Thursday, March 08, 2012

An interesting model of asset bubbles

Yesterday I was lucky enough to catch a talk by Gadi Barlevy of the Chicago Fed, one of the people whose work on bubbles inspired me to tackle the topic. Gadi presented a very interesting theory of bubbles, of a type that I hadn't studied closely before, so I thought I'd blog about it.

The paper, "A Leverage-Based Model of Speculative Bubbles" (Barlevy, 2011) is available here.

For our purposes, "bubbles" are situations in which asset prices rise quickly above fundamental values and then subsequently crash. This captures both the phenomenological notion of a bubble (prices rise and then fall) and the economically interesting possibility that prices might exceed fundamentals (thus indicating a market failure).

In any situation when assets are overpriced, the question is: Why would people pay more for an asset than it is fundamentally worth? There are many possible answers, but most of them involve some irrationality on the part of some subset of traders. It's difficult, but also very interesting, to try to imagine a situation in which a market made up of fully rational individuals would still overpay for something. The Barlevy (2011) model does precisely that. Instead of irrationality, the culprit is asymmetric information.

In the Barlevy (2011) model, which is based on some earlier models by Franklin Allen, people overpay for financial assets because they don't fully bear all of the risk - they buy the asset with borrowed money, so if the price crashes they can just default on their loans.

So why would anybody loan money to people who intend to use the money to buy overpriced financial assets? That sounds like a bum deal! The answer is that the people lending the money may not know what the borrowers are going to do with it. There may be some borrowers who will be able to do something productive and worthwhile with the money they borrow (Barlevy calls these "entrepreneurs" but I prefer the term "productive borrowers"). Lenders can't necessarily tell the difference between these people and the "speculators" who will just dump the money into risky financial assets.

So if lenders want the chance to lend to productive borrowers, they have to accept some of the risk that the people they're lending to are actually just unproductive speculators. In equilibrium, therefore, the speculators may end up getting away with it - by pretending to be productive borrowers, they can get a free ride, pushing up the price of financial assets in the process. Ta da - overpricing!

Now how about the rise-and-crash pattern of pricing? This gets a little trickier. It has to do with uncertainty about the payoff from the risky asset. In the model, there is a chance that the payoff will be revealed sooner, and a chance that it will be revealed later. If the payoff is revealed later - in other words, if traders suddenly discover that they have to wait to find out how much income they can get from the asset - then the bubble will grow. Whether the bubble grows can also can depend on the composition of the market - whether a bunch of new speculators show up in the interim. This latter mechanism is similar to what happens in "noise trader" models of bubbles.

But anyway, there are several features of this model that make it interesting and new. One is that bubbles can grow without people being overly optmistic about future asset prices - in fact, the reason that bubbles grow is precisely because traders are initially afraid that the bubble might pop, which holds down the price! Thus, speculation is based not on "irrational exuberance," but on fear.

Another interesting feature has to do with the type of contracts that lenders make with borrowers. In particular, the Barlevy (2011) model requires that debt contracts are "backloaded" - that borrowers borrow now and pay back later. This gives the bubble - which depends on the risk-shifting caused by borrowing - time to grow. This requirement may initially seem like a weakness of the model, but actually it is a strength, because it allows the model to make a very testable prediction: Bubbles will be bigger when debt contracts are more backloaded. Looking at the recent housing bubble, Barlevy finds that states with more interest-only mortgages (i.e. backloaded debt contracts) experienced bigger house price bubbles.

So that's the model; very interesting stuff. It does raise one big question in my mind, though: What about the tech bubble? The late-90s tech bubble was about the same size, in terms of the size of the price run-up and crash, as well as the total wealth involved, as the mid-2000s housing bubble, but involved far less debt (in fact, many argue that lower leverage is precisely the reason why the tech bubble wasn't as damaging to the real economy). In the Barlevy (2011) model, people only buy into bubbles if they are using borrowed money. Can this be reconciled with the appearance of bubbles that involve mostly non-borrowed money? Is it possible that housing bubbles and stock bubbles are two different phenomena?

Anyway, I encourage everyone who's interested in bubbles to take a look at Gadi Barlevy's work. The financial crisis right refocused the econ profession on financial instability and asset market failures...but Barlevy was doing it before it was cool!


  1. A fundamental difference between the tech bubble and the housing bubble is that the tech bubble largely involved paper gains and paper losses while the housing bubble involved the unproductive, and debt financed, consumption of large quantities of actual building materials, labor and household furnishings.

  2. Anonymous5:20 PM

    Replacing the people giving the loans with venture capital and you can probably recreate the same dynamic. After all- the tech boom was largely about dotcoms.

  3. Great post, very compelling!

    Seeing as your dissertation is in bubbles, would you be able to comment on possible dynamics of deflationary bubbles? Seeing as inflationary bubbles are widely associated with speculation in individual markets, does not similar phenomena happen with speculative acts in a downward way, i.e., bank runs, rapid deleveraging, or when a good becomes otherwise taboo? The model seems to work in my head, but I do not have the pedigree to work it out otherwise. What do you think?

  4. Well, it's difficult to get a "negative bubble" based on higher-order beliefs, due to the zero lower bound on asset prices. And institutionally, many models of bubbles (including Barlevy 2011) rely on constraints on short-selling, which are much easier to justify than constraints on margin buying. So while many models predict that assets can be undervalued, generally it is thought that overvaluation is a bigger deal.

    Does that make sense?

  5. This model could describe other bubbles, but isn’t there a problem with the housing example? The lenders were the ones who knew the score, and the borrowers, at least some of them, were rubes. The asymmetric information was switched around. (One could argue that the buyers of the mortgage-backed assets were taken for a ride, and this was true in many cases, but a lot of sophisticated agents got caught short when the music stopped.)

  6. Anonymous7:06 AM

    I wonder whether there really is a strict fundamental difference between the two descriptions of bubbles. Not as models, but rather in relation to reality. Could it just be a semantic difference to what one may call incomplete information or irrationality? In many, if not all, (economic) relationships there will be information that will be hard to get, and whether that information is available or not may depend crucially on how much effort is done by the parties. However, doing more effort could be more costly and not worth the effort. So when you assume that in the housing crisis there was lack of information, could the lenders have found out (some of) this information by better vetting their borrowers? When would you call it lack of information, and when would you call it irrationality? Also, were investors in the dot-com bubble irrational about what to expect about tech businesses, or would you call it lack of information because they're not tech people, and is there really a difference? Where do you draw the line, and is there a fundamental line? I don't think there is a fundamental difference, only a sliding scale with some arbitrary line drawn. Different models therefore may have similar outcomes, and could even be mathematically equivalent.

  7. Anonymous7:58 AM

    The components of a bubble are as follows:

    1. Very low returns on low risk investments.

    2. Almost no moderate risk investments exist. Low returns push the value of moderate risk investments into high risk territory. Any attempt to balance a low risk portfolio will only add to the bubble (everything not low risk is at an inflated price).

    3. Uncertainty. Assets are in uncharted waters. Their behavior going forward is unpredictable.

    4. The potential for high return is huge when the bubble is expanding. Failure to participate places a portfolio in the grossly underperforming category.

    5. Miscalculation of risk. The housing bubble was created by the willingness of fund managers to underwrite home mortgages partly on the premise that "people do not default on their home." They miscalculated the risk as lower than it actually was. Those that knew it was risky bought insurance, but the insurer miscalculated the risk and was unable to payout.

    Krugman describes the phenomena very well in his "Ice Age Cometh"- an entertaining read.

    Bush policies encouraged an investment bubble by relying solely on private investment to create jobs and expand the economy. Bush failed to make those investments that would create a climate for business investment to succeed. Bush subsidized business such as BigOil and BigEnergy and other BigBusiness that had excess capital.

    Bush failed to raise minimum wage, help the States, or take other steps to improve income to sustain demand. Consumers relied on unsustainable borrowing. The generally poor business climate produced by Bush policies reduced the number of possible moderate risk investments.

    jonny bakho

  8. You should do like Krugman and alert us to posts that are massively wonkish. ;)

  9. This is very similar to my view of bubbles.

    As for the tech bubble, you also had vendor financing -- when that chain broke, everything did. You also had people giving up after-tax income in order to get stock options. The reduction in wages could not be sustained permanently, and the options ended up worthless.

  10. This model could describe other bubbles, but isn’t there a problem with the housing example? The lenders were the ones who knew the score, and the borrowers, at least some of them, were rubes. The asymmetric information was switched around.

    I agree that this is a problem for the story as applied to the mortgage market. One could argue that mortgage lenders couldn't identify borrowers with income from borrowers without income, but then there are all those anecdotes about borrowers actively seeking to ignore information about borrower income.

    But (as you anticipate) I think the story could be more accurately applied to the MBS/CDO/etc. markets. Demand for mortgages was high because of securitization. And securitized products were usually bought using massive leverage. It seems plausible to me that some of the people lending money to, say, Bank of America would have balked at lending that money had they known that BofA was going to just turn around and (through SIVs etc.) buy some of the same securitized products that BofA was originating.

    So I think if we're going to apply the Barlevy (2011) story to the housing bubble, the credit would be going to investors in securitized products, and the demand would simply feed through to mortgages themselves, eventually showing up in the Case-Shiller price index.

  11. Interesting. The argument I'd seen before was closer to the "hold an auction for a dollar" explanation, where it costs more (in marginal cost) not to buy an asset than one risks by buying it, until an outside shock brings the whole thing tumbling down. However, that actually plays very well with this argument, since this information asymmetry lowers the cost of participation without lowering the marginal payout.

  12. Anonymous1:42 PM

    Your comment at 12:58 is not entirely correct.

    The people originating the loans (liar loans etc) were the ones who had some idea about the risk.

    The originators are NOT the same people who were "lending". The people who were lending were lending Investing in a package deal that years afterward, cannot be adequately assessed for value, which is why we have robo signing scandals and the like.

    The lenders were assured by the ratings agency that the products they were buying were triple A, when in reality, the ratings agencies did not know what was in them either.

    Good banking systems have transparency that prevents lying. In this case, investors (lenders) were lied to. Either the liars knew the products were bad and lied that they were good, or more likely, the liars had no clue whether the products were good or not but stamped them AAA anyway.

    Fraud was a big player in the housing bubble. Fraud needs to be a big part of any model of the housing bubble.

    jonny bakho

  13. McMike4:02 PM

    Investors investing borrowed money; lenders lending invested money... the serpent eats its own tail.

    I suppose it's passe, but I am still attracted to theories along the lines of herd/greater fool/pump and dump mechanics.

    Everyone dances until the music stops (h/t J.D.) becuase you can't afford not to play.

    The big winners are the intermediaries (banks) who make money coming and going off the flows and betting off their insider information.

    Just don't get caught holding the hot potato when the music finally stops.

  14. I suppose it's passe, but I am still attracted to theories along the lines of herd/greater fool/pump and dump mechanics.

    Oh no, I don't think that's passe at all! I think that Abreu & Brunnermeier (2003), which is exactly that kind of model, is still by far the most popular model of bubbles out there.

    I'm not saying Barlevy (2011) is "right", I'm saying it's interesting, new, and different. It's possible that different bubbles have different causes, or that several causes operate simultaneously. It's also possible that the Barlevy (2011) model is wrong, but for an interesting reason that reveals something about the way financial markets work.

  15. This is not my field so my question may be elementary, but it's in relation to this:
    "Barlevy (2011) model requires that debt contracts are "backloaded" - that borrowers borrow now and pay back later."
    This sounds true by definition (of debt). What would be an example of a debt contract not backloaded?
    Also, do you or he or anyone around observe the modelled behavior? E.g., borrowers faking bankers into thinking they're going to invest in something productive and then go buy gold or something?
    Finally, if I'm understanding the paper (having read only your summary and the intro of the actual paper, not worked through the model itself), it seems to sneer investment mediated by financial markets (e.g., stock marekts). The entrepreneur is the gal who invests productively, whereas the trader speculates. So direct capital investment is more productive (more virtuous somehow?) than share buying? Why? (Or am I wrong in my understanding?).
    Good luck on your research.

  16. The whole argument is based on a fallacy, that there is such a thing as fundamental value. There isn't. There is only price.

    Once you get this out of the way, you can understand bubbles very simply.

    As prices for an item rise, people expect those prices to continue rising. In cases where there is a mechanism to support those prices - e.g. everyone now has telephone service or an automobile is likely to continue paying for service, gasoline or whatnot - then we simply call it economic growth. If there is no such support mechanism - e.g. house prices are too high for most wage earners or anticipated corporate revenues did not meet expectations - then the bubble bursts. There's the same price rise mechanism, just no hysteresis.

    If you want to tell if you are watching a bubble, just look at what is supporting the prices and see if that mechanism is likely to continue doing so. If you start getting mystical and start thinking about fundamental value and the like, you will be clueless.

  17. Your presentation of this boom'n'burst model is really crystal clear to me. Thanks for this! Barlevy gives a very interesting one.

  18. Anonymous6:02 PM

    sometimes the investors are perfectly rational, but using wrong information. During the internet bubble Bernie Ebbers mis-stated the rate of internet bandwidth growth. Since this was one of the main publicly available measures of internet usage (and growth), this alone would have led to over investment.

    Similarly the assumption about the housing market was that home prices never fall (or fall very much). A single owner may not be able to pay the mortgage, but they can always sell, so the risk of making the loan is small.

  19. It puzzles me that economists don't seem to believe in emergent phenomena when far simpler systems than the economy are full of them. No one individual has to be irrational or misinformed of what everyone else knows; the market can be irrational while its participants behave normally. Prices are an emergent phenomenon with feedback effects that can create a butterfly effect -- the Babysitters club proved that.

    I bought my house in 2006, was that irrational? I'm not sure it is -- I've gotten good use out of it, and I can afford it. I paid as much as I did for a simple reason: because that's what they cost. Would I pay the same price for it now? Of course not, because that's not what they cost now. Even if the market is crazy, you still have to pay what it charges if you want something.

    But isn't that true for investors, too? Sure, rational investors will try to shift their portfolio from overvalued assets to undervalued, but if the market is generally overvalued do they stop investing? Do hedge funds ever start just sitting on their customer's cash? Do you ever stop your 401k contributions? People invest what they have budgeted for investment.

    If you want to turn the money you have today into more money tomorrow, you pay what it costs. If there aren't many investors and there are plenty of investments, you might be able to get $1,000 next year for $900 today. But if a decade later there is a lot more money being invested, the investment opportunities aren't guaranteed to grow to match it. So maybe now you pay $990 for $1000 next year. Is there some fundamental price that that's supposed to cost? If you want your money to work for you, you go for the returns you can get. And if money is flowing into the hands of the wealthy, then you should expect the price of any income stream to go up for simple demand reasons, as they tend to use their money for investment. It only becomes irrational when your crystal ball tells you that prices have gone up to more than they will be tomorrow and it is time to stuff your savings under your mattress. (And regardless of "fundamental values," if people do start stuffing their savings under their mattress instead of in investments, it will turn out to have been a very good time to stuff your savings under your mattress.)

    I laid out my thinking on this here, but generally I think our problem is simply too much money being invested. Unless you know some part of the economy that was severely undervalued where investors are getting unusually high returns?

  20. Anonymous9:51 PM

    There is the possibility that credit extended on cards and home financing, very easy to obtain at the time, was an indirect lending vehicle for the tech bubble. The indirect aspect of such financing may account for the less devastating response of the bubble burst.

  21. Anonymous11:21 AM

    But what about microfoundations?! ;)

  22. Anonymous12:12 PM

    or, you could also encourage people to look at the Leverage Cycles lit,

  23. I think there is a fundamental difference between how an equity financed bubble (internet) and debt financed bubble (housing) unwind.

    What I dont understand is how this is fundamentaly different from the Austrian model, other than describing the information differences.