Poking the hive of DSGE (Distinctly Sensitive Group of Economists)

The other day when I wrote my recent post What you can learn from DSGE, I expected that maybe 6 or 8 people would read it. I mean, it's a fairly tiny fraction of people who really want to read about the methodology of economic modelling, even if some people like myself insist on writing about it occasionally. So I was surprised that this post seems to have drawn considerable attention, especially from economists (apparently) writing on the forum econjobrumors. An economist I know told me about this site a while back, describing it as a hornet's nest of vicious criticism and name calling.

Now I know this first hand: the atmosphere there is truly dynamic and stochastic, choked with the smog of blogosphere-style vitriol (one commenter even suggesting that I should be shot!). Some comments were amusing and rather telling. For example, writing anonymously, one reader commented that....

I like how this blogger cites a GMU Ph.D. student as an example of someone considering alternatives to rational expectations. The author has no idea that such work has been going on for decades. He doesn't know s**t.

Actually, I never implied that alternatives had never been considered before. In any event, I guess the not-so-hidden message here is that grad students from GMU -- and not even in a Department of Economics, tsk! tsk! -- shouldn't be taken seriously. Maybe the writer was just irritated that the graduate student in question, Nathan Palmer, was co-author on the paper, recently published in the American Economic Review, that I just wrote about in Bloomberg. AER is a fairly prominent outlet, I believe, taken seriously in the profession. It seems that some real economists must agree with me that this work is pretty interesting.

Most of the other comments were typical of the blog-trashing genre, but one did hit on an interesting point that deserves some further comment:

...the implication that physicists or other natural scientists would never deploy the analytic equivalent of a representative agent when studying physical processes is not quite correct.

Mean Field Theory:

In physics and probability theory, mean field theory (MFT also known as self-consistent field theory) studies the behavior of large and complex stochastic models by studying a simpler model. Such models consider a large number of small interacting individuals who interact with each other. The effect of all the other individuals on any given individual is approximated by a single averaged effect, thus reducing a many-body problem to a one-body problem.

The ideas first appeared in physics in the work of Pierre Curie[1] and Pierre Weiss to describe phase transitions.[2] Approaches inspired by these ideas have seen applications in epidemic models,[3] queueing theory,[4] computer network performance and game theory.[5]

This is a good point, although I definitely never suggested that this technique is not used in physics. The mean field approach in physics is indeed the direct analogy to the representative agent technique. Theorists use it all the time, as it is simple and leads quickly to results that are sometimes reasonably correct (sometimes even exact). And sometimes not correct.

In the case of a ferromagnet such as iron, the method essentially assumes that each elementary magnetic unit in the material (for simplicity, think of it as the magnetic moment of a single atom that is itself like a tiny magnet) acts independently of every other. That is, each one responds to the overall mean field created by all the atoms throughout the entire material, rather than to, for example, its closest neighbors. In this approximation, the magnetic behavior of the whole is simply a scaled up version of that of the individual atoms. Interactions between nearby magnetic elements do not matter. All is very simple.

Build a model like this -- you'll find this in any introductory statistical mechanics book -- and you get a self-consistency condition for the bulk magnetization. Lo and behold, you find a sharp phase transition with temperature, much like what happens in real iron magnets. A piece of iron is non-magnetic above a certain critical temperature, and spontaneously becomes magnetic when cooled below that temperature. So, voila! The mean field method works, sometimes. But this is only the beginning of the story.

Curie and Weiss wrote down theories like this in the early 1900s and this way of thinking remained in fashion into the 1950s. Famed Russian physicist Lev Landau developed a much more general theory of phase transitions based on the idea. But here's the kicker -- since the 1960s, i.e. for half a century now, we have known that this theory does not work in general, and that the mean field approximation often breaks down badly, because different parts of a material aren't statistically independent. Especially near the temperature of the phase transition, you get strong correlations between different magnetic moments in iron, so what one is doing strongly influences what others are likely to be doing. Assume statistical independence now and you get completely incorrect results. The mean field trick fails, and sometimes very dramatically. As a simple example, a string of magnetic elements in one dimension, held on a line, does not undergo any phase transition at all, in complete defiance of the mean field prediction.

An awful lot of the most interesting mathematical physics over the past half century has been devoted to overcoming this failure, and to learning how go beyond the mean field approximation, to understand systems in which the correlations between parts are strong and important. I believe that it will be crucial for economics to plunge into the same complex realm, if any serious understanding is to be had of the most important events in finance and economics, which typically do involve strong influences acting between people. The very successful models that John Geanakoplos developed to predict mortgage prepayment rates only worked by including an important element of contagion -- people becoming more likely to prepay when many others prepay, presumably because they become more aware of the possibility and wisdom of doing so.

Unfortunately, I can't write more on this now as I am flying to Atlanta in a few minutes. But this is a topic that deserves a little further examination. For example, those power laws that econophysicists seem to find so fascinating? These also seem to really irritate those writing on econjobrumors. But what we know about power laws in physical systems is that they are often (though not always) the signature if strong correlations among the different elements of a system....  so they may indeed be trying to tell us something.

Mortgage dynamics

My latest Bloomberg column should appear sometime Sunday night 7 April. I've written about some fascinating work that explores the origins of the housing bubble and the financial crisis by using lots of data on the buying/selling behaviour of more than 2 million people over the period in question. It essentially reconstructs the crisis in silico and tests which factors had the most influence as causes of the bubble, i.e. leverage, interest rates and so on.

I think this is a hugely promising way of trying to answer such questions, and I wanted to point to one interesting angle in the history of this work: it came out of efforts on Wall St. to build better models of mortgage prepayments, using any technique that would work practically. The answer was detailed modelling of the actual actions of millions of individuals, backed up by lots of good data.

First, take a look at the figure below:

This figure shows the actual (solid line) rate of repayment of a pool of mortgages that were originally issued in 1986. It also shows the predictions (dashed line) for this rate made by an agent-based model of mortgage repayments developed by John Geanakoplos working for two different Wall St. firms. There are two things to notice. First, obviously, the model works very well over the entire period up to 1999. The second, not obvious, is that the model works well even over a period for which it was not designed, by the data, to fit. The sample of data used to build the model went from 1986 through early 1996. The model continues to work well even out of sample over the final three years of this period, roughly 30% beyond the period of fitting. (The model did not work in subsequent years and had to be adjusted due to a major changes in the market itself, after 2000, especially new possibilities to refinance and take cash out of mortgages that were not there before.).

How was this model built? Almost all mortgages give the borrower the right in any month to repay the mortgage in its entirely. Traditionally, models aiming to predict how many would do so worked by trying to guess or develop some function to describe the aggregate behavior of all the mortgage owners, reflecting ideas about individual behavior in some crude way in the aggregate. As Geanakoplos et al. put it:

The conventional model essentially reduced to estimating an equation with an assumed functional form for prepayment rate... Prepay(t) = F(age(t), seasonality(t), old rate – new rate(t), burnout(t), parameters), where old rate – new rate is meant to capture the benefit to refinancing at a given time t, and burnout is the summation of this incentive over past periods. Mortgage pools with large burnout tended to prepay more slowly, presumably because the most alert homeowners prepay first. ...

Note that the conventional prepayment model uses exogenously specified functional forms to describe aggregate behavior directly, even when the motivation for the functional forms, like burnout, is explicitly based on heterogeneous individuals.

There is of course nothing wrong with this. It's an attempt to do something practically useful with the data then available (which wasn't generally detailed at the level of individual loans). The contrasting approach, seeks instead to start from the characteristics of individual homeowners and to model their behavior, as a population, as it evolves through time:

the new prepayment model... starts from the individual homeowner and in principle follows every single individual mortgage. It produces aggregate prepayment forecasts by simply adding up over all the individual agents. Each homeowner is assumed to be subject to a cost c of prepaying, which include some quantifiable costs such as closing costs, as well as less tangible costs like time, inconvenience, and psychological costs. Each homeowner is also subject to an alertness parameter a, which represents the probability the agent is paying attention each month. The agent is assumed aware of his cost and alertness, and subject to those limitations chooses his prepayment optimally to minimize the expected present value of his mortgage payments, given the expectations that are implied by the derivatives market about future interest rates.

Agent heterogeneity is a fact of nature. It shows up in the model as a distribution of costs and alertness, and turnover rates. Each agent is characterized by an ordered pair (c,a) of cost and alertness, and also a turnover rate t denoting the probability of selling the house. The distribution of these characteristics throughout the population is inferred by fitting the model to past prepayments. The effects of observable borrower characteristics can be incorporated in the model (when they become available) by allowing them to modify the cost, alertness, and turnover.

By way of analogy, this is essentially modelling the prepayment behavior of a population of homeowners as an ecologist might model, say, the biomass consumption of some population of insects. The idea would be to  follow the density of insects as a function of their size, age and other features that influence how and when and how much they tend to consume. The more you model such features explicitly as a distribution of influential factors, the more likely your model will take on aspects of the real population, and the more likely it will be to make predictions about the future, because it has captured real aspects of the causal factors in the past.

Models of this kind also capture in a more natural way, with no extra work, things that have to be put in by hand when working only at the aggregate level. In this mortgage example, this is true of the "burnout" -- the gradual lessening of prepayment rates over time (other things being equal):

... burnout is a natural consequence of the agent-based approach; there is no need to add it in afterwards. The agents with low costs and high alertness prepay faster, leaving the remaining pool with slower homeowners, automatically causing burnout. The same heterogeneity that explains why only part of the pool prepays in any month also explains why the rate of prepayment burns out over time.

One other thing worth noting is that those developing this model found that to fit the data well they had to include an effect of "contagion", i.e. the spread of behavior directly from one person to another. When prepayment rates go up, it appears they do so not solely because people have independently made optimal decisions to prepay. Fitting the data well demands an assumption that some people become aware of the benefit of prepaying because they have seen or heard about others who have done so.

This is how it was possible, going back up to the figure above, to make accurate predictions of prepayment rates three years out of sample. In a sense, the lesson is that you do better if you really try to make contact with reality, modelling as many realistic details as you have access to. Mathematics alone won't perform miracles, but mathematics based on realistic dynamical factors, however crudely captured, can do some impressive things.

I suggest reading the original, fairly short paper, which was eventually published in the American Economic Review. That alone speaks to at least grudging respect on the part of the larger economics community to the promise of agent based modelling. The paper takes this work on mortgage prepayments as a starting point and an inspiration, and tries to model the housing market in the Washington DC area in a similar way through the period of the housing bubble.

What you can learn from DSGE

                                       *** UPDATE BELOW ***

Anyone who has read much of this blog would expect my answer to the above question to be "NOTHING AT ALL!!!!!!!!!!!!!!!!!" Its true, I'm not a fan at all of Dynamic Stochastic General Equilibrium models, and think they offer poor tools for exploring the behaviour of any economy. That said, I also think economists should be ready and willing to use any model whatsoever if they honestly believe it might give some real practical insight into how things work. I (grudgingly) suppose that DSGE models might sometimes fall into this category.

So that's what I want to explore here, and I do briefly below. But first a few words on what I find objectionable about DSGE models.

The first thing is that the agents in such models are generally assumed to be optimisers. They have a utility function and are assumed to maximize this utility by solving some optimization problem over a path in time. [I'm using as my model the well known Smets-Wouters model as described in this European Central Bank document written, fittingly enough, by Smets and Wouters.] Personally, I find this to be a rather hugely implausible account of how any person or firm makes decisions when facing anything but the simplest problems. So it would seem like a miracle to me if the optimal behaviors predicted by the models would turn out to resemble even crudely the behavior of real individuals or firms.

Having said that, if I try to be generous, I can suppose that maybe, just maybe, the actual behaviour of people, while it isn't optimizing anything, might in the aggregate come out to something that isn't at least too far away from the optimal behavior, at least in some cases. I would guess there must be armies of economists out there collecting data on just this question, comparing the actions of real individuals and firms to the optimal predictions of the models. Maybe it isn't always bad. If I twist my arm, I can accept that this way of treating decision making as optimization sometimes lead to interesting insights (for people facing very smple decisions, this would of course be more likely).

The second thing I find bad about DSGE models is their use of the so-called representative agent. In the Smets-Wouters model, for example, there is essentially one representative consumer who makes decisions regarding labor and consumption, and then one representative firm which makes decisions on investment, etc. If you read the paper you will see it mention "a continuum of households" indexed by a continuous parameter, and this makes it seem at first like there is actually an infinite number of agents. Not really, as the index only refers to the kind of labor. Each agent makes decisions independently to optimize their utility; there are no interactions between the agents, no one can conduct a trade with another or influence their behavior, etc. So in essence there is really just one representative laborer and one representative firm, who interact with one another in the market. This I also find wholly unconvincing as the real economy emerges out of the complex interactions of millions of agents doing widely different things. Modelling an economy like this seems like modelling the flow of a river by thinking about the behaviour of a single representative water molecule, bouncing along the river bed, rather then thinking about the interactions of many which create pressure, eddies, turbulence, waves and so on. It seems highly unlikely to be very instructive.

But again, let me be generous. Perhaps, in some amazing way, this unbelievably crude approximation might sometimes give you some shred of insight. Maybe you can get lucky and find that a collective outcome can be understood by simply averaging over the behaviors of the many individuals. In situations where people do make up their own minds, independently and by seeking their own information, this might work. Perhaps this is how people behave in response to their perceptions of the macroeconomy, although it seems to me that what they hear from others, what they read and see in the media, probably has a huge effect and so they don't act independently at all.

But maybe you can still learn something from this approximation, sometimes. Does anyone out there know if there is research exploring this matter of when or under what conditions the representative agent approximation is OK because people DO act independently? I'm sure this must exist and it would be interesting to know more about it. I guess the RBC crowd must have an extensive program studying the empirical limits to the applicability of this approximation? 

So, those are my two biggest reasons for finding it hard to believe the DSGE framework. To these I might add a disbelief that the agents in economy do rapidly find their way to an equilibrium in which "production equals demand by households for consumption and investment and the government." We might stay well away from that point, and things might generally change so quickly that no equilibrium ever comes about. But let's ignore that. Maybe we're lucky and the equilibrium does come about.

So then, what can we learn from DSGE, and why this post? If I toss aside the worries I've voiced above, I'm willing to entertain the possibility that one might learn something from DSGE models. In particular, while browsing the web site of Nathan Palmer, a PhD student in the Department of Computational Social Science at George Mason University, I came across mention of two lines of work within the context of the DSGE formalism that I do think are interesting. I think more people should know about them.

First is work exploring the idea of "natural expectations." A nice example is this fairly recent paper by Andreas Fuster, David Laibson, and Brock Mendel. Most DSGE models, including the Smets-Wouters model, assume that the representative agents have rational expectations, i.e. they process information perfectly and have a wholly unbiased view of future possibilities. What this paper does is to relax that assumption in a DSGE model, assuming instead that people have more realistic "natural" or "intuitive expectations." Look at the empirical literature and you find that there's lots of evidence that investors and people of all kinds tend to overestimate recent trends in time series and expect them to continue. This paper explores some of this empirical literature, but then goes to its main purpose -- to include these trend following expectations into a DSGE model.

As they note, a seminal failure of rational expectations DSGE models is that they struggle "to explain some of the most prominent facts we observe in macroeconomics, such as large swings in asset prices, in other words “bubbles”, as well as credit cycles, investment cycles, and other mechanisms that contribute to the length and severity of economic contractions." These kinds of things, in contrast, do emerge quite readily from a DSGE model once the expectations of the agents is made a little more realistic. From the paper:

.....we embed natural expectations in a simple dynamic macroeconomic model and compare the simulated properties of the model to the available empirical evidence. The model’s predictions match many patterns observed in macroeconomic and financial time series, such as high volatility of asset prices, predictable up‐and‐down cycles in equity returns, and a negative relationship between current consumption growth and future equity returns.   

That is interesting, and all from a DSGE model. Whether you believe it or not depends on what you think about the objections I voiced above about the components of DSGE models, but it is at least nice that this single step towards realism pays some nice dividends in giving more plausible outcomes. This is a useful line of research.

Related work, equally interesting, is that of Paolo Gelain, Kevin J. Lansing and Caterina Mendicino, described in this working paper of the Federal Reserve Bank of San Francisco. This paper essentially does much the same thing as the one I just discussed, though in the context of the housing market. It uses a DSGE with trend following expectations for some of the agents to explore how a government might best try to keep housing bubbles in check through change in interest rates or restrictions on  leverage, i.e. how much a potential home buyer can borrow relative to the house value, or restrictions on how much they can borrow relative to income. The latter seems to work best. As they summarize:

Standard DSGE models with fully-rational expectations have difficulty producing large swings in house prices and household debt that resemble the patterns observed in many industrial countries over the past decade. We show that the introduction of simple moving-average forecast rules for a subset of agents can significantly magnify the volatility and persistence of house prices and household debt relative to otherwise similar model with fully-rational expectations. We evaluate various policy actions that might be used to dampen the resulting excess volatility, including a direct response to house price growth or credit growth in the central bank’s interest rate rule, the imposition of a more restrictive loan-to-value ratio, and the use of a modified collateral constraint that takes into account the borrower’s wage income. Of these, we find that a debt-to-income type constraint is the most effective tool for dampening overall excess volatility in the model economy. 

Again, this is really interesting stuff, worthwhile research, economics that is moving, to my mind, in the right direction, showing us what we should expect to be possible in an economy once we take the realistic and highly heterogenous behaviour of real people into account.

So there. I've said some not so nasty things about DSGE models! Now I think I need a stiff drink.

*** UPDATE ***

One other thing to mention. I'm happy to see this kind of work, and I applaud those doing it. But I do seriously doubt whether embedding the idea of trend following inside a DSGE model does anything to teach us about why markets often undergo bubble-like phenomena and have quite strong fluctuations in general. Does the theoretical framework add anything?

Imagine someone said the following to you:

 "Lots of people, especially in financial markets and the housing market, are prone to speculating and buying in the hope of making a profit when prices go up. This becomes more likely if people have recently seen prices rising, and their friends making profits. This situation  can lead to herding type behavior where many people act similarly and create positive feedbacks and asset bubbles, which eventually crash back to reality. The problem is generally made worse, for obvious reasons, if people can borrow very easily to leverage their investment..." 

I think most people would say "yes, of course." I suspect that many economists would also. This explanation, couched in words, is for me every bit as convincing as the similar dynamic wrapped up in the framework of DSGE. Indeed, it is even more convincing as it doesn't try to jump awkwardly through a series of bizarre methodological hoops along the way. In this sense, DSGE seems more like a straitjacket than anything else. I can't see how it adds anything to the plausibility of a story.

So, I guess, sorry for the title of this post. Should have been "What you can learn from DSGE: things you would be much better off learning elsewhere."

FORECAST: new book to be published tomorrow!

That's right, my new book, the cover of which you've seen off to the right of this blog for some time now, will FINALLY be in bookstores in the US tomorrow, March 26. Of course, it is also available at Amazon and other likely outlets on the web. Who knows when reviews and such will begin trickling in. The book was featured in Nature on Thursday in their "Books in brief" section (sorry, you'll need a subscription), but the poor writers of those reviews (I've been one) really have almost no space to say anything. The review does make very clear that the book exists and purports to have some new ideas about economics and finance, but it makes no judgement on the usefulness of the book at all.

Anyone in the US, if you happen to be in a physical bookstore in the next few days, please let me know if you 1) do find the book and 2) where it was located. I've had the unfortunate experience in the past that my books, such as Ubiquity or The Social Atom, were placed by bookstore managers near the back of the store in sections with labels like Mathematical Sociology or Perspectives in the Philosophy of History, where perhaps only 1 or 2 people venture each day, and then probably only because they got lost while looking for the rest room. If you do find the book in an obscure location, feel completely free -- there's no law against this -- to take all the copies you find and move them up to occupy prominent positions in the bestsellers' section, or next to the check out with the diet books, etc. I would be very grateful!

And I would very much like to hear what readers of this blog think about the book.

Quantum Computing, Finally!! (or maybe not)

Today's New York Times has an article hailing the arrival of superfast practical quantum computers (weird thing pictured above), courtesy of Lockheed Martin who purchased one from a company called D-Wave Systems. As the article notes,

... a powerful new type of computer that is about to be commercially deployed by a major American military contractor is taking computing into the strange, subatomic realm of quantum mechanics. In that infinitesimal neighborhood, common sense logic no longer seems to apply. A one can be a one, or it can be a one and a zero and everything in between — all at the same time. ...  Lockheed Martin — which bought an early version of such a computer from the Canadian company D-Wave Systems two years ago — is confident enough in the technology to upgrade it to commercial scale, becoming the first company to use quantum computing as part of its business.

The article does mention that there are some skeptics. So beware.

Ten to fifteen years ago, I used to write frequently, mostly for New Scientist magazine, about research progress towards quantum computing. For anyone who hasn't read something about this, quantum computing would exploit the peculiar properties of quantum physics to do computation in a totally new way. It could potentially solve some problems very quickly that computers running on classical physics, as today's computers do, would never be able to solve. Without getting into any detail, the essential thing about quantum processes is their ability to explore many paths in parallel, rather than just doing one specific thing, which would give a quantum computer unprecedented processing power. Here's an article giving some basic information about the idea.

I stopped writing about quantum computing because I got bored with it, not the ideas, but the achingly slow progress in bringing the idea into reality. To make a really useful quantum computer you need to harness quantum degrees of freedom, "qubits," in single ions, photons, the spins of atoms, etc., and have the ability to carry out controlled logic operations on them. You would need lots of them, say hundreds and more, to do really valuable calculations, but to date no one has managed to create and control more than about 2 or 3. I wrote several articles a year noting major advances in quantum information storage, in error correction, in ways to transmit quantum information (which is more delicate than classical information) from one place to another and so on. Every article at some point had a weasel phrase like ".... this could be a major step towards practical quantum computing." They weren't. All of this was perfectly good, valuable physics work, but the practical computer receded into the future just as quickly as people made advances towards it. That seems to be true today.... except for one D-Wave Systems.

Around five years ago, this company started claiming that it was producing and achieving quantum computing and had built functioning devices with 128 qubits. It used superconducting technology. Everyone else in the field was aghast by such a claim, given this sudden staggering advance over what anyone else in the world had achieved. Oh, and D-Wave didn't release sufficient information for the claim to be judged. Here is the skeptical judgement of IEEE Spectrum magazine as of 2010. But more up to date, and not quite so negative, is this assessment by quantum information expert Scott Aaronson just over a year ago. The most important point he makes is about the failure of D-Wave to really demonstrate that its computer is really doing something essentially quantum, which is why it would be interesting. This would mean demonstrating so-called quantum entanglement in the machine, or really carrying out some calculation that was so vastly superior to anything achievable by classical computers that one would have to infer quantum performance. Aaronson asks the obvious question:

... rather than constantly adding more qubits and issuing more hard-to-evaluate announcements, while leaving the scientific characterization of its devices in a state of limbo, why doesn’t D-Wave just focus all its efforts on demonstrating entanglement, or otherwise getting stronger evidence for a quantum role in the apparent speedup?  When I put this question to Mohammad Amin, he said that, if D-Wave had followed my suggestion, it would have published some interesting research papers and then gone out of business—since the fundraising pressure is always for more qubits and more dramatic announcements, not for clearer understanding of its systems.  So, let me try to get a message out to the pointy-haired bosses of the world: a single qubit that you understand is better than a thousand qubits that you don’t.  There’s a reason why academic quantum computing groups focus on pushing down decoherence and demonstrating entanglement in 2, 3, or 4 qubits: because that way, at least you know that the qubits are qubits!  Once you’ve shown that the foundation is solid, then you try to scale up.   

So there's a finance and publicity angle here as well as the science. The NYT article doesn't really get into any of the specific claims of D-Wave, but I recommend Aaronson's comments as a good counterpoint to the hype.

Third (and final) excerpt...

The third (and, you'll all be pleased to hear, final!) excerpt of my book was published in Bloomberg today. The title is "Toward a National Weather Forecaster for Finance" and explores (briefly) the topic of what might be possible in economics and finance in creating national (and international) centers devoted to data intensive risk analysis and forecasting of socioeconomic "weather."

Before anyone thinks I'm crazy, let me make very clear that I'm using the term "forecasting" in it's general sense, i.e. of making useful predictions of potential risks as they emerge in specific areas, rather than predictions such as "the stock market will collapse at noon on Thursday." I think we can all agree that the latter kind of prediction is probably impossible (although Didier Sornette wouldn't agree), and certainly would be self-defeating were it made widely known. Weather forecasters make much less specific predictions all the time, for example, of places and times where conditions will be ripe for powerful thunderstorms and tornadoes. These forecasts of potential risks are still valuable, and I see no reason similar kinds of predictions shouldn't be possible in finance and economics. Of course, people make such predictions all the time about financial events already. I'm merely suggesting that with effort and the devotion of considerable resources for collecting and sharing data, and building computational models, we could develop centers acting for the public good to make much better predictions on a more scientific basis.

As a couple of early examples, I'll point to the recent work on complex networks in finance which I've touched on here and here. These are computationally intensive studies demanding excellent data which make it possible to identify systemically important financial institutions (and links between them) more accurately than we have in the past. Much work remains to make this practically useful.

Another example is this recent and really impressive agent based model of the US housing market, which has been used as a "post mortem" experimental tool to ask all kinds of "what if?" questions about the housing bubble and its causes, helping to tease out better understanding on controversial questions. As the authors note, macroeconomists really didn't see the housing market as a likely source of large-scale macroeconomic trouble. This model has made it possible to ask and explore questions that cannot be explored with conventional economic models:

 Not only were the Macroeconomists looking at the wrong markets, they might have been looking at the wrong variables. John Geanakoplos (2003, 2010a, 2010b) has argued that leverage and collateral, not interest rates, drove the economy in the crisis of 2007-2009, pushing housing prices and mortgage securities prices up in the bubble of 2000-2006, then precipitating the crash of 2007. Geanakoplos has also argued that the best way out of the crisis is to write down principal on housing loans that are underwater (see Geanakoplos-Koniak (2008, 2009) and Geanakoplos (2010b)), on the grounds that the loans will not be repaid anyway, and that taking into account foreclosure costs, lenders could get as much or almost as much money back by forgiving part of the loans, especially if stopping foreclosures were to lead to a rebound in housing prices.

There is, however, no shortage of alternative hypotheses and views. Was the bubble caused by low interest rates, irrational exuberance, low lending standards, too much refinancing, people not imagining something, or too much leverage? Leverage is the main variable that went up and down along with housing prices. But how can one rule out the other explanations, or quantify which is more important? What effect would principal forgiveness have on housing prices? How much would that increase (or decrease) losses for investors? How does one quantify the answer to that question?

Conventional economic analysis attempts to answer these kinds of questions by building equilibrium models with a representative agent, or a very small number of representative agents. Regressions are run on aggregate data, like average interest rates or average leverage. The results so far seem mixed. Edward Glaeser, Joshua Gottlieb, and Joseph Gyourko (2010) argue that leverage did not play an important role in the run-up of housing prices from 2000-2006. John Duca, John Muellbauer, and Anthony Murphy (2011), on the other hand, argue that it did. Andrew Haughwout et al (2011) argue that leverage played a pivotal role.

In our view a definitive answer can only be given by an agent-based model, that is, a model in which we try to simulate the behavior of literally every household in the economy. The household sector consists of hundreds of millions of individuals, with tremendous heterogeneity, and a small number of transactions per month. Conventional models cannot accurately calibrate heterogeneity and the role played by the tail of the distribution. ... only after we know what the wealth and income is of each household, and how they make their housing decisions, can we be confident in answering questions like: How many people could afford one house who previously could afford none? Just how many people bought extra houses because they could leverage more easily? How many people spent more because interest rates became lower? Given transactions costs, what expectations could fuel such a demand? Once we answer questions like these, we can resolve the true cause of the housing boom and bust, and what would happen to housing prices if principal were forgiven.

... the agent-based approach brings a new kind of discipline because it uses so much more data. Aside from passing a basic plausibility test (which is crucial in any model), the agent-based approach allows for many more variables to be fit, like vacancy rates, time on market, number of renters versus owners, ownership rates by age, race, wealth, and income, as well as the average housing prices used in standard models. Most importantly, perhaps, one must be able to check that basically the same behavioral parameters work across dozens of different cities. And then at the end, one can do counterfactual reasoning: what would have happened had the Fed kept interest rates high, what would happen with this behavioral rule instead of that.

The real proof is in the doing. Agent-based models have succeeded before in simulating traffic and herding in the flight patterns of geese. But the most convincing evidence is that Wall Street has used agent-based models for over two decades to forecast prepayment rates for tens of millions of individual mortgages.

This is precisely the kind of work I think can be geared up and extended far beyond the housing market, augmented with real time data, and used to make valuable forecasting analyses. It seems to me actually to be the obvious approach.
 

Second excerpt...

A second excerpt of my forthcoming book Forecast is now online at Bloomberg. It's a greatly condensed text assembled from various parts of the book. One interesting exchange in the comments from yesterday's excerpt:

Food For Thought commented....Before concluding that economic theory does not include analysis of unstable equilibria check out the vast published findings on unstable equilibria in the field of International Economics.  Once again we have someone touching on one tiny part of economic theory and drawing overreaching conclusions. 

I would expect a scientist would seek out more evidence before jumping to conclusions.

to which one Jack Harllee replied...

Sure, economists have studied unstable equilibria. But that's not where the profession's heart is. Krugman summarized rather nicely in 1996, and the situation hasn't changed much since then:
"Personally, I consider myself a proud neoclassicist. By this I clearly don't mean that I believe in perfect competition all the way. What I mean is that I prefer, when I can, to make sense of the world using models in which individuals maximize and the interaction of these individuals can be summarized by some concept of equilibrium. The reason I like that kind of model is not that I believe it to be literally true, but that I am intensely aware of the power of maximization-and-equilibrium to organize one's thinking - and I have seen the propensity of those who try to do economics without those organizing devices to produce sheer nonsense when they imagine they are freeing themselves from some confining orthodoxy. ...That said, there are indeed economists who regard maximization and equilibrium as more than useful fictions. They regard them either as literal truths - which I find a bit hard to understand given the reality of daily experience - or as principles so central to economics that one dare not bend them even a little, no matter how useful it might seem to do so."

This response fairly well captures my own position. I argue in the book that the economics profession has been fixated far too strongly on equilibrium models, and much of the time simply assumes the stability of such equilibria without any justification. I certainly don't claim that economists have never considered unstable equilibria (or examined models with multiple equilibria). But any examination of the stability of an equilibrium demands some analysis of dynamics of the system away from equilibrium, and this has not (to say the least) been a strong focus of economic theory.   

New territory for game theory...

This new paper in PLoS looks fascinating. I haven't had time yet to study it in detail, but it appears to make an important demonstration of how, when thinking about human behavior in strategic games, fixed point or mixed strategy Nash equilibria can be far too restrictive and misleading, ruling out much more complex dynamics, which in reality can occur even for rational people playing simple games: 

Abstract

Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated. However, economists have argued that iterated reasoning–what you think I think you think–will suppress complex dynamics by stabilizing or accelerating convergence to Nash equilibrium. We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point solution concept. These cycles are driven by a “hopping” behavior that is consistent with other accounts of iterated reasoning: agents are constrained to about two steps of iterated reasoning and learn an additional one-half step with each session. If higher-order reasoning can be complicit in complex emergent dynamics, then cyclic and chaotic patterns may be endogenous features of real-world social and economic systems.

...and from the conclusions, ...

Cycles in the belief space of learning agents have been predicted for many years, particularly in games with intransitive dominance relations, like Matching Pennies and Rock-Paper-Scissors, but experimentalists have only recently started looking to these dynamics for experimental predictions. This work should function to caution experimentalists of the dangers of treating dynamics as ephemeral deviations from a static solution concept. Periodic behavior in the Mod Game, which is stable and efficient, challenges the preconception that coordination mechanisms must converge on equilibria or other fixed-point solution concepts to be promising for social applications. This behavior also reveals that iterated reasoning and stable high-dimensional dynamics can coexist, challenging recent models whose implementation of sophisticated reasoning implies convergence to a fixed point [13]. Applied to real complex social systems, this work gives credence to recent predictions of chaos in financial market game dynamics [8]. Applied to game learning, our support for cyclic regimes vindicates the general presence of complex attractors, and should help motivate their adoption into the game theorist’s canon of solution concepts

Book excerpt...

Bloomberg is publishing a series of excerpts from my forthcoming book, Forecast, which is now due out in only a few days. The first one was published today.

Secrets of Cyprus...

Just something to think about when scratching your head over the astonishing developments in Cyprus, which seem to be more or less intentionally designed to touch off bank runs in several European nations. Why? Courtesy of Zero Hedge:

...news is now coming out that the Cyprus parliament has postponed the decision and may in fact not be able to reach agreement. They may tinker with the percentages, to penalize smaller savers less (and larger savers more). However, the damage is already done. They have hit their savers with a grievous blow, and this will do irreparable harm to trust and confidence.

As well it should! In more civilized times, there was a long established precedent regarding the capital structure of a bank. Equity holders incur the first losses as they own the upside profits and capital gains. Next come unsecured creditors who are paid a higher interest rate, followed by secured bondholders who are paid a lower interest rate. Depositors are paid the lowest interest rate of all, but are assured to be made whole, even if it means every other class in the capital structure is utterly wiped out.

As caveat to the following paragraph, I acknowledge that I have not read anything definitive yet regarding bondholders. I present my assumptions (which I think are likely correct).

As with the bankruptcy of General Motors in the US, it looks like the rule of law and common sense has been recklessly set aside. The fruit from planting these bitter seeds will be harvested for many years hence. As with GM, political expediency drives pragmatic and ill-considered actions. In Cyprus, bondholders include politically connected banks and sovereign governments.  Bureaucrats decided it would be acceptable to use depositors like sacrificial lambs. The only debate at the moment seems to be how to apportion the damage amongst “rich” and “non-rich” depositors.

Also, much more on the matter here, mostly expressing similar sentiments. And do read The War On Common Sense by Tim Duy:

This weekend, European policymakers opened up a new front in their ongoing war on common sense.  The details of the Cyprus bailout included a bail-in of bank depositors, small and large alike.  As should have been expected, chaos ensued as Cypriots rushed to ATMs in a desperate attempt to withdraw their savings, the initial stages of what is likely to become a run on the nation's banks.  Shocking, I know.  Who could have predicted that the populous would react poorly to an assault on depositors?

Everyone.  Everyone would have predicted this.  Everyone except, apparently, European policymakers....
 

Beginning of the end for big banks?

If the biggest banks are too big to fail, too connected to fail, too important to prosecute, and also too complex to manage, it would seem sensible to scale them down in size, and to reduce their centrality and the complexity of their positions. Simon Johnson has an encouraging article suggesting that at least some of this may actually be about to happen: 

The largest banks in the United States face a serious political problem. There has been an outbreak of clear thinking among officials and politicians who increasingly agree that too-big-to-fail is not a good arrangement for the financial sector.

Six banks face the prospect of meaningful constraints on their size: JPMorgan Chase, Bank of America, Citigroup, Wells Fargo, Goldman Sachs and Morgan Stanley. They are fighting back with lobbying dollars in the usual fashion – but in the last electoral cycle they went heavily for Mitt Romney (not elected) and against Elizabeth Warren and Sherrod Brown for the Senate (both elected), so this element of their strategy is hardly prospering.

What the megabanks really need are some arguments that make sense. There are three positions that attract them: the Old Wall Street View, the New View and the New New View. But none of these holds water; the intellectual case for global megabanks at their current scale is crumbling.

Most encouraging is the emergence of a real discussion over the implicit taxpayer subsidy given to the largest banks. See also this editorial in Bloomberg from a few weeks ago:

On television, in interviews and in meetings with investors, executives of the biggest U.S. banks -- notably JPMorgan Chase & Co. Chief Executive Jamie Dimon -- make the case that size is a competitive advantage. It helps them lower costs and vie for customers on an international scale. Limiting it, they warn, would impair profitability and weaken the country’s position in global finance.

So what if we told you that, by our calculations, the largest U.S. banks aren’t really profitable at all? What if the billions of dollars they allegedly earn for their shareholders were almost entirely a gift from U.S. taxpayers?

... The top five banks -- JPMorgan, Bank of America Corp., Citigroup Inc., Wells Fargo & Co. and Goldman Sachs Group Inc. - - account for $64 billion of the total subsidy, an amount roughly equal to their typical annual profits (see tables for data on individual banks). In other words, the banks occupying the commanding heights of the U.S. financial industry -- with almost $9 trillion in assets, more than half the size of the U.S. economy -- would just about break even in the absence of corporate welfare. In large part, the profits they report are essentially transfers from taxpayers to their shareholders.

So much for the theory that the big banks need to pay big bonuses so they can attract that top financial talent on which their success depends. Their success seems to depend on a much simpler recipe.

This paper also offers some interesting analysis on different practical steps that might be taken to end this ridiculous situation.

Megabanks: too complex to manage

Having come across Chris Arnade, I'm currently reading everything I can find by him. On this blog I've touched on the matter of financial complexity many times, but mostly in the context of the network of linked institutions. I've never considered the possibility that the biggest financial institutions are themselves now too complex to be managed in any effective way. In this great article at Scientific American, Arnade (who has 20 years experience working in Wall St.) makes a convincing case that the largest banks are now invested in so many diverse products of such immense complexity that they cannot possibly manage their risks:

This is far more common on Wall Street than most realize. Just last year JP Morgan revealed a $6 billion loss from a convoluted investment in credit derivatives. The post mortem revealed that few, including the actual trader, understood the assets or the trade. It was even found that an error in a spreadsheet was partly responsible.

Since the peso crisis, banks have become massive, bloated with new complex financial products unleashed by deregulation. The assets at US commercial banks have increased five times to $13 trillion, with the bulk clustered at a few major institutions. JP Morgan, the largest, has $2.5 trillion in assets.

Much has been written about banks being “too big to fail.” The equally important question is are they “too big to succeed?” Can anyone honestly risk manage $2 trillion in complex investments?

To answer that question it’s helpful to remember how banks traditionally make money: They take deposits from the public, which they lend out longer term to companies and individuals, capturing the spread between the two.

Managing this type of bank is straightforward and can be done on spreadsheets. The assets are assigned a possible loss, with the total kept well beneath the capital of the bank. This form of banking dominated for most of the last century, until the recent move towards deregulation.

Regulations of banks have ebbed and flowed over the years, played out as a fight between the banks’ desire to buy a larger array of assets and the government’s desire to ensure banks’ solvency.

Starting in the early 1980s the banks started to win these battles resulting in an explosion of financial products. It also resulted in mergers. My old firm, Salomon Brothers, was bought by Smith Barney, which was bought by Citibank.

Now banks no longer just borrow to lend to small businesses and home owners, they borrow to trade credit swaps with other banks and hedge funds, to buy real estate in Argentina, super senior synthetic CDOs, mezzanine tranches of bonds backed by the revenues of pop singers, and yes, investments in Mexico pesos. Everything and anything you can imagine.

Managing these banks is no longer simple. Most assets now owned have risks that can no longer be defined by one or two simple numbers. They often require whole spreadsheets. Mathematically they are vectors or matrices rather than scalars.

Before the advent of these financial products, the banks’ profits were proportional to the total size of their assets. The business model scaled up linearly. There were even cost savings associated with a larger business.

This is no longer true. The challenge of risk managing these new assets has broken that old model.

Not only are the assets themselves far harder to understand, but the interplay between the different assets creates another layer of complexity.

In addition, markets are prone to feedback loops. A bank owning enough of an asset can itself change the nature of the asset. JP Morgan’s $6 billion loss was partly due to this effect. Once they had began to dismantle the trade the markets moved against them. Put another way, other traders knew JP Morgan were in pain and proceeded to ‘shove it in their faces’.

Bureaucracy creates another layer, as does the much faster pace of trading brought about by computer programs. Many risk managers will privately tell you that knowing what they own is as much a problem as knowing the risk of what is owned.

Put mathematically, the complexity now grows non-linearly. This means, as banks get larger, the ability to risk-manage the assets grows much smaller and more uncertain, ultimately endangering the viability of the business.

Strategic recklessness

Some poignant (and infuriating) insight from Chris Arnade on Why it's smart to be reckless on Wall St.:

... asymmetry in pay (money for profits, flat for losses) is the engine behind many of Wall Street’s mistakes. It rewards short-term gains without regard to long-term consequences. The results? The over-reliance on excessive leverage, banks that are loaded with opaque financial products, and trading models that are flawed. ... Regulation is largely toothless if banks and their employees have the financial incentive to be reckless.

Networks in finance

Just over a week ago, the journal Nature Physics published an unusual issue. In addition to the standard papers on technical physics topics, this issue contained a section with a special focus on finance, especially on complex networks in finance. I'm sure most readers of this blog won't have access to the papers in this issue, so I thought I'd give a brief summary of the papers here.

It's notable that these aren't papers written just by physicists, but represent the outcome of collaborations between physicists and a number of prominent economists (Nobel Prize winner Joseph Stiglitz among them) and several regulators from important central banks. The value of insight coming out of physics-inspired research into the collective dynamics of financial markets is really starting to be recognized by people who matter (even if most academic economists won't wake up to this probably for several decades).

I've written about this work in my most recent column for Bloomberg, which will be published on Sunday night EST. I was also planning to give here some further technical detail on one very important paper to which I referred in the Bloomberg article, but due to various other demands in the past few days I haven't quite managed that yet. The paper in question, I suspect, is unknown to almost all financial economists, but will, I hope, gain wide attention soon. It essentially demonstrates that the theorists' ideal of complete, arbitrage free markets in equilibrium isn't a nirvana of market efficiency, as is generally assumed. Examination of the dynamics of such a market, even within the neo-classical framework, shows that any approach to this efficient ideal also brings growing instability and likely market collapse. The ideal of complete markets, in other words, isn't something we should be aiming for. Here's some detail on that work from something I wrote in the past (see the paragraphs referring to the work of Matteo Marsili and colleagues).

Now, the Nature Physics special issue.

The first key paper is "Complex derivatives," by Stefano Battiston, Guido Caldarelli, Co-Pierre Georg, Robert May and Joseph Stiglitz. It begins by noting that the volume of derivatives outstanding fell briefly following the crisis of 2008, but is now increasing again. According to usual thinking in economics and finance, this growth of the market should be a good thing. If people are entering into these contacts, it must be for a reason, i.e. to hedge their risks or to exploit opportunities, and these deals should lead to beneficial economic exchange. But, as Battiston and colleagues note, this may not actually be true:

By engaging in a speculative derivatives market, players can potentially amplify their gains, which is arguably the most plausible explanation for the proliferation of derivatives in recent years. Needless to say, losses are also amplified. Unlike bets on, say, dice — where the chances of the outcome are not affected by the bet itself — the more market players bet on the default of a country, the more likely the default becomes. Eventually the game becomes a self-fulfilling prophecy, as in a bank run, where if each party believes that others will withdraw their money from the bank, it pays each to do so. More perversely, in some cases parties have incentives (and opportunities) to precipitate these events, by spreading rumours or by manipulating the prices on which the derivatives are contingent — a situation seen most recently in the London Interbank Offered Rate (LIBOR) affair.

Proponents of derivatives have long argued that these instruments help to stabilize markets by distributing risk, but it has been shown recently that in many situations risk sharing can also lead to instabilities.

The bulk of this paper is devoted to supporting this idea, examining several recent independent lines of research which indicate the more derivatives can make market less stable. This work shares some ideas with theoretical ecology, where it was once thought (40 years ago) that more complexity in an ecology should generally confer stability. Later work suggested instead that complexity (at least too much of it) tends to breed instability. According to a number of recent studies, the same seems to be true in finance:

It now seems that the proliferation of financial instruments induces strong fluctuations and instabilities for similar reasons. The basis for pricing complex derivatives makes several conventional assumptions that amount to the notion that trading activity does not feed back on the dynamical behaviour of markets. This idealized (and unrealistic) model can have the effect of masking potential instabilities in markets. A more detailed picture, taking into account the effects of individual trades on prices, reveals the onset of singularities as the number of financial instruments increases.

The remainder of the paper goes on to explore various means that may be taken, through regulations, to try to manage the complexity of the financial network and encourage its stability. Stability isn't something we should expect to occur on its own. It demands real attention to detail. Blind adherence to the idea that "more derivatives is good" is a recipe for trouble.

The second paper in the Nature Physics special issue is "Reconstructing a credit network," by Guido Caldarelli, Alessandro Chessa, Andrea Gabrielli, Fabio Pammolli and Michelangelo Puliga. This work addresses an issue that isn't quite as provocative as the value of the derivatives industry, but the topic may be of extreme importance in future efforts to devise effective financial regulations. The key insight coming from network science is that the architecture of a network -- its topology -- has a huge impact on how influences (such as financial distress) spread through the network. Hence, global network topology is intimately linked up with system stability; knowledge of global structure is absolutely essential to managing systemic risk. Unfortunately, the history of law and finance is such that much of the information that would be required to understand the real web of links between financial institutions remains private, hidden, unknown to the public or to regulators.

The best way to overcome this is certainly to make this information public. When  financial institutions undertake transactions among themselves, the rest of us are also influenced and our economic well being potentially put at risk. This information should be public knowledge, because it impacts upon financial stability, which is a public good. However, in the absence of new legislation to make this happen, regulators can right now turn to more sophisticated methods to help reconstruct a more complete picture of global financial networks, filling in the missing details. This paper, written by several key experts in this technical area, reviews what is now possible and how these methods might be best put to use by regulators in the near future.

Finally, the third paper in the Nature Physics special issue is "The power to control," by Marco Galbiati, Danilo Delpini and Stefano Battiston. "Control" is a word you rarely hear in the context of financial markets, I suppose because the near religion of the "free market" has made "control" seem like an idea of "communists" or at least "socialists" (whatever that means). But regulation of any sort, laws, institutions, even social norms and accepted practices, all of these represent some kind of "control" placed on individuals and firms in the aim, for society at large, of better outcomes. We need sensible control. How to achieve it?

Of course, "control" has a long history in engineering science where it is the focus of an extensive and quite successful "control theory." This paper reviews some recent work which has extended control theory to complex networks. One of the key questions is if the dynamics of large complex networks might be controlled, or at least strongly steered, by influencing only a small subset of the elements making up the network, and perhaps not even those that seem to be the most significant. This is, I think, clearly a promising area for further work. Let's take the insight of a century and more of control theory and ask if we can't use that to help prevent, or give early warnings of, the kinds of disasters that have hit finance in the past decade.

Much of the work in this special issue has originated out of a European research project with the code name FOC, which stands for, well, I'm not exactly sure what it stands for (the project describes itself as "Forecasting Financial Crises" which seems more like FFC to me). In any event, I know some of these people and apart from the serious science they have a nice sense of humor. Perhaps the acronym FOC was even chosen for another reason. As I recall, one of their early meetings a few years ago was announced as "Meet the FOCers." Humor in no way gets in the way of good science.

The intellectual equivalent of crack cocaine

That's what the British historian Geoffrey Elton once called Post-Modernist Philosophy, i.e. that branch of modern philosophy/literary criticism typically characterized by a, shall we say, less than wholehearted commitment to clarity and simplicity of expression. The genre is represented in the libraries by reams of apparently meaningless prose, the authors of which claim to get at truths that would otherwise be out of reach of ordinary language. Here's a nice example, the product of the subtle mind of one Felix Guattari:

“We can clearly see that there is no bi-univocal correspondence between linear signifying links or archi-writing, depending on  the author, and this multireferential, multi-dimensional machinic catalysis. The symmetry of scale, the transversality, the pathic non-discursive character of their expansion: all these dimensions remove us from the logic of the excluded middle and reinforce us in our dismissal of the ontological binarism we criticised previously.”

I'm with Elton. This writer, it seems to me, is up to no good, trying to pull the wool over the reader's eyes, using confusion as a weapon to persuade the reader of his superior insight. You read it, you don't quite get it (or even come close to getting it), and it is then tempting to conclude that whatever he is saying, as it is beyond your vision, must be exceptionally deep or subtle or complex, too much for you to grasp.

You need some self confidence to come instead to the other logically possible conclusion -- that the text is actually purposeful nonsense, all glitter and no content, an affront against the normal, productive use of language for communication, "crack cocaine" as the writer gets the high that comes from appearing deep and earning accolades without putting in the hard work to actually write something that is insightful.

Having said that, let me also say that I am not in any way an expert in postmodernist philosophy and there may be more to the thinking of some of its representatives than this Guattari quote would suggest.

In any event, I think there's something deeply similar here to John Kay's point in this essay about Warren Buffet. As he notes, Buffet has been spectacularly successful and hence the subject of vast media attention, yet, paradoxically, he doesn't seem to have inspired an army of investors who copy his strategy:

... the most remarkable thing about Mr Buffett’s achievement is not that no one has rivalled his record. It is that almost no one has seriously tried to emulate his investment style. The herd instinct is powerful, even dominant, among asset managers. But the herd is not to be found at Mr Buffett’s annual jamborees in Omaha: that occasion is attended only by happy shareholders and admiring journalists.

Buffet's strategy, as Kay describes, is a decidedly old-fashioned one based on close examination of the fundamentals of the companies in which he invests:

If he is a genius, it is the genius of simplicity. No special or original insight is needed to reach his appreciation of the nature of business success. Nor is it difficult to recognise that companies such as American Express, Coca-Cola, IBM, Wells Fargo, and most recently Heinz – Berkshire’s largest holdings – meet his criteria. ... Which leads back to the question of why Berkshire has so few imitators. After all, another crucial insight of business economics is that profitable strategies that can be replicated are imitated until returns from them are driven down to normal levels. Why do the majority of investment managers hold many more stocks, roll them over far more often, engage in far more complex transactions – and derive less consistent and profitable results?

The explanation, Kay suggests, is that Buffet's strategy also demands an awful lot of hard work and it's easier for many investment experts to follow the rather different strategy of Felix Guattari, not actually working to achieve superior insight, but working to make it seem as if they do, mostly by obscuring their actual strategies in a bewildering cloud of complexity. Sometimes, as in the case of Bernie Madoff, the obscuring complexity can even take the very simple form of essentially no information whatsoever. People who are willing to believe need very little help:

... the deeper issue is that complexity is intrinsic to the product many money managers sell. How can you justify high fees except by reference to frequent activity, unique insights and arcana? But Mr Buffett understands the limitations of his knowledge. That appreciation distinguishes people who are very clever from those who only think they are.

One final comment. I think finance is rife with this kind of psychological problem. But I do not at all believe that science is somehow immune from these effects. I've encountered plenty of works in physics and applied mathematics that couch their results in beautiful mathematics, demonstrate formidable skill in building a framework of theory, and yet seem utterly useless in actually solving or giving insight into any real problem. Science also has a weak spot for style over content.

Obscurity and simplicity

The British economist John Kay is one of my favorite sources of balanced and deeply insightful commentary on an extraordinary number of topics. I wish I could write as easily and productively as he does. He has a great post that is, in particular, on Warren Buffet, but is more generally on an intellectual affliction affecting finance whereby purposeful obscurity often wins out at the expense of honesty and simplicity. Well worth a read. BUT... I think this actually goes way beyond finance. It's part of the human condition... more on that tomorrow.... 

The housing market in pictures

A blogger named Irvine Renter (aka Larry Roberts) knows an awful lot about the housing market and writes about it here. He also produces (and links to) some great cartoons, like this one...



and this one...



and this one...
 


and this one...

A real model of Minsky

Noah Smith has a wonderfully informative post on the business cycle in economics. He's looking at the question of whether standard macroeconomic theories view the episodic ups and downs of the economy as the consequence of a real cycle, something arising from positive feed backs that drive persisting oscillations all on their own, or if they instead view these fluctuations as the consequence of external shocks to the system. As he notes, the tendency in macroeconomics has very much been the latter:

When things like this [cycles] happen in nature - like the Earth going around the Sun, or a ball bouncing on a spring, or water undulating up and down - it comes from some sort of restorative force. With a restorative force, being up high is what makes you more likely to come back down, and being low is what makes you more likely to go back up. Just imagine a ball on a spring; when the spring is really stretched out, all the force is pulling the ball in the direction opposite to the stretch. This causes cycles.

It's natural to think of business cycles this way. We see a recession come on the heels of a boom - like the 2008 crash after the 2006-7 boom, or the 2001 crash after the late-90s boom - and we can easily conclude that booms cause busts.

So you might be surprised to learn that very, very few macroeconomists think this! And very, very few macroeconomic models actually have this property.

In modern macro models, business "cycles" are nothing like waves. A boom does not make a bust more likely, nor vice versa. Modern macro models assume that what looks like a "cycle" is actually something called a "trend-stationary stochastic process" (like an AR(1)). This is a system where random disturbances ("shocks") are temporary, because they decay over time. After a shock, the system reverts to the mean (i.e., to the "trend"). This is very different from harmonic motion - a boom need not be followed by a bust - but it can end up looking like waves when you graph it...

I think this is interesting and deserves some further discussion. Take an ordinary pendulum. Give such a system a kick and it will swing for a time but eventually the motion will damp away. For a while, high now does portend low in the near future, and vice versa. But this pendulum won't start start swinging this way on its own, nor will it persist in swinging over long periods of time unless repeatedly kicked by some external force.

This is in fact a system of just the kind Noah is describing. Such a pendulum (taken in the linear regime) is akin to the AR(1) autoregressive process entering into macroeconomic models and it acts essentially as a filter on the source of shocks. The response of the system to a stream of random shocks can have a harmonic component, which can make the output look roughly like cycles as Noah mentioned. For an analogy, think of a big brass bell. This is a pendulum in the abstract, as it has internal vibratory modes that, once excited, damp way over time. Hang this bell in a storm and, as it receives a barrage of shocks, you'll hear a ringing that tells you more about the bell than it does the storm.

Still, to get really interesting cycles you need to go beyond the ordinary pendulum. You need a system capable of creating oscillatory behavior all on its own. In dynamical systems theory, this means a system with a limit cycle in its dynamics, which settles down in the absence of persisting perturbation to a cyclic behavior rather than to a fixed point. The existence of such a limit cycle generally implies that the system will have an unstable fixed point -- a state that seems superficially like an equilibrium, but which in fact will always dissolve away into cyclic behavior over time. Mathematically, this is the kind of situation one ought to think about when considering the possibility that natural instabilities drive oscillations in economics. Perhaps the equilibrium of the market is simply unstable, and the highs and lows of the business cycle reflect some natural limit cycle?

Noah mentions the work of Steve Keen, who has developed models along such lines. As far as I understand, these are generally low-dimensional models with limit cycle behavior and I expect they may be very instructive. But Noah also makes a good point that the data on the business cycle really doesn't show a clear harmonic signal at any one specific frequency. The real world is messier. An alternative to low dimensional models written in terms of aggregate economic variables is to build agent based models (of much higher dimension) to explore how natural human behavior such as trend following might lead to instabilities at least qualitatively like those we see.

For some recent work along these lines, take a look at this paper by Blake LeBaron which attempts to flesh out Hyman Minsky's well known story of inherent market instability in an agent based model. Here's the basic idea, as LeBaron describes it:

Minksy conjectures that financial markets begin to build up bubbles as investors become increasingly overconfident about markets. They begin to take more aggressive positions, and can often start to increase their leverage as financial prices rise. Prices eventually reach levels which cannot be sustained either by correct, or any reasonable forecast of future income streams on assets. Markets reach a point of instability, and the over extended investors must now begin to sell, and are forced to quickly deleverage in a fire sale like situation. As prices fall market volatility increases, and investors further reduce risky positions. The story that Minsky tells seems compelling, but we have no agreed on approach for how to model this, or whether all the pieces of the story will actually fit together. The model presented in this paper tries to bridge this gap. 

The model is in crude terms like many I've described earlier on this blog. The agents are adaptive and try to learn the most profitable ways to behave. They are also heterogeneous in their behavior -- some rely more on perceived fundamentals to make their investment decisions, while others follow trends. The agents respond to what has recently happened in the market, and then the market reality emerges out of their collective behavior. That reality, in some of the runs LeBaron explores, shows natural, irregular cycles of bubbles and subsequent crashes of the sort Minsky envisioned. The figure below, for example, shows data for the stock price, weekly returns and trading volume as they fluctuate over a 10 year period of the model:

Now, it is not surprising at all that one can make a computational model to generate dynamics of this kind. But if you read the paper, LeBaron has tried hard to choose the various parameters to fit realistically with what is known about human learning dynamics and the behavior of different kinds of market players. The model also does a good job in reproducing many of the key statistical features of financial time series including long range fundamental deviations, volatility persistence, and fat tailed return distributions. So it generates Minsky-like fluctuations in what is arguably a plausible setting (although I'm sure experts will quibble with some details).

To my mind, one particularly interesting point to emerge from this model is the limited ability of fundamentalist investors to control the unstable behavior of speculators. One nice feature of agent based models is that it's possible to look inside and examine all manner of details. For example, during these bubble phases, which kind of investor controls most of the wealth? As LeBaron notes,

The large amount of wealth in the adaptive strategy relative to the fundamental is important. The fundamental traders will be a stabilizing force in a falling market. If there is not enough wealth in that strategy, then it will be unable to hold back sharp market declines. This is similar to a limits to arbitrage argument. In this market without borrowing the fundamental strategy will not have sufficient wealth to hold back a wave of self-reinforcing selling coming from the adaptive strategies.   

Another important point, which LeBaron mentions in the paragraph above, is that there's no leverage in this model. People can't borrow to amplify investments they feel especially confident of. Leverage of course plays a central role in the instability mechanism described by Minsky, but it doesn't seem to be absolutely necessary to get this kind of instability. It can come solely from the interaction of different agents following distinct strategies.

I certainly don't mean to imply that these kinds of agent based models are superior to the low-dimensional modelling of Steve Keen and others. I think these are both useful approaches, and they ought to be complementary. Here's LeBaron's summing up at the end of the paper:

The dynamics are dominated by somewhat irregular swings around fundamentals, that show up as long persistent changes in the price/dividend ratio. Prices tend to rise slowly, and then crash fast and dramatically with high volatility and high trading volume. During the slow steady price rise, agents using similar volatility forecast models begin to lower their assessment of market risk. This drives them to be more aggressive in the market, and sets up a crash. All of this is reminiscent of the Minksy market instability dynamic, and other more modern approaches to financial instability.

Instability in this market is driven by agents steadily moving to more extreme portfolio positions. Much, but not all, of this movement is driven by risk assessments made by the traders. Many of them continue to use models with relatively short horizons for judging market volatility. These beliefs appear to be evolutionarily stable in the market. When short term volatility falls they extend their positions into the risky asset, and this eventually destabilizes the market. Portfolio composition varying from all cash to all equity yields very different dynamics in terms of forced sales in a falling market. As one moves more into cash, a market fall generates natural rebalancing and stabilizing purchases of the risky asset in a falling market. This disappears as agents move more of their wealth into the risky asset. It would reverse if they began to leverage this position with borrowed money. Here, a market fall will generate the typical destabilizing fire sale behavior shown in many models, and part of the classic Minsky story. Leverage can be added to this market in the future, but for now it is important that leverage per se is not necessary for market instability, and it is part of a continuum of destabilizing dynamics.

Edmund Phelps trashes rational expectations

I'm not generally one to enjoy reading interviews with macroeconomists, but this one is an exception. Published yesterday in Bloomberg, it features an interview by Caroline Baum of Edmund Phelps, Nobel Prize winner for his work on the relationship between inflation and unemployment. This focus of the interview is on Phelp's views of the rational expectations revolution. He is not a big fan:

Q (Baum): So how did adaptive expectations morph into rational expectations?

A (Phelps): The "scientists" from Chicago and MIT came along to say, we have a well-established theory of how prices and wages work. Before, we used a rule of thumb to explain or predict expectations: Such a rule is picked out of the air. They said, let's be scientific. In their mind, the scientific way is to suppose price and wage setters form their expectations with every bit as much understanding of markets as the expert economist seeking to model, or predict, their behavior. The rational expectations approach is to suppose that the people in the market form their expectations in the very same way that the economist studying their behavior forms her expectations: on the basis of her theoretical model.

Q: And what's the consequence of this putsch?

A: Craziness for one thing. You’re not supposed to ask what to do if one economist has one model of the market and another economist a different model. The people in the market cannot follow both economists at the same time. One, if not both, of the economists must be wrong. Another thing: It’s an important feature of capitalist economies that they permit speculation by people who have idiosyncratic views and an important feature of a modern capitalist economy that innovators conceive their new products and methods with little knowledge of whether the new things will be adopted -- thus innovations. Speculators and innovators have to roll their own expectations. They can’t ring up the local professor to learn how. The professors should be ringing up the speculators and aspiring innovators. In short, expectations are causal variables in the sense that they are the drivers. They are not effects to be explained in terms of some trumped-up causes.

Q: So rather than live with variability, write a formula in stone!

A: What led to rational expectations was a fear of the uncertainty and, worse, the lack of understanding of how modern economies work. The rational expectationists wanted to bottle all that up and replace it with deterministic models of prices, wages, even share prices, so that the math looked like the math in rocket science. The rocket’s course can be modeled while a living modern economy’s course cannot be modeled to such an extreme. It yields up a formula for expectations that looks scientific because it has all our incomplete and not altogether correct understanding of how economies work inside of it, but it cannot have the incorrect and incomplete understanding of economies that the speculators and would-be innovators have.

I think this is exactly the issue: "fear of uncertainty". No science can be effective if it aims to banish uncertainty by theoretical fiat. And this is what really makes rational expectations economics stand out as crazy when compared to other areas of science and engineering. It's a short interview, well worth a quick read.

Highly ironic also that, nearly half a century after Lucas and others began pushing this stuff, the trend is now back toward "adaptive expectations." Is rational expectations anything other than an expensive 50 year diversion into useless nonsense?