"Words ought to be a little wild, for they are the assault of thoughts on the unthinking" - JMK
- Regular commenter stickman has a relatively new blog called Stickman's Corral that is worth following. He recently had a post up on "Why we need maths in economics". It's not every day you get to read a blog post where you agree with every single word. You all know I like to caveat and agree with parts of posts and disagree with other parts. I found myself agreeing with every single word of this post - it's worth a read.
- Stickman also has a newer post up illustrating his point about math in economics using a simple model of investment in oil fields. It's worth reading through the whole post. First, it's nice to see an actual model in a blog post. I'd never have the balls to put one up (right now at least) - I just blog on whatever comes to mind between 5:30 and 7:00 am, which usually isn't a full-fledged model. If you've had calculus you should be fine with this one. He demonstrates that the impact of the interest rate on investment is indeterminate because of the opportunity cost of capital. Now, there's a certain bit of irony in this conclusion. I've stumbled on several Austrians who think that they're the only ones that think about the opportunity cost of capital, and yet it's precisely this cost that introduces a stumbling block for cavalier assumptions (derived from less formal, less precise deductions) about the interest rate. Two thoughts on the model for stickman (which he is free to disregard, since it's not like I'm going to put in the work of implementing them): First, if you remove the assumption of up front payments, does that change anything? Second, usually Austrians (and honestly I'm not sure if you had them in mind when writing this up) think of the impact of the interest rate on investment as affecting investment in higher order vs. lower order production - i.e., causing malinvestment rather than overinvestment. Your result varies with c/p - the opportunity cost of capital, with some value of c/p where there would be no impact. If there were reason to believe that higher order production has a lower c/p and lower order production has a higher c/p, this would affirm the Austrian view (granted, I'm not sure if or why there would be any reason to believe that). Nice post.
- Jonathan Catalan also posts on math and the Austrian school, specifically econometrics. I have a few concerns with it - first, he cites Mises as if econometrics were used to derive theory rather than test theory. I'm not aware of any work that really does this, so I'm not sure exactly what Mises was thinking. We certainly theorize with some sense of the world (you can't theorize about the interest rate without observing the world and knowing about this thing called an "interest rate") but that's different from using econometrics inductively, which isn't done. The qualification Jonathan suggests Mises makes of mathematical models is that "those relationships are subject to change depending on the different factors that the model does not account for (thus, models rely on ceteris paribus)" - again, this isn't really a point that anyone would really dissent on. I'm not sure why Austrians have to go to Mises for approval, but if this is what Mises thought then there shouldn't be any major obstacles to mathematical and empirical Austrian economics. After all, this is how the vast majority of economists view math and empiricism. So maybe there's no problem? Perhaps Mattheus will weigh in on this - I know he sometimes differs from Jonathan on these points. One of the frustrating things about Jonathan's post is that he claims that math is less precise than using words, and he points out that people may get slopppy with their assumptions or premises with math. This is taking the standard argument in favor of math and standing it on its head. The whole point of math is precisely that you have to explicitly state all your assumptions or you can't solve the damn problem. This isn't the case with language. With language, the assumptions are implicit in the words themselves. Stickman can't write out his initial NPV equation without telling you what each symbol means. That's considerably more precise and the assumptions are considerably more out in the open than anything I've read on the Economic Thought blog about the determinants of oil rig investment. That's the whole point. Just saying it doesn't make it true, Jonathan. The English language is versatile and useful, but it is not more precise or clear than math.
- Scott Kuhagen continues his coverage of our activist Attorney General in Virginia. Jefferson would be rolling in his grave if he knew about this assault on academic freedom at his university. I don't like to use the memory of the founders to make a political statement. I hate it when the Tea Party does that. It oversimplifies very complex positions that they held and tries to pretend that the late 1700s are comparable to the 21st century. But in this case, I'm pretty confident Jefferson would abhor what Cuccinelli is doing at the University of Virginia.
- Lee Kelly has a post on currency, deposits, and monetary disequilibrium. He suggests private banknotes as a solution. I have a few concerns about that, which I note in the comment section of the post. Not a terrible idea - not even something I'd be especially opposed to - but I don't think it's quite the solution that Lee suggests it is.
- Evan had an interesting post up a little while back on Stephen Hawking's recent statements about God. He connects the spontaneity of Hawking's universe to the theological concepts of the "freedom" of God. I will stress that these are developed theological concepts - just like I talk in jargon here, he'll talk in his jargon there - so read with interest and google some stuff if you need more background on it, but know that there is a bit more depth and background to the concepts he's discussing than might meet the eye. I have comments in this comment section as well.
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In the main, the theologians who are responding toe Hawking's work don't know enough physics to make a useful response to Hawking. Really, people should ignore theologians and read what other scientists (particularly physicists) say about the work.
ReplyDeleteProbably the best review I have read of it so far is here: http://www.math.columbia.edu/~woit/wordpress/?p=3141
Well part of the problem is that Hawking doesn't know much about theology (but can say whether he thinks God is necessary for the universe), and theologians don't know much about physics (but can say things about the "nature of God" as they understand it).
ReplyDeleteWhat I like about Evan's post is that he's taking Hawking at face value and instead of challenging Hawking on his point, he's trying to understand what that means for theologians.
I think for a physicist to say "I know there is no God" or for theologians to say "Hawking is wrong - the universe needs a God" are equally wrong.
I think for Hawking to say "the universe doesn't of necessity need a God" and for theologians to say "we think there is a God, but the lack of a necessity for that God has implications about how we think about him" are equally fine.
Daniel,
ReplyDeleteI realize that is the part getting all the press, but it is really his discussion of M-theory that is far more interesting. Of course M-theory is hard to wrap your head around, so the default for most people is "He said what about God?"
Oh right - I wasn't approaching this as a book review. I've heard some of what he's had to say about M-theory but I haven't read the book itself yet. I'm interested in the dialogue that's come out of this that I have read.
ReplyDeleteHave you read the book? Is it a good one? I read his older ones - Brief History and Black Holes. Didn't read that newer one he wrote.
"The whole point of math is precisely that you have to explicitly state all your assumptions or you can't solve the damn problem. This isn't the case with language. With language, the assumptions are implicit in the words themselves. Stickman can't write out his initial NPV equation without telling you what each symbol means."
ReplyDeleteYou are saying that words are imprecise. Fine. But the symbols in Stickman's model point to an initial set of words/phrases (ie. Q = Amount of oil that can be recovered, r = Interest rate). The words/phrases in Stickman's model come loaded with the sorts of pre-existing assumptions you talk about in your post. (How many battles have been fought over interest rates, what they are, and how they're determined?). Therefore, Stickman's symbols and mathematical model are weighed down with the same imprecision that the underlying words are.
Economic arguments couched in math never lose their connection to language, after all, variables must point to some set of words, so that if the words are not precise, so is the math derived from the words.
Before mathematical symbols can point to a set of words, economists must use their intuition and logic to turn the morass of real economic structures and activity into language. Economic reality must first be translated into words - we can't tranlate economic reality directly into math because we don't think in terms of math. Only with a good set of words can the math point to anything meaningful and proceed accordingly.
I like to think that it needn't be math vs. language, but more a division of labour between the two. Economists who work in words must formulate the proper phrasing and terminology to hand off to the mathematical economists.
JP -
ReplyDeleteDefinitely - I'm not claiming that math isn't also imprecise. The point is, when you violate mathematical laws it is more easily identifiable than if you violate logical laws. You also are forced to understand the full impact of, say, the opportunity cost of capital in stickman's model. When you use words, you can raise the issue of or drop the opportunity cost of capital where it's convenient.
Economic arguments couched in math never lose their connection to language, after all
I should hope not!!! The models would be useless is they did!
I like to think that it needn't be math vs. language, but more a division of labour between the two.
I think what we have is math vs. math and language vs. language. I think math alone and language alone are both fallacious.
Economists who work in words must formulate the proper phrasing and terminology to hand off to the mathematical economists.
But should there be any non-mathematical economists? That seems extremely dangerous. I would say all economists should be mathematical economists and they should all think hard about how they're modeling phenomena and what assumptions they're using.
The White House and libertarians against Obama: http://reason.com/archives/2010/10/08/austan-powers
ReplyDeleteDaniel,
ReplyDeleteFirst, thanks for the props and favourable comments on my post(s)... You've helped to push my audience stats into double figures for the first time on any single day! (In blogging terms, I feel like I just made it to second base.)
W.r.t. your questions:
1) I haven't actually worked through the math with staggered investment costs, but I see no immediate reason why it would change the conclusion. Cost would, after all, still be a negative component in the analysis. It seems to me that we'd still be left with an ambiguous numerator (in terms of sign) for the final equation. Although, yes, the way we discount costs does affect how much we value those costs; making the outcome potentially more sensitive to the magnitude of the parameters.
2) I wouldn't say that I had Austrians in mind for the Oil Tank model (although they were certainly among those that I was talking to in my first maths post). Regardless, I'd be very cautious in extending the implications of this particular model to a "higher" vs "lower" order goods scenario... This is a singular investment and the only decision variable at stake is how many (homogeneous) wells to drill. Also, to be pedantic, c/p itself is not the opportunity cost of capital, but rather the relative cost of capital/investment. So it's not that some c/p would have no impact, but rather that a "low" (c/p) relative to the interest rate would be superseded by the "impatience effect"... But of course I know what you meant ;)
PS - If I'd known what a mission it was going to be putting those formulas up into a blog post (converting them into picture format, etc), then I might have avoided doing it in the first place!
ReplyDeleteStill, I do think that it's good to provide some examples to back up your claims (especially on something like this math discussion). On that note, I've already decided that my next example will summarise the insights from Schelling's famous segregation model. A lot of you may already have seen this one before, it deserves "popularising" in blog format and it's certainly relevant to the discussion at hand. Of course, it helps that segregation is a topic that's probably much more relevant to most people than optimal oil depletion!
JP,
ReplyDeleteReading my original post on this maths question, I think you'll see that we agree on most things. (That maths and language should be considered as compliments rather than substitutes, etc)
Still, I will object to your concerns about "pre-loaded assumptions" in this context,as these are empirical - not theoretical - problems. Indeed, the model in question is actually completely free of the definitional imprecisions that you are worried about, since the relationships hold not matter what the chosen interest rate is.
Put differently, the exact point is that the model is a "pure" skeleton upon which different (observed) values can be imposed, not the other way around. The values of the individual parameters (r, c/p, etc) have no bearing on the relationship between those variables; although they will clearly affect the final outcome... (Which is part of what I was trying to show.)
"I think math alone and language alone are both fallacious."
ReplyDeleteWait. It may be the case that when you violate mathematical laws it is more easily identifiable than if you violate logical laws, but that doesn't mean you *can't* identify errors in language. One must be rigourous with words.
So I'd agree, math alone is wrong. But language alone is possible. It's not a false notion, as you seem to believe. Perhaps it isn't ideal, but that's much softer than fallacious. Daniel, you must realize that if you hold the idea that an economics based purely on language is a fallacy, you are writing off all economics done from the early Greeks to the early 1900s. I think we can agree, along with Adam Smith and David Ricardo, that such a write off would be a bit presumptuous.
"Put differently, the exact point is that the model is a "pure" skeleton upon which different (observed) values can be imposed"
ReplyDeleteI like that. My point may be pedantic. But in order to create that skeleton, economic reality must have been already transcribed into words. How else could you properly delineate the concepts of interest rates or present value? Each bone in your "skeleton", these are the variables of your model, is equated to a set of pre-existing words, while your PV equation derives itself from pre-existing phrases about the interaction between time and interest rates. If your words and phrases are wrong, the skeleton is wrong. I'm sure your model is completely free of definitional imprecisions, but that's because you got the language right to begin with.
You're right JP - fallacious was the wrong word. Let me just say that the extreme view that it's somehow illegitimate to use math in economics is fallacious - and an over-reliance on words alone is just very suspect.
ReplyDeleteSo what do we do with economics before substantial mathematization? Probably the same thing we do with physics before substantial mathematization - note the contributions, but not be afraid to acknowledge that it was still a very immature stage in the science.
"So what do we do with economics before substantial mathematization? Probably the same thing we do with physics before substantial mathematization - note the contributions, but not be afraid to acknowledge that it was still a very immature stage in the science."
ReplyDeleteThis is just a subtle repetition of your idea that a purely language-based economics is a fallacy. You're saying... ignore old economics because no math. Only pay attention to the economics that comes after some arbitrary line demarcating "herein lies sufficient mathematics."
No. You can safely ignore old economic ideas only because they have been superseded by better ideas. It is irrelevant if these better ideas came from the pen of an economist working purely in words or one working with words & numbers.
In sum, the demarcation line between the economics you-must-know and the economics you-can-ignore is *not* determined by math/no math, but good ideas vs. bad ideas.
No, it's not a repetition of that. I fully retract that. Language-based economics is not a fallacy. You can do good language-based economics. It is insufficient for thoroughly understanding the economy. That's a real difference, not a subtle repetition. It is what I should have said the first time.
ReplyDelete