Gene Callahan takes on Murray Rothbard and stickman channels Paul Krugman, critiquing the math-haters and Luddites. It's extremely fashionable to be down on math today, particularly among bloggers (a medium that perhaps caters to math skeptics???). Unfortunately, fashionability isn't a good measure of utility and math will always be essential for clarifying the messiness and confusion of human language. They're partners, not enemies. Math clarifies language, language translates math into intuition, etc. It's an iterative, constructive process.
The funniest thing is that the deductive logic partisans don't even seem to realize that logicians utilize math all the time for just this reason. The philosophers of math out there aren't German idealists or post-structuralists, after all!
I shared this with stickman, which I think readers will appreciate:
"This past fall I was at a conference with Richard Freeman and I was talking to him after dinner. He told me something I think you'd like.
He said that whenever you see anything by him where the math is extremely dense, he's probably talking about something he's not very confident about or that he fully understands yet. He said that when he starts to think about a problem he writes it all down formally. As he continues to work through it the math becomes more elegant and readable and he is able to focus on the key elements of the model. When you come across a paper of his that is easily readable it's usually a more mature idea. He's fully digested the insights from the math so he can express the intuition in words, and he's also had the opportunity to clean up the model a little. But he only gets there by thinking the models through several times and trying to figure out the intuition behind the model."
The funniest thing is that the deductive logic partisans don't even seem to realize that logicians utilize math all the time for just this reason. The philosophers of math out there aren't German idealists or post-structuralists, after all!
I shared this with stickman, which I think readers will appreciate:
"This past fall I was at a conference with Richard Freeman and I was talking to him after dinner. He told me something I think you'd like.
He said that whenever you see anything by him where the math is extremely dense, he's probably talking about something he's not very confident about or that he fully understands yet. He said that when he starts to think about a problem he writes it all down formally. As he continues to work through it the math becomes more elegant and readable and he is able to focus on the key elements of the model. When you come across a paper of his that is easily readable it's usually a more mature idea. He's fully digested the insights from the math so he can express the intuition in words, and he's also had the opportunity to clean up the model a little. But he only gets there by thinking the models through several times and trying to figure out the intuition behind the model."
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Rohbard's complaint about using differential equations in economics is also fatuous. Sure, people can't buy continuous quantities of things at continually varying prices... so what? The physical sciences differentiate what are really discrete functions all the time, as with animal populations. You just have to remember you are assuming a smooth function where one doesn't exist.
ReplyDeleteIt's not a serious argument.
ReplyDeleteThe same goes for complaints about the marginal efficiency of capital on the grounds of complementarity of capital. Yes, a given entrepreneur probably has to deal with things more discretely than that implies - but if you're talking about capital markets as a whole, continuity and differentiability is a quite reasonable assumption.
They take real world intuition at an extremely micro level - that we don't do calculus at the grocery store - ignore the fact that what we do do is still constrained optimization, and then just wave their hands and suggest that at the market level the same degree of discreteness applies.
Here is an interesting thought.
ReplyDeleteAt the college library, I was once reading Science For The Citizen. The author had a remark on math and science.
He said that it was newly fashionable among economists (the book was in the late 19th century) to support their theories with mathematical models, to show economics as a science.
But science preceded math. Not the other way round. He said that in the beginning of time, man is known to have quietly observed the stars, sun, and weather patterns. He made some conclusions about it. Only afterwards, to test the conclusions, he put a stick on the ground to see the angle of the sun and shadow. It was so that man started using angles before lengths. For some time, man understood angles better than dimensions, because angles were useful for his prime purpose in knowing the weather.
So math followed after actual observation, not before.
PS: Yes, I know that calling economics a science is disputed, even by economists, but never mind.
"But science preceded math. Not the other way round. He said that in the beginning of time, man is known to have quietly observed the stars, sun, and weather patterns."
ReplyDeleteAnd only when we finally reached Galileo WHO SAID THAT NATURE'S LANGUAGE IS MATHS did we come to the scientific revolution that brought you blogs like this one.
Plus, your case, which prioritizes "observation" still tears Austrian epistemology to shreds.
Good post, Kuehn. I'm so sick of the math-haters.
Don't you realize that the time wasted on translating between clear and precise math language and fuzzy natural language is better spent debating what Rothbard really said or what Mises actually meant?
ReplyDeleteAs I've already told Daniel, I'm not certainly not trying - let alone qualified - to become the poster boy for using maths in economics... However, this fixation against it in some quarters of the blogosphere makes me chuckle. So, yes, I would agree that blogs do provide an enabling environment for increased maths scepticism, without particularly rigorous argumentation.
ReplyDeleteOn that note, Gene... I have had similar things to say about Rothbard's charge against differential equations, e.g.:
http://www.economicthought.net/2010/10/math-and-the-austrian-school/comment-page-1/#comment-2963)
(For what it's worth, while Jonathan and I clearly didn't see eye-to-eye on a lot of issues in the above post, I respect his efforts at reconciling the use of maths within Austrian Ecos. That being said, the marshalling the use of, say, MV = PQ, the equation of exchange, as evidence against mathematical economics still strikes me as a non sequitur. Actually, I recall Daniel had a good post on this a while back: http://factsandotherstubbornthings.blogspot.com/2010/11/equation-of-exchange-and-metaphysics-of.html)
Righteo, stickman.
ReplyDeleteJonathan calls the equation of exchange a "model" there, which is quite a misunderstanding of its use.
The equation of exchange, like the Keynesian cross or the national income equation, are simple facts - simple accounting identities.
When you construct models to actually tell you something you have to nail things down.
y=mx+b does not do a damned thing for you if you're looking for a solution.
y=mx+b
y=nx+c
Takes you from an infinite number of solutions to (potentially) one solution. This is basic alegbra. We include these key identities to nail things down and (hopefully) find a unique solution.
Citing one component as a model and then denouncing said model is bad economics.
Citing MV=PQ to say that when you increase M you increase P as well as citing Y=C+I+G to say that when you increase G you increase Y are both bad economics and a horrible misuse of math in economics.
These equations are useless on their own. They are there to nail things down.
@ scineram
ReplyDeletehahaha, well, when you put it that way...!
In other words, anyone that wants to try to use MV=PQ to promote inflation scare-mongering is short at least two equations - or to put it another way, they only have a third of an argument.
ReplyDeleteWell, Friedman and Schwartz tried to show that V changed only slowly over time, which gives MV = PQ a little more oomph, if true.
ReplyDeleteV=V* adds one more constraint :)
ReplyDeleteSo why is all the fretting over the fact that it will increase P and not Q?
Two more quotes - which I happen to have stumbled upon via a link on my blog today - and then I'm done with this maths in economics thing for a while:
ReplyDeleteFirst, from Léon Walras... in anticipation of all the "maths haters", as StrangeLoop put it:
[A]s to those economists who do not know any mathematics, who do not even know what it meant by mathematics and yet have taken the stand that mathematics cannot possibly serve to elucidate economic principles, let them go their way.
Walras 1974/1900 (Jaffe 1954), Elements of Pure Economics, p. 47.
Second, another (older) Krugman quote. This time pertaining to the usefulness of accounting identities in economics:
ReplyDelete"Many, indeed probably most, of the non-economists who attack the field's formalism do so not because that formalism makes the field irrelevant, but on the contrary because economists insist that their equations actually do say something about the real world. And since the critic's view conflicts with what the equations say, this whole business of using mathematics to think about economics must be a bad thing.
What sort of equations are we talking about here? Well, how about the equation that says that the sum of a nation's capital account and current account is zero?
This is not meant to be a joke. While a number of issues motivate outsider critics of the economics profession, surely the most prominent and emotional involves concerns about the impact of globalization. Many people[...] who regard themselves as knowledgeable about economic affairs are convinced that growing international trade and investment are bad things for workers everywhere. The typical story - as found, for example, in the 1994 World Competitiveness Report (World Economic Forum 1994) or in Greider (1997a) - goes like this: Multinational corporations and other investors are massively relocating capital to low-wage countries, undermining traditional employment in the advanced countries. Meanwhile, hopes that these newly industrializing economies will provide export opportunities and thus alternative jobs for the displaced workers are a mirage: wages and hence purchasing power in these countries will remain low, both because of the sheer size of their labor forces and because they need to keep wages low to attract a continuing inflow of capital. Thus workers in the Third World will see no benefit from the process - their economies will achieve high productivity while continuing to pay low wages - while those in advanced countries will find their position undermined both by trade deficits and by capital outflows.
What is wrong with this story? Economists quickly notice that it violates the equation that says that current account plus capital account equals zero. It cannot be true that newly industrializing economies are or will be the recipients of large capital inflows and at the same time export much more than they are importing. And once one tries to fix this aspect of the story, the whole thing falls apart. In particular, suppose that one decides that newly industrializing economies will, in fact, attract large capital inflows. Then one must conclude that they will run current account and probably trade deficits rather than surpluses. But how can they run trade deficits when their productivity rises but their wages remain low? Doesn't this cost advantage ensure a trade surplus? Well, something must be wrong with the premise; perhaps wages will not remain low after all.
[...]
...The popular story is literally nonsense: that crucial equation is not some abstract theory, it is a simple accounting identity - and there is no way to save the story while getting the accounting right."
Krugman, Two Cheers for Formalism (http://web.mit.edu/krugman/www/formal.html)