December 15, 2003
Daniel Davies Defends "Theory"
Daniel Davies comes up with the most eloquent and insightful justification for the heavy use of mathematical tools within academic economics that I have ever seen:
Crooked Timber: The War On (some kinds of) Theory : ...And the point I'm trying to make is this; in the construction of arguments of this kind [within economics], there are certain kinds of mistake which it is fearfully easy to make. It's easy to spot particular benefits and miss the fact that their counterparts are costs elsewhere in the system. To come up with arguments which, if true, would imply that people systematically allowed others to impoverish them without changing their behaviour. To miss the fact that your model requires the build-up of debts forever that never get repaid. Etc, etc. The bestiary of really bad economic commentary is full of all sorts of logical howlers. And the good thing about building mathematical models is that, in general, it acts as a form of double-entry book-keeping, to make sure that, if you've followed the rules of the game, your economic argument will not have any of these most common and most egregious flaws. It doesn't mean that it won't be bad or misleading for other reasons, of course, but it does mean that you'll at least be saying something that makes sense...
Two comments. First, I wasn't "proudly boasting": I was "lamenting". Second, while it is true that a discipline's "formal language... (its jargon) has... the function of making it more difficult to make the characteristic mistakes of that discipline. In economics, itís politically convenient adding-up errors..." it is also true that the formal language has the function of serving as a barrier to entry: of excluding outsiders from being allowed to say anything. Whether the jargon is useful or harmful depends, of course, on its marginal costs and benefits, which are different for different disciplines. I see powerful benefits from the use of mathematics in economics. I see no benefits from (say) the use of functionalist jargon in sociology. And in literary criticism... I don't see any marginal benefit at all from writing like, say, Judith Butler in The Psychic Life of Power...
Posted by DeLong at December 15, 2003 11:33 AM
Formalism creates a collective illusion of objectivity in economics; the idea that economic ideas are divorced from material conditions and justifications because they can be described in mathematical terms is different than Butler using complex language because she at least acknowledges and attempts to incorporate the social embeddedness of abstract reasoning.
I've no problem with formalism in economics, but the idea that it thereby places the field in the realm of Platonic truth is comically transparent self-justification.
I wrote about Paul Krugman's take on this here
"the idea that economic ideas are divorced from material conditions and justifications because they can be described in mathematical terms is different than Butler using complex language because she at least acknowledges and attempts to incorporate the social embeddedness of abstract reasoning."
Do economists argue that their ideas are divorced from material conditions? I thought the standard complaint against economics was more along the lines of, 'precisely *because* economists use mathematics in order to create certain models of material conditions, they tend to think they are accurately reflecting an underlying material reality that is pure and unmediated and divorced from the social and political questions, biases and concerns that actually help construct the models'?
But I could be wrong. I'm stuck in the 18th century and can't get past "das Adam Smith problem."
That's the same point phrased differently. It'd be better to say that they argue (or assume) that their material conditions do not constrain the ideas they express, which are instead discovered exclusively through mathematical analysis of data, like the Laffer curve, e.g.
In defense of Brad, a good economist will not confuse his model with reality any more than, say, an evolutionary biologist will (to continue on a Krugman theme). Even a physicist has to deal with the existence of wind resistance or the gravitational pull of the moon but whether to correct for it depends on the situation.
But a little bit of math even when not exactly right can be awfully useful to cut through logical errors, letting researchers move on to more interesting empirical questions. Think of how much more understandable Keynes would have been with a small amount of algebra. "Oh, THAT's what he meant when he was talking about liquidity preference. Does this make sense? Do people behave broadly like this?"
Not that there isn't a lot Laputa-like of abuse of math out there--go to a theory seminar or check the NBER website sometime--but it's nice to transparently see the inner workings of a model, moving the argument to assumptions and empirical evidence instead. And unlike literary devices which tend to encourage dogmatism, this method at least allows for a researcher to say, "I thought that X caused Y but now I just don't know. Maybe my assumptions are wrong; I've been missing something in the data; or there's just another approach that works better."
Let me use a macro example. Think of the original real-business-cycle theorists--even Bob Lucas--who've been forced to admit that there has to be some kind of friction causing business cycles based on the evidence. At the same time, they forced the old Keynesians to reexamine some of their treasured assumptions after the accelerating inflation episode of the 1970s, introducing dynamics. It's still too early to see where this synthesis is going but it's bound to be better than the dogmatic quarrels of the 1960s.
Economics isn't perfect; in particular I think that the seams between theory as taught to graduate students and empiricism are just a little too great--one of the McCloskey critiques. That, and it's a little too easy to make a hash of statistics since we're economists first, statisticians second. Every profession has its imperfections. But there's still a lot of good work being done out there and I'd rather not throw the baby out with the bathwater.
I think the idea that there is no benefit to formal language in Sociology is as unfair to that profession as a similar statement would be to an Economist. The formal language in sociology serves the same role as Prof. Delong describes for Economics except that every ____ who watches the evening news thinks he is a Sociologist. You might as well say Sociology doesn't exist. (I'm sure that view was held by the people who planned the occupation of Iraq.)
Suppose we compare Orlando Patterson and Charles "Bell Curve" Murray. Yes, my dear, there is a discipline to sociology and psychology and even even even philosophy. Really.
Two comments: I really can't take credit for this defence of maths in economics; it's simply a paraphrase of Krugman's.
Second, Brad says:
"I see no benefits from (say) the use of functionalist jargon in sociology. And in literary criticism... I don't see any marginal benefit at all from writing like, say, Judith Butler in The Psychic Life of Power... "
Well, you wouldn't would you ...? You're outside the barrier to entry.
Chun: "I've no problem with formalism in economics, but the idea that it thereby places the field in the realm of Platonic truth is comically transparent self-justification."
I'd like to think that mathematical formalism helps open theories up for criticism and scrutiny. It is not there to provide an impression of truth. Obviously the reader will have to know mathematics, but is that really such an unreasonable request? Should we limit economics to only theories readily explainable in layman's terms? Few people would impose the same restriction on physics, or medicine.
The trouble is that economics is inherently political, which means that people want to be able to check the political implications of models themselves. But shouldn't we try to understand economic systems better, even if it leads us to complex theories?
Speaking as a non-economist fairly familiar with math and behavioral science... economics is WAY too full of mathematical jargon. I've read paper after paper - including decent stuff by well known economists, not wannabes trying to hide that they aren't saying anything intelligent - that use 10 pages of math to say nothing that couldn't be said in 1 page of clear text. (This is in stark contrast to math and computer science papers I read, where 1 page of math could take 10 pages of text to explain). Ridiculous amounts of formal notation are used to describe simple linear systems, to talk about the intersections of a couple of curves, and so on.
I actually don't buy the argument that this avoids mistakes. The level of obscurism that I've seen makes it relatively easy to HIDE things such as "proof by assumption", and assumptions that are flat out ridiculous - anyone reading it has to wade through a lot of notation to notice where the magic happens. In particular it makes it particularly difficult for people from other disciplines to interpret economics. There has been a great coming-together of most behavioral science research in the last two decades. There is increasing overlap and cooperation between psychology, evolutionary biology, artificial intelligence, cognitive science, anthropology, and behavioral economics. But looking at all those things, behavioral economics is most on the fringe of its parent discipline (economics), and in my experience economics is the discipline least affected by - or even aware of - the new convergence in behavioral science.
All of the other disciplines use math. AI researchers use math that would blow the minds of most economists. But the other disciplines use relatively "practical" math - it's closely tied to modeling a real-world system, it's not too hard to check against what is being modeled, and because the models are complicated enough to start with the application of mathematical formalisms generally isn't used to obscure them further. Much of economics seems quite a different experience - models often rely much more their assumptions, and there is a tradition starting at the level of undergraduate teaching to describe even very simple ideas with the most complex, "rigorous" formal notation.
Somewhere I read an anecdote about some physicists who asked an economist "Why do you use so much math for so little data?"
Psychology of certain types uses rigorous-looking, impenetrable statistics to dress up what seems to be (judging by the descriptions given of the actual research, as well as what I've seen of psychological research) rather mushy data. The DSM-IV diagnosis standard is also full of what seems to be false rigor. Some of the categories don't seem to have much to do with either treatment or causes, but just to be codings for insurance and malpractice purposes.
Economics also lacks good popularizers of the underlying theory. I have a pretty good understanding of economics but as a non-econ major I had to fight for it. In contrast, other disciplines have excellent popularizers who can give people a good understanding of a subject without having to take them through all the math.
Where is the economic equivalent of Richard Dawkins, for example? In evolutionary biology Dawkins' earlier books provide excellent "big picture of what's going on" books. You can learn an amazing amount just by reading "The Selfish Gene" and paying close attention, to say nothing of "The Extended Phenotype". Without going into the math - which is complicated - he still provides an excellent explanation of not only some of the details and hot button issues of evolutionary biology, but also some pretty deep theoretical insights.
The closest economics writer I've found is Paul Krugman. However, while Krugman is an excellent writer, he tends to focus on explaining a single contentious issue, explaining just enough theory so that the reader can understand that issue. So he doesn't really cater to the person who wants to know in a broader sense, "just how does the prevalent view of microeconomics and/or macroeconomics work, anyway?" Most fields have a slew of popularizers that are accessible to a non-professional, but still generally rigorous and reliable. Krugman is the only such person I know of in economics. Other economics "popularizers" tend to be outside-the-field types with an axe to grind and arguments that an attentive undergrad could puncture.
Physics is another area that has some great popularizers. Of course you can get a fairly lite big picture from books by Hawking and Sagan as everyone knows. But there are other excellent popularizers who can give a more in depth big-picture understanding, still without going into the utterly nasty details of the maths. Victor Stenger fits this bill quite nicely for physics, but I have never found a Victor Stenger in economics.
Yes, psychology has often suffered from a related disease - obsession with coming up with a study that passes a significance test. Psychology makes HEAVY use of statistics, without most researchers really understanding it. So passing a statistical significance test has come to be the be-all and end-all of much research. The problem is that a significant result may mean very little in real world terms.
Traditional psychology research had a similar problem to one I've seen in much traditional economics. Namely, ideas became judged by a standard (whether significance testing, or proper derivation from rational actor axioms) that does not in itself guarantee that the ideas have any value. Passing a significance test, or following all the right mathematical rules, is just a first-pass way to eliminate some obviously bad results. But it can become pathological if you accept passing such tests as a sort of important proof, and don't bother to test alternative theories that could crush the whole edifice you've built.
Significance testing has actually become a disease in psychology. It's hard to publish a paper at all unless it was set up to allow you to pass .05 significance - despite the fact that as a good statistician will tell you, significance testing can be quite meaningless without a good real-world handle on alternative hypotheses you're comparing your theory to. "My experiment got results that couldn't be explained by pure randomness" means extraordinarily little, especially since a big enough sample size virtually _guarantees_ that your experiment will catch _some_ phenomenon not attributable to chance, but also not at all related to your theory. (This is one of Gerd Gigerenzer's favorite subjects - he's a statistician and behavioral scientist).
So anyway the result was that entire psychological research programs could pass significance tests for decades, but then end up completely demolished because the true theory was something they'd never even bothered to test. This happened, for example, in the evolutionary psychological revolution that came to the forefront in the 1990s. What had been a bunch of fringe researchers destroyed many consensus results in psychology by challenging underlying assumptions that had always been ignored, rather than by pitting their favorite theories against blind chance.
I've already seen a similar thing start to happen in economics. Economists have their own version of significance testing - the use of rigorous derivations from standard axioms of market behavior. Time and time again I've seen economists pay so much attention to properly deriving their model from their assumptions, that it obscures what the assumptions are and what problems there might be with them. The attention some economists pay to their math can be likened to the good ol' castle built on sand - too much time spent cutting blocks of stone and teaching students the exact method of laying out a defensible keep, so you don't take time to look down at what you're standing on. Game theorists and behavioral economists have already started to come up with some very different results that cast doubt on founding assumptions of economics (as foundational as the assumption that more wealth is an inherently good thing). But their models are either heavily empirical, or based on mathematical techniques that don't lead to the simple static equilibrium solutions of neoclassical economics. The formalisms that most economists are taught, and taught to respect, have no application to this type of research.
I think that plays a big part in resistance to these new ideas. Resistance to evolutionary psychology was heavily ideological/philosophical - people weren't comfortable with accepting such a large role for evolved biology in human behavior. But most economists basically agree with the idea that not everything's a static equilibrium, and rational actor models can't be a precise description of human behavior. But from what I've seen, when push comes to shove, they don't see how to connect this research with what they know how to do so they don't pay attention to it. If it can't be derived from the standard models, well, gee it's a nice idea but what can I do with it? (This is in contrast to other disciplines more used to "real" and empirically based math, where new models seem much more readily adopted by mainstream researchers, provided they can explain something).
I've had two friends who did statistics for researchers in bio and psych at OHSU (not quite a major research center, but reasonably close). One (a sociologist) said that the researchers he worked with really had no concept at all of experiment design, scientific method, or stats. They were biologists and knew about biology.
The other said that bio researchers wanted a strong (~90%) correlation, whereas his psych researchers were happy with anything that wasn't completely random.
At a different school, a MA candidate hired someone to put stats into his thesis because the program director liked stats. His stats guru told him that his statistical results contradicted the main point of his thesis. So he hired a new guru.
Thank you Ian Montgomery.
The problem I see, perhaps stating the same thing that has been stated better and at greater length by others, is that the formal assumptions that underly so much economics are simply wrong. As Montgomery points out, if your foundations are faulty, the rest of the structure is likewise faulty - and it only gets worse the more you build on it. To an outsider who has taken a few coruses and read a fair bit the entire edifice looks like the sort of building which it would be foolish to buy.
As for functionalist jargon - functionalism is only one theoretical framework in sociology, and is understood to be a theory - there are other theoretical perspectives and other sets of words that can be used descriptively. There is little that someone explains functionally which couldn't also be explained from the point of view of conflict theory, or Marxism, for example. (Which is is suspicious in and of itself - any theory that explains everything has moved beyond its proper sphere.)
I think economists get biased by the very existance of their theories towards a view of economic systems as based on 'natural laws'. So many numbers must point to something quantitatively verifiable, right? So there is a lack of historical, social, political sophistication in many practicioners in the field. Of course I am an outsider, but I am compelled by the lack of useful comment by economists on how best to handle dislocations and conflicts associated with free-trade, for example.
Ayn Rand popularized some of the more bogus free-market ideologies masquerading as 'laws of nature'. It is interesting that no less an economist than our Federal Reserve Chair has a past sullied by an infatuation with Miz Fountainhead. Yuck!!
I spent a thoroughly interesting morning digesting all this material. As someone trained in religion, I think offering an opinion borders on absurd. I have no idea what the jargon of econ is. As you note, in other disciplines, it doesn't improve comprehension. In fact, it generally replaces a pre-existing, precise term with an ambiguous one. Perhaps there's a reason the term gets introduced, but in the end, it shields poor scholars from the scrutiny of better ones.
Davies, though, seems to be making two points simultaneously--about math an language. I wonder what you think of his sense that econ should be regarded as a form of rhetoric rather than a science (leaving aside issues of how either might be best communicated)?
Just one example of problematic foundations...
The standard model of neoclassical economics assumes that people are rational utility maximizers. It's easy to find arguments about how the assumption of rationality fails. But what about the one on "utility"?
Economics has a quite strange concept of utility. Utility is supposed to be a measure of how satisfied someone is with things (their life, their possessions, what they did today, whatever). Utilitarian philosophy, and most everyday "common sense" ethics on the subject of utility, treats it sort of like a number. It makes a sort of sense to say "I'm twice as happy as he is today", "I'm half as happy today as I was yesterday", and "a new widescreen TV would improve my life but only by a tiny amount". In other words you can at least roughly compare satisfaction between people, and talk about how much satisfaction something might give you.
Economics rejects that. It is based on a concept of "ordinal" utility. In ordinal utility there is no comparison between people, and no "amount" of satisfaction given by something. All you can know is that for any two alternatives, a person may prefer one of those alternatives to the other. You can "sort of" talk of strength of preferences by involving the idea of how much you'd want to risk for something. But when an economist talks about the "efficient" outcome, know that fundamentally there are some big differences between that and what an ordinary person might consider the outcome producing the "most wellbeing" for people. One big difference is that economic efficiency makes no comparison between the wellbeing of people.
Creating a ten course meal for Bill Gates is more efficient than creating a two dollar sandwich for a starving paralyzed man, essentially _by assumption_. Because under the economic theory you can't say that the starving man's cheap meal preference generates more wellbeing than Bill Gates' expensive meal preference. But you can say that if the starving paralyzed man doesn't have goods/labor that other people want, he can't create an "everybody wins" market transaction that gets him fed, whereas Bill Gates can. In technical terms, the economists' decision to base efficiency on "pareto optimality" (win-win transactions) rather than "wellbeing" (where a win-lose transaction may be a net gain because the win is big and the loss is small), results in conclusions about market efficiency having a huge built-in ideological assumption. An assumption which, moreover, only a tiny portion of people on the libertarian right actually accept when you put it to them as a question of ethics.
Of course, measuring wellbeing is messy and empirical, and coming up with models based on pareto optimality is relatively simple. So economists by and large have chosen to build a mighty fortress on sand, rather than a humble hut on rock. And it's not like they actually empirically studied wellbeing and made a college try of incorporating it into their models - rigorous study of wellbeing has only recently been started by psychologists, and introduced by them into the fringes of economic research. The perception is more "wow that stuff is so much harder to measure, let's not bother trying". Economists primarily create economic models based on Pareto optimality, then run the result through their personal "common-sense interpretation" to try and take actual human wellbeing into account.
Another example is how actual peoples' wellbeing isn't directly proportional to how much stuff they have. Economic models assume that if you voluntarily acquire something then it must increase your wellbeing, and the more stuff you acquire the more wellbeing you have. Psychologists who have actually studied wellbeing believe this to be completely false. Especially, acquiring the material consumer goods that the middle/upper classes in the developed world buy so much of, makes essentially no long-term contribution to wellbeing. A few economists are actually aware of this - Robert Frank's work in the 1990s has some examples, as does his book "Luxury Fever". These findings totally call into question pretty much all arguments about economic efficiency. But economists aren't sitting up and taking notice - if you kick such a big foundation of the standard neoclassical microeconomics out from under them, the techniques they know provide no path for them to get back on firm ground. When I've talked to economists about these findings, their reaction usually reminds me of the old joke about the man looking for his glasses under a streetlight. He lost them in a dark alley, but he was looking under the streetlight because that's where he has enough light to see.