What’s the use of econophysics?

Mark Buchanan has the answers:

1. More than anything, physicists have helped to establish empirical facts about financial markets; for example, that the probability of large market movements (up or down) decreases in accordance with an inverse cubic power law in many diverse markets…

4. Work in econophysics — through the study of minimal models such as the minority game — has also revealed surprising qualitative features of markets; for example, that a key determinant of market dynamics is the diversity of participants’ strategic behaviour…

7. On a similar theme, fundamental analysis by physicists has examined the relationship between market efficiency and stability.

Go read about 8 success stories of econophysics. Whenever I delve into the econophysics literature, it mostly seems…pretty boring and bad. But there’s some good stuff out there! You just have to find it.

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The economic and geographic environments of cities

Just like plants and animals, cities compete with each other and attempt to take advantage of the local environment in which they find themselves. Some cities are founded on oceans or rivers, others on plains, mountains, deserts or at the crossroads of trade networks. Yet, just like any organism that may find begin itself in an advantageous environment one day and find its environment transformed the next, the fundamental geographic advantages of cities can shift.

Guy Michaels and Ferdinand Rauch examined the shifting fortunes of cities in Europe as Empires ebbed and flowed:

Around the dawn of the first millennium Rome conquered and subsequently urbanised areas, including those that make up present-day France and Britain (as far north as Hadrian’s Wall). Under the Romans, towns in France and Britain developed similarly in terms of their institutions, organisation, and size. Around the middle of the fourth century, however, their fates diverged.

Roman Britain suffered invasions, usurpations, and reprisals against its elite. Around 410CE, when Rome itself was first sacked, Roman Britain’s last remaining legions, which had maintained order and security, departed permanently. Consequently, Roman Britain’s political, social, and economic order collapsed. From 450-600CE, its towns no longer functioned. The Roman towns in France also suffered when the western Roman Empire fell, but many of them survived and were taken over by the Franks.

…Medieval towns in France were much more likely to be located near Roman towns than their British counterparts (Figure 1). These differences in persistence are still visible today: only three of the 20 largest cities in Britain are located near the site of Roman towns, compared to 16 in France.

Cities exhibit a ‘path dependence’, where their fortune is linked to the experience of their specific history. Of course, they can impact their own environment in ways that can manifest physically – such as through the building of canals – or the establishment of trade networks and specialization. They can even spawn the growth of nearby towns to create their own trading microenvironments.

When crowds aren’t so wise

Alex Tabarrok recently related a familiar story about the ‘wisdom of the crowds’:

I ask the audience to guess my weight. They all wrote their guesses on a piece of paper. All the guesses was collected and an average guess – the “consensus forecast” – was calculated, while I continued my presentation.

I started my presentation and I naturally started telling why all of my forecasts would be useless – or at least that they should not expect that I would be able to beat the market. I of course wanted to demonstrate exactly that with my little stunt. It was a matter of demonstrating the wisdom of the crowds – or a simple party-version of the Efficient Market Hypothesis.

…I usually think of my own weight as being just below 80 kg…As always I was completely confident that the “survey” result would come in close to the “right” number. So I was bit surprised when the  ”consensus forecast” for my weight came in at 84.6 kg…So once I came back home I immediately jumped on the scale – for once I hoped to show that the Efficient Market Hypothesis was wrong. But the verdict was even more cruel. 84 kg!

And so, Tabarrok concludes, the market does not lie! Or at least, does not spread deliberate falsehoods. Except that’s a bit of a non sequitor, because there are two independent issues here: are crowds wise? And do markets reflect this wisdom?

One reason that crowds might be wise is that they are noise canceling. You and I may be able to guess something like someone’s weight from visual information fairly well but we can never be perfect – even a machine-like ‘optimal decoder’ will give a range of possible values due to little visual and personal quirks. But if we are all noisy in the same way, guessing independently from each other then the noise should disappear. Think of it like a drawing from a gaussian probability distribution – the more guess you make, the closer you get to the correct number.

Crowds can also be wise because they can generate more possible ideas. Just like the old saying goes, everyone is a bit different and will offer slightly different perspectives. Though you don’t even need that difference! A group of foraging animals aren’t all going to be checking the same areas for food, so when one finds a great food source others can join in.

There are a few clear problems that arise from trusting a crowd. A vast literature in ecology is dedicated to the question of when you should use social information instead of just your own personal information. Somewhat unintuitively, when the quality of personal information is lower it is less useful to pool with the crowd! And the size of the crowd matters; individuals in large crowds have an easier time of maintaining high group information even when personal information is of low quality.

Unfortunately, this assumes that there’s no talking in the group; nothing is being coordinated. Because when you start coordinating, when one person starts having influence, then suddenly opinions are correlated and can get dragged around in unfortunate ways. Now things are less diverse and you’re in a functionally smaller group (funnily enough, it also makes people more confident in the quality of their personal information).

Of course, this assumes you can trust others. Why should they provide you with their information? In the real world, my ability to get a good deal or an animal’s ability to find food may mean that if you find out, then I can’t get that deal! And the animal can’t get that food! Generally, it is better to trust the information from those whose goals don’t totally overlap with your own. In the wild, animals often do better when they don’t trust non-related animals of their own species (conspecifics) and trust other species (heterospecifics). And they prefer information from animals that have small home ranges, leading to information parasitization from animals that have larger home ranges! (I think that’s a pretty cool concept.)

And that brings us back to markets. Are crowds wise? Sometimes; but more importantly, should we trust the wisdom of the crowds? In a properly designed market, sure. I can’t think of why a one-time, everybody wins market wouldn’t be great. But when there are is low personal information (aka noise traders), group information goes down. When markets are small – and they are often quite finite! – group information goes down. When I can temporarily mislead an opponent about a reward, group information goes down. Markets can always lie.

References

Seppänen JT, Forsman JT, Mönkkönen M, & Thomson RL (2007). Social information use is a process across time, space, and ecology, reaching heterospecifics. Ecology, 88 (7), 1622-33 PMID: 17645008

King AJ, & Cowlishaw G (2007). When to use social information: the advantage of large group size in individual decision making. Biology letters, 3 (2), 137-9 PMID: 17284400

Lorenz J, Rauhut H, Schweitzer F, & Helbing D (2011). How social influence can undermine the wisdom of crowd effect. Proceedings of the National Academy of Sciences of the United States of America, 108 (22), 9020-5 PMID: 21576485

Economics may be a science, but it is not one of the sciences

(Begin poorly-thought-out post:)

Raj Chetty wrote an article for the New York Times that has been being passed around the economics blogosphere on why economics is a science:

What kind of science, people wondered, bestows its most distinguished honor on scholars with opposing ideas? “They should make these politically balanced awards in physics, chemistry and medicine, too,” the Duke sociologist Kieran Healy wrote sardonically on Twitter.

But the headline-grabbing differences between the findings of these Nobel laureates are less significant than the profound agreement in their scientific approach to economic questions, which is characterized by formulating and testing precise hypotheses. I’m troubled by the sense among skeptics that disagreements about the answers to certain questions suggest that economics is a confused discipline, a fake science whose findings cannot be a useful basis for making policy decisions.

He goes on to argue, strangely, that economics is a science because it is now primarily empirical. I’m not particularly interested in the argument of who is a “real” science – when I did physics, I remember people liked to make fun of biology as not a real “hard” science, etc.

But I spend a lot of time talking to people across the scientific spectrum – physicists, biologists, psychologists, economists. And economists are consistently the outlier in what they think about and who they reference. They are simply not a part of the broader natural sciences community. Look at the interdisciplinary connectivity between fields in the picture above. There is a clear cluster in the center of social studies and a largely separate ring of the natural sciences. Here’s another way of viewing it:

No matter how you slice it, economics is just not part of the natural sciences community. It’s starting to edge there, with some hesitant links to neuroscience and genomics, but it’s not there yet. I find it all a bit baffling. Why has economics separated itself so much from the rest of the natural sciences?

Richard Thaler on behavioral economics and nudges

Since the Nobel Prize committee decided to honor the rationality of the markets (or lack thereof), here’s a well-timed interview with behavioral economist RIchard Thaler:

Region: It’s hard to summarize the field, but you’ve written that there are three characteristics that differentiate Homo economicus from Homo sapiens: bounded rationality, bounded self-interest and bounded self-control.

Thaler: Those are the three things that—in the terminology Cass Sunstein and I use in our book Nudge.—distinguish humans from “econs,” short for Homo economicus. But I’ve now added a fourth “bound” that we also need in order to have behavioral economics: bounded markets.

If you had asked me in 1980 to say which field do you think you have your best shot at affecting, finance would have been the least likely, essentially because of the arguments that Becker’s making: The stakes are really high, and you don’t survive very long if you’re a trader who loses money.

Region: And you found that investors overreacted to both good and bad news; also, they were overconfident in their investing ability. The implication was that market prices weren’t always right. In other words, markets weren’t necessarily efficient, in contradiction to the efficient market hypothesis (EMH). Then in 2001, with Owen Lamont, you studied equity carve-outs and found more evidence that markets aren’t good at estimating fundamental value.

Thaler: Yes. Those papers highlight the two aspects of the efficient market hypothesis that I sometimes call the “no free lunch” part and the “price is right” part.
De Bondt and Thaler, “Does the Stock Market Overreact?” was about the no- free-lunch argument. When we were writing that paper in the early ’80s, it was generally thought by economists that the one thing we knew for sure is that you can’t predict future stock prices from past stock prices.

He goes on and talks about his work with the British government putting in successful ‘nudges’ and his relationship with Fama (they sit in mirror opposite offices at Chicago). He points out that when behavioral economics started with ‘bounded rationality’, a lot of the criticism was that it didn’t appear consistently or at the macro level. If you can’t aggregate the behavior, who cares? Well the more we investigate, the more important it turns out to be. I think neuroeconomics is in a similar stage – I’m not sure many economists really care, yet, because it will take time to figure out how to aggregate it. I wish I knew what Thaler thought about neuroeconomics. Anyone have a link to remarks of his on the topic?

Here’s an interview with Shiller who is teaming up with Akerlof to write a book about manipulation and deception in markets.

Nobel Prize in Economics: Fama, Hansen, and Shiller (link round-up)

The winners of this year’s pseudo-Nobel Prize in Economics are Fama, Hansen and Shiller. Marginal Revolution has a good series on what Fama did, what Hansen did, and what Shiller did. Hansen’s work is the hardest to understand in that it is basically stats. Here are more explanations.

Shiller of course had a lot of commentary on the recent bubble and crash which you should read.

I have nothing useful to add that is not in these links.

How little we know

In a recent issue of Nature there is a discussion of the history of utility theory:

Three centuries ago, in September 1713, the Swiss mathematician Nikolaus Bernoulli wrote a letter to a fellow mathematician in France, the nobleman Pierre Rémond de Montmort. In it, Bernoulli described an innocent-sounding puzzle about a lottery…The result is surprising. Each product — 1 × ½, 2 × ¼, 4 × ⅛, and so on — is a half. Because the series never ends, given that there is a real, if minute, chance of a very long run of tails before the first head is thrown, infinitely many halves must be summed. Shockingly, the expected win amounts to infinity…

In May 1728, writing from London, the 23-year-old mathematician Gabriel Cramer from Geneva weighed in. “Mathematicians value money in proportion to its quantity, and men of good sense in proportion to the usage that they may make of it.” This was a far-ranging insight. Adding a ducat to a millionaire’s account will not make him happier, Cramer reasoned. The usefulness of an extra coin is never zero, but simply less than that of the previous one — as wealth increases, so does utility, but at a decreasing rate. Assuming that utility increases with the square root of wealth, Cramer recalculated the expected win to be a little over 2.9 ducats.

Daniel encapsulated the probability scenario in a plot of utility versus monetary value, now known as a ‘utility function’ (see ‘Risky business’)… The curve’s diminishing gradient implies that it is always worth paying a premium to avoid a risk. The consequences of this simple graph are enormous. Risk aversion, as expressed in the concave shape of the utility function, tells us that people prefer to receive a smaller but certain amount of money, rather than facing a risky prospect.

It was a bit shocking to me how advanced these concepts were for the year 1700 – and how we haven’t come very far from those insights from the mathematicians of the 18th century. It’s a testament to the lack of experiment in economics that it took until the 1900s for Allais (and his “paradox”) and Kahneman and Tversky‘s theories to come about.

How trade develops: thinking in terms of “we”

This is an absolutely fantastic classroom experiment by Bart Wilson:

In the traditional market experiment, the experimenters explain to the participants how to trade. For this experiment that seemed more than a little heavy handed if the question is, what is the process by which exchange “gives occasion,” as Adam Smith says, to discovering the “division of labour”? …Thus the first requirement in building the design was that participants would have to discover specialization and exchange…

The participants choose how much of their daily production time they would like to allocate to producing red and blue items in their field. They are then told, deliberately in the passive voice, that “you earn cash based upon the number of red and blue items that have been moved to your house.” What they have to discover is that not only can they move items to their own house, but that they can move items to other people’s houses…

At one extreme, the economy achieves 88% of the possible wealth above self-sufficiency by the last day[.] And at the other extreme, only 6% of the possible wealth above autarky is realized[…] Why the disparity? These students are immediately engaging their counterparts as part of an inclusive “we”. The same is not true in group 4 [which achieved less wealth].

He then goes into detail on the words and mode of thinking that different groups used to develop the idea of trade and markets. The conclusion is that the development of trade and specialization arises from considering the group and not the individual. And this is in a capitalist society! It is not to say that the only way for trade and specialization to develop is a kind of group-consciousness, and it is not to say that it wouldn’t have developed anyway. But it’s a bit of evidence that it can foster the conditions that make mutually beneficial trade networks increasingly likely.

As a second experiment, I would be interested in how quickly students familiar with the idea and the mathematics would find the optimal solution, and how it would evolve in a ‘noisy’ environment. I’d really like to see more advanced analyses of the text as well, the communication networks that evolve, and how they coordinate the development of the intellectual idea. Is there a tipping point? Is it a steady accumulation towards the optimum? Are there ‘laggards’ that are unconvinced?

But this is a great experiment and a great teacher.

The young and the restless

Elderly chinese men playing chess

It struck me recently that one of the key differences between economists and neuroscientists studying decision-making is their interest in dynamics.  Economists seem more interested in explaining how behavior operates (or should operate) on average whereas neuroscientists would like to explain trial-to-trial variability.  Decisions are rarely made just once in a lifetime, but are instead made repeatedly.  Any behaviorist would instantly tell you that this means that there will be a learning component, something that I hardly see in the economic decision-making literature (feel free to correct me if this is wrong).

In many of these repeated decisions, people are not simply making a decision in a vacuum but are responding to the actions of others.  The decision must then be balanced by their prior beliefs, the results of recent decisions, and their predictions of how other people will act.  All of this can be incorporated into a reinforcement learning (RL) paradigm, where the expected value of any action is a combination of classical RL – where every payoff suggests future payoffs, and every loss suggests future losses – as well as a ‘mentalizing’ component that predicts how the opponent is likely to act, and how the opponent will react.  By fitting the responses of different brain regions to this type of model, one can get a sense of what each region is (kind of) doing.  One region that instantly pops out is the medial prefrontal cortex (mPFC): this region is highly correlated with the prediction of other people’s behavior.

I once took a behavioral economics class in which the professor pointed out that deviations from rational behavior are only important if they translate to something in aggregate.  In other words, who cares if just a few people have abnormal mPFC function.  In a large population you won’t notice them.  But in fact there is a very large group of people with degraded mPFC: the elderly.  13 percent of the US is over the age of 65, and this group is known to have significant loss of volume in mPFC.  The prediction, then, would be that older individuals would be less inclined to take into account the behavior of other individuals when making decisions.

To test how they will act, we can take the experimental game the “Patent Race”.  In this game, two players are selected from a pool to compete for a prize.  They are each given either a large five credit or a small four credit endowment, and are asked to “invest” some portion of that.  They then get to keep whatever is left over, and the person who “invested” the most wins ten extra credits.

Cumulative distribution plots of how influential other individual's behavior is in determining one's own behavior.  Blue represents young adults and purple-dashed represents the elderly.

Cumulative distribution plots of how influential other individual’s behavior is in determining one’s own behavior. Blue represents young adults and purple-dashed represents the elderly.

There does exist a Nash equilibria to this game, and young adults will play the Nash equilibria exactly.  Old adults, on the other hand, play a significantly different strategy.  What is more interesting, though, is half of elderly adults behave as if they did not care at all about the strategy of the other player.  In other words, they are making decisions using a pure reinforcement learning strategy where they only cared about payoffs, not about how the other player was going to act.  In contrast, no young adults played like this: they all took into account the strategy that the other player would use.

References

Hampton, A., Bossaerts, P., & O’Doherty, J. (2008). Neural correlates of mentalizing-related computations during strategic interactions in humans Proceedings of the National Academy of Sciences, 105 (18), 6741-6746 DOI: 10.1073/pnas.0711099105

Zhu, L., Walsh, D., & Hsu, M. (2012). Neuroeconomic Measures of Social Decision-Making Across the Lifespan Frontiers in Neuroscience, 6 DOI: 10.3389/fnins.2012.00128

Photo from

Life is not in an equilibrium

Much of economics is built upon the idea of equilibrium: supply equals demand, and if there are opportunities to drive down price to equilibrium, they will immediately be taken.  Economists assume this because it is hard to predictions otherwise.  Important assumption though this is, this can be hard to empirically test; all such tests are necessarily indirect approximations.  So what happens when you have a virtual economy and can empirically test this?  Well, it turns out that the economy is frequently out of equilibrium:

The data makes it look like external shocks take you out of equilibrium (unsurprisingly) and that equilibrium returns fairly quickly.  But just look at how often the economy is out of equilibrium!  It’s all the bloody time!  It almost looks like instead of a fixed point we’ve got a limit cycle with varying amplitude.  This shouldn’t be a surprise, but it is nice to get real data.  Next the question is: which are the equilibrium and which are the non-equilibrium situations, how often do they each occur, and how big are the differences between markets?