Bubbles are supposed to be cyclical. Presumable, before the bubble there is a steady state situation, what causes the bubble mechanism to start? On the light side, your model does not take into account that a new sucker is born every minute.

Someone has actually come up with an economic theory on why we have price bubbles:

http://en.wikipedia.org/wiki/Hym...ki/ Hyman_Minsky

Minsky believed that stability bred complacency in financial systems and that this encouraged borrowers and lenders to become ever more reckless.
Minsky's Actual Paper (PDF form)

http://www.levy.org/pubs/wp74.pdf

Another author also wrote something about economic bubbles:

http://www.amazon.com/Dollar-Cri...s/dp/ 0470821027

Duncan that the dollar acted like steroids for economies running large trade surpluses with the US and believe this led to hyperlending and the Asian currency crisis of 1997

Last but not least there is too big to fail:

http://www.amazon.com/Too-Big-Fa...50767678&sr=1- 1

The author of this book believes that financial institutions are inherently reckless because of government guarantees that underwrite reckless behaviour.

Yes I did get a degree in economics but I didn't read any of the aforementioned texts for school and hardly covered any of the issues that the authors raised in my classes.

You may wish to look at some of the results coming out of experimental economics.

How steady state passes into the bubble phase?

Bubbles are supposed to be cyclical.

Right, this model just shows that we can at least get boom-and-bust. I'll bet that if I allow the retireds to re-join the suckers, it will produce cycles. It's like when an epidemic hits, and the people who are recovered and immune eventually lose their immunity and become susceptible to infection again.

Presumable, before the bubble there is a steady state situation, what causes the bubble mechanism to start?

In this model it's an exogenous event. Somehow, a group of people get it in their heads to start speculating in some market. In the early 1990s, there was speculation in comic books. Starting in the late 1990s, they were speculating in houses. Why is it one thing at one time, and another thing at another? The model doesn't try to explain that, only how the dynamics unfold once the initial speculators have arrived.

agnostic,

Retards DO rejoin suckers all the time, because they retired with money from the market, that is, they feel good about their chances to do it again.

Be kind enough to "allow" them to rejoin.

I just checked what happens when we let retireds re-enter the suckers, i.e.:

S' = -aSI + lR

Where l is the rate at which retireds decide to come out of retirement. This assumes that they decide to do so independent of what other retireds are doing, and again ignores price or price trend, which is unrealistic.

It does not produce cycles. Rather, there is a single stable fixed point that has a positive value for both S and P -- meaning that the suckers are never completely used up (now they can be replenished by retireds) and there will always be some degree of price hype. Moreover, if l is less than aI, the price hype will go up and then down, although not to zero; but if l is greater than aI, price hype only goes up to its stable value and never declines. So for some parameter values, this model doesn't even produce a semi-boom-and-bust.

So, even allowing for retireds to get back in on the bubble won't produce cycles in this model. We probably need a more realistic picture where P' affects the rate at which suckers become investors, as well as the rate at which retireds decide to re-join the suckers.

There's a paper by Doyne Farmer, among others, carrying out this kind of modeling experiment in more detail. IIRC, his three groups are fundamental investors, momentum investors and noise investors. The main result was that his market didn't settle down to an equilibrium. And his momentum investors aren't necessarily dummies. There are models in which information about fundamental values percolates down slowly to retail investors and stodgy fund managers. Under those assumptions, the movement of share prices does convey useful information.

The characteristic features of bubbles include the involvement of new players and the use of debt. The sign of new players is the magazine cover indicator in which news magazines at the peak all have covers devoted to real estate, internet startups, etc. So perhaps an epidemic model would provide better insights.

I haven't read Minsky, but the secondary accounts emphasize his point that debt acquired for productive investments is ok, but debt acquired to buy assets with the intent of flipping them is a Bad Thing.

The standard source for the descriptive history is Kindelberger. He has a bestiary of perhaps 200 of these cycles from the GD down to real estate speculation in a single European city. And yes, the tulip bulbs are there.

the magazine cover indicator has been improved on by google search word count and other data mining indices. Not that it did any good in recent housing bubble case.

Let me see if I can summarize your model.

First, you define a system wherein "investors" sell an asset to a pool of "suckers" until the pool of suckers is depleted. Then, you define the (extra) price of said asset to be 0 when the pool of suckers is full, 0 again when it is empty, and positive everywhere in between. Finally, you declare that this system - which is tautologically defined to produce a bubble - produces a bubble. And people wonder why Austrian economists don't like mathematical models?

Not to be rude, I don't think you need to do all this work. The logic behind the greater fool theory is already simple and clear: If Steve thinks he can find an idiot to pay $100 for a $75 barrel of oil, he'll probably buy some oil. If enough Steves are doing this, oil prices will rise. QED. To me, grafting equations onto this logic just distracts from and conceals the logic. Maybe there's some use to this I'm not seeing, but I'm really not seeing it.

I do mean to be rude, and you need to learn more math before you criticize models. It is not built in that there will be a bubble (a boom-and-bust). It happened that way. That's the point of modeling -- sometimes it will turn out that the price will only increase or only decrease from start to finish. It's harder than you think to build models where there is a boom-and-bust, let alone where there are sustained boom-and-bust cycles.

Indeed, earlier in these comments I noted that when we allow the retireds to re-join the suckers, if their rate of leaving (l) is greater than a*I (the leaving rate of investors times the number of investors), we do NOT get a bubble. Price hype only increases to a point where it stays put.

This is why we model -- to see what assumptions about the world can produce what we observe. You can argue among those that can produce real patterns, but we can immediately discard those that cannot produce them.

As an aside, whenever someone uses the word "tautology," the conditional probability that they don't know what they're talking about is high.

I think the implicit question that everyone needs to ask is this: do markets price things properly? That may sound like an easy question but it's underlying assumption that underlies all economic pricing.

For example during the bubble days a few years ago the average median house price in California was $450,000. I think everyone implicitly believed that a house was worth that much. If not no one would have bought a house, because no rational investor will buy something if believes the prices will come down substantially.

I haven't read Minsky, but the secondary accounts emphasize his point that debt acquired for productive investments is ok, but debt acquired to buy assets with the intent of flipping them is a Bad Thing.

This is where ecology and economics in theory converge. One of the unstated assumptions of both is that systems tend to converge towards some sort of equillibrium state. However as a believer of the Medea Hypothesis:

http://en.wikipedia.org/wiki/Pet...paleontologist)

I believe life is inherently self destructive we only have to look at the "oxygen holocaust" that occurred because the first life on earth produced oxygen,a substance that was poisonous to those organisms but which allowed higher life to flourish. Or own produced of C02, incidently the ideas for curbing global warming by spraying sulfer particles in the air strike me as really dumb and probably even worse than global warming.

Economic systems are very similar in the fact that stable systems lead to ever increasing levels of instability. In this case it's investors who invest with a false sense of security, which is my read on Minsky. All economic systems eventually evolve into systems of "Ponzi Finance". What a great name it describes our credit system to a tee.

Of course if you really want to get crazy with this analysis there is another great book on economics written by a religion professor called. Confidence Games about how the markets are really based on faith:

http://www.amazon.com/Confidence...50880709&sr=8- 1

The author doesn't come out and say it but he infers that all markets function because of faith. Once that faith is lost things go to hell in a handbasket. From a GNXP point of view this is more evolutionary psychology than biology.

As far as mathematical modeling is concerned Nicholas Taleb wrote some great stuff on it:
http://www.amazon.com/s/ ref=nb_s...=nicholas+taleb
In his lay books he believes that most models make an assumption that most distributions are gaussian when in fact they are not. He believes in "fat tails" or black swans. Hence the title of his one book. The fact that quants and economists seem to get things consistently wrong supports this hypothesis.

Personally I think the problem with economics is that we fail to ask some obvious questions. Is this price rational? Do we act on the basis of faith(much like religion)? Is the system inherently unstable?

If not no one would have bought a house, because no rational investor will buy something if believes the prices will come down substantially.

Many speculators buy into bubbles, even believing that the price will come down eventually - because they think it still has a ways to go up, and they think they can get out before the tipping point. Or soon enough after to still make a profit. This kind of buyer contributes to the asymmetrical shape of the rise and collapse in speculative bubbles (they jam the exits once the bubble pops).

I think globalization encourages bubbles because it increases the plausibility of the idea that there are enough greater fools out there eager to be bilked. In 2006, it was obvious that very few people currently living in California could afford to buy a house there, but the feeling was that there was a near infinite supply of people from somewhere else (China? Mexico? The ex-Soviet Union?) who would pay to live in California. And since factual discussions of groups of people are discouraged, it was easy to dream.

agnostic,

Perhaps the language of of math is not as intuitive to some people as it is to others. Personally, I find it much more satisfying to take the logic from your models and see it expressed it in English.

For instance, will the price of an asset experiencing "greater fool demand" eventually collapse, popping the bubble, or will it not collapse, preserving the bubble? The answer to this question is clear in English. If your investors run out of suckers to sell to, then the price of your asset will collapse. If they don't run out, then it won't.

On the other hand, you can set up two models, one with an exhaustible supply of suckers, and one with an inexhaustible supply. Then, you can define the "extra price" of the asset to be the supply of suckers times some other stuff. This means that the "extra price" will reach zero when the supply of suckers reaches zero, i.e. it will collapse when the supply of sucerks collapses. Now you can check your models and find that the price in the exhaustible supply model eventually collapses, whereas the price in the inexhaustible supply model permanently remains afloat. Thus, you reach the same conclusion. To me, you have just taken a more unintuitive and roundabout path to this conclusion.

In my opinion, math is most useful when you need to make precise calculations. For example, if I thought that you could use your models to make precise, real-world predictions, then I would think them useful. I.e. if you could predict how high real-world bubbles would go, when they would collapse, etc. But you can't make those kinds of predictions, because in economics there is no method to determine your input variables with any kind of precision.

Most of the data available in economics is qualitative and order-of-magnitude, and this sort of data is best analyzed and integrated using your God-given ability to reason with language. Think about this fact: the best economic predictor in the world is Warren Buffett. Buffett ridicules mathematical models. His method is purely one of common sense and sound judgment. This suggests to me that economic models are extraneous.

One other issue I have with models is that they allow previously accessible fields of study to be transformed into mysterious arcanum, only meant to be understood by trained experts. This effectively shields the field from scrutiny by outsiders, making it much easier to be dishonest (either with yourself or with others). I'm not saying you were being dishonest here, since you clearly weren't. But think about the ways you could massage the model in your favor, if you wanted to. Just drop in covariance amplifier term here, an animal spirits coefficient there, and suddenly the behavior of your model changes completely, and math illiterate folk like me can just scratch our heads.