.

And as Spiegler has it — to think we solve the problem by reforms to mathematical modeling is nothing but “a more refined version of the wrong tool for the job, like sharpening one’s knife when what is needed is a spoon.

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Dave, can you use your math to explain the “red herring” allegation, or should I just have faith? (Does the Banach-Tarski proof strictly follow the two criteria cited by the Peter Spiegler quotation in the blog post immediately following this one?)

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Why does it seem to me that the real reason some mathematicians would deny the meticulous mathematical rationality of the Banach-Tarski proof, is that there is an implicit social understanding that propriety demands that a professor may only be heterodox in one field at a time? Thus is it a safe bet that the math professor that taught me the mathematical rigor of the Banarch-Tarski paradox is perfectly orthodox, when it comes to economics?

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As for coercion, why do I (a mere proletarian) fear the unintended coercive consequences (for non-ergodic me) of zealous yet ignorant financial regulation more than I fear the observably nonviolent actions of traders?

Comment by rsm— 1 Jan, 2023 #

I am not sure why, but I have only just come across your question here. I think I have answered it elsewhere, but at the risk of repeating myself.

Banach-Tarski proves that not every sub-set of a measurable set is necessarily measurable. This is only a paradox if you believe otherwise. For example, some people suppose that every possibility can be assigned a numeric probability, in which case an argument of Wittgenstein would show that such sets are measurable. But why do they think that? See djmarsay.wordpress.com for more on this general point.

Comment by Dave Marsay— 12 Jan, 2023 #

《Using formal mathematical modeling, mainstream economists sure can guarantee that the conclusions hold given the assumptions.》

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Did Hilbert’s program fail? Can “proper math” prove its consistency? Does Combinatorics VI require the Axiom of Choice (AC), because otherwise a book by John Locke might be both a philosophy and an economics book?

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《”If AC holds, then the decomposition in the Banach–Tarski paradox exists.”》- Wikipedia

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If Banach-Tarski is a true paradox, why isn’t trivialism entailed, due to explosion?

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《mainstream macro modellers of various ilks construct microfounded DSGE models that standardly assume rational expectations […]》

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What if the biggest economic agents are financial firms that are self-consciously rational in a mainstream economic sense because they choose to be? What if supply and demand for the paper contracts they trade really determine prices? Can the Fed set a floor on prices by printing money to buy assets until markets clear?

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《to think we solve the problem by reforms to mathematical modeling is nothing but “a more refined version of the wrong tool for the job, like sharpening one’s knife when what is needed is a spoon.”》

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Sure but isn’t the statistical, model-agnostic ChatGPT about as good as any of us on the Combinatorics problems?

Comment by rsm— 1 Jan, 2023 #

Banach-Tarski seems a ‘red herring’. But on ‘rationality’, I was taught that the concept goes back to the ancient Greeks, who promoted the idea that certain methods were ‘rational’ so they could persuade hoi polloi to comply and justify punishing them for dissent.

Much economic orthodoxy might be regarded as reasonable unless and until someone comes up with an alternative. But let’s not require the alternative to be too ‘rational’ in an inappropriate, coercive sense. (I agree with Lars on that.)

Comment by Dave Marsay— 1 Jan, 2023 #

https://nicolaswuethrich.com/Spiegler_Published.pdf has a review of this book, which suggests that its framework is ‘inspired by’ Maki 2009.

Maki notably suggests that models (mathematical or otherwise) ought to be accompanied by a ‘commentary’.

I am not quite clear what Spiegler means by ‘mechanical’, but any commentary would surely have to guard against common misuse of mathematical models, such as by too many economists, and provide advice on better practice.

Some people regard a ‘mechanism’ as something that can be ‘analysed’ into structured parts to provide a ‘map’ that one can use ‘as if’ it somehow corresponded to the ‘territory’. One can use mathematical modelling ‘qualitatively’ to show the dangers of this, just not the kind that Spiegler (rightly) critiques.

As for your own comments, you seem to use ‘formal’ as a synonym for ‘mechanistic’. In this sense pseudo-mathematics and scientism can be formal in your sense without involving ‘proper’ mathematics. It seems to me that economics would benefit from a better appreciation of the distinction.

Comment by Dave Marsay— 31 Dec, 2022 #