Dani Rodrik on math and models (VI)

21 Dec, 2015 at 11:28 | Posted in Economics | 5 Comments

According to Dani Rodrik — as argued in Economics Rules — an economic model basically consists of ‘clearly stated assumptions and behavioral mechansisms” that easily lend themselves to mathematical treatment. Furthermore, Rodrik thinks that the usual critique against the use of mathematics in economics is wrong-headed. Math only plays an instrumental role in economic models:

First, math ensures that the elements of a model … are stated clearly and are transparent …

The second virtue of mathematics is that it ensures the internal consistency of a model — simply put, that the conclusions follow from the assumptions.

What is lacking in this overly simplistic view on using mathematical modeling in economics is an ontological reflection on the conditions that have to be fullfilled for appropriately applying the methods of mathematical modeling.

Using formal mathematical modeling, mainstream economists like Rodriik sure can guarantee that the conclusion holds given the assumptions. However, there is no warrant that the validity we get in abstract model worlds automatically transfer to real world economies. Validity and consistency may be good, but it isn’t enough. From a realist perspective both relevance and soundness are sine qua non.

broken-linkIn 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.

In all those economic models that Rodrik praise — where the conclusions follow deductively from the assumptions — mathematics is the preferred means to assure that we get what we want  to establish with deductive rigour and precision. The problem, however, is that what guarantees this deductivity are as a rule the same things that make the external validity of the models wanting. The core assumptions (CA), as we have shown in previous posts, are as a rule not very many, and so, if the modellers want to establish ‘interesting’ facts about the economy, they have to make sure the set of auxiliary assumptions (AA) is large enough to enable the derivations. But then — how do we validate that large set of assumptions that gives Rodrik his ‘clarity’ and ‘consistency’ outside the model itself? How do we evaluate those assumptions that are clearly used for no other purpose than to guarantee an analytical-formalistic use of mathematics?  And how do we know that our model results ‘travel’ to the real world?

On a deep level one could argue that the one-eyed focus on validity and consistency make 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. The time is due and over-due for getting the priorities right …


  1. Wren-lewis’s recent posts give a good illustrative case study of some of the comments made here.

    “The belief that people would need to have for the FTPL to be relevant – that the government would not react to higher deficits by reducing government spending or raising taxes – does not seem to be credible, given that austerity is all about them doing exactly this despite being in a recession.”

    What evidence is there about such beliefs? Would people even know the government’s fiscal position or have the slightest interest in it? There may have been a perception, for example that an incumbent government mismanaged an economy say in the UK after the 2008 – and this would have been directly felt by people in the form of difficulties in getting mortgages, job insecurity etc, and this was the background to the entry of a new government which wished “fix the economy” by reigning back spending – but the link being made between people’s beliefs, deficits, and reduced government expenditure does not seem to be on a very informed level. This is what happens when people are incapsulated in the world of Model – absolute detachment and a lack of interest in going out on the field and finding out what the causal mechanisms actually are. The result is pure speculation and story telling.

  2. “the more mainstream economists insist on formal logic validity, the less they have to say about the real world”.
    This indeed true if they proceed with “arguments [which] show amazingly weak relationship to their everyday real world equivalents”.

    In other words, you are right that: ‘Garbage in, garbage out’.
    However, this is entirely consistent with Rodik’s argument: ‘good/realistic assumptions in, maybe interesting results out’.

    • Analysis is never descriptive. It does not matter how good Euclid’s assumptions are, his geometry never becomes a universal map of the world. Knowledge does not work like that. To make a map, geometry is useful but not sufficient onto itself. The actual economy — its institutional structure — is adapted to uncertainty; that fact alone contradicts the key core assumptions. Economists have to observe and study how people use institutions to cope with uncertainty, because you cannot assume a realistic uncertainty axiomatically and still crank out a deductive result — uncertainty breaks the nomological machine. You can creep up on the logical implications of uncertainty with clever assumptions, but the blanket uncertainty of real life remains beyond the reach of pure speculation and the universalism of logical rigor. Knowledge of the actual economy will require making maps of specific times and places and the institutions found there, and those maps will never be general in their implications or rigorously certain. A realistic economics is much, much harder than what economists are accustomed to do with their toys.

  3. I have been wondering about mathematics in economics and the question of tractability. For instance, there is mathematics to handle non-transitive preferences or partially ordered utilities, but the reduction of preferences and utilities to real numbers makes the math more tractable. Is that one reason for such assumptions?

  4. Thanks Lars. If you read spanish please to see: https://www.academia.edu/19758095/Analog%C3%ADas_entre_las_pol%C3%ADticas_de_Mart%C3%ADnez_de_Hoz_y_las_de_Cambiemos



    Pedro Dudiuk Profesor titular de Macroeconomía II FCE-UNLP. La Plata, Argentina Director de K-TIC, “Software de Decisión Strat Pro”. http://www.pedrodudiuk.com.ar TEL 0221 474 2640 CEL 15 5070 450 Skype: pdudiuk

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