tag:blogger.com,1999:blog-26706564.post6032017893753637139..comments2024-03-25T07:51:47.758-04:00Comments on Thoughts On Economics: Steve Keen: Economists Are "Insufficiently Numerate"Robert Vienneauhttp://www.blogger.com/profile/14748118392842775431noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-26706564.post-7666745094156727462014-01-19T06:43:17.157-05:002014-01-19T06:43:17.157-05:00It wasn't that, it was a working paper, and I ...It wasn't that, it was a working paper, and I can't find it now for the life of me.<br /><br />I brought it up because in the discussion on "The Moving Finger Writes..." I speculated that agents would find some way to stay at the unstable equilibrium. This working paper seems to have shown that is not the case.YouNotSneaky!https://www.blogger.com/profile/06378267534638281151noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-15985699627981527162014-01-17T13:52:41.166-05:002014-01-17T13:52:41.166-05:00Using Google, I find Sean Crockett's Price Dyn...Using Google, I find Sean Crockett's <a href="http://aux.zicklin.baruch.cuny.edu/crockett/GESurvey121205.pdf" rel="nofollow">Price Dynamics in General Equilibrium Experiments</a> surveys experiments, including with the Scarf instability example.Robert Vienneauhttps://www.blogger.com/profile/00872510108133281526noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-7964961185933800622014-01-17T06:02:29.591-05:002014-01-17T06:02:29.591-05:003Yes, there is a connection but it's not the s...3Yes, there is a connection but it's not the same thing. You can reduce a nth order DE to a system of n 1st order DEs. Is there an "only if" arrow going the other way (I actually don't know, but I suspect, no)?<br /><br />And that sort of highlights that you don't need to study 3rd+ order DEs to play with chaotic systems. Really all you need is to know that higher order DEs can be reduced to 1st order systems. Which is why standard ODE courses focus on 1st and 2nd order DEs.<br /><br />I'm not disagreeing with you, just Keen.<br /><br />BTW, I saw a paper not too long ago where something like what you outline in your "The Moving Finger Writes..." post was implemented in a laboratory/classroom setting. The motivation for the paper was that there was a disagreement between the co-authors, one of whom believed that agents would find *some* way to get to the interior, unstable, equilibrium. The other one thought it was going to go wacky, as the tatonnment dynamics suggest. In the experiment, it went wacky with price dynamics unraveling away from the equilibrium. I wish I could find it but it was just something I noticed in passing.YouNotSneaky!https://www.blogger.com/profile/06378267534638281151noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-55695177701172265022014-01-16T12:55:38.863-05:002014-01-16T12:55:38.863-05:00I've demonstrated awareness in past posts of t...I've demonstrated awareness in past posts of the possibility of chaos in discrete time systems.<br /><br />Anyways, a clear connection exists between the order of a single ODE and the dimensions of a system of differential equations.<br /><br />Let <i>f</i>(<i>x</i>''', <i>x</i>'', <i>x</i>', <i>x</i>) = 0 be a third-order ODE. Then:<br /><br /><i>y</i> = <i>x</i>'<br /><br /><i>z</i> = <i>y</i>'<br /><br /> <i>f</i>(<i>z</i>', <i>y</i>', <i>x</i>', <i>x</i>) = 0<br /><br />is a system of three first-order differential equations.<br /><br />A forced, damped pendulum, apparently, is a counter-example to Keen's claim. It is anon-homogeneous example, if I understand correctly; and it is a system defining a flow in a three-dimensional space, anyways.Robert Vienneauhttps://www.blogger.com/profile/00872510108133281526noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-61082268697134356722014-01-16T06:19:00.453-05:002014-01-16T06:19:00.453-05:00Yes, but that's about dimension not order. Mos...Yes, but that's about dimension not order. Most well known chaotic systems are first order (for example, Lorenz). And in a way that's the whole point of "chaos" - that really complex dynamics can result from fairly simple relationships.<br /><br />(Also, with discrete time difference equations you don't even need three dimensions, and that's pretty much what most models use, not just in economics)YouNotSneaky!https://www.blogger.com/profile/06378267534638281151noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-65808892134000519922014-01-15T11:23:26.497-05:002014-01-15T11:23:26.497-05:00In my browser, footnote 5 is there. Maybe I mucked...In my browser, footnote 5 is there. Maybe I mucked up the HTML.<br /><br />I suppose some of the dynamic concepts can be introduced at an introductory level.<br /><br />That bit about "second-order..." is apparently known as the Poincaré-Bendixon Theorem.Robert Vienneauhttps://www.blogger.com/profile/00872510108133281526noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-59695536777545268212014-01-15T07:33:51.522-05:002014-01-15T07:33:51.522-05:00"Students may learn some of the basic techniq..."Students may learn some of the basic techniques for handling what are known as 'second-order linear differential equations,' but chaos and complexity begin to manifest themselves only in 'third order nonlinear differential equations.'"<br /><br />Uh... say what?YouNotSneaky!https://www.blogger.com/profile/06378267534638281151noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-49660891774905141222014-01-02T06:47:34.572-05:002014-01-02T06:47:34.572-05:00Having taken some (basic) applied maths, I was sho...Having taken some (basic) applied maths, I was shocked at the way differential equations were 'used' in my mathematical economics classes. There's a strange focus on equilibrium properties over actual exploration of the dynamics of the system.Unlearningeconhttps://www.blogger.com/profile/13687413107325575532noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-17145300914258026312013-12-30T14:46:08.948-05:002013-12-30T14:46:08.948-05:00You wrote: "How can they learn all of this ne...You wrote: "How can they learn all of this necessary background and the needed mathematics[5], as well?" But footnote [5] is missing...pqnelsonhttps://www.blogger.com/profile/12779680952736168655noreply@blogger.com