August 11, 2004

Marty Weitzman Is *Much* Smarter Than I Am

Marty Weitzman is smarter than I am:

This paper attempts to shed light on the equity-premium, risk-free-rate, and excess-volatility puzzles by rooting all three issues together deeply into the core structure of Bayesian statistical inference. The basic idea of the paper is that a seemingly innocuous change in the specification of uncertainty from classical to Bayesian can have very powerful effects on this family of risk aversion issues because it is capable of fattening critically the tails of the posterior distribution of future growth rates. The paper shows how a transition from a model based on stochastic uncertainty to a model based on statistical uncertainty can increase significantly the properly-calculated value of the equity premium while simultaneously decreasing significantly the value of the properly-calculated risk-free interest rate.

To convey the essential statistical insights as sharply as possible, the simplest imaginable specfication.... two time periods... pure endowment-exchange economy... lognormal future endowments... single utility function... isolelastic.... The most striking result... as the modeler makes a simple continuous transition... from stochastic Gaussian towards statistical Bayesian... the equity premium increases without bound, while the risk-free rate simultaneously decreases, also without limit... the basic insights have broader application...

Martin Weitzman (2004), "The Bayesian Equity Premium" (Cambridge: Harvard University xerox).

This is brilliant. I should have seen this. I should have seen this sixteen years ago. I *almost* saw this sixteen years ago.

Posted by DeLong at August 11, 2004 02:19 PM | TrackBack | | Other weblogs commenting on this post
Comments

What are the implications of this for Dow 36,000?

Posted by: Fabio Lanzoni on August 11, 2004 02:30 PM

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Well, both of you are smarter than I am. Sounds brilliant. Just wish I had a clue what he was saying. If you get a chance, Professor DeLong, I am sure many of us would greatly appreciate a translation.

Posted by: Casey Flaherty on August 11, 2004 02:32 PM

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As a non-economist, all I can say is "Whaaaaaaa??!!!?" Martha, is the Wheel on yet?

Posted by: Cheney's Third Nipple on August 11, 2004 02:33 PM

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Under what "prior"? The fattening of the tails wouldn't seem necessarily be due to Bayesian learning, per se, but due to the choice of the prior...

Was he assuming uninformative priors? If so, improper uniform? or Jeffreys' prior?

I do research on Bayesian uncertainty in the assessment of medical technology. Sounds like I have to get this paper/book!

Posted by: Dave on August 11, 2004 02:36 PM

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Dear Brad,

Please add more from Weitzman as well as DeLong. I wonderful topic.

Posted by: anne on August 11, 2004 02:38 PM

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Electronic version, for pity's sake! All SSRN has is some guff about Icelandic fisheries!!

Posted by: dsquared on August 11, 2004 02:39 PM

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Second thoughts ... hang on a minute. The stochastic Gaussian assumption is not a mere simplifying assumption and changes to it are not innocuous, unless you're prepared to make much, much more fundamental changes to the way you do economics. In particular, if you're going to take a Bayesian approach to the uncertainty in returns, then it strikes me that you're not going to be able to make anything like as much use of dynamic programming methods as today's economists are habituated to. I don't see how this sort of idea can be fit into anything which resembles a CAPM framework at all. Which I'd say is all to the good, but I'd really like to see the paper.

Posted by: dsquared on August 11, 2004 02:45 PM

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why can't I get the phrase..."lies, damn lies, and statistics" out of my head now?

Posted by: p. lukasiak on August 11, 2004 02:45 PM

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What D^2 said. I'd really like to see the paper. "Xerox" ?! They pass around Xerox and don't put it online?!

Posted by: Jonathan Goldberg on August 11, 2004 03:01 PM

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"How extremely stupid not to have thought of that!"

Posted by: Paul on August 11, 2004 03:34 PM

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I'm not going to bother paying attention to this new theory until it's been properly vetted by John Crudele and Mickey Kaus.

Posted by: Kuas on August 11, 2004 04:31 PM

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I was thinking that Brad could do a big favor for us non-economists by explaining what exactly is the equity premium etc. etc. puzzle. Fortunately, there are readable references that come up in a google search:

http://economics.about.com/library/glossary/bldef-equity-premium-puzzle.htm
"Definition of The Equity Premium Puzzle: Real returns to investors from the purchases of U.S. government bonds have been estimated at one percent per year, while real returns from stock ("equity") in U.S. companies have been estimated at seven percent per year (Kocherlakota, 1996). General utility-based theories of asset prices have difficulty explaining (or fitting, empirically) why the first rate is so low and the second rate so high, not only in the U.S. but in other countries too. The phrase equity premium puzzle comes from the framing of this problem (why is the difference so great?) and the attention focused on it by Mehra and Prescott (1985);"

OK, that's clear enough. At least I understand what the big deal is all about. I need a substantially better appreciation of Bayesian statistics to appreciate Weitzman's insight.

Now if I could only read "fattening critically the tails of the posterior distribution" without picturing a voracious Gila Monster (a type of lizard, not actually a monster) gorging on Bayesian statistics in anticipation of the winter when it supposedly "lives off the fat it has stored in its tail during the warmer months" (http://centralpets.com/pages/critterpages/reptiles/lizards/LZD5833.shtml)


Posted by: Paul Callahan on August 11, 2004 05:13 PM

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Brad or DD

Pleeease help with the understanding!

Posted by: Terri on August 11, 2004 05:29 PM

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I have learned over at Crooked Timber that sometimes it s better to keep quiet and watch, and maybe google a little. Brad D is not going to catch you up on his 16 years or whatever of economic thought in a few posts. Anyway, I'm too busy trying to understand Condorcet voting and the Sen Paradox this week to spend my time on the likes of this.

As a Joyce fan, I am used to not understanding a word of what I read, and just enjoying the musical rhythyms of the jargon.

Posted by: bob mcmanus on August 11, 2004 05:45 PM

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Quick, forward it to Donald Luskin.

Posted by: Mike on August 11, 2004 05:47 PM

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There are times for an explanation or for the source, so we can learn. That is what Brad is about.

Posted by: Terri on August 11, 2004 05:50 PM

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In latin please?

Posted by: Palolo lolo on August 11, 2004 05:53 PM

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OK, a few comments to at least define terms.

"Equity risk premium". This is the excess return that you should anticipate if you choose to own risky assets (as a class) rather than risk-free assets (as a class, although obviously any two risk free assets have the same return in all states of the world, so it makes no odds to suppose that there is only one risk free asset). Some version of the equity risk premium appears in any theory of equilibrium in capital markets, because it tells you what rate of return the class of risky assets earns in equilibrium. Despite the name, it doesn't just mean equities, but various hack econometricians estimate it as if it does.

"Equity risk premium puzzle". Basically, if you want to estimate what the equity risk premium *is*, then one seemingly sensible thing to do would be to assume that markets in the past have been kinda-sorta efficient (or at least, kinda-sorta in equilibrium), and that therefore a good estimator of the equilibrium ERP would be the actual rate of return earned by risky assets in the past (which hack econometricians proxy as the rate of return on the S&P500, hence the name), minus the "risk free rate" (which hack econometricians proxy as the interest rate on 10 year government bonds, despite the fact that you can get your face ripped off trading this "risk free" asset).

Anyway, the "puzzle" is that even if you aren't a hack econometrician, and you take care to the nth degree to estimate a realistic rate of return on risky and risk-free assets in the past, you get a number for the equity risk premium which is *much* too high. Specifically, if we assume that capital markets have been in equilibrium even most of the time in the past, then the premium earned on risky assets would imply a level of risk aversion in the general population which is completely inconsistent with everything else we know about economic behaviour (in particular, it would imply utterly implausible money demand equations).

The "risk free rate" puzzle is similar; the realised risk-free rate in the past has turned out to be much too low relative to everything else we know about time preference. Personally I regard the RFR puzzle as a bit of a joke; the very fact that people are in the business of statistically estimating a "risk-free" rate of interest shows that it wasn't risk free. I've always assumed that it was the result of serious misspecification of all past estimates of the ERP, but some people more knowledgable than I take the problem seriously.

The "excess volatility puzzle" is simply the fact that in equilibrium or efficient markets, prices ought to represent a coherent expectation of the present value of future dividends. If they are, then the mathematical definition of the term "expectation", which matches up quite well to its everyday use in most other contexts, suggests that (by something called Jensen's Inequality) stock prices should not be more volatile than the dividends which they forecast. But they are, big time.

So we're left with the unpalatable (and not mutually exclusive) possibilities that capital markets are almost always out of equilibrium, that stock market investors are utterly unlike the general public, that expectations in financial markets have very little to do with the mathematical concept of an expectation, or that all econometric work on financial markets is seriously flawed. Hence, this is one of the *big* ones in financial economics.

"Bayesian versus classical statistics" in this context. Basically, the assumption of classical statistics (which I think is what's meant by "stochastic Gaussian" in this sense) is that there is, out there in the Platonic realm, an actual Equity Risk Premium, but that we can only see the shadows it casts on our cave wall, and so when we do statistics, we are attempting to strip away the variance and get a consistent estimate of the actual value of ERP; the variance in the data is a measure of our confidence in that estimate.

Bayesian statistics, on the other hand, treats the ERP as being itself a random variable with a mean and variance, and sees our job over time as being to estimate both the mean and variance of that random variable.

It is possible (and the sonic boom you just heard was me reaching the outer edge of my training) to get statistical techniques which are mixtures of the two; as in, the ERP is a variable with a mean and variance, but we only observe both of them with noise. That seems to be what the last quoted paragraph is driving at. I *think*.

Weitzman is also unlikely to be blowing smoke when he says that "the basic insights have broader application". As I hinted above, this sort of thing matters for money demand functions and all sorts. If he's come up with a sensible and soluble way of modelling behaviour under uncertainty (the old "unknown unknowns"), then this is very big stuff.

please note the time of day in London, and make allowances for the incoherence above, btw.

Posted by: dsquared on August 11, 2004 06:16 PM

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I think that the fattening-of-tails bit relies a little too much on third-derivative conditions for my liking. But the approach is interesting and just starting to become popular with good reason--Woodford and Sargent have been working on this sort of stuff in their own complicated ways.

This hits pretty close to home because it relates to a research topic that I'm pursuing. Don't spit coffee out of your nose, dsquared, but it involves doing dynamic programming taking these expectations as, well, what people actually expect, rather than assuming certainty about the present state of the world. This could lead to, among other things, slow learning and excessive skepticism on the part of agents. It would lend some truth to the idea that recessions are times of uncertainty and confusion.

The interesting questions at this point are empirical. This sort of thing might not explain very much, or it could explain all sorts of things like autocorrelation and heteroskedasticity in financial returns as well as business-cycle propagation. The interesting questions here are empirical, not conceptual.

Brad, this isn't an issue of intelligence. The fact that all sorts of people are developing this technique independently now but not before seems to indicate that there's a deeper reason for this. What we now call rational expectations has run its course with seriously mixed results. Nobody could have predicted this thirty years ago when dynamic stochastic general equilibrium models were just becoming part of the average grad student's toolkit. This stuff is so computationally intensive that it took a generation to sort out basic results.

Also, certainly here at UCSD, there seems to be a mathematical arms race. Students are encouraged to take large doses of probability theory but no history. Insert teeth-gnashing here.

Time to write Prof. Weitzman and ask for a copy. Sounds like it could be good.

Posted by: Chris on August 11, 2004 06:26 PM

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Marty Weitzman is smarter than you. You're surprised? Marty Weitzman is one of the greatest economists of my generation. He thinks deeply, writes well, and has the gifted economist's sense of what is important. He's exceptional. You know that; I know that. The general public don't know that. He was one of the four horsemen who came to Yale in 1968 or 1969 -- Stiglitz, Nordhaus, Klevoric and Weitzman. What a team! What Yale could have been had they kept them, and Paul Krugman ten years later! Missed opportunities.

Posted by: Knut Wicksell on August 11, 2004 06:39 PM

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To all of you who have trouble with the equity premium, fat tails of distributions etc. I recommend Benoit Mandelbaum and Richard L. Hudson's "The (Mis)behaviour of Markets: A Fractal View of Risk, Ruin, and Reward". Basic Books, 2004.

Posted by: Thomas T. Schweitzer on August 11, 2004 06:41 PM

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Chris: I'm sure you know what you're doing, but to me it seems weird to use dynamic programming methods when you're not working backward from a boundary condition.

Brad: Chris has a point. Sixteen years ago there was no such thing as BUGS, so nobody outside Louvain was interested in Bayesian statistics, so nobody was taught it.

Posted by: dsquared on August 11, 2004 06:42 PM

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"Brad, this isn't an issue of intelligence. The fact that all sorts of people are developing this technique independently now but not before seems to indicate that there's a deeper reason for this."

Probably because there has been an explosion of research using bayesian statistical methods in all fields of science, and some of it is trickling into economics. The hard sciences and computer science were the first big users, and the "bayesian revolution" in artificial intelligence has been going on for over a decade now.

Posted by: Ian Montgomerie on August 11, 2004 06:48 PM

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Good exposition, dsquared. Interestingly, the specification issue for quantifiable uncertainty is not so bad--this has been worked out. Google the phrase "Kalman Filter" to see where I would go with this--think of trying to model people's beliefs over nonstationary and maybe nonergodic parameters like productivity or money growth rates. In order to run decent simulations, however, we need to calibrate parameters like signalling noise and transition equations, and that's where things get hairy. At least that would force the econometrics to serve the economics, not the other way around. Maybe a little too ambitious.

There's also a bit of an infinite-regress problem here but that's one of the lesser problems compared to the econometrics. Basically, if people can be uncertain about parameters, they can be uncertain about parameters that govern these parameters, and so on.

On the whole, I'm excited about this new economics of confusion. Being a bit freshwater myself, I'll hold off on the congratulations until someone shows me some interesting quantitative results.

Posted by: Chris on August 11, 2004 07:00 PM

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Gee, so no one has a sense of humor? I think there may be, well, just a teensy weeny bit of irony in Brad's set up.. The equity premium will be explained (if atall) by a combination of experimental economics and evolutioooonary [whoops, too much Shiraz] psychology..!

Posted by: Roland Stephen on August 11, 2004 07:42 PM

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My brain hurts... I wish I could add something intelligent here, but I am a free loading lurker right now :) Thanks guys!

Posted by: fester on August 11, 2004 07:43 PM

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As a non economist who is a fan of Mitchell Waldrop's "Complexity", the Santa Fe Institutes "The Economy as an Evolving Complex System" and Aristotles "Nicomachean Ethics", I paraphrase a quote from the later. "Do not measure with a micrometer what you will cleave with an ax".

If this post by Brad is not a joke, it is the biggest waste of intellectual talent since the brilliant scholars of scholasticism explained the Trinity.

Sam

Posted by: Sam Taylor on August 11, 2004 07:47 PM

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No it's not (and, btw, nor was scholasticism). If there is a good explanation of the ERP here, then it has all sorts of implications for capital budgeting, government versus private provision of services and just about any matter related to investment you can think of. If the key conclusions have general application as a method of modelling expectations, the sky's the limit.

If, on the other hand, it's a dead duck, then how disappointing.

Posted by: dsquared on August 11, 2004 08:07 PM

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What reasons do we have to believe capital markets are in equilibrium?

Equilibrium works in the hard sciences because we're dealing with partition functions of O(10^23) particles, and the fewer the particles, the greater the fluctuations.

During the 20th century, all it took was some diplomatic failure between O(10^1) state actors to produce the WWI-depression-WWII sequence, which may have hammered equity investors, but ripped the faces right off of "risk free" security holders.

Posted by: Dave on August 11, 2004 09:00 PM

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Dear dsquared-

You are right about scholasticism. Many aspects of this discipline were not a waste and helped establish the basis for muddling through to what have turned out to be better insights into how the world works.

As one who was struggling with the Ibbettson-Sinquenfeld data 25 or so years ago, I have trouble believing that there is not some uncertainty surrounding the ERP ( which I presume means Equity Risk Premium). If one believes that the ERP trends to infinity while the Risk Free Rate (RFR?) trends to zero, would one make different policy choices than if we thought the ERP was about 3%? (I incidentally believe that this description is probably fairly close to accurate since otherwise there is no one to borrow but the distinction is trivial. The compounding of the difference has always been huge.)

What policy does one change as a result of this miracoulous insight? Do you believe as Stephen Pinker does about the insights of evolutionary psychology that they are so precise as to be "like gravity"? What would you do differently if some God suddenly revealed to all of us that these insights were "true"?

In short, if Brad's post is not a joke, I have no reason to dispute the math. In the interim, if you have not read those much more informed (and smarter) than I about the assumptions made by many academic economists as theories are formed, you might enjoy the books I referenced in my earlier post.

Cordially,

Sam


Posted by: Sam Taylor on August 11, 2004 09:27 PM

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D^2: "capital markets are almost always out of equilibrium, that stock market investors are utterly unlike the general public, that expectations in financial markets have very little to do with the mathematical concept of an expectation, or that all econometric work on financial markets is seriously flawed."

What about your description of the "general public"?

Posted by: Mats on August 11, 2004 11:40 PM

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For instance - a "general public" experiencing relative utility from their income could generate quite some equity volatility. If the Joneses buy or sell, you have to as well, just for hedging.

Should one ever be puzzled when puzzles arise in economics? Shouldn't one really be surprised when economics actually explains things out of its highly idealized set of assumptions?

Posted by: Mats on August 12, 2004 02:21 AM

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“...fattening critically the tails of the posterior distribution of future growth rates” : In English, does this mean that sane investors have to worry about all old-company profits tanking and their whole portfolio becoming as worthless as Antonio’s in the Merchant of Venice?

“..the risk-free rate simultaneously decreases, also without limit” : so investors in the model can’t be sure of keeping even one cent in the dollar? Shades of Germany in 1922.

This is fun even if you don’t understand a word.

Posted by: JamesW on August 12, 2004 03:38 AM

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My suspicion is that "the equity risk premium increases without limit" and "the risk-free rate decreases without limit" is the model's way of telling us that in a purely Bayesian world these concepts don't really make sense. But, I reiterate, I haven't read the bloody thing.

Posted by: dsquared on August 12, 2004 04:25 AM

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"or that all econometric work on financial markets is seriously flawed"

We Have A Winner!!!

When the real world is wildly at variance with your theories, junk the theories and start studying the real world. Instead of starting with a blue-sky (I'm tempted to say "rectally-extracted") theory, then building a mathematical fortress around it, then tinkering with the fortress because it doesn't really describe reality (which is the way economics is usually done, and what's going on here), why not start WITHOUT a theory, examine the real-world data, and let it TELL you what's going on.

That's the difference between sciences (Physics, for example) and pseudo-sciences (Economics springs to mind). When a physicist propounds a theory, it's to explain observed phenomena. WHen an economist does, it's to foster some pet idea.

Posted by: Chuck Nolan on August 12, 2004 04:48 AM

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When a physicist propounds a theory, it's to explain observed phenomena

Have you had a look at the arXiv recently, Chuck?

Posted by: dsquared on August 12, 2004 05:14 AM

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No, dsquared, my course work does not allow me time for much else.

But I stand by my comments. I just finished a paper for my PhD on Friedman and the Chicago school. Admittedly, he's an extreme example of this phenomenon. But every econ book I've read, every paper I've seen, and every professor I've quizzed all exhibit these same symptoms. A theory is propounded in space, purely by intuition, and then tinkered with because it doesn't match real-world observations. Much better to START with real-world observations, and construct a theory to explain what has been observed. That's what physics does, in general, and what economics does NOT do.

I believe the term is Ricardian, but that's from memory and since I'm at work I'm trying to do two things at once, here.

Posted by: Chuck Nolan on August 12, 2004 05:36 AM

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Isn't it a corollary to Godwin's Law that as soon as someone involved in a scientific or technical debate mentions philosophy of science, then the conversation is over and that person loses?

Posted by: JO'N on August 12, 2004 05:56 AM

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yo -wheres the paper?

Posted by: mickslam on August 12, 2004 06:16 AM

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Mo one starts

WITHOUT a theory, examine the real-world data, and let it TELL you what's going on.

because it's not possible. There is a large literature on this. Francis Bacon started it with the comment "Truth emerges more readily from error than from confusion." I don't agree with much else he said, but he nailed it with this one.

Posted by: Jonathan Goldberg on August 12, 2004 07:28 AM

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in re the "equity premium puzzle"

Before Inflation 1901–2000 1801–1900
Stocks 9.89% 6.51%
Bonds 4.85% 4.99%
After Inflation (Real Return)

Stocks 6.45% 6.76%
Bonds 1.57% 5.23%

The 20th century saw an exceptionally high level of inflation, both in the U.S. and globally. Fixed-coupon investments thus under-performed profit-linked investments for much of the century. In the 19th century, which saw no overall inflation, stock and bond real returns were much closer. Equity out-performance in the 20th century is not necessarily due to an unexpectedly high equity risk premium.

NM

p.s. Most people use the CRSP/Ibbotson's data for asset class returns, but there were markets around before 1926.

Two sources of older returns data:
The 2004 Ibbotson's SBBI Yearbook
Bill Bernstein's "Efficient Frontier"
(from whence the figures quoted above)

http://www.efficientfrontier.com/ef/402/index402.htm

Posted by: Nicholas Mycroft on August 12, 2004 07:56 AM

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I'd like to tell a story and see if it relates.

You have a long-term investment to make, you won't need the money for a long time and you don't want to churn it and pay fees. You can put it into bonds or into a diversified basket of stocks.

On average in the past the stocks have paid off much better, but there's a lot of variation in how well they pay off. That's OK, if you measure the historical data and get a mean and variance for the past performance, you can see whether that amount of performance is worth that amount of risk to you. Assume a lognormal distribution and you're set.

But if you think a little more, the stocks aren't independent. The whole economy has good years and bad years, so the variance in the result you're likely to get down the road is bigger than the variance in past performance of stocks. The market might go bad for years at a time, and most of your stocks then would do worse than expected.

Even worse, the performance might appear to fit a lognormal distribution but if you think about it, your basket won't represent the whole market. I'll simplify it and talk like companies have three modes. They can be in exponential growth mode. Or they can be in stasis, where they make decent profits on average but they aren't really doing anything. Or they can be in a slow death phase. (Or not so slow.) If you pick stocks for a long term, you'll get some that are in exponential growth -- but how long will they keep growing? You'll get some that are in stasis, and those are more likely to die than to go exponential. So at any given time the economy has a few companies that are growing fast, and a lot that are stable. Pick a bunch of existing companies and you won't do as well as the market because a lot of the ones that go into exponential mode will be new companies that weren't even around when you made your choices. And if you keep buying and selling to pick the good stocks, you're likely to catch them at high prices just as they're slipping into stasis again. The companies that just keep growing for a very long time like IBM are rare. Average a few companies growing exponentially with a larger number of companies that are declining logarithmically and it will come out a nice growth; the more any one loser loses the less effect it will have on the averages. But that doesn't tell you how to pick the rare good ones.

So pick a stable stock and it's unlikely to go exponential, it's more likely to go bad. Pick an exponential stock and it's likely to go stable or bad. Pick a bad stock and it's likely to die. Exponential stocks are more likely to come from new companies than otherwise, but they're rare among startups too.

Fat tails. To do as well as the market over a long time you need to pick some exponential companies early, and they're rare. Unless you really know how to pick them, it's hard to do as well as the market without sampling all the good candidates. The stocks you pick will on-average not be as good as the average, because a few IBMs will bring up the average too much.

So, people look at how much the stock market has improved since 1933 and say if you'd just bought stock then and held onto it.... And if you had, you'd have Union Carbide, Penn Central, US Steel, etc. Stocks that look safe for short times are very likely to do badly in the long run. They have a niche, they're much more likely to go bad than to get into a new niche where they can expand quick. But anything else you pick is also more likely to go bad than to be the rare one that brings up the average a lot. It's Gambler's Ruin all over again.

The problem comes from assuming an undifferentiated lognormal distribution and then supposing you can get average performance.

I think if I wanted to model the stock market along those lines, I might rather assume that companies have lifetimes, and my first stab at a distribution for that might be a Weibull. I'd look at the Weibull parameters and see if I could fudge them into exponential growth, stasis, and decline. And then....

Chuck, that isn't what physics does either. Physicists started out making math that described what they saw, yes. Their model was what they saw. But pretty quick they got away from seeing and they started making models and trying to fit them. The heliocentric model didn't work with circular orbits so they tried ellipses. The model came first, and they eventually hammered it into shape to fit the data. The trouble in economics is that it's harder to get reliable data. Like, it's very hard to control for independent variables.

That might be possible. Like, you could give money to experimental subjects and put each of them alone in a featureless room that has a vending machine full of various things at various prices, and see which things they buy knowing that they'll lose both their purchases and their money in a few hours when the door opens. Study buying behavior with lots of independent variables controlled. Maybe you'd learn something that way that would apply to real life.

But as it is, economists *know* that complex interactions are important, they know that the very simple models don't work, but it's very hard to measure the parameters for the complex models.

Life is hard.

Posted by: J Thomas on August 12, 2004 08:13 AM

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The 19th vs. 20th century difference seems a classic issue of risk vs. uncertainty. With the possible exception of the bit of bayesianism currently under discussion, I haven't seen economics ever actually deal with uncertainty, just with risk (mind you I Am Not An Economist).

To put it simply using extreme examples, risk is "will this coin come up heads or tails?" and uncertainty is "will the dollar still be the dominant currency in 100 years"?

Risk happens when you don't know what will happen, but you know the probabilities. Flip a coin and you don't know whether it will come up heads or tails, but you know the chances of each. When dealing with risk, you either know the exact probabilities involved or can come up with pretty good guesses (guesses which will be within some predictable boundary of the real answer), and so you can very precisely balance the risk vs. reward of various choices and figure out what gives you the best expected returns. There is a huge body of math available to analyze risk.

Uncertainty is when you don't know what will happen and there's no clear way to figure out what the chances are. Ultimately something will happen or it won't, something is true or it isn't, but uncertainty occurs when you simply don't have the means to figure it out accurately. How, for example, would you calculate the probability of the US dollar being the dominant currency in 100 years? How could you possibly attach a probability to the chances of the Euro being dominant vs. the chances of China or India getting the dominant currency in the very long term vs. the chances of a massive meteor strike or nuclear war causing a huge realignment in global politics vs. intelligent robots taking over the world and doing away with the concept of currency? You don't - the real answer depends on information about the future that is simply beyond our knowledge. We can guesstimate based on some of our current knowledge - that so far dominant currencies have come from wealthy trading nations, and there are certain trends we can see that may change the relative ranking of those nations in the future. But there are also other major trends that will be important in the future, but are still completely invisible to us.

This creates a huge problem for economists studying long term investment, a problem which as far as I can tell is usually pushed into a corner and ignored because it's very hard to deal with mathematically or in any other way. Try taking the historical perspective for a moment. In 1900, who the hell knew what the world would look like in 1950, let alone 2004? Absolutely nobody. Who had an inkling of what it would look like in 1925, in the aftermath of the First World War? Also nobody - a few people may have expected a brutal general war (though I don't specifically know of any, and from my knowledge of history, most never would have imagined it), but even prescient Cassandras couldn't predict specifically what the shape of the world political system and economy would be in the aftermath of it.

So how do you model informed investment decisions over the long term, when it's an obvious fact that the long term behavior of the market may completely defy expectations?

If you're most economists, you assume that out-of-the-blue uncertain events like the World Wars simply never happen, from the perspective of your theory.

And bayesian modeling isn't some immediate magical answer to this. The problem of uncertainty is that instead of the current economic theory (where we have an idealized conception of how the market should act, and economists try and encourage people to adhere more closely to it), it produces a reality where there is no idealized answer, and all you could do is study what causes people to actually make decisions without having a convenient universal "rational answer" to compare it to.

For example, people probably make investment decisions informed by the lessons of the recent past (especially the past few decades). They can look at 20th century stock and bond returns because those are not too hard to find in economics texts. Someone looking into specific fund classes, on the other hand, may only have a few decades of data to go on, because precise segment-by-segment market information isn't even available for the whole 20th century. And even then, their methods tell them to treat price variance within this region as establishing a risk around a certain level of average return.

But no matter how precise the calculations, this is all nothing more than a seat-of-the-pants guesstimate, because the underlying economic landscape can undergo dramatic sea changes due to uncertainty. As Nicholas Mycroft pointed out, one of the big risks for bonds is what the level of inflation would be. Inflation isn't a random variable, but neither is it all that predictable in the long term - it has depended on political events that are difficult to predict. So if you want to guess stock vs. bond returns in the next few decades, what data do you use? Returns in the last 20 years? The last 100? The last 200? You'll get very different answers in each case. But there is NOT any good reason to expect that the longest-term answer is the "right" one. It's not like getting more samples to more accurately measure one underlying probability. A lot of that data involves the gold standard, so it's not particularly relevant to an era where we don't expect the gold standard to return. The most recent data is in fact produced by circumstances that are probably most similar to what we can expect in the near future - but then again, there might be some great political change that we can't predict. Terrorists might nuke somebody and spark events plunging the world into a new depression. What's the risk of that? Who knows?

Posted by: Ian Montgomerie on August 12, 2004 08:49 AM

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I don't want to thread-jack the good professor's bandwidth any further than I already have. Is there a more appropriate forum where issues of this type are being discussed?

I believe I'm not quite explaining exactly what I mean, and I believe what I mean is a quite valid criticism of economics and the application of mathematics thereto. I dopn't really have time to construct the argument correctly, because I'm at work now, but I would like to make this argument when I do.

In fact, at one time it was a dissertation candidate for me. I believe it would have been a winner.

Posted by: Chuck Nolan on August 12, 2004 09:12 AM

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For clarity, I'll add a quote from Bill Bernstein (who I suspect may be as bright as Marty Weitzman)--from the article I referenced above:

"With hindsight we can see that the 5% stock-bond return gap in the 20th century was the result of a totally unexpected inflationary burst produced by the abandonment of hard money. You can’t abandon hard money twice, so a repeat is not possible. Though inflation might increase dramatically in the future, resulting in another high stock-bond return gap, it’s at least as likely that inflation will remain tame for the foreseeable future, producing nearly equal stock and bond returns. More importantly, we now live in a world where investors have learned to extract an inflation premium from bonds and to expect inflation protection from stocks. This increases expected bond returns and reduces expected stock returns."

I'd add "massive government indebtedness due to the unanticipated costs of wars that required total or near-total economic mobilization" as a cause of 20th-century inflation, but other than that, this makes sense to me.

NM

Posted by: Nicholas Mycroft on August 12, 2004 09:14 AM

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DD

You are terrific. I am thinking through each points. Thank you for these most careful posts.

Posted by: Anne on August 12, 2004 09:33 AM

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Just wanted to second Anne and others' comments on dsquared. Brad's excerpt was nearly incomprehensible to me, but after dsquared's explanation, I feel I understand the basic puzzle and maybe even why it makes a difference if you used classical vs. Bayesian statistics (the part about ERP being treated as a random variable as opposed to an unknown constant to be determined).

Posted by: Paul Callahan on August 12, 2004 11:21 AM

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Brad is lying again. Everything he writes in the post is false false false. Brad is much smarter than Weitzman and he did see this sixteen years ago. My source on any stock price goes if people are Bayesian is Barsky and Delong "why have stock prices fluctuated" Pdf available on this web page.

For shame Brad, you have slandered yourself. Now I note you posted an e-mail from Donald Luskin's lawyer threatening to sue Donald Luskin for slander so you are familiar with the issue.

Posted by: Robert Waldmann on August 12, 2004 12:38 PM

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Chuck Nolan wrote, "Much better to START with real-world observations, and construct a theory to explain what has been observed. That's what physics does, in general, and what economics does NOT do."

Wasn't there a meeting of physicists and economists, where the physicists thought the economists were too close to their equations/models and too far from their data?

I think Brian Arthur (?) was there. Maybe also Philip Abelson (who died the other day).

Posted by: liberal on August 12, 2004 01:11 PM

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Chuck Nolan wrote, "Much better to START with real-world observations, and construct a theory to explain what has been observed. That's what physics does, in general, and what economics does NOT do."

Wasn't there a meeting of physicists and economists, where the physicists thought the economists were too close to their equations/models and too far from their data?

I think Brian Arthur (?) was there. Maybe also Philip Abelson (who died the other day).

Posted by: liberal on August 12, 2004 01:14 PM

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Chuck Nolan wrote, "Much better to START with real-world observations, and construct a theory to explain what has been observed. That's what physics does, in general, and what economics does NOT do."

Wasn't there a meeting of physicists and economists, where the physicists thought the economists were too close to their equations/models and too far from their data?

I think Brian Arthur (?) was there. Maybe also Philip Abelson (who died the other day).

Posted by: liberal on August 12, 2004 01:15 PM

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Also you and Weitzman are cheating. Isoelastic utlity is a standard assumption, but it must be subject either to a st petersburg paradox or the opposite (burgpetersaint paradox). With isoelastic utility happiness can go either to infinite (crra 1) or both (logarithmic). This is crazy.

If people aren't infinitely excited about a 1 in a trillion chance of being very very risk or infinitely afraid of a 1 in a trillion chance of personal bankruptcy, the tails can not be so critical.

In effect the isoelastic assumption is roughly universal and totally crazy. Only with something like lognormality (log has a distribution with a finite variance) does it make any sense. Bayesian means that the posterior on resolutions (distribution of outcomes integrated over posterior on paramters) is not log normal.

For any distribution of value of stock with positive weight on 0 you get an infinite risk premium. Does this make sense ? How much were russian shares worth in 1920 ? yes it makes sense. Rational people with isoelastic utility crra > 1 would buy a balanced portfollio of gold and other durable goods of real value and bury it in a hidden location.

The fact that no one does this implies that we don't have isoelastic utility which is obvious to begin with.

Posted by: Robert Waldmann on August 12, 2004 02:18 PM

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i have just started working for a major investment bank, and during training last week we learned that most financial markets exhibit high kurtosis (leptokurtic lognormal returns). i think that one explanation for these "fat tails" is the impact of block trades (e.g. Putnam decides to liquidate a large position in IBM, moving the price more than the "efficient markets hypothesis" would suggest).

given that the marginal investor is aware of the leptokurtic distribution of lognormal returns of risky assets, can this serve to explain a portion of the observed equity premium? or is there some math that i'm not thinking about that essentially reduces this situation to the same puzzle?

Posted by: noto on August 12, 2004 07:07 PM

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i have just started working for a major investment bank, and during training last week we learned that most financial markets exhibit high kurtosis (leptokurtic lognormal returns). i think that one explanation for these "fat tails" is the impact of block trades (e.g. Putnam decides to liquidate a large position in IBM, moving the price more than the "efficient markets hypothesis" would suggest).

given that the marginal investor is aware of the leptokurtic distribution of lognormal returns of risky assets, can this serve to explain a portion of the observed equity premium? or is there some math that i'm not thinking about that essentially reduces this situation to the same puzzle?

Posted by: noto on August 12, 2004 07:09 PM

____

i have just started working for a major investment bank, and during training last week we learned that most financial markets exhibit high kurtosis (leptokurtic lognormal returns). i think that one explanation for these "fat tails" is the impact of block trades (e.g. Putnam decides to liquidate a large position in IBM, moving the price more than the "efficient markets hypothesis" would suggest).

given that the marginal investor is aware of the leptokurtic distribution of lognormal returns of risky assets, can this serve to explain a portion of the observed equity premium? or is there some math that i'm not thinking about that essentially reduces this situation to the same puzzle?

Posted by: noto on August 12, 2004 07:10 PM

____

i have just started working for a major investment bank, and during training last week we learned that most financial markets exhibit high kurtosis (leptokurtic lognormal returns). i think that one explanation for these "fat tails" is the impact of block trades (e.g. Putnam decides to liquidate a large position in IBM, moving the price more than the "efficient markets hypothesis" would suggest).

given that the marginal investor is aware of the leptokurtic distribution of lognormal returns of risky assets, can this serve to explain a portion of the observed equity premium? or is there some math that i'm not thinking about that essentially reduces this situation to the same puzzle?

Posted by: noto on August 12, 2004 07:10 PM

____

i have just started working for a major investment bank, and during training last week we learned that most financial markets exhibit high kurtosis (leptokurtic lognormal returns). i think that one explanation for these "fat tails" is the impact of block trades (e.g. Putnam decides to liquidate a large position in IBM, moving the price more than the "efficient markets hypothesis" would suggest).

given that the marginal investor is aware of the leptokurtic distribution of lognormal returns of risky assets, can this serve to explain a portion of the observed equity premium? or is there some math that i'm not thinking about that essentially reduces this situation to the same puzzle?

Posted by: noto on August 12, 2004 07:12 PM

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sorry about all the posts. i blame IE.

Posted by: noto on August 12, 2004 07:15 PM

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Ian,
The difference between risk and uncertainty
HAS been considered by economists, in particular
Nicholas Kaldor. But you're right, it has been
mostly ignored for a long time though it's making a bit of a comeback (Mark Machina's work in
particular - one of the implications seems to
be that the two concepts are not as seperable as
you seem to suggest). It's also
related to the difference between UNCERTAINTY
(close to what you describe as RISK) and AMBIGUITY
(close to what you describe as UNCERTAINTY).
And yes, all this has been applied in the context
of the EPP.


Posted by: radek on August 12, 2004 11:13 PM

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Chuck:"Much better to START with real-world observations, and construct a theory to explain what has been observed. That's what physics does, in general, and what economics does NOT do."

Ah yes, I forgot. Einstein wrote the General
Theory to explain the frequently observed
phenomenon of time travel.

Facetiousness aside, I think you have little idea
of how either economics or physics proceed in
their respective endeavors. And, more importantly,
of the fact that this particular topic has been
a running controvery in philosophy since, oh,
I don't know, Aristotle.
(ok so the facetiousness wasn't really aside)

Posted by: radek on August 12, 2004 11:22 PM

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Correction to the above. I meant Frank Knight,
not Nicholas Kaldor. I always confuse the two.
I should have known though. "Knightian Uncertainty" rolls off the tongue better than
"Kaldorian Uncertainty".

Posted by: radek on August 12, 2004 11:53 PM

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Does Marty only send out paper copies of these things to friends? No electronic version? Inquiring minds would like to see it, if possible without bugging the author.

Posted by: James Galbraith on August 13, 2004 08:10 AM

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Sig. Waldmann, do you mean this paper?

Barsky & DeLong, "Bull and Bear Markets in the Twentieth Century", JEH Jun 90
http://www.j-bradford-delong.net/pdf_files/Bull_and_Bear.pdf

Would "fundamentals felt fads" be a fair summary?

Posted by: Dave on August 14, 2004 12:17 PM

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To amplify a bit on what radek wrote to Chuck...you're right, but not nearly as right as you think you are. The truth of the matter, both historically and from a "philosophy of science" point of view, is that there is a synergy between a priori modeling and empiricism. A strong awareness of the history of science demonstrates this. Many contemporary scientists are unaware of this, and thus have a naive conception of science.

From my perspective, economics, which I think is the most "advanced" of the social sciences, is pretty much following the same historical progression that the hard sciences did. That is, it began with very strong a priori models and assumptions, used them as a lens with which to "discover" empiricism, then subsequently used that empiricism to modify the model. Rinse and repeat. Paradigm shifts occur when big model changes become necessary because the tension between the abstract modeling and empricism become too great.

As someone with very little schooling in economics—so with little credibility—it's my impression that economics is right on the cusp of making the transition that, say, chemistry made between Lavoisier and Dalton. It's about to become what by contemporary standards would be a "real" science. You're too hard on it.

Posted by: Keith M Ellis on August 14, 2004 10:58 PM

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Radek,

Einstein developed General Relativity to explain the frequently observed phenomenon that inertial mass appears to be equivalent to gravitational mass. Just as he developed Special Relativity to explain the newly discovered phenomenon that light has the same speed for all observers.

Posted by: wcomer on August 15, 2004 02:33 PM

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