Imagine an economy in which the following hold true: (a) it is ruled by a dictator who has unlimited powers of intervention, (b) this dictator likes to think of himself as maximising the welfare of his society, (c) he thinks many market participants have some kind of bias (e.g. sexism) which he believes results in a suboptimal economic outcome, (d) he wants to know: how much of society’s resources should be allocated to fighting bias?
Now clearly the answer, given those assumptions, is going to be “some”, with the details depending on the benefit versus cost of fighting bias, which will probably exhibit diminishing returns. Any more specific answer will be sensitive to the precise parameters, in ways which are likely to be fairly predictable. (E.g. the longer it takes to shift bias, and the more impatient the average person is, the less we should devote to fighting it.)
So you might think that mathematicising the problem is not going to prove particularly illuminating. However, this is to misunderstand the role of modern academia, which is not to illuminate but to provide an ersatz product that will conceal the absence of genuinely progressive intellectual activity. This object is achieved by demonstrating technical expertise in a way which is difficult to criticise by outsiders and which also provides, where possible, incidental reinforcement for the prevailing ideology.
Here is how a trained economist (1) would nowadays be expected to present the above problem:
Now this looks very clever. And anyone except another trained economist would find it difficult to recognise that the mathematics does not really add much. This model, which is fairly typical, suffers from several flaws:
a) It does not really contribute anything to understanding the problem.
b) The conclusions it yields cannot go beyond what could be ascertained by non-mathematical logic.
c) It conceals its most crucial assumptions (2), e.g.
- that individuals are homogeneous,
- that a meaningful ‘welfare function’ can be constructed as a proxy for an aggregate ‘good of society’,
- the presupposition of a 'benevolent dictator',
- and the idea that the choices of an exogenous welfare-maximiser shed light on what is desirable in practice for a real economy.
As someone who was on the inside of academic economics not so long ago, I can confirm that much of contemporary economics is like this. And I suspect many other areas of social science suffer from similar pseudo-scientification. Now wouldn't it be interesting if Professor Dawkins had a go at that?
(1) Although the author of this model appears to be a young economics graduate — whom I certainly do not mean to single out for criticism — his model is a variation on a fairly standard workhorse of economics 'research'.
(2) When I say the most important assumptions are concealed, I don't mean specifically in the context of the blog post from which this model is taken, which I realise is not intended to be a full-blown academic contribution. Nevertheless, the assumptions I list are ones which are typically not stressed and heavily signposted (as they should be) in papers that use such models.
Update: trained economist Gabriel replies.
9 comments:
Ok, now I'm scared :O
Going to university soon to study economics, hoping to be a lecturer or some other form of academic... rubbish at maths :|
I'm sure you're being overly modest.
But, for anyone who is rubbish at maths (or who doesn't get anything out of doing it for its own sake): I strongly recommend staying clear of pure econ degrees, and going for a mixed course such as phil/pol/econ.
Thanks for the link. The only problem I have with it is that you picked a post/model where I couldn't go anywhere with it. (I'll return with another, equally mathy, post in a few days).
There is *something* to your criticism and I think everyone will agree to that. I just wouldn't take it as far as you have.
These exercises are not meant for the general public. They're primarly meant for oneself and for one's community. It takes a certain amount of hubris to second-guess a community re: its internal standards of discourse.
But, beyond the live and let live point, in regard to the way people choose to structure their thinking, I will also take issue with the claim that such formalizations don't prove valuable.
It's not that math is particularly insightful on its own. It's that loose, verbal arguments can easily turn self-serving and they generaly make unforeseen and unintuitive implications harder to address.
Plus, the best economists never seem to have trouble expressing themselves to a wider audience even if most of their research is far more mathematically refined than my amateurish attempt at formulation above.
P.S. Your list of (unstated) assumptions is artificially large. For a competitive economy with complete markets, there will exist "welfare weights" as to make it representationally equivalent with a "planner problem".
P.P.S. :-) You might think that your second paragraph is obvious but that's because you're an economists. That sort of thing is not obvious to most people. It takes some training (and work with marginal conditions and constranied optimization!) to see that as obvious, I'm affraid.
Thanks for commenting.
I’m not convinced that another model, where you could “go with it”, would not also suffer from my criticisms. I suppose there are, occasionally, highly mathematical models which lead to some genuine counter-intuitive insight. But I feel these are in the minority. Meanwhile, the bulk of economics research could be described as “high on technicality, low on content”.
You talk about “exercises not meant for the general public”, and of course that may be true in the case of your blog post. You may feel I singled you out unfairly, but you were a convenient place from which to take an illustration. If I had access to online current journals, which I don’t, I would have taken it from one of them instead. So, apologies for using you as a demonstration, but I think your approach is actually fairly representative.
I happen to think there is something wrong with theoretical research the content of which can only be grasped by someone who has had years of training. And this applies particularly to disciplines dealing with human behaviour. I like the advice allegedly given by Marshall to Pigou:
"(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."
I’m familiar with the defensive argument that mathematicisation is valuable because it prevents “loose, verbal arguments becoming self-serving and generally making unforeseen and unintuitive implications harder to address.” I’m not entirely convinced the benefits of this are as great as tends to be claimed. Against any such putative benefits has to be placed the risk that, by making the technicality impenetrable, more important questionable fundamental assumptions are lost sight of.
The level of mathematicisation used in much of contemporary economic theory seems to me to go well beyond the level of insight which economics actually has into real life phenomena. Ergo, the level seems to me to be excessive. (In contrast to, say, certain branches of applied physics.)
“the best economists never seem to have trouble expressing themselves to a wider audience even if most of their research is far more mathematically refined than my amateurish attempt at formulation above.”
Could that be because their points are actually far simpler than is suggested by the mathematical sophistication employed, and that the sophistication is unnecessary?
“You might think that your second paragraph is obvious but that's because you're an economist. That sort of thing is not obvious to most people. It takes some training (and work with marginal conditions and constrained optimization!) to see that as obvious”
I agree a little training would be necessary, but frankly I don’t know that anything beyond first year undergrad theory gets you much further in terms of understanding than it's possible to get with this kind of problem. Anything more is in danger of being delusory: it’s possible to feel one has achieved some fabulous model, with the mathematics meeting all kinds of stringent criteria (although I note that, even so, economic theory is criticised by some mathematicians for not being stringent enough) but the applicability is so marginal that, if anything, one has gone backwards rather than forwards in terms of understanding.
Right!
So, some of the issue ends up as being empirical (how much is much?) but there's something else...
You CAN'T talk your way through large, dynamic, stochastic systems. It's a speculation but much of the impoverishment of early macro theorizing was caused by the lack of a language suited for such systems. I'm not qualified to assert such as thing but I suspect it.
Plus, mathematicians do sometimes like what they see in Economics:
http://www.mth.kcl.ac.uk/~pushn/cm354x-page-0607/Franklin.pdf
Michael has been hosting a few discussions on the value of formalism, on a more sympathetic note, which your readers might enjoy, e.g.
http://yetanothersheep.blogspot.com/2007/04/point-of-pointless-economic-theory.html
P.S. I don't feel singled-out and I don't have a problem with it. I just like the fact that someone, somehow read my blog. :-)
Gabriel,
You don't think that mathematical arguments can be loose and self-serving?
A pesky critic might suggest that mathematics is the ideal form in which to present a loose and self-serving argument. It's much harder, for example, to conceal unrealistic assumptions when you have to reason syllogistically in English.
In the comment thread you link to, you write:
I'd bet that many heterodox folk are driven to their "heresies" by technicalities. Of course, they won't admit it. But if you like to think about economic issues and you're not capable of (or good at) following proof after proof, what are you to do?
Indeed. However, once upon a time, "literary economics" was orthodox and Marshall, Walras, etc, were heterodox.
You strike me as quite literate. And even if you weren't, it would hardly be polite of me to explain your preference for mathematics as a consequence of illiteracy. So I suspect you might enjoy engaging with a modern treatise of literary economics, such as Rothbard's Man, Economy, and State.
Usually published in PEER REVIEWED journals you have to explicitly say what assumptions you are making. You had to single Gabriel out for this where you could have went to professional economists around the web that have their papers available on their sites. Using mathematics is not the problem, a model could be too simplistic of reality and should be regarded as such. I agree that Economists should do a better job communicating with the public but quite a bit of top Economists write best selling books already.
"Usually in peer reviewed journals you have to explicitly say what assumptions you are making."
I think you may have missed footnote 2 of my post. I don't accept that peer reviewed papers adequately flag their most crucial assumptions, e.g. that it even makes sense to talk about a welfare function.
I happened to pick on Gabriel because I happened to come across his model without actively searching for one. I pointed out (in footnote 1) that it was not intended to be specifically a criticism of his particular model, but of contemporary economic models in general. But I think in some ways his was a good case to use because it illustrates how such (in my view pointless) technification is expected even at his level, and is not confined to advanced level research.
"A model could be too simplistic". That's precisely the problem with many current models, IMO. The mathematics merely conceals this. And perhaps that is part of its function. It means only trained economists are capable of noticing the oversimplification or unrealism. But, if they are all playing the same game, what incentive do they have to call bull?
"Economists should do a better job communicating with the public."
That may be impossible in some cases, given how abstruse and unrealistic some of their research has become.
"Quite a lot of top economists write best selling books already."
That is proof of public appetite for understanding economic phenomena. But how much of what is written in these books has benefited from the economic theory of the last forty years? Relatively little, in my opinion.
I think you've come to the core of the matter... Would you say that, on the net, the research over the last 40 years has been worthless?
If no, then that's something. If no, then we're dealing with a matter of degree, not categoricals.
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