RE: Re: Re: Rigor mortis?
Alan writes:The problem I see with the (mainstream) economics profession---and I suspect that this is what many people on this list rightly object to---is the exaltation of mathematical formalism above all else. If formal models were taken as just _one more_ tool in the economists' toolkit then we probably wouldn't be having this discussion. right. The problem is that economists use math as a way of proving and gaining status in the profession. If you don't do math, you don't rise to the top. Speaking of which, though I learned a bunch from the post-Keynesian economist Paul Davidson, I found that the few times he tried to use math were the most illuminating. This suggests that the problem isn't the math as much as the equilibrium conceptions that math encourages. More generally, math by its very nature describes an idealized world. That doesn't mean that it shouldn't be used as much as that it has to be used _very carefully_ if one's goal is to understand the world. But the vast majority of economists aren't careful. -- Jim Devine
RE: Re: Rigor mortis?
Michael Perelman writes:Marshall's biography -- he is also a villian in this piece -- shows that he pushed formalization of econ. to prevent outsiders from taking part in the subject. this fits with my sense that economists embrace math so fervently partly because it provides a basis for Mandarinism. (Mandarinism refers to the pre-20th century practice of requiring would-be Chinese state bureaucrats to take examinations in stuff like calligraphy that had nothing at all to do with their ability to rule.) I have little faith that formal models clarify much or avoid misrepresentations of reality. I have asked the list for examples of formal models that have taught them anything that they could not have learned by other means. I think Peter Dorman may have been the only one who responded. I found that in order to talk about -- and to understand -- dynamic-disequilibrium growth theory (in my dissertation), math was totally necessary. In one model, the equilibrium is stable in the short run, but as the equilibrium persists, it becomes unstable. Nicholas Kaldor had a business cycle model along those lines. One of the big differences between my models and those of the orthodox school is that like Joan Robinson, I believe that we need to understand processes in historical time rather than in the totally hypothetical and unrealistic logical time of neoclassical economics. Jim Devine
Re: RE: Re: Rigor mortis?
Daniel, I don't disagree with you, although the PBS television show, Nova, did do a pretty good job. I was asking about the examples of models that were able to teach something about the nature of the economy. Obviously, mathematics is important in finance, but I'm not sure how much it can teach about how financial machinations affect the economy. Davies, Daniel wrote: I've yet to see a decent explanation of risk-neutral pricing (most normally seen in the context of the Black-Scholes and/or Cox/Ingersoll/Ross options pricing models, but a very powerful economic idea of very general application) which didn't involve some sort of formalism. I'm not saying it can't be done, but I don't know how one would go about it. -- Michael Perelman Economics Department California State University [EMAIL PROTECTED] Chico, CA 95929 530-898-5321 fax 530-898-5901
RE: Re: RE: Re: Rigor mortis?
-Original Message- From: Michael Perelman [mailto:[EMAIL PROTECTED]] Sent: 04 March 2002 16:43 To: [EMAIL PROTECTED] Subject: [PEN-L:23467] Re: RE: Re: Rigor mortis? Daniel, I don't disagree with you, although the PBS television show, Nova, did do a pretty good job. I was asking about the examples of models that were able to teach something about the nature of the economy. Obviously, mathematics is important in finance, but I'm not sure how much it can teach about how financial machinations affect the economy. == here beginneth the apologia I tend to think that option theory actually has a much wider application than just in finance. For example (to plug the only piece I've ever published in anything even resembling an academic journal), you can model the payoffs to the owner of a limited liability company as the equivalent of the payoffs on a strip of put options. The idea is that, if the firm's assets are worth more than its liabilities on the next audit date, the owner gets a payoff equal to the positive difference between assets and liabilities (plus the ability to play the game for one more year), whereas if the assets are lower in value than the liabilities, the owner's losses are capped. For this reason, owners of limited liability firms have an incentive to maximise the volatility of their assets, and this incentive increases the futher out of the money the option moves. This explains the Nick Leeson gambling for redemption phenomenon. It's possible to put it in less mathematical terms, but I don't think you get the feel of it unless you know how to interpret vega (the sensitivity of the value of an option to a change in the volatility of the underlying). And that's not even touching the general issue of risk-neutral pricing, which I am currently constructively proving my point by not being able to give a sensible example of without using maths. Basically, this is an issue in the selection of the appropriate discount rate for a set of risky future payments under particular assumptions about one's ability to manage the risk. There are a knot of finance theory concepts here, but they're all terribly important: The CAPM tells me that if the risk of an investment I propose to make is like that of a lottery -- it's more or less a completely random number, like prospecting for opals in Australia --, then I ought to make an unbiased forecast of the future payoffs, and discount these back to the present at the *risk-free* rate. I use the risk free rate in this case because if I have enough of these projects, I can diversify this risk away and be more or less certain of getting the actuarial expectation. The CAPM also tells me that if my investment is correlated with the wider economy, and if the nature of the project is that I basically invest my capital now, and find out in the next time period whether I'm a winner or a loser (say, I'm thinking about distilling Scotch, and once I've put it in the barrels, there's nothing I can do except hope that people want to buy it in fifteen years), then I should adjust my discount rate upwards according to the *covariance* of the return on the project with my expected consumption. So if my Scotch is Johnnie Walker Black Label, then I should want a higher discount rate, because the event under which I get rich out of this business is one in which I'm rich anyway (a stock market boom in Japan), whereas if it's rotgut hooch, then I'd be prepared to accept a lower rate of return than Treasury bonds, because the rotgut hooch business would make me a big winner exactly in the sort of recessionary economy in which I'd need the money. I'll assume that this sort of intuitive explanation will do; in actual fact, to prove that covariance rather than variance is the relevant measure of risk, you need some pretty hairy maths. But risk-neutral pricing is something else. It says that if the nature of my business is one where I can make day-to-day changes to my output -- if I can *manage* the risk -- I ought to be setting out a plan to manage this risk, counting up the payoffs on various branches of the plan, and then discounting these cashflows at the *risk-free* rate of interest. The reason for this is (I contend) impossible to describe without getting into some sort of formalism, but it's got a lot to do with the fact that at any one stage in my plan, I can be hedged against the next small movement, so each node of my decision tree has me in a situation where (consistent with the plan) I have no risk, so the whole plan should be treated as a risk-free project. Which sounds awfully like a fallacy of composition, and you need the maths to prove that it isn't. Broadly speaking, finance (and its close cousin actuarial science) is the branch of economics which deals with uncertainty and time, so I don't see how it can fail to be relevant to the central questions of economics. Even something as simple as compound
RE: Re: Rigor mortis?
Eric writes: This does not mean that math models are not helpful when we consider the real world. They can point out possible mechanisms and connections that are unlikely to be discovered in other forms of discourse. I think it's important to remember that the phrase the real world is redundant. Also, isn't it more accurate to say tht math models can clarify one's thinking about possible mechanisms and connections instead of allowing them to be discovered? The discovery seems to be a pre-mathematical stage of the analysis. Jim Devine [EMAIL PROTECTED] http://bellarmine.lmu.edu/~jdevine
RE: Re: Rigor mortis?
Jim D wrote, I think it's important to remember that the phrase the real world is redundant. I guess this depends on one's epistemology, but I don't want to start any discussion about epistemology. Pen-l seems to have a lot on its plate now. ;) Also, isn't it more accurate to say tht math models can clarify one's thinking about possible mechanisms and connections instead of allowing them to be discovered? The discovery seems to be a pre-mathematical stage of the analysis. I think that both things can happen but I that sometimes that discovering stuff with a math model can be more interesting than clarifying one's thinking. Having said that, the math work I'm doing now fits into the latter approach (clarifying).. Eric .
Re: Re: Rigor mortis?
At 3/3/2002, you wrote: I have little faith that formal models clarify much or avoid misrepresentations of reality I have asked the list for examples of formal models that have taught them anything that they could not have learned by other means I think Peter Dorman may have been the only one who responded Michael Perelman I have problems with the way this issue is posed in the above paragraph 1) Any explanation of an economic issue can have misrepresentations of reality and not clarify much regardless of the method chosen (a formal model, plain text, or whatever method one chooses) 2) For some, formal models may be an easier way to understand what an economist is trying to say than plain words This has to do with the way a particular individual learns and with the ability of the one doing the explaining, among other variables (so to speak!) For example, doing a static CGE model helped me understand the inner workings of the neoclassical framework a lot better than many critical texts Not that the texts themselves were bad, things clicked with the model in a way they haden't before The problem I see with the (mainstream) economics profession---and I suspect that this is what many people on this list rightly object to---is the exaltation of mathematical formalism above all else If formal models were taken as just _one more_ tool in the economists' toolkit then we probably wouldn't be having this discussion Alan _ Do You Yahoo!? Get your free yahoocom address at http://mailyahoocom
RE: Re: Rigor mortis?
I have little faith that formal models clarify much or avoid misrepresentations of reality. I have asked the list for examples of formal models that have taught them anything that they could not have learned by other means. I think Peter Dorman may have been the only one who responded. I've yet to see a decent explanation of risk-neutral pricing (most normally seen in the context of the Black-Scholes and/or Cox/Ingersoll/Ross options pricing models, but a very powerful economic idea of very general application) which didn't involve some sort of formalism. I'm not saying it can't be done, but I don't know how one would go about it. dd ___ Email Disclaimer This communication is for the attention of the named recipient only and should not be passed on to any other person. Information relating to any company or security, is for information purposes only and should not be interpreted as a solicitation or offer to buy or sell any security. The information on which this communication is based has been obtained from sources we believe to be reliable, but we do not guarantee its accuracy or completeness. All expressions of opinion are subject to change without notice. All e-mail messages, and associated attachments, are subject to interception and monitoring for lawful business purposes. ___
