A Question for Ben Golub

Colleges and Universities A-Z California Institute of Technology
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<p>Part two:</p>

<p>The math in empirical work is absolutely necessary in that it helps statisticians deal with the problems inherent in teasing out inferences from imperfect data not derived from controlled experiments. One of the reasons that a lot of the most convincing stats work in many areas of social science is done by economists (cf. recent work by Levitt but also by others on the value of education, development spending, or the sources of AIDS in Africa) is that economists have probably done more than most other social scientists to worry about the mathematics of teasing out causal inferences from observational data. Compare for example, the level of empirical work in many journals of education or sociology vs those in the econ journals.</p>

<p>It is also NOT true that poli sci is indifferent to this. There is a strong branch of poli sci that is pretty much economics applied to political science models. Munger -- chair at Duke -- is an econ Phd. Weingast -- former chair of Stanford poli sci -- was a professor of econ at Wash U. Former Harvard chair Shepsle was a mathematical theorist doing econ style models in Poli Sci. A lot of the best poli sci stats work looks much like the equivalent in Econ. And Econ Phds often look to Poli Sci as part of their job market.</p>

<p>Finally, undergrad econ is still seen as general liberal arts training. The basic econ ideas are still so powerful and useful that those who never plan to do research can still benefit from learning to think a certain way. I believe that econ may be the most popular major at HYP (or one of the top 3) and certainly econ reasoning permeates the campus these days. Nonetheless, most top schools usually have a more mathematical track (sometimes official, sometimes informal) for those contemplating advanced work.</p>

<p>So there are lots of good reasons and a few bad ones for the current state of affairs. I predict that social sciences which can adapt more of the econ-flavored reasoning without necessarily swallowing all the excesses of the outer reaches of math econ will be likely to flourish in the coming century.</p>

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<p>Here's an interesting book on the problems with the traditional mathematical theories of economics:
<a href="http://www.amazon.com/Origin-Wealth-Evolution-Complexity-Economics/dp/157851777X/ref=cm_cr-mr-title/104-3850307-3231111%5B/url%5D"&gt;http://www.amazon.com/Origin-Wealth-Evolution-Complexity-Economics/dp/157851777X/ref=cm_cr-mr-title/104-3850307-3231111&lt;/a&gt;&lt;/p>

<p>What do you all think of it (along with the approaches used by Samuel Bowles and Herbert Gintis?) The novel approach that some desire to take in economics now happens to be along the lines of game theory and non-deterministic models that use non-linear differential equations, and that the predictions of the previous models of economics were overly idealistic and impractical. The complaint that both Bowles and Gintis raise, of course, is that economics departments are still filled up with economists who use the wrong methods (and change is often slow in university departments, due to tenure and the like). </p>

<p>I'm somewhat partial to the approaches used by modelers such as Bowles, Gintis, and John Maynard Smith, however (and the whole venue of Sociobiology as explained in E.O. Wilson's "Consilience" in general).</p>

<p>The way I see it though, game theory is still rarely taught in many universities. Of course, that's where self-study comes in. ^_^</p>

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<p>Erm. I'm a little bit confused. Game theory is a major foundation (along with general equilibrium) of core microeconomics courses at every good department. Certainly all serious economists must be comfortable with the approach. Even political scientists can now scarcely afford to ignore it.</p>

<p>As for people who write books condemning most of economics to date as "simplistic", there's scarcely a professional economist who would disagree. Of course the models we have are extraordinarily stylized. We are always looking for better ones. </p>

<p>The Amazon review says that "he outlines an open, adaptive system with interlocking networks that change organically, reflecting the interaction of technological innovation, social development and business practice." If he can make these notions precise enough to generate real predictions, then more power to him. Otherwise, anyone can talk -- that doesn't mean you're within 5 miles of doing real science.</p>

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<p>Oh, I think that part of my argument had to deal with points discussed previously - the lack of game theory in many economics undergraduate courses may be related to the lack of math in such courses in general (I think I may have given the impression of "departments" instead of "courses" - of course game theory is heavily used in econ departments). I don't know a whole lot about economics departments in general (I'm just interested in the application of complexity theory to any of the social sciences), although the book that I showed on Amazon.com gave me the impression that traditional economic theory still dominates econ departments in the nation.</p>

<p>Granted, though, the book did not elaborate too much on the specifics of complexity theory. In this case, it may be wiser for me to check out the latest book of Gintis. Both Gintis and E.O. Wilson, in any case, say that economics is the social science that has got things right more so than any other social science, due to (a) its non-conformance to the standard model of social science and (b) to its use of mathematics, esp. game theory. It's just complexity theory that the book cited above talks about. Though that theory is very controversial (and we don't know how far its predictions can go, considering that it's a new field)</p>

<p><a href="http://www.amazon.com/Game-Theory-Evolving-Herbert-Gintis/dp/0691009430/sr=1-1/qid=1170696132/ref=sr_1_1/104-7963058-4683965?ie=UTF8&s=books%5B/url%5D"&gt;http://www.amazon.com/Game-Theory-Evolving-Herbert-Gintis/dp/0691009430/sr=1-1/qid=1170696132/ref=sr_1_1/104-7963058-4683965?ie=UTF8&s=books&lt;/a&gt;&lt;/p>

<p><a href="http://www-unix.oit.umass.edu/%7Egintis/%5B/url%5D"&gt;http://www-unix.oit.umass.edu/~gintis/&lt;/a&gt;&lt;/p>

<p>This seems particularly intriguing</p>

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<p>I recommend the following book critical of economics by David Colander. I especially recommend the last chapter which DEFENDS mainstream econ from its naive critics. While I don't agree with large chunks of the book, Colander is quite sophisticated in his understanding of the problems of the profession. Nonetheless, he defends the core work in mainstream econ as generally successful and he argues, rightly in my view, that any improvements will come from encouraging the evolution of the standard model, and not its overthrow.</p>

<p><a href="https://mywebspace.wisc.edu/morrow1/link/colander/garbagemen.pdf%5B/url%5D"&gt;https://mywebspace.wisc.edu/morrow1/link/colander/garbagemen.pdf&lt;/a&gt;&lt;/p>

<p>I might add that he also touches on the grad undergrad split that was brought up earlier.</p>

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<p>Wow, interesting, thanks! =)</p>

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<p>Thanks guys, for your helpful and interesting thoughts on my questions. Ben Golub, I like your example of Arrow's impossibility theorem---the math behind it is necessary to give the useful insights that it provides. And, of course, there are plenty of similar examples. It'd be interesting, though, to consider if there are any specific interesting "bad" examples as well. For example, just how scientifically valid/founded are the fundamental</a> theorems of welfare economics? (That's a genuine question, not a rhetorical one, since for all I know they could be amazingly sound.)</p>

<p>I noticed that both of you (Ben Golub and Not quite old) mentioned that economics is an "immature" science. I'm not sure exactly what you mean by that. If you date it from Smith's Wealth of Nations, then it's about 225 years old. Saying a science is immature when it's 225 years old is a little discouraging! (When physics was that old in the mid 1800s, it was already quite mature, although of course its subject matter is simper than economics'.) If, however, you meant mathematical economics is immature, then I'd certainly agree with you, as it only really began around the turn of the century. And regardless of maturity, I'd imagine you're right that not teaching undergrads a bunch of math is at least partly the researchers' way of admitting the math may or may not be valid in some cases. (Odd that they are hell-bent on teaching all the grad students a whole bunch of math, though.)</p>

<p>Not quite old, I see what you're saying w.r.t. empirical work. Certainly empirical examination of econ requires sophisticated statistics. And this sentence of yours caught my eye: "The basic econ ideas are still so powerful and useful that those who never plan to do research can still benefit from learning to think a certain way." The funny thing is, an economist I know has said almost the opposite thing, that in undergrad econ you learn a bunch of stuff and then in grad econ you have to un-learn it in order to learn the "real" stuff. That attitude is partly why I asked the questions here; I plan on majoring on econ (and then possibly going on for econ grad school), and I was concerned that undergrad econ might just be a waste of time. If that's not the case, that's good news, then.</p>

<p>And that book you linked to looks interesting. I'll check it out.</p>

<p>Thanks, guys!</p>

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<p>Hmm... your posts make me feel bad about myself. I was not asking questions anywhere near this sophisticated when I was where you are in my education. :)</p>

<p>My personal opinion on your questions:</p>

<p>"Modern" economics should probably be dated to around the time Pareto worked -- so early 1900's. But in some ways Adam Smith is quite modern in spirit, so those things are always a judgment call. I am by no means an expert on the history of economic thought, and NQO knows an order of magnitude more about that than I do, so let's wait to hear what he says about it.</p>

<p>As for things like the welfare theorems... that's a good example to bring up. Unlike the assumptions of Arrow's theorem, the more restrictive assumptions of general equilibrium theory are somewhat harder to accept. So it's not clear whether the theorems have any testable implications, especially since things like individual utility functions are very hard to measure. (To their credit, economists recognize this, and the empirical testability of general equilibrium is a big topic of research.)</p>

<p>On the other hand, the welfare theorems make precise Adam Smith's "invisible hand" intuition, and are valuable for that reason. If you read Smith's argument, you might say "well, sure, imbalances in supply and demand will lead to correction, but does it really follow that the resulting allocation is efficient in some sense?" There are a lot of points where you could quibble with his intuitions about how the system will work. If you formalize it mathematically, you can see that there is no room for doubt -- in the general equilibrium model, market outcomes are Pareto efficient and (with a few more assumptions) any Pareto efficient outcome can be achieved with a price system after transfers. It's a way, once again, to get from handwaving to a precise statement, at least in a particular model. It also puts economists on firmer ground when they say things "at least in our model, most desired welfare programs can be implemented without price controls." It's better when there's math to back it up than if it were just said based on intuition.</p>

<p>That really illustrates the divide between the empirical math that NQO was talking about and the "theory math" that usually gets the criticism. The former is 100% data-focused and interested in getting real-world answers to real-world questions. The latter kind (topology, analysis, fancy dynamical systems theory, etc.) is more about checking whether our intuitions work in an idealized model. Often they don't, and we can chuck them right there -- they certainly won't work in the world. At other times, intuitions like the "invisible hand" can be confirmed rigorously, and then we can go find ways to apply the theory in a more down-to-earth way. Both are valuable, and it's important, I think, that both are developed in tandem, so they can enrich each other.</p>

<p>Just my two cents.</p>

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<p>Since people are talking about economics here, I'd like to check assertions about taxation made in an online discussion. The first assertion was, </p>

<p>
[quote]
Things "paid for completely by the government" are really paid for by taxpayers. NO form of taxation has incidence only on the rich.

[/quote]
</p>

<p>A response to that statement, the second assertion, was, </p>

<p>
[quote]
This is, in fact, wrong. The estate tax affects only the estates of those who die with more than x million dollars (whatever x happens to be right now). I think it's safe to say that this has incidence only on the rich.

[/quote]
</p>

<p>What do those of you who study economic theory think about those two assertions? The context was a discussion of whether schools should be both government-operated and government-subsidized.</p>

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<p>Just my two cents as usual -- keep in mind that I'm only a student.</p>

<p>The first guy is right in principle, because generally transfers (i.e. taxes) on a particular group will change their consumption choices, which will change a variety of prices and optimal production decisions, which will influence other markets (in particular, labor markets) and people who were not taxed at all. </p>

<p>In particular examples, these effects may be small, but it is hard to know for sure in advance. In general it is a mistake to tax a single brakcet and expect that the effects will be confined to only a few markets. At the very least, you have to check (typically using an econometric model) that the effects on "unrelated" markets are expected to be small.</p>

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<p>You guys are really getting into this. I don't think I started thinking this hard about econ till grad school. Maybe, never :)</p>

<p>Since I'm in a rush to head out of town this weekend, I can't comment in detail, but some simple remarks:</p>

<p>1) At the level of Arrow's Imp Thm or similar, the math suits the intuition. But formal econ has gone, way, WAY beyond that without any evidence of a large payoff. I have argued long and hard with guys about whether any of the insights using heavy duty math could not have been made without the heavy math and whether they are made plausible to econs who are not already predisposed to drink the higher math KoolAid. There's a lot of post Arrow formalism that -- in my humble view -- doesn't get us farther than Arrow.</p>

<p>2) Economists are always talking about the virtues of substitution. So in theory, a good enough idea without heavy math should be publishable. In practice that is not the case. The greatest ideas of Buchanan, Coase, North, Olson, Williamson would simply not be publishable in a top journal unless dressed up in model form (assuming a new idea with similar insight). This is a weird lexicographic ordering for the profession. Since none of the newer math has direct empirical operationalizability (is that a word?) it's not clear why we should treat them as other than sophisticated gedanken. In which case interesting, less formal gedanken should also be publishable. But I have even heard people say in seminars Well, the econ is probably wrong, but it's a really cool model while dismissing a good idea because, the model was too elementary.</p>

<p>The fixed costs are rising yet correspondence with empirical testing is weak.</p>

<p>3) I am especially disturbed by the post Debreu turn. This began the importation of Bourbaki to econ. If you read the Theory of Value (going through all those theorems in grad school traumatized me I think) there is actually no correspondence to any empirical reality. The model is formal, but in fact it is not scientifically rigorous in the sense that the primitives are not strictly tied to real world entities. There isn't even the hint of testability, nor does Debreu seem to care. When Debreu defines prices, he basically says, "It's what you usually think prices are." So if we want to make this empirical we can't say Oh, Debreu got this wrong, because he can always redefine terms to make things work out. And Debreu is nothing compared to lots of stuff after.</p>

<p>4) The math can be a hindrance to new work. Vernon Smith always talked about the fact that when he first tried to get a paper showing that in real experiments, the descending Dutch Auction resulted in higher prices than the First Price Sealed Bid Auction, editors and refs kept rejecting the results on the grounds that "Oh, those two equilibria are trivially equivalent. That's what the math tells us." There's a longer version of this story that's more fun.</p>

<p>Anyway, just some quick shots. If you're still interested, I'll post more late next week.</p>

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<p>Oh, and with respect to estate taxes: </p>

<p>There are in theory many ways that a tax on the rich can have much incidence on the poorer. For example if someone with an estate of say, 5 million were to lose most of it, he might 1) not have incentives to accumulate that estate in advance and 2) engage in early transfers to his heirs that are second-best and that result in lost benefits for the economy as a whole. Moreover, imagine that the estate is used to fund a small business. Taxing those assets at a high rate could easily have a bigger effect on the employees of the business than the dying capitalist himself.</p>

<p>Of course the size of the effect is complicated, but you can't say just because the LEGAL incidence hits only millionaires that only millionaires will bear the ECONOMIC incidence of the tax. Indeed, the irritating thing about taxes is that it is so very hard to calculate the economic incidence in the real world of just about anything.</p>

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<p>The example I remember from the early 1990s was a "luxury tax" imposed on buyers of yachts. I don't ever expect to buy a yacht--that's a purchase for rich people only, as near as I can tell. But, sure enough, blue-collar workers who built yachts lost their jobs because of the tax, so the tax was eventually repealed.</p>

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<p>I just wanted to confirm Ben's point about political science. Some political scientists are wary of the mathematical bent of the newer work, but it seems to me (as a grad student and as a watcher of political science in general) that most poli sci departments are moving to the quantitative direction these days.</p>

<p>I have some objections to it, however. For one, without a good qualitative foundation, many political science models simply fall apart once scrutinized. You can punch as many numbers you want into Stata and get good (mathematically speaking) results, but that doesn't mean that your model will actually predict anything. I think that for this reason, Keohane is probably my favorite example of a political scientist who straddles both the qualitative and quantitative and actually tells us something useful. John Zaller is another good example.</p>

<p>As for econ and math, what everyone else said is right. I can't add much there.</p>

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<p>No question that Arrow is a giant and that his Impossibiity theorem is an incredible mixture of great insight with comparatively little formal machinery.
-But-</p>

<p>a) the earlier post grouping Coase, Friedman, Schelling and Spence as "soft theorists" is misleading, as Friedman was much more mathematical than Coase, and Spence was much more mathematical than Schelling. </p>

<p>b) Whille Scheliing is also a giant, his discussion of plausible and implausible commitments in "Strategy of Conflict" proceeds only by example, so it was hard for others to know how to apply these ideas to new situations; Selten's mathematical formalism provided a way to make these ideas precise.</p>

<p>c) Similarly, Williamson is often too vague to be testable. Good empirical work doesn't need a big theorem, but it does help to have a clear idea in one's head about what one is trying to test. I think the related work of eg Hart, Holmstrom, and Tirole has greatly advanced our understanding of the organization of firms.</p>

<p>d) I agree that there are a lot of uninteresting poorly motivated theoretical models. There are also a lot of unintersting poorly motivated emprical papers, experiments, etc.; in each case papers are held to a higher level of craft/technical competence than say the AER of 50 years ago. Still, I prefer the current system to the former one; if we went back to verbal theory and casual empiricism, there would be a lot of poorly motivated verbal models, with the additional problem that it would be harder to tell what each other was talking about.</p>

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<p>
[quote]
b) Whille Scheliing is also a giant, his discussion of plausible and implausible commitments in "Strategy of Conflict" proceeds only by example, so it was hard for others to know how to apply these ideas to new situations; Selten's mathematical formalism provided a way to make these ideas precise.

[/quote]
You said it quite well. Noticing that sometimes a commitment doesn't make sense is a big leap, but defining subgame perfectness so that this idea can be applied to arbitrary situations did much more for economics. The moderately sad thing is that, in hindsight, it might seem like it was "obvious" that subgame perfectness was the right way to formalize it and that the math is just pointless symbols. It only becomes clear how subtle and challenging it all is if you try to do it youself. (Avinash Dixit has a</a> great short paper of advice in which he recalls [page 3] how hard it was when he had to invent some of it himself.)</p>

<p>A large fraction of the mathematical formalism invented in economics comes to nothing. But the few things that "stick" because they're truly good ways to parsimoniously capture a system make up for the chaff, in my humble view.</p>

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<p>I do not deny that formal theory is beautiful and has produced great insight. I argue that as economists we should be focused on the opportunity cost of a system that overemphasizes formal theory ** at the margin **.</p>

<p>Many of the sciences value a great deal of descriptive, statistical, and even theoretical work that is not particularly formal. Biology, geology, astronomy, routinely give space to work whose econ analog gets pushed out of the top journals.</p>

<p>Evidence for the disjunction in econ theory is the enormous disconnect between the top empirical work and top theoretical work. Mind you, this does not mean that all empirical work excludes high formalism. It is quite relevant, however, that the Levitt's of this world, as well as some of the best macro does not depend for the most part of the most formal theoretical work. Indeed, it is a sign of the problem that in many departments top empiricists clash with top theorists about which margins should be rewarded. It is likely that if you cut out 99% of the formal work in Econometrica from the last 25 years that almost none of the major strands of empirical work today would be displaced.</p>

<p>At the margin, the insights of Coase, Williamson, North, etc have easily matched the impact of the top theorists on non-theoretical economists. I bow to no one in my respect for Arrow or the best work in game theory but I don't think we should dismiss the contributions of intuitive workers such as Coase. Similarly, Acemoglu, Johnson, Robinson's work in macro institutional effects would be unthinkable without the highly verbal work of North that preceeded them. Moreover, even though Friedman was mathematical by the standards of the day, it is not clear that the increases in math sophistication are a necessary condition for further breakthroughs. Friedman himself often said so in person. He told me on more than one occasion that he was unpersuaded that most of the macro formal machinery was an advance over the state of the art circa 1970.</p>

<p>Even some of the biggest supporters of math in macro (and believers that only formal theory is serious theory) -- Lucas and Sargent -- have been dipping their toes in historical waters because they realize that there are insights to be gained from ideas that are not yet fully formalizable. Yet most young people who made those same points would find it hard to publish. The post Romer growth models have not necessarily changed the way empirical and historical work on growth has been conducted and indeed, often depends on work that was much more verbal (or mathematically lowtech) from the past.</p>

<p>Finally, even the work of Caltech experimentalists and behavioralists -- such as Camerer -- is sometimes pooh-poohed because it hasn't all been neatly tied in to the formal standard model. (I heard more than one theorist over th e years make such dismissive remarks.) Yet I doubt that Ben would deny the relevance of Colin's work even when it isn't based on fully worked out models that satisfy the dominant elites in the profession. Indeed, I've often heard the following: "So-and-so's current interest in behavioral work/neuroeconomics is crazy, but I'll cut him some slack because of his rep as a theorist." This suggests that the theory per se isn't driving the esteem.</p>

<p>Again, we won't settle these issues in a few posts. And I'm not opposed to either high math or formalism per se. But this is about the relative value at the margin of the current strictures on research in econ. I'm well aware of the professions' biases and reasons on this. Heck, I have paid the price on more than one occasion of thinking as I do. But there's no doubt that the profession is divided on this subject. And that divide seems like more of a consensus simply because there is much tighter control of the journal market by those in power.</p>

<p>But there are alternatives and the success and recognition given to many suggest that even the high formalists are conceding at the margin. Certainly the turn in the late 90s towards valuing hot young empiricists (almost none of whom pays more than lip service to the really funky math) testifies to the fact that at the top of the profession, the big theoretical push of the late 80s and early 90s has not always led to fully satisfying economics.</p>