PCES Myth-Busting: One-and-a-Half Cheers for Maths

This is the third edition of our ‘PCES Myth Busting’ series, which will talk  about our view on the use of mathematics in economics (and for this reason may be a bit more technical than the others). The previous myth-busting post, which is about our relationship with the Manchester economics department, is here.

You do not have to look hard to find arguments to the effect that criticising mainstream economics makes one anti-mathematics. According to a 2014 Financial Times article by John Kay: “much of the ‘heterodox economics’ the Manchester students suggest including is flaky, the creation of people…who cannot do the mathematics the dominant rational choice paradigm requires.” Blogger Tony Yates similarly quipped that “students wanting to draw the analogy between the financial crash and organic processes had better stop chatting about Austrian economics and start crunching exotic nonlinear ordinary differential equations.” In his review of our book The Econocracy, Michael Ben-Gad implied that we were unable to “master the language of mathematics and engage with the difficult task of understanding economies as complicated dynamic systems”. 

There a few claims – implicit or explicit – in these quotes, which need unpacking:

  1. Disliking the use of maths in economics is a signal that you don’t understand maths.
  2. Disliking the use of maths in economics shows you don’t understand its connection to economic issues.
  3. Disliking the type of maths used in economics means that you dislike all types of maths.

(1) is petty and shallow, but since it seems to come up so much it’s worth addressing briefly. If it were true that PCES, and more broadly Rethinking Economics, were all bad at maths, then those who champion our cause would be disadvantaged in math heavy qualifications, which is just not true – the movement contains plenty of economics postgraduates, as well as some mathematicians and physicists. Aside from students, Ben Fine and Tony Lawson are two famous heterodox economists who largely reject the use of mathematics but were originally trained as mathematicians. Fine has actually used Godel’s incompleteness theorem to argue against mainstream economics, something rarely discussed or understood by many of the pro-maths crowd. Thus it cannot credibly be argued that people dislike maths in economics because they don’t understand maths.

(2) is a more interesting debate. A key bone of contention for PCES is that the maths in economics is rarely linked to the real world. The charge that many of us don’t understand why there’s maths in economics is therefore true on one level: we do not understand because nobody tells us! Mathematical models are often learned by rote instead of being introduced to solve an economic problem. As one student put it, ‘you learn to solve models before you even know what a model is and its purpose.’ Economics students typically come from very different backgrounds and so expecting them to automatically understand the purpose of maths is unfair – in fact, we believe that grounding the teaching of maths in real world problems would help many students to understand it better.

Should economics use maths? Since large parts of economics deal with mathematical quantities and dynamic processes, the subject can clearly benefit from quantitative analysis and mathematical modelling. The question is whether it is appropriate to use maths in a particular case, and what is gained by doing so. For example, looking at financial flows and balance sheets surely invites the use of mathematics, as do macroeconomic quantities such as GDP, unemployment and inflation. At a micro level, it seems absurd to study the impact of (say) sugar taxes on sugar prices and consumption without using mathematical quantities.

On the other hand, modern economics is rife with mathematics used to represent things which are simply unquantifiable in the real world. One example is ‘effort’, a key variable in the kind of contract models for which the 2016 Nobel Prize was awarded to Oliver Hart and Bengt Holmströmand, and which are the bane of all Manchester Micro III students. We have no real way of measuring effort, so it cannot be used as an empirical input into the model to yield quantitative predictions. Economists might respond that it nonetheless provides useful insights, but many of these are quite obvious – for example, one of the Micro III models implies that higher wages might be needed to induce higher worker effort (in absence of monitoring). Hart’s recent lecture at the Royal Economic Society conference contained many such intuitive statements, such as that “with good collateral the entrepreneur can borrow more and long-term”. As always, we’re not dismissing these models altogether, we’re just calling for skepticism about whether expressing something in maths necessarily adds value.

Turning to the related but distinct point in (3), it often goes unsaid in economics that the mathematics used is only of a certain type: constrained optimisation. Some agent(s) optimises some objective function under a resource constraint, and the outcome gives our mathematical predictions. But there is so much more to mathematics than this: Ordinary Differential Equations (ODEs) deal with dynamic systems which change over time; Agent-Based models and others use programming techniques to simulate economies; graph theory deals with network connections, which are crucial in interlinked markets (especially finance). Steve Keen and Mattheus Grasselli in particular have used the ODE approach extensively to model economic fluctuations, an approach that – going back to point (2) – is technically much more difficult to deal with than many economic models.

In summary, PCES do not dislike maths. What we dislike is the near-universal use of a particular type of maths to model all economic (or sometimes non-economic) problems. We embrace maths and statistics as invaluable tools in the study of economics, but believe that students should learn a variety of these tools so that they can know which types of maths to use and when. Perhaps most importantly, students should be made aware of times where maths is not appropriate so that they have a critical grasp of how to use it most effectively in economics.



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