Economics and similar, for the sleep-deprived
Does anyone have any idea what might be done about the pointless blob of white space above this paragraph? It seems to be resistant to all my efforts. Update haha, it succumbed.
Friday, July 25, 2003
DeLong and the shorts
Schopenhauer correctly pointed out that "Buying books would be a good thing if one could also buy the time to read them in: but as a rule the purchase of books is mistaken for the appropriation of their contents". If you're wondering why the book reviews promised "tomorrow", several days ago, aren't here, that's why. I am working on a solution to this problem, which will be posted soon.
But in the meantime, I started reading my own archives, and was impressed by two things. First, how good my comments section is (no really, I love you guys, sob), and second, how much better this weblog was when I used to stick to the rubric and write more stuff about economics than anything else. The shift wasn't really a matter of policy; it's just that the economics stuff takes rather a while to write and I have less spare time than I did a year ago. So I'm going to try and keep this short; if it is too dense and incomprehensible as a result, say so in comments and I'll have another go. I've posted it here rather than Crooked Timber because I think it fits better.
The question I'd like to address is one that Brad DeLong asked a while ago with respect to the dot com bubble. Now, Brad actually wrote one of the seminal papers on how it is that markets can get so wildly out of control without someone coming in a turning a profit by taking the other half of all the suckers' trades and waiting them out until they run out of money ("Noise Trader Risk", or something it's called and it's a goody). But he confessed on his weblog to still being a bit surprised that the DeLong/Shleifer1/Summers1 effect seemed to dominate so completely. The question he asked was "Why are there no rational, well-financed players to come in and bring the market back to its senses?"
My answer to this question is that the reason there are none is that it is logically impossible for the kind of market participant Brad is thinking of to exist.
Consider the very simplest model of a stock market bubble there could be. (I have a mathematical version of this first bit on paper, so either it definitely works (10% chance) or I have made a mathematical error and maybe it works (90% chance)). There are two players; "the crowd", who are noise traders, and one single player (call him "Soros") who is rational and has access to unlimited investable capital. The crowd have the normal Blanchard-style bubble dynamics (non economists; basically, every day, the market has to either crash, or rise by enough to compensate the crowd for bearing the risk of a crash). On any given day, unless a crash has already happened, Soros can decide to commit his capital to short positions. If he does this, he sucks up all the excess demand for stock and a crash is inevitable on the next day.
So, in this model, when does Soros decide to pop the bubble? Well, think about it this way. Number the days 0, 1, 2, ..n, and call P(t) the profit for Soros from the strategy "Wait until day T and then pop". Call B(t) the level which the market has reached by day T as long as the bubble is still going (one can read this out of the standard bubbles model) and R(t) the probability of a spontaneous collapse on day t conditional on no collapse before t. I'll use cum(R(t)) to refer to the cumulated version of R(t), ie the unconditional probability as of T=0 that the market has collapsed before T. Clear as mud? Thought so.
Anyway we can say the following things about P(t) as a function of t:
P(t) is equal to B(t) conditional on no collapse before t and 0 otherwise. Therefore:
- As B(t) is assumed a monotonically positive function of t, for every day that passes, Soros can commit more capital to the market when he decides to pop, and earns a greater return on every unit of capital committed. This would tend to make P(t) increase with respect to t.
- Since cum(R(t)) is also a monotonically positive function of t, every further day also increases the risk that the eventual profit will be zero.
- Whatever happens, Soros can't lose money in this deal, because he is assumed to have perfect information that the market is in fact overvalued. Therefore there is an option-like structure here, meaning that there is a positive reward to waiting. Note that there is no "noise trader risk" in this model.
I think you can solve this model for the optimal value of t in P(t), and that this value could be quite large. The idea is that even for a rational well-financed arbitrageur, it is actually rational to see if a bubble gets bigger so that you get more bang for your buck when popping it (this is the flipside of the noise trader risk in Brad's paper; there, the danger was that it would get bigger and bust smaller arbitrageurs).
So anyway, we've established that a Soros-type investor - a monopolist in the provision of arbitrage - will not pop bubbles but will allow them to get bigger. But a single large monopolist of capital is not the typical way in which we think about stock markets. Typically, we assume that there is a very large number of investors on an equal footing. And obviously, if there is an infinity of Soroses, things are very different. If we call the optimum bubble-popping day for the monopolist T*, then if there is a second Soros in the market, he knows that he can get a smaller return, but take it all for himself by popping on T*-1. But a third Soros could pop on T*-3 and so on, until we get the standard Steve Ross view of the world in which the Soroses are competing with each other tooth and nail, and are content to scalp the tiny return they can get by jumping on the market the moment it gets even a tiny bit out of line with fundamentals.
But hang on ... isn't there something a bit funny about assuming an infinite number of Soroses? Well yes. What we're being asked to believe here, is something akin to the "small firm assumption" of perfect competition; that each individual Soros is so small relative to the total community of Soroses that he can't influence the price (can't prop up the market on T*-1 so as to ensure he can be the one to pop it on T*). But this assumption is indefensible. The Soroses are part of the market. It is not consistent to both assume that any given Soros is large enough to be a price maker with respect to the whole market (a necessary condition for him to be a Soros in this model), but simultaneously small enough to be a price taker with respect to a subset of the market (Soroses). This is the logical inconsistency above; if an arbitrageur is big enough to pop bubbles, he won't do so until he's good and ready. And if he doesn't have the liberty to wait until he's good and ready, then he may call himself an arbitrageur, but he's actually part of the crowd.
There is a lot more to this; particularly, I have to deal with the cases where there is neither a monopoly nor a continuum of Soroses, but rather a small number of them interacting strategically. But I am afraid that, Fermat-like, I have to just say that the solution to that problem is truly marvellous, but is slightly to long for the 45 minutes (1321 words, yo JQ) I have allocated to this post.
1Imagine me booing and hissing like the crowd at a pantomime at the mention of these two names ....
posted by the management 7/25/2003 06:50:00 AM
Tuesday, July 15, 2003
Heavy paratroopers
There was a bit of a kerfuffle in the comments section on this matter not so long ago. My dad has now weighed in:
"I know its old stuff now but here's my two pennyworth on falling parachuters. Large persons do indeed fall faster than small ones, but on account of their size rather than their weight. Terminal velocity is reached when the air resistance force becomes equal to the weight. Approximating a person to a sphere of radius a (more appropriate with some than others [yes yes dad you could stand losing a few pounds yourself -- d^2] ) the person's weight is proportional to a-cubed, whereas the air resistance is proportional to a (Stokes Law). As a result, the terminal velocity becomes proportional to a-squared."
This is, as far as I am concerned, the official view of the physics community on the subject. Any physicist wanting to disagree, go ahead, but please be aware that you are disagreeing with Mr Davies Sr and therefore wrong. I am treating the paragraph above as the definitive truth on heavy versus light paratroopers and their rates of descent. If anyone who reads this site is a paratroop or ex-paratroop and remembers falling more quickly than their heavier comrades-in-arms, I might revise this view, but not otherwise (recreational skydivers, keep your views to yourselves).
In semi-related news, I'd be interested in anyone's opinion on the subject of which is more of a stretch; to assume that a person is a rational utility-maximiser, or to assume that he's a sphere of radius a. Actually, from now on, it is probably official policy of this site that homo economicus is spherical, except in contexts where we have to work on the economics of overcrowding, in which case we'll assume he's a cuboid or other tessellating polyhedron.
posted by the management 7/15/2003 09:59:00 AM
Thursday, July 10, 2003
Review corner
Haven't done one of these in a while ...
My current musical obsession is the 1983 recording of Brahms' Violin Concertos featuring Itzhak Perlman and Vladimir Ashkenazy. If you're in a bad mood with the State of Israel (and we all are, from time to time), I heartily recommend it as the best kind of evidence that the original Zionist dream of creating a state (and specifically a socialist state, something unaccountably forgotten by non-Israeli Zionists) was at its heart motivated by the best kind of aspiration.
An actual violinist could presumably explain to me how it is that Perlman's tone seems to be so much fuller and more rounded than any other violinist I've heard; it's almost like Jacqueline du Pre's cello at points in the Brahms recording. I suspect that it might have something to do with the painstaking recording done by good old EMI back in the days when people spent money on this sort of thing, or even that there is something to do with the fact that he plays sitting in a wheelchair rather than standing. But lying back with a glass of wine and listening to the confident, lubricious, opening section of the Second Concerto, I couldn't help hearing it as the sound of a Jew at ease with himself. Perlman was born and grew up in Israel; he was three years old when the State was formed; unlike almost any other great Jewish musician you care to mention, he didn't have the diaspora experience. The contrast with his accompanist's approach to Romantic piano playing is extraordinary; Ashkenazy was a Soviet Jew and he approaches the piece with massive nervous energy; he always seems to be pushing the piece frantically forward. Perlman is sitting back and relaxing, letting Ashkenazy wear himself out doing the heavy lifting while savouring the warm, open melody for himself. You can clearly hear that one of these men has got demons and the other one hasn't. Although I have very little time for most of the things that the Israeli government does, particularly when Likud are in charge, the truth has to be recognised that this music could not have been produced if the Jewish people were still living as guests and squatters everywhere in the world. And for this reason it reminds us not to always judge them too harshly when they fight like tigers to protect something that they lacked for a very long time.
On a similar theme, my other current musical obsession is "The Soul of Mbira: Traditions of the Shona People". It's a reissue of a 1970s anthropological recording originally titled "Traditions of the Shona People of Rhodesia" and it's fantastic. The mbira is a thumb-piano, made out of strips of metal that vibrate when plucked and placed inside a large gourd which acts as a resonator. It's a sort of deep guttural sound halfway between a stringed instrument and a xylophone or marimba and the music played on it is astonishingly complex in its polyphony. It's a somewhat humbling experience to listen to it if you're white, and particularly British, as the sleeve notes to the reissued edition tell us that several of the players featured were executed in the revolution which brought independence to Zimbabwe. But more than that, it is a racing certainty that some time in the nineteenth century in Africa, the British put a genius of the calibre of Beethoven onto a slave ship and didn't even realise we'd done it.
Finally, I'll briefly point out that if you liked the Norah Jones album, a) you sad cliched thirtysomething bastard and b) you will find that you like Eddi Reader Sings The Songs Of Robert Burns (with the BBC Scottish Orchestra and various Jock musos) much better. Trust me on this one. One of my minor magical powers is "music retail luck", in that I can walk into a record shop and I don't need to look at what I'm buying in order to know that it's going to be both unusual and good. I would normally have recoild in revulsion from this one because a) Scottish (minus a few points) b) Robert Burns (minus a few more, though I must say I'm warming to him) c) Eddi Reader has known form with both "folk" and "jazz" music d) the cover photograph has a rather alarming chin sticking out of it. But I actually picked it up by mistake while reaching for the CD behind it, and when the universe hands you something, it's usually a good idea to buy it. I must say I didn't regret it; it's a great record. As I say, trust me on this one.
Tomorrow, books ....
Update: Askenazy and Perlman play the Brahms Violin Concertos? Sonatas, you bloody idiot.
posted by the management 7/10/2003 11:59:00 AM
Crooked Timber
I'm a terrible academic groupie, as you might guess from the posts below. I really would have loved to have had a career as a prof; the only thing that stopped me was the realisation that it would involve being financially dependent on my parents for another three years. So I'm really quite chuffed to be joining Crooked Timber, the new group blog that's setting the world on fire. I think I'm the only person there who doesn't work for an academic institution. They're all frighteningly highbrow, which is why I decided to come out all guns blazing with a post more or less entirely made up of obscure literary references to Jorge Luis Borges. In all honesty, it might have been a bit more impressive if the references hadn't all been to stories in the same Penguin anthology, but I think I got away with it.
I'll be keeping D2D going at roughly its current rate of (in)frequency of posting, however. For one thing, it can only be a matter of time before I get found out and chucked out of the Crooked Timber gang. For another, there are a fair few things I like doing that wouldn't really fit in there because they're too long, contain obscene language or excessive facetiousness, or are only concerned with personal hobby-horses of mine. And also because I'm incredibly vain.
Everyone who likes this weblog will like Crooked Timber much more. If you're worried about the number of weblogs you find yourself having to keep up with, might I suggest that Matthew Yglesias' site has begun to suck a bit recently and is probably the best candidate for pruning from your bookmarks.
posted by the management 7/10/2003 10:52:00 AM
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