by From Lars Syll If 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
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from Lars Syll
If 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.