Maths and economics

There has been a lot of negative talk about the maths in economics – like a huge amount.  Just look at these links, some of them are poor and reactionary, but some of them are excellent and the last two are my favourite (*, *, *,*,*,*).

Now although I believe much of this attack is excessive, and I believe the role of maths in economics is very very important, like all protestations there is a grain of truth to be found.

The way I see it, the role of maths is as a language – Mario Rizzo covers that off in more detail here.  Now, maths is not the only language that can provide clarity and solidity to the discussion of a given issue – words are still effective if treated with the same structural integrity.  The prime example of this is the work of Spinoza.

Maths was useful as it helped to drive structure and clear up arguments.  It helps to clarify thoughts, and acts as a clear linguistic device.

However, as with any language the main issue with maths in economics is when it loses its ability as a clear linguistic device,  namely when:

  1. people using it become overconfident of their assumptions, thereby missing some implicit assumptions in their modeling
  2. people use mathematical notation to hide their results.

However, both of these errors aren’t a problem of too much mathematical use in economics – they are an issue of too little concentration on the formal, logical, elements of using maths as a language!

The lesson here is that economists have to be aware of exactly what the elements of their models represent, and should be able to evaluate these elements when moving on to make recommendations – at least in some sense.  The maths is not the problem, and an arbitrary crusade against mathematics would only serve to reduce the usefulness of economic analysis.

An economist with a strong eye for mathematics and a strong nose for elements of reality can overcome these issues and use mathematics to provide a clear, incisive, and valuable contribution to the study of the economy and society as a whole.  I am glad to say that I believe many theoretical economists do possess these traits – hence why I am confident about the future of the discipline.

Note:  I am not a theoretical economist, and spend most of my time using words and numbers – not maths.  Even from my position of weakness I can see the important role that mathematical rigor plays in economics.

  • What would Hayek say

    I agree – I also like this quote from Alfred Marshall(http://en.wikipedia.org/wiki/Alfred_Marshall)

    (1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This I do often.”

    Point Three on translating into English I think is important – its not sufficient that just quants understand. I also find point 4 as a good proxy for suggesting that something is wrong with the model/maths (normally the assumptions) if the result cannot be illustrated by examples from real life – does not mean always wrong – just more likely to be wrong.

    Biggest issue from experience is not the maths – its normally the assumptions and this tend to occur because the model works backward, i.e. the result a person wants and then fitting the maths and assumptions to create this. Recent examples of using scarey social cost numbers spring to mind 🙂

  • steve

    theoretical economics is basically applied maths so I would give it a little more credit than you have here. but I certainly agree with your comments on assumptions and with the above post about Marshall. Its about how it is translated and its examples which really make maths useful in economics.

  • @What would Hayek say

    “Biggest issue from experience is not the maths – its normally the assumptions and this tend to occur because the model works backward”

    Definitely. It isn’t the maths that is the problem, its how were using it 😛

  • @steve

    “theoretical economics is basically applied maths so I would give it a little more credit than you have here”

    More credit? I’ve said that maths is essential as a language for describing social situations. I don’t know how I could have been “more” supportive of the use of maths in economics.

    Yes, theoretical economics is applied maths – applied maths is the application of maths – “Mathematics is the study of quantity, structure, space, and change” (http://en.wikipedia.org/wiki/Mathematics).

    So theoretical economics applies knowledge of how we study “quantity, structure, space, and change” to issues related to economics/society. In other words it uses the structure and language associated with mathematics to clearly study questions about economics/society.

    The post said that applying the language and methods of mathematics to economics was appropriate – therefore it was stating that theoretical economics effectively being applied maths was appropriate. As a result, I do not believe it was physically possible for me to be more supportive of the role of maths in economics 😛

  • steve

    @Matt Nolan
    my apologies – on a re-read you certainly are supportive of maths as part of economics. I think I was confused by “there has been a lot of negative talk about the maths in economics – like a huge amount. Just look at these links, many of them absolutely excellent and the last two are my favourite”.

    it sets the context at the start. I haven’t read the arguments just yet (will take a look when I have more time) but if I found only a “grain of truth”, I wouldn’t describe the argument as excellent. I think we’re on the same page, I just mis-understood because of the change in direction.

  • @steve

    “I think I was confused by “QUOTE””

    Good point. I will change that sentence actually, thanks for the pointer!!

    The “grain of truth” is that maths can be used poorly – to hide ceteris paribus assumptions, either on purpose or accidentally.

    For example, this is one of my concerns with “agent based” economic modeling (the numerical kind, not the standard intertemporal stuff). I think it is more realistic and can provide a lot of useful analysis – but it is so complex that it is hard for people to truly “understand” what the model, and the model results, are saying. In this case there is a lot of room for spurious results – which could translate into poor policy decision making.

    However, theoretical economists are generally aware of this – they tend to be more methodologically sound then alot of people give them credit for. As a result, I think the “grain of truth” provides an important lesson, which economists already know 🙂

  • My problem with this whole debate is that 99% of all math used in econ is trivial. Just go to any maths department and tell them that the math we use is high tech and they will laugh you out of the room. There are a few areas of GE, macro modelling and finance etc where the maths can get serious but very few economists work in these areas. Even for a lot of theory the maths is straight forward. Look, for example, at the theory of the firm stuff, very low tech maths, I’m very pleased to say!

  • @Paul Walker

    I suspect people just get caught up about the maths and state that it is the problem – when what they mean is that they have an issue with some underlying assumptions of some economic analysis. After all using mathematics as a language is hardly contentious 😛

    If people just said what assumptions they disagreed with we could have a useful discussion – instead all we get is vitriol 😛