Not PC has a critique of the use of mathmatics in economics. Critising the discipline of economics has been especially popular lately. I have had engineers (and some physicists) call me up to tell me that we do economics wrong and we need more maths (to which my reply would be to look more closely at the methodology of your own discipline before even trying to apply it to our one). I have had business people (and my dear mother) call me up and say that there is too much “voodoo maths” and economists need to work in real jobs first.
What I have found in common with all these criticisms is that their implicit view of what an economist does, and the point of economics, differs remarkably from my own. The scope, methods, and reasoning behind economic analysis which we are imbued with at university most definitely differ from the scope, methods, and reasoning which I often hear people accuse economists of using/making.
Now I don’t agree with either side except my own here, as I think the current implementation of maths in the study of economics makes sense. In fact, I don’t believe the level of maths is a fixed thing – it merely depends on what “language” people who use economics are willing to use. This is because maths is merely a language. Using mathematical form, economists are able to place down ideas and clarify thinking, as long as economists understand the implicit assumptions they make when writing out a mathematical model then this is a valuable way of doing things.
Rather than reiterating my defense of economics, I will link to things. Here is where I last discuss math and economics, here I mention “Marshal’s view” of maths, which is close to the way economists still function. Here is a set of links where I build up an idea of “what is economics“. And before anyone says that predictive failure indicates that maths is an issue, I say that the purpose of economic language and discussion is trying to build a case for description and explanation. There are a myriad of links saying this (*, *, *,*).
So the typical conclusion from this is that maths is useful in economics as it provides a powerful tool/language that allows us to set issues down – in the hope of being able to describe/explain relationships in reality.
Not PC adds another element though. Specifically he counters by calling on the lack of causal inference available from pure mathmatics – however, when this is the case we have to rely on explicit judgments and theory. In this situation we can DEBATE causality when we set up the mathmatical model – but it does not make the use of such models invalid.
That is why I always say – use the theory as much as possible before you get onto using the data. Now I have no doubt that the data may then impact on the way you view the theory, there is a significant circularity problem here, but that is part of the reason why economists are so determined to formalise and set down in mathmatical stone the theoretical roots of their analysis. And this is, of course, the main area where economics is trying to improve itself and evolve at the moment – hence why I don’t think there is an issue with training and research in the discipline per see.