Broken Symmetry

Symmetry and Entropy in Market Bubbles and Crashes

From Dion Harmon, Marcus A. M. de Aguiar, David D. Chinellato, Dan Braha, Irving R. Epstein, Yaneer Bar-Yam:

Predicting panic is of critical importance in many areas of human and animal behavior, notably in the context of economics. The recent financial crisis is a case in point. Panic may be due to a specific external threat, or self-generated nervousness. Here we show that the recent economic crisis and earlier large single-day panics were preceded by extended periods of high levels of market mimicry --- direct evidence of uncertainty and nervousness, and of the comparatively weak influence of external news. High levels of mimicry can be a quite general indicator of the potential for self-organized crises.

Via Physics arXiv blog.

What I like about this work is how at the conceptual level it fits with other theories of markets making phase transitions between high and low entropy states, with symmetries breaking as the transition begins and picks up steam.

There is a lot of talk about whether Quantitative Easing has done much. Folks like Scott Sumner seem to be arguing that it has not because market expectations were adjusted at the moment QE was announced (or quickly thereafer). I'm more skeptical about that claim because I imagine that it takes more than days or even weeks for organizations to propagate new information about prospective rates through their entire ranks, such that there remains an impedance mismatch between Fed signals and market reactions. But at an even more fundamental level, the market response to Fed signals does not appear to be linear within some regimes, including the one we live in now, which looks to me like a liquidity trap, albeit not homogeneously sticky for all industries and firms. (Consumer internet, in particular, seems to be attracting capital investment at an accelerated pace compared even with hardware and software solutions providers.)

High-Frequency Trading Fact of the Day

From an interesting paper on the flash crash by Easley, Mailoc Lopez de Prado, and O'Hara:

Since 2009 high-frequency trading firms, which represent approximately 2% of the nearly 20,000 trading firms operating in the U.S. markets, have accounted for over 73% of all U.S. equity trading volume.

Via Computational Legal Studies

Valuing Patented Features of Complex Systems Using Frequency-Averaged Measures of Demand

[Submitted today in response to this call for papers. -MFM]

ABSTRACT

Thanks to the ubiquity and integration of digital computers, each consumer of a product or service now produces a digital stream of data. Bundled together, these streams of data record how particular products or services, including any patented features, are valued by actual consumers in different geographical regions and in different windows of time. Most relevant to patent royalty calculations are the histories of transactions for a particular product or service. These transactions eventually show up in financial statements, which permit top-down estimates of value, such as revenue or gross margins. But alternative metrics drawn from these streams, such as change in the frequency of transactions before and after the introduction of a patented feature, also permit bottom-up estimates of the value of patented features. Demand can also be estimated using metrics for customer engagement, such as the frequency and length of visits to a particular website or the conversion ratio of number of independent visits per completed transaction. In some cases, analyses of these data permit calculation of a more reliable lower bound for the marginal value of a patented feature to a complex product or service. More generally, time-frequency analyses of data on consumer behavior complement existing methods for calculating lost profits or reasonable royalties, and can help resolve questions about the marginal value a patented feature adds to a complex or highly integrated product or service.

The Damages Apportionment Problem for Complex Systems

Under 35 U.S.C. § 284, “[u]pon finding for the claimant the court shall award the claimant damages adequate to compensate for the infringement but in no event less than a reasonable royalty for the use made of the invention by the infringer, together with interest and costs as fixed by the court.” Famously, the Southern District of New York laid out a “comprehensive list of [fifteen] evidentiary facts  relevant, in general, to the determination of the amount of a reasonable royalty for a patent license” Georgia-Pacific Corp. v. U.S. Plywood Corp., 318 F.Supp. 1116, 1120 (S.D.N.Y.1970). The thirteenth in this list is “[t]he portion of the realizable profit that should be credited to the invention as distinguished from non-patented elements, the manufacturing process, business risks, or significant features or improvements added by the infringer.” Id.

When Georgia-Pacific was decided in 1970, Jimi Hendrix was still performing, the Internet was known only as ARPANET, and access to information about cutting edge research and development usually required national security clearance. Four decades later, instead of secrets about national defense leaking to the press through a former first lieutenant in the Marine Corps with high-level security clearance, an Australian hacker is leaking them to the Internet. Instead of a carefully choreographed ballet of contractors producing a 747, a globally distributed swarm of programmers continuously releases new features and combinations of features in an effort to attract a stable base of users. Consumers depend upon producers – producers who compete vigorously with each other to make the sales necessary for their own survival – to cooperate in the development and adoption of industry standards that are necessary for complex, integrated systems to exist at all. The Federal Circuit put it well in describing one of the most commercially successful productivity software products as “an enormously complex software program comprising hundreds, if not thousands or even more, features.” Lucent Technologies, Inc. v. Gateway, Inc., 580 F. 3d 1301, 1333 (Fed. Cir. 2009). The Federal Circuit found “it inconceivable to conclude, based on the present record, that the use of one small feature … constitutes a substantial portion of the value.” Id.

Most lawyers agree with the Federal Circuit that the base for calculating royalties should be discounted to adjust for the value that other features contribute to a product. Other features may include features themselves covered by other patents (not owned in common with a patent-in-suit), or features not easily protectable through patents (such as the durability of parts, precision of manufacturing tolerances, or the timely availability of the product or service at a requested order volume). Moreover, what feature or features were sufficient or necessary to the completion of a sale may vary from customer to customer, or even for the same customer over time. In most cases, it is indeed inconceivable that any single patented feature could be responsible for the entire revenue (much less profit) generated by a complex or highly integrated product or service.

On the other hand, the very fact that an infringer has chosen to implement a patented feature rather than a non-infringing alternative is strong evidence that the patented feature most likely contributes some finite value to the product or service. That value, in turn, is ultimately reflected in the revenue and profit generated by the sale of the complex product or service that includes the patented feature.

[Discussion of economic case for patents, focusing on the potential social benefit of granting property rights in easily appropriable innovations in markets with high barriers to entry. Exclusionary rights permit supracompetitive prices in proportion to inelasticity of demand for patented innovations. Thus, measuring inelasticity of demand is core problem for patent valuation in general, and for damages apportionment in particular.]

Measuring the Price Elasticity of Demand

The Federal Circuit has acknowledged that price elasticity is at the core of the problem of patent valuation. The opinion in Crystal Semiconductor v. Tritech Microelectronics, 246 F. 3d 1336 (2001) is particularly instructive, although it deals specifically with price erosion. In Crystal Semiconductor, the Federal Circuit explained the economic theory of price elasticity:

For example, if substitution of a product were impossible and the product were a necessity, elasticity of demand would be zero — meaning consumers would purchase the product at identical rates even when the price increases. This very rare type of market is called inelastic. On the other side of the spectrum, if any price increase would eradicate demand, elasticity of demand would be infinite — meaning consumers would decline to purchase another single product if the price increases by any amount. This very rare type of market is called perfectly elastic. Markets typically have an elasticity greater than zero and less than infinity.

Crystal Semiconductor, 246 F.3d at 1359 (italics added). In other words, the market value of a patented feature should be tied to its effect on price elasticity, and price elasticity can be estimated by reference to the relative rate of sales at different price levels. The Federal Circuit went on to rule that the patentee in Crystal Semiconductor had failed to show sufficient evidence of whether or how much the rate of sales would have declined as a result of a price increase. Id. at 1360-1. It is enough for my purposes, however, to note that the Crystal Semiconductor case provides a legal precedent for the use frequency-averaged measures of the value of patented innovations, such as relative rates of sales.

Top-Down Estimates from Time-Averaged Revenues and Profits

The approach to estimating price elasticity described in Crystal Semiconductor requires the use of revenue and profit figures, which would typically be derived from financial statements. Financial statements provide a highly compact summary of the entire history of transactions that occurred among a company and its many stakeholders, from the purchasing of capital equipment and parts from suppliers, to the payment of labor for design and assembly, to the actual payments of cash from customers for delivery of the final product. Thus, financial statements provide a good foundation for what I will call “top-down” estimates of the value of patented features.

[Discussion of the information architecture of financial statements: Income and cash-flow statement record time-integrated flow of revenue and expenses; balance sheet records snapshot in time of assets and liabilities. The information architecture of financial statements lends itself to optimization of time-averaged measures of efficiency in increasing sales, decreasing costs of sales. Trends in sales or costs of sales are visible only after two or more periods have elapsed.]

Top-down estimates of the value of patented innovations are most appropriate for valuation of products or services that are protected by a single patent. Top-down estimates provide only a ceiling on valuation when multiple patents cover each product or service sold in the transactions that ultimately result in the financial statements from which the top-down estimates are drawn.

Frequency-Averaged Measures of Productivity

Every time-averaged measure of profitability has a frequency-averaged counterpart. In practice, experienced investors and managers use both to develop a picture of the health of an organization. For example, in addition to gross margin – a time-averaged ratio of profit to revenue – experienced investors and managers also track inventory turnover – a frequency-averaged ratio of costs of goods sold to average inventory. A company with high gross margins but dropping inventory turnover is unlikely to maintain its margins going forward. Conversely, low margins with increasing inventory turnover signals that higher margins might be available in the future. [Discuss analogy to driving without a tachometer.]

Inside large corporations, managers don’t wait until the end of the quarter to spot trends in supply or demand for a particular good or service. Rather, managers monitor daily reports about order and inventory volume to ensure that the supply of products and services stays synchronized with customer demand.

Bottom-up Estimates from Frequency-Averaged Measures

The stream of data that management uses for frequency-averaged measures of productivity provides the basis for alternative, bottom-up estimates of demand for patented innovations. Bottom-up estimates derived from frequency-averaged measures are useful in valuing patents on innovations introduced as features of an existing product or service, or in valuing patents on products or services that are sold as a bundle with many other products or services. Bottom-up estimates may also be helpful in putting a more reliable floor on the minimum value of a patented innovation. A variety of techniques may be used to produce bottom-up estimates using frequency-averaged measures. I give two as examples: Fourier analysis of a time-series of transactions and A|B testing of a web service.

Sales of a particular product are recorded as a time-series of transactions, each of which is associated with a particular price. Within a particular window of time, one can count up the number of transactions and the total sales. The former is a frequency-integrated measure of sales, the latter the time-integrated measure of revenue. Focussing on the former, we can see how the frequency of sales changes within different same-width and different-width windows of time. Most relevant to patent valuation, we can look at how the frequency of sales changes before and after the introduction of a new patented feature. If frequency increases even as price is held constant or decreased, the patented feature probably increased the demand for the product or service.

Because frequencies change seasonally, many web services rely upon a more direct method for testing demand for a feature, called A|B testing. Using A|B testing, managers can watch how actual consumers interact in real-time with a web service that includes slightly different features. It is conceivable that A|B testing could be used in some cases to demonstrate that a patented feature is less desirable than an existing version of web service, effectively resolving some disputes that cannot be resolved using only top-down estimates of value. [Discussion of A|B testing, Google Analytics, Optimizely, &c.]

Broken Symmetries and the Culture of the Ants

From Deborah M. Gordon:

Ants can show us how the rhythm of local interactions creates patterns in the behavior and development of large groups.

Via Teppo Felin at Orgtheory What Gordon suggests is that spatial and temporal periodicities could be used to coordinate (unconsciously) the behavior of groups of people. Isn't this what Thomas Schelling suggested decades ago? Why haven't economists (in particular) made more progress on these fronts? Here are my guesses:

1. The rational expectations model of group behavior is operationalized through revealed preferences, and tests of the model have been possible only through aggregate statistics like the CPI. (Maybe Google will have a hand in more fine-grained tests.)
2. Most economists never ask the why or how questions when it comes to preference formation. Take the Becker and Stigler classic as evidence.
3. (Most importantly) The data didn't exist at least until Csikszentmihalyi started handing out pagers for the ESM project in the 1980s.

One and two haven't changed.

Improving on the Signal to Noise Ratio -- Stadium Edition

From Wired's Gadget Lab:

Squarehead’s new system is like bullet-time for sound. 325 microphones sit in a carbon-fiber disk above the stadium, and a wide-angle camera looks down on the scene from the center of this disk. All the operator has to do is pinpoint a spot on the court or field using the screen, and the Audioscope works out how far that spot is from each of the mics, corrects for delay and then synchronizes the audio from all 315 of them. The result is a microphone that can pick out the pop of a bubblegum bubble in the middle of a basketball game...

Storytelling Synchronizes Neural Networks

From the Wired Science blog:

When two people experience a deep connection, they’re informally described as being on the same wavelength. There may be neurological truth to that. Brain scans of a speaker and listener showed their neural activity synchronizing during storytelling. The stronger their reported connection, the closer the coupling.

Links to earlier related posts:

Focal Points Constitute Organizations by Synchronizing the Phase of Human Rhythms

The Synchronized Flow Theory of the Firm

Organic Economics

Popping Bubbles With Sornette

Here's the arXiv blog's summary of his latest gambit:

Sornette says there are two parts to his forecasting method. First, he says bubbles are markets experiencing greater-then-exponential growth. That makes them straightforward to spot, something that surprisingly hasn't been possible before.

Second, he says these bubble markets display the tell signs of the human behaviour that drives them. In particular, people tend to follow each other and this result in a kind of herding behaviour that causes prices to fluctuate in a periodic fashion.

I find the particular mathematical model (of log periodic oscillations) less interesting than what it's trying to capture in the underlying market dynamics. Canonical neoclassical models of markets give no insight into correlation and synchronization of market actors. These dynamics are the most obvious and important new facts about markets we (as global market participants) have learned as a result of the ongoing crisis. It would be nice to see more of these ideas percolate out into economic analysis of law, for example.

See here for an earlier post on Sornette. And here for my favorite model of synchronization -- introduced in a paper by Zanette and Kuperman.

What do B.S. readers think of Sornette's work?

Reprise: An Economy Made of Glass

Want a handwavy physics-based explanation for what happened at 2:45 p.m. on Thursday, May 6, 2010? Here's a post from the B.S. archives:

[I]f an economy is modeled as cross-linked clusters of synchronized oscillations, then we might expect to see viscoelasticity and time-dependent transitions in its equilibriums also. Should bubbles and crashes be modeled as viscoelastic creep?

Such an analogy might offer practical value to financial regulators. Generally speaking, the fragility of a glass will depend on the size and shape of the molecular clusters and the number of cross-links among them. The bigger the clusters and the more the cross-links, the more fragile the glass to external shocks. Smaller clusters and fewer cross-links mean less viscosity and elasticity.

We're so heavily cross-linked through digital exchanges and statistical arbitrage, when that big market sell order came through for P&G, the whole market splintered into a thousand desynchronized clusters.

Something I'd like to read more about is what happened in the bond markets at 2:45 p.m. Anybody have a link? Is it the case that credit still gets traded almost entirely by humans? I generally wonder why we don't trade credit the way we trade equity. What are the historical and practical reasons for the fact that we have public indices for equity, but not debt?

Do Market Prices Synchronize Input and Output?

A couple of years ago I was reading Schelling's Micromotives and Macrobehavior, and was struck by his description of the phase mismatch in the marriage market. I wondered (out loud here, using sloppy terminology) whether market price signals couldn't be understood as a mechanism for ameliorating phase mismatch (or "latency"). Williamson identifies "frequency" as a category of transactions costs. But in fact it isn't frequency so much as differences in frequency (or differences in phase when buyers and sellers operate at the same frequency) that raises transaction costs.

If we think about markets as networks, then we can identify market makers as important nodes -- like train junctions or airports in transportation networks. Market makers and market prices haven't been studied much this way. But transportation networks have.

A paper by Lacasa, Cea, and Zanin is particularly suggestive in this regard. Lacasa et al. show that as the density of flow within an air transportation network increases, the network undergoes a phase transition above a certain threshold, whereby nodes of intermediate traffic density display "Brownian motion" in delay times. This "Brownian motion" ends when the traffic density increases still further, resulting in bottlenecks that, like traffic lights, effectively limit the rate of flow through the network.

Today the Physics arXiv blog calls my attention to a new paper by Fretter, Krumov, Weihe, Müller-Hannemann, and Hütt, which arrives makes similar observations about the traffic through rail and gene networks. But the newer paper takes a very interesting step forward by applying a phase synchronization analysis (related to the Kuramoto Model) to its data. Here's one of their conclusions:

We believe that a quantitative view on synchronization of arrival/departure events in the network of long-distance train connections, as presented here, can similarly serve as a starting point for a theoretical understanding, and subsequently systemic optimization, of the balance between eciency and robustness for such timetables underlying public transportation.

This work has direct relevance to scalable plans for regulation of systemic risk within our global economy.

Phil Weiser on the Topology of Innovation Networks

From a speech by Deputy Assistant AG to the Antitrust Division Phil Weiser on 31 January 2010:

One fascinating dynamic in today's entrepreneurial economy is that the world is simultaneously more locally driven and more interlinked. It is more local because clusters of business start-up and expansion activity can create local symbiotic relationships that fuel further growth and innovation; it is more interlinked because ongoing technological development and races to innovate have created internationally interconnected networks for product development, production, and distribution. A key challenge, recognized and engaged by the Obama Administration's Strategy for American Innovation is understanding how best to balance these local and global forces. For countries, it creates an awkward dynamic insofar as modern economic forces are making both local geography and global connections more important. Thus, to be economically successful, countries must both support local economic clusters to spur entrepreneurship and innovation as well as participate and compete in global markets.

I like almost everything Weiser has to say here, although he is as optimistic about the accuracy of antitrust regulation as you would expect for a government agent. To take the Microsoft case, for example, I have previously blogged that the best result might have been for Microsoft to license in browser technology from Netscape.

Weiser's ultimate suggestion is an excellent one. The government would do well to leverage the comparative advantage of private institutions, such as standards-making bodies, in balancing exclusivity and access in order to achieve the right balance between competition and innovation. See here for a few additional thoughts along these lines.

Weiser and I also share the view that natural monopolies ought to be subject to compulsory licensing -- a fact I discovered on reading a post he did on SSOs for the Truth on the Market blog a few months ago. Where we may disagree more is over the question of who and how natural monopolies are to be identified.

Asynchrony in the Frontal Cortex

Jonah Lehrer provides some interesting description of research on synchronized brain activity in -- of all things -- a review of Avatar:

The most notable of these "non-synchronous" regions is the prefrontal cortex, an area associated with logic, deliberative analysis, and self-awareness. (It carries a hefty computational burden.) Subsequent work by Malach and colleagues has found that, when we're engaged in intense "sensorimotor processing" - and nothing is more intense than staring at a massive screen with Dolby surround sound while wearing 3-D glasses - we actually inhibit these prefrontal areas.

What I want to know is how mirror neuron theory is considered by some to be discredited for lack of precise mechanism despite these kinds of studies? Who cares whether it's a single neuron or single group of neurons that permits these social effects?

Meditations on Calendar Reforms

From the WSJ:

Creating a calendar is like fitting a lot of round pegs into not quite as many square holes. Western tradition demands a seven-day week. Ancient custom, rooted in moon cycles, calls for a 12-month year. The Earth's tilted axis produces four seasons. But the Earth, uncooperatively, takes 365 days, plus a tad more, to go once around the sun, and 365 is divisible by none of seven, 12 or four. And thanks to the extra bit of time -- about one-fourth of a day -- required for a complete orbit, leap years are needed to keep things on track.

Religious and civil authorities in the past have reformed the calendar in ways not unlike how local and state authorities govern daylight savings time today. Calendar reform is a historical subject that gives us insight into what organizations had true authority over everyday lives at a given moment in history.

Such reforms are also a direct regulation of how people synchronize activities. But unlike the bells of Venice, which lengthened in the summer and shortened in the winter, the intent of reformers now seems to be achieving a more symmetrical match between the frequency of astronomical and human activities.

But why should we prize symmetry with the stars above human needs? Consider the Pythagorean comma. The fact that perfect fifths cannot be made to coincide with octaves does not prevent us from making beautiful music. What a comment on our culture: Calendar reformers seek not to accommodate the human need for stability and consistency, but to measure life out in a more symmetrical (and hence aesthetically pleasing?) increment.

The calendar should be our slave, not we its servant.

Easley and Kleinberg on Synchronization

From Chapter 21 of their treatise on Networks, Crowds, and Markets:

When looking at public-health data, it is natural to look at periodic oscillations in the number of cases of a disease and to try positing external causes for the effect. For example, cycles in the prevalence of syphilis across the U.S. over the past 50 years have traditionally been attributed to large-scale societal changes, including changes in sexual mores and other forces [194]. While such factors clearly play a role, recent research has shown that oscillations and synchronization over time can in fact result largely from the contagion dynamics of the disease itself, and that similar patterns can be created in direct simulations of the disease using the types of models we have been considering here [194, 264].

We now describe how such effects can be produced using simple epidemic models. The crucial ingredients appear to be a combination of temporary immunity and long-range links in the contact network. Roughly, long-range links produce coordination in the timing of flare-ups across dispersed parts of the network; when these subside, the temporary immunity produces a network-wide deficit in the number and connectivity of susceptible individuals, yielding a large “trough” in the size of the outbreak that directly follows the “peak” from the earlier flare-ups. We now describe how to make this intuitive picture concrete using simple models.

Want an explanation for how markets all over the world seem to have become more correlated?

As financial institutions have become more densely coupled through new financial instruments and leverage, what used to be only local bubbles and crashes are now global epidemics.

Distinguishing Exogenous from Endogenous Market Crashes

Simoleon Sense links to what could be a useful bit of anlaysis from Sornette et al.:

[W]e have provided an objective test of the hypothesis that the largest negative markets moves are special and form two distinct populations. The exogenous crashes can be attributed to extraordinary important external perturbations and/or news impacting the market. The endogenous crashes can be seen as the natural deaths of self-organized self-reinforcing speculative bubbles giving rise to specific precursory signatures in the form of log-periodic power laws accelerating super-exponentially.

Sornette applied a similar approach to analyzing YouTube video traffic here.

I'm slowly warming up to Sornette's idea of log-periodic scaling. The mathematical part of this model, at bottom, arises from a treatment of fractional dimensions as complex rather than real-valued quantities.

What Mandelbrot and Fama Both Got Wrong: Buyers and Sellers Can Synchronize

I've been working through a paper by Eugene Fama, titled "Madelbrot and the Stable Paretian Hypothesis." The paper is from 1963. I found it in Modern Developments in Investment Management, edited by Lorie and Brealey and published in 1976. It was in the free books bin outside a bookstore in Noe Valley!

As a historical record, this is a wonderful article. In the article, Fama finds the data inconclusive as to whether the Pareto distribution applies better as a fit to the distribution of price changes during a given period of time. The punchline, of course, is that Fama's efficient market hypothesis (which he developed in the decade after this paper was published) gave the confidence at least to Black and Scholes and many others to base their models of price changes on Gaussian distributions. At least at one point, Fama was open to another possibility.

But what is more interesting is the evidence from this paper, which suggests that both Mandelbrot and Fama may have made the same mistake in analyzing time series of prices. In particular, it seems that both Mandelbrot and Fama wanted to maintain the assumption of independence in price changes in successive intervals. They seem to have had the same reason too. Both wanted whatever distribution that might apply in a shorter interval to apply also in longer or successive intervals -- the very condition that fails when the price changes are not independent. Here's how Fama puts it:

If the changes between transactions are independent, identically distributed, stable Paretian variables, daily, weekly, and monthly changes will follow stable Paretian distributions of exactly the same form, except for origin and scale.

Mandelbrot, recognizing that a Gaussian was not a good fit, picked the Pareto distribution as an alternative. Why did he choose the Pareto distribution? I'm not sure, but there is a good chance that he did so because while its infinite variance permitted wider swings in price than the Gaussian, the Pareto distribution is still stationary in the sense that it treats the price changes during particular intervals as wholly independent.

Both Mandelbrot and Fama seem to have let themselves be guided too strongly by their theoretical ambitions. If we observe what actually happens in crowded marketplaces (such as a crowded trading floor), it is easy to observe how buying and selling behavior is correlated. This kind of correlation (which Keynes attributed to "animal spirits") destroys the very independence that is necessary to the assumption of stationarity made by both Mandelbrot and Fama in their models of market prices!

What alternative models might we use to understand price changes? We have to start from models like the 1D Ising model described in the last post, models which show how correlations at the microeconomic scale can aggregate up into macroeconomic fluctuations. We must begin with the assumption that buying and selling decisions are at least weakly coupled, so that market price changes reflect the large swings that can result from synchronization. In future posts, I shall attempt an explanation for how the Kuramoto Model of synchronization could be used to model the non-stationary distribution(s) of market prices.

UPDATE: My sincere apologies to Mandelbrot. I find in this early work that he did not assume stationarity, and was aware of the non-stationarity in these distributions all along.

Ecological and Constructivist Rationality

Vernon Smith has articulated a distinction between "constructivist" and "ecological" rationality in economics:

We have become accustomed to the idea that a natural system like the human body or an ecosystem regulates itself. To explain the regulation, we look for feedback loops rather than a central planning and directing body. But somehow our intuitions about self-regulation do not carry over to the artificial systems of human society...

"[C]onstructivist rationality (or ‘constructivism’) ... stems particularly from Descartes (also Bacon and Hobbes), who believed and argued that all worthwhile social institutions were and should be created by conscious deductive processes of human reason...In summary, constructivism uses reason to deliberately create rules of action, and create human socioeconomic institutions that yield outcomes deemed preferable, given particular circumstances, to those produced by alternative arrangements...

Since our theories and thought processes about social systems involve the conscious and deliberate use of reason, it is necessary to constantly remind ourselves that human activity is diffused and dominated by unconscious, autonomic, neuropsychological systems that enable people to function effectively without always calling upon the brain’s scarcest resource– attentional and reasoning circuitry...

These considerations lead to the second concept of a rational order, as an undesigned ecological system that emerges out of cultural and biological evolutionary processes: home grown principles of action, norms, traditions, and ‘morality’.

An analogy may be helpful in understanding and remembering the difference between these two concepts of rationality. In a dance performance, the choreographer may exercise constructivist rationality by designing and explaining the moves to the individual performers. But it is ecological rationality that takes over as the individual performers together -- though practice and attention to their neighbors -- execute the performance:

Both forms of rationality are necessary to the pleasing result.

Here's an interesting question to consider: By what mechanism does constructivist order become embedded in ecological order? By reference to the analogy we can make this question more concrete: By what mechanism does the choreography influence the performance of the dancers?

In considering the dance analogy, the answers are not so difficult to see, although the details are surely interesting and important. The choreographer communcates her design with verbal or written instructions to the dancers, who then practice under the choreographer's direction until the design is reproduced. But when we drop the analogy and consider the question more broadly in the context of markets and market-based institutions, the answers seem fuzzier and more difficult to envision.

Perhaps one slice at the answer is provided in a paper by Barbara Drossel reviewed earlier here on Broken Symmetry:

These systems essentially have three states which are called quiescent, excited, and refractory. If there is an excitation, it spreads to the quiescent neighbors. After excitation, a region is refractory to further stimulation and needs some time to recover its quiescent state. The model discussed in this paper describes an excitable medium in the limit where excitation spreads fast on the scale of the refractory time, and where spontaneous excitation is rare. In cases where this limit can be realized experimentally, such a system should show either synchronization or SOC, depending on whether the transition from the refractory to the quiescent state and from the quiescent to the excited state are deterministic or stochastic.

Within Drossel's terminology, sync is acheived through excitation from a quiescent to a refractory state. When in a refractory state, any additional excitation will be passed onto neighboring states. In this regard, Drossel's model seems to have fundamental links to models of population inversions, which produce the coherent radiation of masers and lasers.

Given the right circumstances, even a weak coupling between the neural networks of individuals might be enough to induce a group of people into a state of sync or self-organized criticality.

The Great Synchronization

From the Vox blog, a post by Sónia Araújo and Joaquim Oliveira Martins

The current trade crisis is a uniquely synchronised fall. A pattern standing out from Figure 4 is that periods of abrupt decline of total trade flows were not uncommon at the individual country level, but these drops were not occurring simultaneously. The unique feature in the current crisis is the negative growth rates exceeding -10%, from November 2008 onwards for all six countries depicted,3 with the fall increasing to more than 20% as of January 2009.

Figures 4-5 try to uncover this striking synchronisation with an aggregate indicator. The figures display, for exports and imports separately, the percentage of OECD countries that exhibit a monthly year-on-year trade growth rate that is: i) negative, ii) below -5%, and iii) below -10%. To focus on the current decline, the analysis includes all 30 OECD member countries since January 1998.

The remarkable degree of synchronisation emerges rather neatly. There have been episodes of synchronised trade declines, namely following the dot.com crisis and September 11, but by end-2008 suddenly more than 90% of OECD countries exhibit simultaneously a decline in exports and imports exceeding 10%. It is the synchronised and large drop in trade in every OECD country that explains the collapse in international trade.

At this scale, psychology is not the right modeling tool. "Animal spirits" are real, but they do not provide an adequate explanation for how behavior gets correlated across continents. Click on the "Sync" category at the right and explore some of the mathematical models of sync. Markets are global now; market price signals are a mechanism for an all-to-all coupling of trade flows. The Kuramoto Model could provide insight into global sync of trade flows.

What is the Systems Theory of Economics?

Systems theory is an attempt to put Hayek, Coase, Williamson, North, and Ellickson on more quantitatively rigorous foundations. Systems theory is an umbrella term for physics models of networks and dynamical systems that are used to understand how interconnected flows can end up in stable or unstable local equilibria, spontaneously synchronize, and generally evolve over time in feedback loops.

Here are some of the basic hypotheses about human behavior that might be associated with systems theory:

• Individuals have preferences for goods that can be measured in units of flow (quantity consumed/produced per unit time).
• Individuals seek to optimize the fit between their flow preferences and available flow using available information about past and present available flow.

These together suggest that individuals can be modeled as a nexus of flows of cash and other goods. In turn, the interconnected streams of these flows lead to additional hypotheses about the behavior of the integrated system of flows.

• Feedback loops in flow among individuals can result in more spatially and temporally stable preferences by synchronization of flow.
• A nexus of synchronized flows may be a firm or a market depending on the structure of interconnections. (I.e., the ability to synchronize flow over time determines what structures will persist.)
• Firms that synchronize with higher-bandwidth can operate at lower cost, sell at higher margin, or both.
• Firms with scale-free architecture are the most cost-efficient, but also the most susceptible to catastrophic failure.
• (Perhaps most surprisingly) Under certain circumstances, individual preferences will spontaneously synchronize through market price signals.

There is an evolutionary mechanism at work here in that the nexus of flows that constitutes a firm is in competition with other nexuses of flows for additional flow. Over time, some network structures will survive better. And the success or failure of a particular network will, of course, have an impact on how the preferences of individuals within it will evolve over time. There are deep connections between systems theory and the evolutionary theory of psychologists like Mihaly Csikszentmihalyi and sociologists like Donald T. Campbell. But the kind of data and scale of the models used by systems theory is more traditionally associated with economics.

Much of systems theory has been anticipated by New Institutional Economics, and in some cases sociology and psychology. The work from Haidt and Ehrenreich on hive psychology and collective joy, for example, is consistent within broad contours of the physics models of self-organized synchronization. Robert H. Frank's work on positional goods can be understood in terms of the sustainability of certain integrated flow structures over long times. In general, Thomas Schelling seems to have had these sorts of models in mind in his writing, although he tended to focus on the potentially destructive outcomes after long periods of repeated interactions.

I'm going to try to turn each of these bullet points into a separate post over the next few weeks or months.

More Systems Theory from Judge Posner

My remaining proposals are of measures to improve regulatory performance, as distinct from the organization of financial regulation. First, we need a program that will rotate financial regulatory staff among the different financial regulatory agencies, to broaden the perspectives of regulators, reduce the "stovepiping" of information that may relate to a wide range of companies and financial markets, expose regulators to new ideas, reduce turf warfare based on misunderstandings, and make a career in financial regulation more interesting and challenging.

At his Atlantic Correspondents blog. This is a prescription that could be drawn directly from Ciskszentmihalyi's systems theory as applied to cultural economics.

Judge Posner on the Systems Theory of the Financial Crisis

Yet even if all firms that create systemic risk decided to shrink, or to reduce their interactions with other financial firms, systemic risk would not be eliminated. For such risk is a property of the financial system rather than of individual firms. That is, systemic risk is correlated risk. If the entire banking industry were heavily invested in home mortgages, and a housing bubble caused a drastic fall in the value of those mortgages, it wouldn't matter if the industry consisted of 10,000 banks of equal (and therefore equally small) size that had no dealings with other financial firms. The whole industry would be brought down.

Read the whole post here.

Feedback Loops in the All-to-All Network in which we live

Story I heard from Congressman Bill Foster this morning: Last fall, when the Stimulus Bill first went to the House for a vote, Congress members on the floor were watching the markets drop in real time on their blackberries. At the same time, traders in the pits on Wall Street were watching Congress voting on the Bill. Pro voters began berating Con voters as they came to the floor to vote. In effect, traders and their thousands of customers, spread all over the world, were doing the same.

Pause and let that sink in. We live in Robert Musil's world now. If we aren't careful, our decisionmaking can become very tightly correlated very fast.

Consider how many steps the framers of the United States Constitution took to avoid their decisionmaking during the Convention -- or the decisionmaking of actors in different branches of government -- from becoming too correlated.

How to Reduce Systemic Risk: Look at the Rates of Growth and Cross-Correlations

The White Paper last week was a disappointment. It was long on generalities and short on specifics of how and why we ended up in this mess. Lots of people are throwing their hands up in the air. A few are saying that the only way to avoid this problem is to go back -- i.e., to keep banks from ever growing so big again. Both of these are counterproductive. We have learned a few things from watching this crisis enfold that may help us avoid similar crises in the future.

One of those lessons is directly relevant to the argument that banks should simply be limited to a particular size. If there is any lesson that we have learned from this crisis, it is that size doesn't matter. Banks big and small all over the world have been brought to their knees by this crisis.

Systemic Risk = Large-Scale Correlations in Risk

What brought the financial industry all over the world to its knees can be attributed to a single mistake in reasoning, which was made by managers at every bank that ended up insolvent. Their mistake was in assuming that their risk of loss would range only within the boundaries set by local and recent events. The Royal Bank of Scotland, Kaupthing Bank in Iceland, Lehman Brothers in the United States, and your local Savings & Loan -- all made the same basic mistake of assuming that even if things got ugly for them, then there would be plenty of other banks around to pick up the slack. So long as I can depend on my counter-parties to behave exactly as we expect by contract, we will survive.

One thing that's worth noting is that this mistake wasn't fatal to the financial industry before the subprime mortgage bubble. The financial industry survived several bubbles before that, including the dot com bubble only ten years before. What changed?

The answer is cross-correlation. Over the past ten years, the financial industry became more interconnected through the financial engineering of derivatives and increased leverage than it has been ever before in history.

When any system becomes cross-linked beyond a certain low threshold, correlations in the dynamics of the system can spread from local to global. And this is exactly what we are living through. Although the system became exponentially more interconnected over the last ten years, the individual decisionmakers within the system (for the most part) kept their horizons relatively local and short-term. Nobody was looking at the large-scale, long-term trends and worrying about how those could ripple out in the event of a single default. Nobody was looking because no such cascade had ever occurred before.

The first role of any systemic risk regulator should thus be to quantify and limit the amount of cross-correlation in risk within the financial industry. We just can't afford to have every financial institution making the same kinds of bets. If a few are taking their cut from poker players, then the others need to take their cut from craps-players or roulette-players.

Regulating at Scale: Measuring Fundamental Limits to Growth

Systemic risk regulators have to be especially careful about the problem of scale. As numerous commentators have pointed out, there were a few people within the SEC that noticed the problems that might be caused by the unregulated sale of over-the-counter derivatives and the explosion in growth of the subprime mortgage market. How is putting a new agency in charge -- even if it has access to more information -- going to avoid such cascades in the future? In general, I don't think that any such agency will be able to prevent such cascades without having unintended negative consequences. And the scope of the authority needed to effect system-wide regulations is worrisome too from the point of view of suceptibility to political influence. A thumb on the scale at that scale is enough to crush entire markets.

To deal with systemic risk, any actual regulation will have to gloss over many of the fine details of what particular parties and counter-parties are doing. Getting too involved in these details simply invites corruption anyway. To deal with systemic risk, regulators need to change focus from the short-term and local, to the long-term and global.

For example, has anybody in government ever tried to figure out the highest rate of growth that has ever been achieved by a legitimate (i.e., non-fraudulent, sustainable) large corporation? If a company is growing faster than a certain rate then risk is being spread through the system. Such a company is either a Ponzi scheme or a gamble that some market exists that has not been demonstrated to exist.

A perfectly legitimate way for a systemic risk regulator to operate would be to set a threshold internal rate of return on cashflow -- say 30% annualized -- and then to demand that anybody with a higher IRR has to report to the systemic risk regulator on from whom and to whom that cash is flowing. Such a policy would have flagged the problem with subprime mortgages immediately. The size of the subprime mortgage market did not suddenly go from a few hundred million to billions in a year or two. At the very least, the government should have been carefully scrutinizing it after the cashflow increased by that number of orders of magnitude.

The Big Picture: A Network of Cashflows

At the end of the day, an economy is a network of cashflows. What makes our economy unique in the history of the world is its degree of interconnectedness. Those interconnections are both a blessing and a curse. They are a blessing in that they lower the costs of lending so that more and more people can get access to financing. (Think of Kiva, which is part of that interconnectedness.) The curse is that they permit for system-wide fluctuations to develop even from relatively small losses when decisionmaking is too tightly correlated.

Our goal should not be to go back to the smaller, less interconnected world. It should be to forge ahead into a fully networked economy, but with awareness of and capabilities to manage these global and long-term patterns of growth and decay in the network.

We need to think bigger.

The Glassy State of the Financial Services Industry

How might financial regulators have identified a problem with our market? By looking at cross-correlations like this one:

Again, this is from the paper on synchronized clusters reviewed here.

More on the Glassy Economy

I had to revisit the paper by Yik Wen Goo, Tong Wei Lian, Wei Guang Ong, Wen Ting Choi, and Siew-Ann Cheong, which I reviewed earlier here. As explained in the earlier review, these researchers found correlations in public security prices by looking for cross-correlation at successively longer and longer time scales. Lo and hehold, they were able to identify synchronized clusters that way:

We call these small clusters of very strongly correlated stocks financial atoms. The correlation levels within financial atoms rise significantly above the background level c0, because the dynamics of atomic stocks are coherent over time scales much longer than the average trading interval, which plays the role of the ‘nuclear/electronic’ time scale. The existence of such financial atoms is evident from earlier studies [citations omitted], where they are referred to as synchronized clusters. However, the separation of ‘nuclear/electronic’ and atomic time scales was not recognized. The potential of using financial atoms as effective variables to describe real financial markets is also not widely appreciated.

So not only is it possible that the economy is in a glassy state, there is some numerical data demonstrating that it actually is.

Their use of terminology is unfortunate, because it would be better to think of individuals as the "atoms" of an economy on my view. In that case, corporations would be molecules, and what they call "financial atoms" would be analogous to the chains and sheets of molecules described in the post yesterday on an economy made of glass.

Before I saw the White Paper from the Obama administration, I was hoping they had people that were already doing this kind of analysis. I'm no longer so optimistic. Can I ask for help from anybody and everybody who understands this type of analysis in educating the public and government in its implications? We'll all be better off that way in the end.

More Evidence for Synchronized Flow

Ironman provides an excellent review of some posts on Broken Symmetry, and (even better) provides a beautiful review of how the frequency spectrum of price fluctuations alternates between Gaussian and Levy statistics at Political Calculations:

We thought it would be appropriate to close out this post by reviewing the modern era of the stock market (or rather, most of it!) with our charts that identify the periods where Gaussian rules would apply, and the periods where Lévy flights rule. While we consider the modern era of the U.S. stock market to have begun in January 1952, we'll pick up the action in June 1954, extending to when the most recent period of disorder began in January 2008:

The bottom line here is that you can't understand build up a realistic model of an economy starting from the assumption that preferences are time-independent. The better way to start is with the assumption that preferences are oscillatory. I call this "the fundamental hypothesis of periodicity," and it produces the hypothesis of rationality at the limit of ergodicity -- i.e., when preferences behave the same way from one time-window to the next.