Broken Symmetry

Rolfe Winkler Looks Like a Major New Blogging Talent

From his post "Markets need rules":

Anyone in business knows how much trust matters on both sides of any transaction. When trust disappears, transactions stop. The market breaks down and individuals are forced to rely on themselves. In a perfectly free market, where economic Darwinism means competition always trumps cooperation, trade quickly grinds to a halt.

No one wants this. As economist Russell Roberts has argued, “self-sufficiency is the road to poverty.”

Laws align incentives so that cooperation can be more profitable than competition. So that individuals in the free market don’t have to worry about the market eating them alive.

Winkler's take is slightly different than mine. What I would (and did) say is this:

What Adam Smith taught us is that cooperation is the source of endogenous growth within an economy. Voluntary exchanges and divisions of labor literally create wealth within society. When it's money rather than goods or services that are exchanged, residual income (i.e., profit) is an excellent proxy for cooperation and endogenous growth. In fact, it's the best the world has ever known.

Crucially, the argument is that cooperation creates wealth, and that laws (or social norms) promote wealth creation to the extent that they facilitate and encourage cooperation. This claim may be quite counterintuitive to competition regulatory authorities, in particular, because much of competition regulatory theory is premised on the notion that competition is the engine of growth, with a few recognizing exceptions for temporary and otherwise limited monopolies (for example, for intellectual property). Winkler falls into the same trap by treating cooperation and competition as dichotomous. Competitions are simply one way to get people to cooperate.

Consider the facts of the American Needle case, for example. An unfettered market for NFL souvenirs is one form of private cooperation. The NFL IP licensing group is another. Both are procompetitive and anti-competitive, but among different stakeholders. NFL IP Licensing group promotes competition among professional leagues (MLB, NHL, etc.). A free market among manufacturers and distributors promotes competition among NFL teams, and probably lower prices and lower average quality in souvenirs overall. The question, which I think the Seventh Circuit got right, is what kind of cooperation/competiton we want to promote. The institution of market competition merely pushes people to differentiate or operate with more efficiency. When the market is already operating at peak technological efficiency and peak diversity, competition will be degrading and wasteful.

More fundamentally, the divisons of labor and voluntary exchanges that create wealth are acts of cooperation. In some cases, competiton is necessary to close the gap between bids and asks. In others, there are enough levers on the transaction such that competition isn't necessary to get overlap. In cases where transactions are occurring despite lack of competition, government should be careful not to destroy social capital -- often hard won over generations. That was Ellickson's central insight.

A Short Explanation of the Relationship Between Broken Symmetry and Systems Theory

W. Edwards Deming defines a "system" as follows:

A system is a network of interdependent components that work together to try to accomplish the aim of the system. A system must have an aim. Without an aim, there is no system. The aim of the system must be clear to everyone in the system. The aim must include plans for the future. The aim is a value judgment. (We are of course talking here about a man-made system.)

When Deming says, "[w]ithout an aim, there is no system," he is not saying (of course), that the people who would make up the system disappear. What he is saying is that the aim, by giving each of the people who accept it a shared purpose, modifies the behavior of the people such that activities are no longer random with respect to the aim, but ordered in a way believed best suited to achieve the aim.

In an earlier post on the Ising Model of consumption and savings, we identified individual agents as spins on a one-dimensional lattice. Spin up means consumption; spin down savings. With no magnetic field, the spins are randomly aligned according to the temperature (i.e., money supply) available to them. When a uniform magnetic field is applied, however, that lack of symmetry is broken, and a measurable magnetization (i.e., net savings or consumption) emerges. This broken symmetry is most dramatic when the system approaches the critical point at near zero temperature -- the system spontaneously orders into all savings or all consumption.

In other words, what Deming is saying is that a shared goal, an "aim," acts as field that breaks the symmetry of the system, giving rise to a finite order parameter. (Careful readers will note that my use of the term "system" in describing the Ising Model's behavior is inconsistent with Deming's, which requires an applied field.) In the case of the Ising Model of savings and consumption, the order parameter is aggregate savings or consumption. But other order parameters will emerge in response to other applied fields.

Functionalism and Systems Theory and the Supreme Court's Upcoming Review of American Needle

(If you need background on the case, skip to the * * * * * below.)

For proponents of functionalism and systems theory, there is no more important case before the Supreme Court right now.

Robert Ellickson is perhaps most famous for showing how the Coase Theorem does not hold among ranchers in rural Shasta County in California. His explanation is that shared cultural values are more important than legal rules in many particular social contexts. What the Seventh Circuit has done in American Needle is prevent antitrust law from interfering with privately evolved social norms of cooperation. The theory that individuals can evolve into groups with common norms is part of the sociological theory of functionalism.

In an earlier post on Robert Ellickson's Order Without Law, I pointed out how Ellickson's reasons and evidence for dismissing functionalism as a useful and valid part of systems theory are no longer sound. First, Ellickson rejected functionalism because of a fight among evolutionary biologists that was going on contemporaneous with his publication of Order Without Law. Functionalism is enjoying a resurgence among some evolutionary biologists, notably including E.O. Wilson, whom Ellickson cites in Order Without Law as an opponent of group selection theory. Wilson and Holldobler recently published, The Superorganism, which lays out a functionalist theory of group selection for how cooperation evolved among insects.

Second, there are now better theoretical tools for getting quantitative about functionalism. In particular, associating a group with a network, and individuals with nodes therein, permits evolution of group behavior to be modeled using mathematical models for network growth and decay, or phase transitions. Such models help to eliminate much of the conceptual circularity to which Ellickson objects in this passage.

The upshot is that social norms can evolve to facilitate group cooperation. These norms, in turn, can play a huge role in promoting health and economic growth. The case of IP licensing by the NFL is an easy example of the economic benefits of cooperation. Competition among the teams for licensing revenue -- which I understand is the norm among MLB teams -- leads to less social benefit for consumers and less revenue for the league. In many contexts, cooperation creates wealth that competition would destroy.

This is not to say that there is no role for antitrust regulation. The point is that regulators should not rely on the prescription of methodological individualists (including, most notoriously, neoclassical economists) that competition is a uniform good. Neither perfect competition nor perfect cooperation is optimal for a society. We must find a balance in which enough competition is permitted to allow existing relationships to be broken so that new experiments with resources, capital, and people can be tried. But we should remember that these experiments have an opportunity cost of stability and efficiency, which is too expensive when there is no theory tested by the experiments.

The Seventh Circuit's ruling on the "single-entity" doctrine should be upheld by the Supreme Court. It is a sophisticated answer to the question of how functional groups should be defined. The Seventh Circuit refuses to accept the oversimple definition of a group as a particular group of people. Rather, the group is defined (as W. Edwards Deming suggests it must be) by its shared purpose. Each individual has many goals, but a group of individuals will have only as many as are shared by each individual within it. This counterintuitive fact accounts, to a considerable extent, for the success of neoclassical theory -- only a handful of goals are shared by large groups of people over long periods of time, with the rational pursuit of happiness being the most obvious.

Long time readers will appreciate why I feel this decision is so important for the future prospects of our country. But to give just one illustration, refer back to the description of the effects of individual versus group competition described in this earlier post on executive compensation:

Chickens have always lived in groups, and in the modern egg production industry they are crammed inhumanely into cages usually containing nine to twelve hens. [Biologist William Muir] wanted to increase egg production by selective breeding, and he tried to do it in two ways. The first method involved selecting the most productive hen from each of a number of cages to breed the next generation of hens. The second method involved selecting all the hens from the most productive cages to breed the next generation of hens. You might think that the difference between the two methods is slight and that the first method should work better. After all, it is individuals who lay eggs, so selecting the best individuals directly should be more efficient than selecting the best groups, which might include some individual duds. The results told a completely different story.

When Bill presented his results at a scientific conference that I attended several years ago, he showed a slide of hens selected by the first method after six generations.The audience gasped. Inside the cage were only three hens, not nine, because the other six hens had been murdered. The three survivors had plucked each other during their incessant attacks and were now nearly featherless... What happened? The most productive individuals had achieved their success by suppressing the productivity of their cagemates.

By contrast, the second method resulted in higher production, and a cage that looked almost happy. If group selection could have such a dramatic impact on egg production, what impact might they have on the characteristics of individuals and groups in other situations in which group selection criteria are at work?

What kind of world do we want to live in? There is more at stake in how the Supreme Court decides this case than seems to be apparent to most people.

* * * * *

Here's how the Seventh Circuit summarized the facts and record on appeal (see here for links):

For those who do not know, the NFL is an unincorporated association of (now) 32 separately owned and operated football teams that collectively produce an annual series (or “season”) of over 250 interrelated football games. Each season culminates in a championship game—a game better known as the Super Bowl. As such, the product that the teams produce jointly—NFL football—requires extensive coordination and integration between the teams. After all, NFL football is produced only when two teams play a football game. Thus, although each team is a separate corporate entity or partnership unto itself, no team can produce a game—the product of NFL football—by itself, much less a full season of games or the Super Bowl. Likewise, the teams’ individual success is necessarily linked to the success of the league as a whole; to put it another way, it makes little difference if a team wins the Super Bowl if no one cares about the Super Bowl.

Realizing that the success of the NFL as a whole was in their best interests, in the early 1960’s the individual teams sought to collectively promote the NFL Brand—that is, the intellectual property of the NFL and its member teams—to compete against other forms of entertainment. With this promotional effort in mind, in 1963 the NFL teams formed NFL Properties: a separate corporate entity charged with (1) developing, licensing, and marketing the intellectual property the teams owned, such as their logos, trademarks, and other indicia; and (2) “conduct[ing] and engag[ing] in advertising campaigns and promotional ventures on behalf of the NFL and [its] member [teams].” Among other things, the NFL teams authorized NFL Properties to grant licenses to vendors so the vendors could use the teams’ intellectual property to manufacture and sell various kinds of consumer products that bear the teams’ logos and trademarks—products such as team jerseys, shirts, flags, and, as pertinent here, headwear, like baseball caps and stocking hats.

For a while after its establishment, NFL Properties granted headwear licenses to a number of different vendors simultaneously; one of those vendors was American Needle, which held an NFL headwear license for over 20 years. But then in 2000, the NFL teams authorized NFL Properties to solicit bids from the vendors for an exclusive headwear license. Reebok won the bidding war, and in 2001 the NFL teams allowed NFL Properties to grant an exclusive license to Reebok for ten years. NFL Properties thus did not renew American Needle’s headwear license, or the licenses of the other headwear vendors.

American Needle responded to the loss of its headwear license by filing an antitrust action against the NFL, NFLProperties, the individual NFL teams, and Reebok. As relevant here, American Needle claimed that the exclusive headwear licensing agreement between NFL Properties and Reebok violated § 1 of the Sherman Antitrust Act, which outlaws any “contract, combination . . . or conspiracy, in restraint of trade.” 15 U.S.C. § 1. As American Needle saw it, because each of the individual teams separately owned their team logos and trademarks, their collective agreement to authorize NFL Properties to award the exclusive headwear license to Reebok was, in fact, a conspiracy to restrict other vendors’ ability to obtain licenses for the teams’ intellectual property. American Needle also contended that, by authorizing NFL Properties to award the license to Reebok, the NFL teams monopolized the NFL team licensing and product wholesale markets in violation of § 2 of the Sherman Antitrust Act. See id. § 2.

And here's how the Seventh Circuit ruled on the question of whether the NFL can be considered a "single entity":

American Needle first contends that the district court erred by granting the NFL defendants’ summary judgment on its § 1 claim. Specifically, American Needle argues that the district court incorrectly concluded that the NFL teams constitute a single entity under Copperweld when collectively licensing their intellectual property. American Needle’s argument leads us into murky waters. We have yet to render a definitive opinion as to whether the teams of a professional sports league can be considered a single entity in light of Copperweld. The characteristics that sports leagues generally exhibit make the determination difficult; in some contexts, a league seems more aptly described as a single entity immune from antitrust scrutiny, while in others a league appears to be a joint venture between independently owned teams that is subject to review under § 1. See Brown v. Pro-Football, Inc., 518 U.S. 231, 248-49 (1996) (“[T]he clubs that make up a professional sports league are not completely independent economic competitors . . . . In the present context, however, that circumstance makes the league more like a single bargaining employer . . . .”); Bulls II, 95 F.3d at 597-99 (“To say that the league is ‘more like a single bargaining employer’ than a multi-employer unit is not to say that it necessarily is one, for every purpose.”); see also Super Sulky, Inc. v. U.S. Trotting Ass’n, 174 F.3d 733,741 (6th Cir. 1999) (“[T]he notion of concerted action liability in the field of professional sports is at best confusing.”). For instance, from the perspective of fans, a professional sports league can be seen as “a single source” of entertainment that produces “one product,” even though the league’s member teams are distinguishable. Bulls II, 95 F.3d at 599. Yet at the same time, individuals seeking employment with any of the league’s teams would view the league as a collection of loosely affiliated companies that all have the independent authority to hire and fire employees. See Brown, 518 U.S. at 249 (noting that professional football players “often negotiate their pay individually with their employers,” NFL teams); Bulls II, 95 F.3d at 599 (“[F]rom the perspective of college basketball players who seek to sell their skills, the teams [in the National Basketball League (NBA)] are distinct . . . .”).

That being said, we have nevertheless embraced the possibility that a professional sports league could be considered a single entity under Copperweld. Bulls II, 95 F.3d at 598. But see Fraser v. Major League Soccer, L.L.C., 284 F.3d 47, 55-56 (1st Cir. 2002) (citing Sullivan v. Nat’l Football League, 34 F.3d 1091, 1099 (1st Cir. 1994), to note that Bulls II has not yet been adopted by United States Court of Appeals for the First Circuit). But because of the many and conflicting characteristics that professional sports leagues generally exhibit, we have expressed skepticism that Copperweld could provide the definitive single-entity determination for all sports leagues alike. See id. at 599-600. This skepticism, in turn, has led us to opine that the question of whether a professional sports league is a single entity should be addressed not only “one league at a time,” but also “one facet of a league at a time.” Id. at 600. Thus, in reviewing the district court’s decision, we will limit our review to (1) the actions of the NFL, its members teams, and NFL Properties; and (2) the actions of the NFL and its member teams as they pertain to the teams’ agreement to license their intellectual property collectively via NFL Properties.

With this compartmentalization of Copperweld in mind, we turn to American Needle’s challenge to the district court’s single-entity determination. According to American Needle, the district court applied the wrong legal standard when concluding that the NFL teams were a single entity. As American Needle sees it, the district court concluded “that the NFL [t]eams are a single entity because they ‘act’ as a single entity in licensing their intellectual property.” American Needle asserts that this approach undercuts the Supreme Court’s central teaching in Copperweld: that the Sherman Antitrust Act was designed to combat the deprivation of independent sources of economic power in the marketplace. See 467 U.S. at 469-71.

Therefore, American Needle continues, instead of asking whether the NFL teams merely “ ‘act’ ” as a single entity, the district court should have inquired into whether the NFL teams’ agreement to license their intellectual property collectively deprived the market of sources of economic power that control the intellectual property. That question, the company contends, can be answered by looking to whether the teams could compete against one another when licensing and marketing their intellectual property. If so, American Needle posits, then it is the individual teams who actually control their intellectual property, meaning that they cannot be considered a single entity for the purposes of licensing their intellectual property.

We agree with American Needle that the Supreme Court in Copperweld was concerned about the anti-competitive effects that collective action might introduce into the market. We further agree that when making a single-entity determination, courts must examine whether the conduct in question deprives the marketplace of the independent sources of economic control that competition assumes.

But we are not convinced that the NFL’s single-entity status in the present context turns entirely on whether the league’s member teams can compete with one another when licensing and marketing their intellectual property. American Needle’s proposed approach is one step removed from saying that the NFL teams can be a single entity only if the teams have “a complete unity of interest”—a legal proposition that we have rejected as “silly.” Bulls II, 95 F.3d at 598. As we have explained, “Copperweld does not hold that only conflict-free enterprises may be treated as single entities”; “[e]ven a single firm contains many competing interests.” Id. at 598 (discussing Robert G. Eccles, Transfer Pricing as a Problem of Agency, in Principals and Agents: The Structure of Business 151 (1985)). Thus, though the several NFL teams could have competing interests regarding the use of their intellectual property that could conceivably rise to the level of potential intra-league competition, those interests do not necessarily keep the teams from functioning as a single entity. Id. at 597-98. We therefore cannot fault the district court for not considering whether the NFL teams could compete against one another when licensing and marketing their intellectual property.

And with that said, American Needle’s assertion that the NFL teams have deprived the market of independent sources of economic power unravels. Certainly the NFL teams can function only as one source of economic power when collectively producing NFL football. Asserting that a single football team could produce a football game is less of a legal argument then it is a Zen riddle: Who wins when a football team plays itself? See Nat’l Collegiate Athletic Ass’n v. Bd. of Regents, 468 U.S. 85, 101 (1984)(“‘[Some] activities can only be carried out jointly. Perhaps the leading example is league sports. When a league of professional lacrosse teams is formed, it would be pointless to declare their cooperation illegal on the ground that there are no other professional lacrosse teams.’ ” (quoting Robert Bork, The Antitrust Paradox 278 (1978))); Bulls II, 95 F.3d at 599 (“[T]he NBA has no existence independent of sports. It makes professional basketball; only it can make ‘NBA Basketball’ games . . . .”). It thus follows that only one source of economic power controls the promotion of NFL football; it makes little sense to assert that each individual team has the authority, if not the responsibility, to promote the jointly produced NFL football. Indeed, the NFL defendants introduced uncontradicted evidence that the NFL teams share a vital economic interest in collectively promoting NFL football. After all, the league competes with other forms of entertainment for an audience of finite (if extremely large) size, and the loss of audience members to alternative forms of entertainment necessarily impacts the individual teams’ success. See Bulls II, 95 F.3d at 597; see also Brown, 518 U.S. at 248 (“[T]he [teams] that make up a professional sports league are not completely independent economic competitors, as they depend upon a degree of cooperation for economic survival.”); Nat’l Football League v. N. Am. Soccer League, 459 U.S. 1074, 1077 (1982) (Rehnquist, J., dissenting) (“The NFL . . . competes with other sports and other forms of entertainment in the entertainment market. Although individual NFL teams compete with one another on the playing field, they rarely compete in the market place.”).

But most importantly, the record amply establishes that since 1963, the NFL teams have acted as one source of economic power—under the auspices of NFL Properties—to license their intellectual property collectively and to promote NFL football. Tellingly, American Needle does not dispute that the NFL teams collectively license their intellectual property to promote NFL football; in fact, when opposing the NFL defendants’ motion for summary judgment, American Needle relied on NFL Properties’s Articles of Incorporation, which state that the teams formed NFL Properties “[t]o conduct and engage in advertising campaigns and promotional ventures on behalf of the [NFL] and the member [teams].” And our review of the record reveals no evidence that requires us to question the purpose of the teams’ licensing agreement.

Simply put, nothing in § 1 prohibits the NFL teams from cooperating so the league can compete against other entertainment providers. Indeed, antitrust law encourages cooperation inside a business organization—such as, in this case, a professional sports league—to foster competition between that organization and its competitors. See Bulls II, 95 F.3d at 599. Viewed in this light, the NFL teams are best described as a single source of economic power when promoting NFL football through licensing the teams’ intellectual property, and we thus cannot say that the district court was wrong to so conclude.

Moving on, the failure of American Needle’s § 1 claim necessarily dooms its § 2 monopolization claim. As a single entity for the purpose of licensing, the NFL teams are free under § 2 to license their intellectual property on an exclusive basis, see Cook Inc. v. Boston Scientific Corp., 333 F.3d 737, 740 (7th Cir. 2003), even if the teams opt to reduce the number of companies to whom they grant licenses, see Bulls II, 95 F.3d at 598 (“To say that participants in an organization may cooperate is to say that they may control what they make and how they sell it: the producers of Star Trek may decide to release two episodes a week and grant exclusive licenses to show them, even though this reduces the number of times episodes appear on TV in a given market . . . .”); Gregory J. Werden, Antitrust Analysis.

of Joint Ventures: An Overview, 66 Antitrust L.J. 701, 730-31 (1998) (“An antitrust claim based solely on a single firm’s denial of a license to a trademark would readily be dismissed . . . .”). As such, American Needle has no colorable claim that the NFL teams and NFL Properties created a monopoly by awarding Reebok the exclusive headwear licensing contract. See Cook Inc., 333 F.3d at 740 (discussing competitive effects of exclusive-licensing agreements); Bulls II, 95 F.3d at 598. The district court was therefore correct to grant summary judgment to the NFL defendants on American Needle’s § 2 monopolization claim.

The New Economics by W. Edwards Deming

Recently, I stumbled upon the work of W. Edwards Deming while doing some reading on the applicaton of stastical control to quality improvement. I'm not sure for whom Deming would today be a recognized name, and after reading The New Economics I have a few guesses as to why his reputation may not have persisted for as long after his death as has the reputation of F.W. Taylor, for example.

Deming, unlike Taylor, was not offering easy solutions to his clients, his clients being managers at for-profit companies, teachers and administrators in schools and universities, and politicians or public servants in government -- really anybody who cared to listen. Rather, he was offering a theory about how organizations could improve their overall performance.

The Systems Theory according to Deming

Of special significance to your author is the fact that Deming chose to call his theory "systems theory." Deming defines a "system" as follows:

A system is a network of interdependent components that work together to try to accomplish the aim of the system. A system must have an aim. Without an aim, there is no system. The aim of the system must be clear to everyone in the system. The aim must include plans for the future. The aim is a value judgment. (We are of course talking here about a man-made system.)

Included in this chapter 3 of The New Economics is Figure 6, which Deming calls a "flow diagram" of "Production viewed as a system":

Figure 6 illustrates the interdependence of the components (most economists would call them agents today) within the system. Deming uses the figure to explain how the product is the result not only of how each agent does his or her job, but of how well the agents cooperate to achieve their mutual goal of a happy consumer.

As Deming sees it, "[a] system must be managed. It will not manage itself. Left to themselves in the Western world, components become selfish, competitive, independent profit centers, and thus destroy the system." By contrast, "[t]he secret is cooperation between components toward the aim of the organization. We cannot afford the destructive effect of competition."

More specifically, Deming places the responsibility with management for studying the market, identifying and selecting goals, and clarifying and facilitating the communication of those goals among agents. In practice, this involves listening to agents more than talking, since it is the agents (especially the agents in contact with people outside the firm) that have the freshest information to guide goal development.

Deming suggests that the ultimate goal should be for every stakeholder in the organization -- stockholders, employees, suppliers, customers, community, the environment -- to benefit over the long term. Contrast this with fiduciary duty to maximize profits for shareholders instituted by Dodge v. Ford..

On my view, Deming was prophetic. This book was published in 1993, when the first of two major financial bubbles were just getting started. But now that the global economy has exploded into a chaotic frenzy of new markets and firms, most of which only roughly fit within traditional geographical or jurisdictional boundaries, it is now obvious that there is no institution in the world powerful enough to guarantee to any stakeholder that it will be favored over all others that contribute to an organization. Until a few decades ago, capital was king. No wonder that the owners of capital, often being the scarcest resource available to a firm, got special protection from government. What is the scarcest resource over the very long haul? As Deming could see even in 1993, the answer is human capital -- people power. The systems theory that Deming espoused is about optimizing firms to make the best use of human capital, and it is completely consistent with the systems theory Broken Symmetry seeks to understand in gory detail. Get in the habit of thinking this way, and life will not be the same.

Let's take one example of Deming's application of systems theory to the problem of optimizing firms. Deming attributes this application to Shewhart, who Deming says:

invented a new way to think about uniformity and nonuniformity. He saw two kinds of variation -- variation from common causes and variation from special causes. Common causes of variation produce points on a control chart that over a long period all fall inside the control limits. Common causes of variation stay the same day to day, lot to lot. A special cause of variation is something special, not part of the system of common causes. It is detected as a point that falls outside of control limits.

According to Shewhart, a lack of knowledge about common and special causes of variation leads to two mistakes:

Mistake 1: To react to an outcome as if it came from a special cause when actually it came from a common cause of variation.

Mistake 2: To treat an outcome as if it came from common causes of variation, when actually it came from a special cause.

The "Common Cause of Variation" is a Martingale

At this point, I can explain to my readers why I believe Deming's representation did not last long beyond his death. These statements, devoid of any experience with statistical or physical theory, must seem completely obvious, even trivial. They are not if one can understand and interpret what Shewhart and Deming (both trained as physicists) are talking about here.

What Deming and Shewhart call a "common cause of variation" is what most engineers, scientists, and even economists and other social scientists would recognize as a normal or Gaussian distribution in outcomes. As wikipedia explains:

By the central limit theorem, the sum of a large number of independent random variables is distributed approximately normally. For this reason, the normal distribution is used throughout statistics, natural science, and social science as a simple model for complex phenomena. For example, the observational error in an experiment is usually assumed to follow a normal distribution, and the propagation of uncertainty is computed using this assumption.

By contrast, when Deming and Shewhart talk about "special causes of variation," they're talking about distributions of outcomes with fat tails -- pareto distributions (a/k/a power laws), Levy distributions, and so on. Deming and Shewhart were studying Martingales and non-convergent stochastic dynamics decades before these became popular in academic fields! Even better, they were teaching managers inside large corporations how to recognize non-Markovian dynamics and correct system design without making the problem worse.

An Application to Financial Regulatory Reform

How might this be applied to the financial system? Fat tails developed, which almost destroyed the system. Lots of folks are jumping in now with reform proposals that promise to make the system more efficient, more stable. What would Deming and Shewhart have to say?

Chapter 9 provides some tantalizing clues. Chapter 9 is called "The Funnel," and describes a process whereby marbles are dropped through a funnel (which is wide enough for each marble to have some clearance) onto a table cloth, with the position at which the marbles come to rest being marked. Without doing the experiment yourself, you can imagine that the actual pattern of marks formed after such an experiment will be a cluster of marks on the table under a target under the funnel -- not one spot right on the target. As Deming explains by successively considering various alternatives, most active efforts to reduce the radius of the cluster of marks will not be successful.

1. If at each drop, the funnel is moved from its last position to a new position to compensate for the last error (for example, by moving northeast to compensate for a mark southwest of the target), then the results are worse -- the pattern of marks has an even wider radius.
2. If at each drop, the funnel is moved from its starting position to a position equal in distance and opposite the direction of the last error, then the results are even worse -- a plot of the radius of marks now shows distinct oscillations.
3. If at each drop, the funnel is moved over the mark where the last marble fell, then the marks will merely drift off "to the Milky Way."

What's going on here and how is this relevant to the financial system? Banks are funnels for cash and other assets -- the marbles flowing through our system. The marks on the table are the marks on the books of each bank -- marks of how each asset is valued at a given moment. The various alternative rules for moving the funnel around represent the effects of mark-to-market rules on the financial system -- rules intended to correct for the default gaussian spread of marks!

1. When corrections are made to book value in each period to account for newest market prices, volatility in asset value is increased. This is equivalent to moving the filter in a direction equal and opposite to the last mark after each drop.
2. Making corrections to book values of cost only makes things worse, increasing volatility in the system even further!
3. Marking assets to exactly the last market price (i.e., without taking into account historical value at all) sets the whole system adrift.

How and why was FAS 157, which implemented these rules, ever put into place? The answer is that the accountants who work on these regulations work for the banks and institutions that wanted to mark up their book value during the Great Moderation that preceded the present financial crisis. And they're not entirely to blame because most of these people do not have a systems-wide view of the consequences of these rules. But it should be clear how important they can be.

I hope this example demonstrates the instrumental value of systems theory to policymakers. Until now, law and economics (the economics being mostly neoclassical) was the only quantitative tool in the toolbox. What this example shows is that systems theory can provide insight. As Deming points out, none of the active efforts to correct the error would have been as helpful as simply moving the funnel closer to the table cloth or using a sticky table cloth (by analogy to the financial system, this could mean better matching the frequency of marks to market to the frequency of transactions or increasing the transactions costs relative to the size of the transaction).

The Problem with American Anti-intellectualism

From W. Edwards Deming's The New Economics at 173:

On arrival [at] Western Electric, following directions, I found my way to Mr. Chester Coulter on the fifth floor. I was to join a group of about two hundred people working in so-called research and development. The head of the organization was a Dr. H. Rossbacher. My esteem for him increased year by year. He had a respect for theory. In a conversation that I overheard one time, somebody complained to him that the way we were starting off was too theoretical. HIs reply was that if we have ever accomplished anything here, it started off with studies that some people complained were too theoretical. He had no use for the word practical.

On that note, I plan to post a review of Deming's New Economics sometime soon. Deming is fuzzy on the distinction between special and common causes of variation in production, and it's no accident why. Statistical models of special variation are very sophisticated.

What data sets should be used to test models of agent dynamics?

Geanakoplos and Farmer observe:

What is still largely lacking is an empirical foundation on which to build an evolutionary theory. This ultimately depends on developing a taxonomy of real nancial strategies together with a database of studies of nancial ecologies as they change through time.

It's out there. The right data sets for modeling agent dynamics are the time series of cash-flows into and out of firms. These data sets are obscured by accounting rules right now. Moreover, the time series of security prices are far too complex a phenomena to give any insight into individual or firm agent behavior.

It's always easier to build models for the data you have in front of you than it is to go out and get the best data. But it surprises me that no academic anywhere has ever tried to collect historical journal entries from several companies in a given market, and then modeled their behavior.

The authors also note that previous attempts at nonequilibrium models have failed because they made too many assumptions. How about making just one -- that particular activities of agents have a characteristic frequency. Start from their and work backwards in modeling the dynamics, and we may get further than if we start from the time-series of market prices.

Geanakoplos and Farmer on the Nonequilibrium Statistical Mechanics of Markets

The WSJ leads with Geanakoplos today and Marginal Revolution picks the story up. Skimming through SSRN publications by Geanakoplos, I find this chestnut:

An alternative point of view is that, due to a lack of a perfect rational ity, the market is not in perfect equilibrium and thus prices do not simply passively reflect new information. Under this view the market acts as a non-linear dynamical system: agents process information via decision-making rules that respond to prices and other inputs, and prices are formed as a result of agent decisions. Since this information processing is imperfect, the resulting feedback loop amplies noise. As a result a signicant component of volatility is generated by the market itself.

From a paper co-authored with J. Doyne Farmer.

Are markets flawed? Or is it competition?

Soros has this to say about the role of markets:

But markets are suitable only for individual choices, not for social decisions. They allow individual participants to engage in free exchange; but they are not designed to exercise social choices such as deciding the rules that should govern society, including how the market mechanism should function. That is the purview of politics. Extending the idea of a free-standing market, self-governing and self-correcting, to the political sphere is highly deceptive because it removes ethical considerations from politics which cannot properly function without them.

Soros didn't go far enough with reflexivity. But here he goes too far. It is not markets that are responsible for the emphasis we place on individual choice. It is the value placed on competition that devolves markets into individual free-for-alls. Competition, as currently understood by market actors and government regulators, has the underpinnings of the methodological individualism on which all of modern economics rests. Alternative methodologies and understandings of competition would not produce the same market dynamics, as comparison of various industries makes obvious (to borrow examples from Charlie Munger, consider cereal manufacturers on the one hand and airlines on the other).

Individuals spontaneously order into firms. What benefit is there to such integration if markets put less constraints on the same individuals? The function of markets is to synchronize buyers and sellers who cannot otherwise integrate their needs within a firm. Soros has it exactly backwards. It's not that markets are suitable only for individual choices; it's that individual choices are suitable only for markets.

In this context, Soros would do well to consider some of the New Institutional Economics and Organizational Theory literature, which provides theory on how and when institutional culture develops. I don't disagree with his point that institutional rules are needed. Just his point that government institutions are necessary or sufficient to meet those needs.

Reflexivity Goes Deeper than Soros Himself Seems to Realize

I was piqued by this bit at the end of Soros's recent lecture on his "general theory of reflexivity":

I am somewhat troubled, however, about drawing too sharp a distinction between natural and social science. Such dichotomies are usually not found in reality; they are introduced by us, in our efforts to make some sense out of an otherwise confusing reality. Indeed while a sharp distinction between physics and social sciences seems justified, there are other sciences, such as biology and the study of animal societies that occupy intermediate positions.

But I had to abandon my reservations and recognize a dichotomy between the natural and social sciences because the social sciences encounter a second difficulty from which the natural sciences are exempt.

And that is that social theories are reflexive. Heisenberg’s discovery of the uncertainty principle did not alter the behavior of quantum particles one iota, but social theories, whether Marxism, market fundamentalism or the theory of reflexivity, can affect the subject matter to which it refers. Scientific method is supposed to be devoted to the pursuit of truth. Heisenberg’s uncertainty principle does not interfere with that postulate but the reflexivity of social theories does. Why should social science confine itself to passively studying social phenomena when it can be used to actively change the state of affairs? As I remarked in The Alchemy of Finance, the alchemists made a mistake in trying to change the nature of base metals by incantation. Instead, they should have focused their attention on the financial markets where they could have succeeded.

Why piqued? Because Soros seems oblivious to the fact that Heisenberg's uncertainty principle implies exactly what it is that makes social science distinguishable from natural science! Part of what Heisenberg's principle tells us (in mathematically precise terms) is that what we decide to measure will have an infuence on the system we choose to measure. We cannot treat our probe as independent from the system it measures except as an approximation. In many cases, the interaction of the system and probe through a measurement will irreversibly alter the system, making additional measurements impossible to reproduce without reproducing a copy of the system. That is all part of quantum mechanics.

To his credit, Soros acknowledges that there may not be a clean cut between the two -- he points to biology and animal sociology as intermediate cases. But his mistake is clear. His assumption that nature has not changed as a result of new theories and measurements is false. Sure enough, the changes are not as immediate or obvious. Yet there can be no doubt that the world is a different place because of quantum mechanics. What world would we live in had there been no Manhattan Project? Poverty of theory in Germany and Japan in WWII decided the fate of the world. The history of science is replete with similar examples of successful and failed experiments with nature, which have rippled out in their consequences for the rest of mankind.

But far from being fatal to Soros's "general theory of reflexivity," this observation of his mistake actually solidifies its claim to both validity and relevance. Instead of a dichotomy between natural and social science, What should Soros have called for? A better understanding of the system in which both natural and social scientists work. Our knowledge is a physical manifestation of the activities of scientists and non-scientists. What we measure is merely a function of the various activities of the system.

Many philosophers have made similar observations. In the legal context I think of Wittgenstein and H.L.A. Hart who wrote about how a rule does not include within it a rule for deciding how and when it should be enforced. But W. Edwards Deming had a simpler way of summarizing the point in a book of his that I've been reading with interest:

There is no true value of any characteristic, state, or condition that is defined in terms of measurement or observation. Change of procedure for measurement (change in operational definition) or observation produces a new number... There is no such thing as a fact concerning an empirical observation. Any two people may have different ideas about what is important to know about any event. Get the facts! Is there any meaning to this exhortation?

Communication and negotiation (as between customer and supplier, between management and union, between countries) require for optimization of operational definitions. An operational definition is a procedure agreed upon for translation of a concept into measurement of some kind.

Our perception of reality itself is more socially constituted than most of us appreciate! Consider how physicist Roger Penrose chose to depict reality as a cycle:

The cycle is manifest in the activities of people. The mathematical world is revealed, step by step, through consensus among living and dead mathematicians. The mental world represents the model everybody has, including mathematicians, of what exists. Both of these are embedded in a physical world along with a Noah's ark of other animals and a Garden of Eden of other living things.

We exercise control over our existence by formulating theories about what exists. There are plenty of things that exist that no person imagined to exist until a theory was developed that permitted for experiments, which in turn were consistent with other experiments, and so on. Nobody doubts anymore that we are made of atoms, quarks, and leptons. Yet none of us has seen any of these things. And if we were to stop looking for them, there is no doubt in my mind that we would eventually forget about them -- leaving their existence as ghostly as it was a hundred years ago.

There is no dichotomy between social and natural science. Rather, social science should embrace these constraints that have been on all science for as long as we've been doing experiments.

George Soros Explains His Worldview

And it is surprisingly fascinating:

While I was reading Popper I was also studying economic theory and I was struck by the contradiction between Popper’s emphasis on imperfect understanding and the theory of perfect competition in economics which postulated perfect knowledge. This led me to start questioning the assumptions of economic theory. These were the two major theoretical inspirations of my philosophy. It is also deeply rooted in my personal history.

The FT has a whole website up with transcripts from each of his lectures, which are ongoing this week. It's little things like this that make my day.

Transcripts of first three lectures are here, here, and here.

For an earlier post on epistemlogical and ontological questions that offers one version of reflexivity, see here.

In reponse to Soros's proposal that we dichotomize the natural and social sciences, I have this to say: His misinterpretation of Heisenberg's uncertainty principle kills his proposal. In fact it is true of both natural and social scientific theories that our theories influence how reality evolves. It is true too that bad natural science may not have as catastrophic or immediate consequences for us as bad social science. But what we perceive depends in part on our theory of what exists, and those theories are not social. Soros's dichotomy is in fact a continuum.

To wit, from whence did Soros derive his understanding of positive and negative feedback loops? By analogy to the natural sciences. Our exploration of nature is the ultimate origin of all of our theories, bot natural and social.

Mandelbrot and the Glassy State of the Economy

From Fractals and Scaling in Finance, page 367:

Everyone agrees that the distribution of firm sizes is far from Gaussian, hence the proper metaphor is not a "soft," but a "hard" object. This leaves open the question of whether it is a real solid or a glass. Physics describes glasses as being extremely viscous liquids that mimic solids and happen to be particularly difficult to study. In the same way, the lognormal distribution averages mildly in the very long run, but in the short run it mimics the wild randomness of the scaling in a very treacherous fashion. One can call it a sheep in wolf's clothing.

Why is Mandelbrot skeptical of lognnormal distributions of firm size? Because market concentration appears to be a scale invariant quantity -- i.e., the amount of concentration appears not to vary as much with the number of firms in the market as one would expect from distributions with finite variance.

W. Brian Arthur on How Science and Technology Evolve

From the NYT:

“What I began to realize as I got into the project is that everything emerges out of technology,” Dr. Arthur said in a recent interview. “It’s technology that gives rise to both modern science and the economy, and we tend to think of it in reverse — that science gives rise to technology and the economy gives rise to technology. But technology is more fundamental than either one.”

Think about what this means for how we view the relationship between industry and universities.

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.

The Wire and Csikszentmihalyi's Theory of Flow

Last night I finished the last episode of Season 1 of The Wire. If you haven't seen any of this, check it out. The show compares favorably with any film or lit I've consumed in many years.

The show, in fact, provides a good fictional depiction of a complex system, of the kind discussed repeatedly on Broken Symmetry. Of particular note in this regard is the term chosen by characters in the show to describe the complex system of which they are a part -- "the game."

The term naturally calls to mind Csikszentmihalyi's theory of flow, which was discussed in an earlier post, which included this excerpt C.'s book Flow: The Psychology of Optimal Experience at 81:

Cultures are defensive constructions against chaos, designed to reduce the impact of randomness on experience. They are adaptive responses, just as feathers are for birds and fur is for mammals. Cultures prescribe norms, evolve goals, build beliefs that help us tackle the challenges of existence. In so doing they must rule out many alternative goals and beliefs, and thereby limit possibilities; but this channeling of attention to a limited set of goals and means is what allows effortless action within self-created boundaries [i.e., flow]."

It is in this respect that games provide a compelling analogy to cultures. Both consist of more or less arbitrary goals and rules that allow people to become involved in a process and act with a minimum of doubts and distractions. The difference is mainly one of scale. Cultures are all embracing: they specify how a person should be born, how she should grow up, marry, have children, and die. Games fill out the interludes of the cultural script. They enhance action and concentration during "free time," when cultural instructions offer little guidance, and a person's attention threatens to wander into the uncharted realms of chaos.

When a culture succeeds in evolving a set of goals and rules so compelling and so well matched to the skills of the population that its members are able to experience flow with unusual frequency and intensity, the analogy between games and culture is even closer. In such a case we can say that the culture as a whole becomes a "great game." Some of the classical civilizations may have succeeded in reaching this state. Athenian citizens, Romans who shaped their actions by virtus, Chinese intellectuals, or Indian Brahmins moved through life with intricate grace, and derived perhaps the same enjoyment from the challenging harmony of their actions as they would have from an extended dance. The Athenian polis, Roman law, the divinely grounded bureaucratcy of China, and the all-encompassing spiritual order of India were successful and lasting examples of how culture can enhance flow -- at least for those who were lucky enough to be among the principal players.

On my view, this is the most compelling explanation for why the characters are at once enthralled and entrapped by the institution of which they are a part.

How Things Break

From Michael Marder and Jay Fineberg:

Galileo was seventy-two years old, his life nearly shattered by a trial for heresy before the Inquisition, when he retired in 1635 to Florence to construct the Dialogues Concerning Two New Sciences. His first science is the study of the forces that hold objects together, and the conditions that cause them to fall apart, the dialogue taking place in a shipyard, triggered by observations of craftsmen building the Venetian fleet. The second science concerns ``local motions:'' laws governing the movement of projectiles. The two subjects Galileo founded have fared differently. One is a respectable branch of mechanical engineering, while the other is a core subject that physicists learn at the beginning of their education. Although now, as in Galileo's time, ship-builders need good answers to questions about the strength of materials, the subject has never yielded easily to basic analysis. Galileo identified the main difficulty: ``one cannot reason from the small to the large, because many mechanical devices succeed on a small scale that cannot exist in great size.[1]'' Nearly three hundred years elapsed after Galileo wrote these lines before science reached the atomic scale and began to answer the questions he had posed on the origins of strength, and the relation between large and small.

...

An engineer and a physicist compete to find the best material to build a house. The engineer chooses brick because she knows it is what everyone else uses. The physicist decides to conduct some basic research. Turning to the periodic table, he finds the element with the highest bonding strength and melting point, and first proposes diamond. Trying to find something cheaper, he next proposes a vitreous mixture of silicon and oxygen, since the raw materials are abundant and safe and form strong bonds. All is well until someone throws the first stone. In fact, the relation between bonding energies and strength of materials is far from direct; physicists had best respect the practical experience of engineers until they can really explain why one should not build glass houses.

...

Take a slab of material, make a saw cut in it, and pull. In a brittle material, the tip of the saw cut spontaneously sharpens down to atomic dimensions, and like a knife blade one atom wide slices its way forward[3]. In a ductile material the tip of the saw cut blunts, broadens and flows, so that great effort is required to make it progress.

See earlier post: An Economy Made of Glass

More on the Long Tail

As Michael Nielsen explains, the value of the exponent in your power law matters a great deal:

If you’re developing a long tail business or collaboration, you need to make sure the exponent in the power law is less than one. The smaller the exponent, the better off you’ll be.

How can you make the exponent as small as possible? In particular, how can you make sure it’s smaller than the magic value of one? To understand the answer to this question, we need to understand what actually determines the value of the exponent. There’s some nice simple mathematical models explaining how power laws emerge, and in particular how the power law exponent emerges. At some point in the future I’d like to come back and discuss those in detail, and what implications they have for site architecture. This post is already long enough, though, so let me make just make three simple comments.

First, focus on developing recommendation and search systems which spread attention out, rather than concentrating it in the short head of what’s already popular. This is difficult to do without sacrificing quality, but there’s some interesting academic work now being done on such recommendation systems – see, for example, some of the work described in this recent blog post by Daniel Lemire.

Second, in collaborative projects, ensure a low barrier to entry for newcomers. One problem Wikipedia faces is a small minority of established Wikipedians who are hostile to new editors. It’s not common, but it is there. This drives newcomers away, and so concentrates edits within the group of established editors, effectively increasing the exponent in the power law.

Third, the essence of these and other similar recommendations is that they are systematic efforts to spread attention and contribution out, not one-off efforts toward developing a long tail of sales or contributions. The problem with one-off efforts is that they do nothing to change the systematic architectural factors which actually determine the exponent in the power law, and it is that exponent which is the critical factor.

If the power law is a description of network clustering, then you could say that the power law is likely to shift from less than 1 to greater than 1 as the strength of preferential attachment increases.

What's Wrong with HHI? Or: What Kind of Competition is Bad for Consumers?

The DOJ/FTC have announced upcoming workshops to review the Merger Guidelines, which are now (depending on whether you count the 1997 revision) either about to start or about to end their teenage years -- i.e., in an awkward stage.

Recently the paper by Shapiro and Farrell on upward price pressure came to my attention:

We propose a simple, new test for making an initial determination of whether a proposed merger between rivals is likely to reduce competition and thus lead to higher prices. Under current antitrust policy, the government can establish a presumption that a proposed horizontal merger will harm competition by defining the relevant market and showing that the merger will lead to a substantial increase in concentration in that market. However, this approach can perform poorly in markets for differentiated products, where market boundaries are unclear and the proximity of the products sold by the merging firms is a key determinant of the merger's effect on competition. Our test looks for upward pricing pressure (UPP) resulting from the merger. We develop a simple diagnostic for UPP based on the price/cost margins of the products sold by the merging firms and the magnitude of direct substitution between the two firm's products. We argue that our approach is well grounded in economics, workable in practice, and superior to existing methods in a substantial class of mergers.

In general, I am enthusiastic about this paper and what it signifies about how this administration will approach these complex problems. In short, UPP avoids the rather artificial analysis of market share using HHI by substituting a direct measure of relative cross-elasticity (or, more precisely, the diversion rato) adjusted by profit margins. In other words, within the UPP framework, the higher the profit margins and the lower the cross-elasticity, the more likely the merger will be bad for consumers. Both economists and lawyers should appreciate how this is a vast improvement over the entirely static calculation of HHI for the market pre- and post-merger.

But for me the problems with HHI suggest a different angle of attack. More specifically, if we agree that one of the core problems with HHI is that it provides too static a picture of competition, then one can justly ask whether UPP really solves the core problem rather than substituting a different (albeit better) measure of the prospective effect of the merger.

What is HHI? For the uninitiated, HHI is an index calculated by adding in quadrature the market share (usually in percentage units) of various companies pre- and post-merger. One of the consequences of adding in quadrature, of course, is that the square of the post-merger market share will always be less than the sum of the two pre-merger companies' market shares squared. Why is that?

I do not know what H and H or others have to say. At first, I was putting off this post until I could find out. Today I realized that that could be a long while. So I will offer my own thoughts.

In probability theory, we add the error of normal variables in quadrature. In other words, if a calculation depends on two measurements, each of which has a certain tolerance for error (e.g., 10 meters plus or minus 2 meters and 4 meters plus or minus 1 meter), then the result of the calculation will be the sum of the measurements, but the error will be the sum of the squares of the errors (i.e., here, 2^2 + 1^2 = 5), not merely the sum of the errors (i.e., 2 + 1 = 3).

The reason errors are added in quadrature is because an error in one direction can cancel an error in the other. That is, if the two measurements are made along the same dimension of units, a statistical fluctuation in the positive direction for one can cancel a statistical fluctuation in the negative direction for the other.

This all carries over very naturally to our analysis of HHI. At bottom, what HHI invites us to imagine is that our market share percentages are actually the variance (or, if the distribution is gaussian, the "standard deviation") of some distribution of possible market share. Hence, to determine market share after combining two distributions associated with two companies, we add in quadrature.

Notice that if we think about market share in these terms, then there is an implicit role for time in the picture. Namely, the distributions are produced by "measurements" in the form of dealflow that result in a distribution with particular variance over some period of time. If the distributions are not stationary (and why would they be?), then that variance should fluctuate. But only when two distributions are combined in the sense that they stop competing for the same dealflow will their variance change discontinuously. That fits nicely with the HHI picture.

But what does it leave out? How about how the variance is changing over time? Wouldn't you like to know whether the distributions are getting fatter are narrower over time?

On my view, the key parameter for defining competition is change in distribution width per unit time. In practice, this would produce a dimensionless number, the internal rate of return, or IRR. If, even adjusting for mergers, a company has posted an IRR over a certain percentage, then there is a reasonable chance that their growth has been built through the use of unsustainable modes of operating, such as fraud.

UPP is an improvement, but doesn't really get to the core problem, which is dynamic.

UPDATE: Investigation of Herfindahl's early papers shows an infatuation with the chi-squared distribution. There are serious fundamental problems with relying upon a chi-squared distribution to fit market concentration, perhaps the most important of which is that market shares cannot and should not be assumed to be independent. Another is that any actual distribution of market shares will probably not be stationary, either over same-width intervals or at different length intervals. We should have cast this kind of theory to the flames a long time ago.

The entropy concentration index is an interesting slice at the problem of characterizing concentration, and brings out the fact that it is the correlation of market shares rather than their statistical independence per se that makes HHI unrealistic. But the entropy index fails for the same reason -- i.e., that market share measurements are not uncorrelated, as they must be for entropy to be an extensive quantity (i.e., for S of 1 and 2 combined to equal S1 + S2). In this regard, a generalization to nonextensive entropy metrics might be considered useful. But there are conceptually and practically simpler ways to get at the degree of correlation in market share, such as cross-correlations in the time-series of cash-flows of different firms.

Thouhts on Nick Paumgarten's "The Secret Cycle"

Nick Paumgarten's piece, "The Secret Cycle" in the 12 October 2009 New Yorker is probably worth a read for some readers of Broken Symmetry. The article, which is unfortunately gated, retells some of the history of technical forecasting based on observed periodicities in a variety of independent variables, including (naturally) market prices.

Armstrong sounds like an idiot savant to me. He probably is quite good at the technical analysis, but is full of @#$# when it comes to his speculations about what mechanisms might account for observed periodicities. So are most people who claim to see signal in the noise of market prices. For the record, your author endeavors to invest only with a margin of safety calculated Graham-and-Dodd-style (or, better, Buffett and Munger-style) from fundamentals.

But long-time readers of Broken Symmetry may recall earlier posts on a "fundamental hypothesis of periodicity." Also for the record, I will say that I believe there are probably collective modes of oscillation produced by organizations of individuals that arise from weak nonlinear couplings of human behavior. That belief is not pure speculation, as the papers from Malmgren and Watts and on synchronized clusters demonstrate.

I am profoundly skeptical -- in fact, I believe it's impossible -- for us to accurately forecast market price cycles out for years into the future with day-level precision as people like Martin Armstrong claim to be able to do. Yet I believe it's not impossible that much more of our social and economic lives are governed by low frequency, but large-scale and low-magnitude "forces" than most economists would admit. It's just that the higher energy noise of everyday life makes the influence of these weak forces much harder to discern. It's only in moments of profound social uncertainty -- such as the present crisis -- that people begin to wonder how much of their individual destiny is truly independent of their neighbors'.

Robert Musil says somewhere that we are as connected to each other as two drops in a river. That has always sounded about right to me. And if you're thinking, "That's not too connected!" then I refer you to consider the chemistry of water more carefully (and particularly the hydrogen bond), and remind you that Musil was trained in that chemistry.

Hayek and Group Selection Theory

From the first volume of Law, Legislation, and Liberty:

The other view, which has slowly and gradually advanced since antiquity but for a time was almost entirely overwhelmed by the more glamorous constructivist view, was that orderliness of society which greatly increased the effectiveness of individual action was not duly solely to institutions and practices which had been invented or designed for that purpose, but was largely due to a process described at first as 'growth' and later as 'evolution,' a process in which practices which had first been adopted for other reasons, or even purely accidentally, were preserved because they enabled the group in which they had arisen to prevail over others.

(Italics mine.)

Interesting Interview of Michael J. Mauboussin

At Simolean Sense:

Q: You were a top analyst for many years, can you pinpoint when you first became interested in a multidisciplinary approach to finance/investing?

A: I’d trace my thinking back to the moment I read Creating Shareholder Value by Al Rappaport, who I had the honor of working with on Expectations Investing. That book encouraged me to approach stock valuation in a way that was—and still is, to a large degree—different than the rest of the financial community. Specifically, he emphasized the importance of long-term cash flows, showed how competitive strategy analysis should be used, and made a persuasive case that expectations are the key to stock prices.

As I was implementing Rappaport’s ideas in the early 1990s, I started to read more widely in areas like evolutionary theory and psychology. Around the mid 1990s, Bill Miller, who’s now my boss, invited me to visit the Santa Fe Institute. SFI is dedicated to multidisciplinary research in the physical and social sciences. Immersion into the research at SFI really catalyzed my interest in applying multi-disciplinary approaches to the world of investing.

Via Reflections on Value Investing

Interesting to note Mauboussin's choice of words in a few places -- a perfect match to Charlie Munger's. Who is mimicking whom I cannot say for sure, but I'm guessing Munger has priority here.

How to Think about the Single Sentence Claiming Rule

PatentlyO and Hal Wegner have stirred up discussion of this issue again. Hal points out that it was raised first (at least in the recent past) by Federal Circuit Judge Plager:

a topic that gained much attention when first proposed by a respected former Law School Dean and member of the Federal Circuit. See S. Jay Plager, Challenges for Intellectual Property Law in the Twenty-First Century: Indeterminacy and Other Problems, 2001 U. Ill. L. Rev. 69, 72 (2001).

This is a topic that I touched on briefly in a letter comment to the FTC I submitted earlier this year. In a nutshell, I think patent reform needs to focus on fixing the quid pro quo of the patent system -- exclusive rights for teaching the world something new or nonobvious. People talk about the notice function of patents not working, and there are certainly fairness issues raised by that dysfunction, but what's even worse is the teaching function of patents not working. When engineers and scientists skilled in a given technology cannot read a patent and learn anything from it -- especially what it claims to be its invention -- then the system is broken.

So changing the single sentence rule of claiming could be a big improvement. But the way to change it -- the guiding principle for such a reform -- should be to make the claim language conform more closely to the set of symbols or nomenclature used by the field of engineers and scientists who work with a given technology. This is how claiming works already for chemicals and pharmaceuticals. Why shouldn't it be the same for software? Why not have pseudocode or UML diagrams in the claims?

The "Liquidity Trap" in the Ising Model of Consumption and Savings

According to Wikipedia:

The term liquidity trap is used in monetarism to refer to a situation where a country's nominal interest rate has been lowered nearly to or equal to zero to avoid a recession, but the liquidity in the market created by these low interest rates does not stimulate the economy to full employment.

It's worth pointing out that the Ising Model of Consumption and Savings (introduced here) predicts that liquidity traps can occur in certain scenarios.

Recall that the system of N agents (individuals or firms) is subject to the influence of announced interest rates (by analogy to the magnetic field) and a money supply independent of the announced interest rates (by analogy to the heat bath). The situation where interest rates have been lowered to near zero is reflected by the curves for H=0. Notice that even at finite temperatures below the critical temperature Tc (i.e., when Tc/T > 1), agents may be self-organized into saving as a group.

Thus, within the Ising Model, the critical point marks the threshold amount of money supply necessary to prevent spontaneous symmetry breaking into either hoarding or spending behavior. Even crude estimates of this critical point might prove useful to policymakers.

It's worth noting a further prediction of the Ising Model -- that shifting to negative nominal interest rates might not be enough to shift the population from savings to consumption. Note the wide gap between the states of synchronized consumption and savings for the H=0+ and H=0- curves. It will take a very large negative move in interest rates to induce a phase transition from savings to consumption below the critical point. Good luck Sweden!

Douglas McGregor on Systems Theory

We study characteristics of cells, of organs, of the nervous system as a whole, of the human being as an organism, of groups, and of larger aggregations of human beings. Certain characteristics are common to all these "systems"; others are unique at each level. Water, for example, is composed of atoms of hydrogen and oxygen. Knowledge about these at the level of the atom would not give us knowledge of the properties of water, nor of the fact that water at temperatures below 32 degrees Fahrenheit becomes solid and floats.

Management's insistence that the individual is the unit of organization is as limiting as an engineer's insistence that the atom is the unit of physical systems. The limitations of a physical technology based at one level alone would be great indeed. A molecule is an assembly of atoms, to be sure, but certain relationships among the atoms result in molecules with given properties, whereas other relationships result in entirely different properties. These properties of molecules cannot be predicted solely on the basis of knowledge of the properties of atoms.

That's from The Professional Manager, published in 1967, which I picked up at D.G. Wills in La Jolla while on vacation. I'm still in the first chapter, but have been delighted with what I've discovered so far. McGregor points to Maslow as the foundation for his theory of human behavior, and comes out (in the passage above and its surrounding pages) very strongly in favor of group selection theory. This was just a few years before the new Atheists, especially Dawkins, effectively put the kibosh on multilevel selection theory in evolutionary biology -- a trend that has recently reversed.

A friend tells me that McGregor taught both Warren Bennis and Peter Drucker. It's very intellectually satisfying to find that McGregor shared so many of my personal inclinations. I may have more to say about this book in the future.

If one were to quibble with McGregor's last claim in the quoted passage (that properties of molecules cannot be predicted solely on the basis of properties of atoms), then one would point out that renormalization group methods give us some insights into how relationships at one scale affect dynamics at larger scales.

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.

A Systems Theory of "Animal Spirits": an Application of the 1D Ising Model

According to Keynes, it is "animal spirits" that drive shifts in consumption and savings:

Even apart from the instability due to speculation, there is the instability due to the characteristic of human nature that a large proportion of our positive activities depend on spontaneous optimism rather than mathematical expectations, whether moral or hedonistic or economic. Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as the result of animal spirits - a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.

Condensed matter physicists, including Leo Kadanoff, developed a mathematical model that we might find useful in modeling what Keynes described as a "spontaneous urge to action." Although a toy model even for physicists, the 1D Ising model (described by Kadanoff here and by wikipedians here) provides a useful way of understanding the relationship between symmetries in microdynamics and the coarse-grained, macrodynamical variables that are used to categorize the state of a system.

In condensed matter physics, the system is a large number N (at least thousands) of magnetic dipoles arranged on a line, which are exposed both to a heat bath (that guarantees a certain average temperature for the overall system) and a magnetic field (that can be turned on and off to introduce more energy and order into the system). Each of these dipoles can point either up or down (i.e., parallel or antiparallel to the magnetic field).

For economists, the system is a large number N of individuals (or firms), each of which can exhibit either a preference for consumption or a preference for savings. We shall keep track of these preferences by assigning a preference for consumption to a dipole pointing down (i.e., by analogy, against the magnetic field) and a preference for savings with a dipole pointing up (i.e., by analogy, aligned with the magnetic field). Rather than a magnetic field, these individuals are subject to the influence of an interest rate announced by some regulatory authority. Rather than a heat bath, we're going to have a regulated money supply, which guarantees that there is a certain total amount of cash in the system.

Most importantly, the Ising model postulates a link or coupling to the two nearest neighbors. In the condensed matter case, this means that the overall energy of a local region of the system is lower (or higher depending on the type of magnetism) when the individuals in that local region are either all parallel with the magnetic field or all anti-parallel. In our case, this means that the average cashflow in a local region is lower (never higher as it might be in the condensed matter case) when the individuals in that local region are all either saving or consuming. What's the explanation for this coupling? "Animal spirits."

Before proceeding to the most surprising results, let's get a feeling for the microeconomics of our system to make sure they make sense. Given a fixed amount of cash in the system, if we increase the interest rate, we expect the number of individuals expressing a preference for consumption to decrease -- i.e., for their preferences to flip from consumption to savings. By contrast, given a fixed interest rate, we expect the absolute amount of consumption to increase as the amount of cash in the system is increased because the real cost of interest payments decreases with inflation in the money supply.

Now for the results. Without bothering to reproduce the detailed mathematical analysis (the most elegant solution involves use of renormalization group methods), here is what one finds from the exact solution of the 1D Ising model: (the graph is reproduced from the paper by Kadanoff):

The y-axis on the graph corresponds to the average rate of savings (positive values) or consumption (negative values). The x-axis corresponds to the reciprocal of money supply so that the origin of the x-axis corresponds to an infinite money supply. The x-axis is also scaled by a factor, Tc, which corresponds to a critical threshold for money supply to the system (further explained below). The different plots correspond to different values of the interest rate (note that these can go negative, a scenario that has obtained only in Sweden so far).

The amount of insight this diagram gives us into the system is extraordinary. Consider the interpretation of these various plots:

• High positive interest rate: (H=0.5) As money supply decreases from infinite to fractions of its critical value, the average amount of savings smoothly increases from about 75% of the population saving to the point at the top right where everybody in the system is saving.
• High negative interest rate: (H=-0.5) As money supply decreases from infinite to fractions of its critical value, the average amount of consumption smoothly increases from about 75% of the population consuming to the point at the bottom right where everybody in the system is consuming.
• Zero interest rate: (H=0) The average amount of consumption and savings is perfectly balanced, even with an infinite money supply. In other words, when the system is flooded with money and interest rates are held at zero, exactly half of the population consumes and exactly half of the population saves. When interest rates are zero and money is plentiful, individuals basically act as if independent of their nearest neighbors. But note well what happens when interest rates are zero and the amount of cash in the system is withdrawn. At a critical threshold (Tc in the diagram), individuals spontaneously start to align with their nearest neighbors by either saving or consuming -- either is possible -- even when interest rates are zero. This is a textbook example of spontaneous symmetry breaking, which is the phenomenon from which this blog takes its name. The broken symmetry is a consequence of the coupling among nearest neighbors -- i.e., "animal spirits."

I realize that most economists have never heard of the 1D Ising model. But don't you think this kind of model might be useful in understanding macroeconomics? In subsequent posts, I will try to discuss how the Ising model has been extended into higher dimensions -- an important generalization for economics. For the time being, it must suffice to say that this toy model has nonetheless been highly influential among physicists in understanding nonequilbrium dynamics.

Update: A reader comments:

One problem with this model is that as the money supply goes to infinity, you get hyperinflation. This makes interest rates rise sharply. But your model has rates go to zero.

The answer to this comment is that interest rates might still depend on money supply. Referring back to the diagram, we can see that interest rates and money supply are treated as independent variables -- i.e., both are independent of the dependent variable (average consumption/savings). So in the zero interest rate case (H=0), interest rates are held as money supply is increased and decreased to see what happens to savings and consumption. The diagram doesn't make obvious how interest rates might depend on money supply (or vice versa).

Nonethelesss, we can deduce a few things about such a relationship from the diagram. For example, from the diagram it is clear that if we were to set a very high or very low interest rate (i.e., an H near +1 or -1), then everybody would be either saving (H=+1) or consuming (H=-1) regardless of whether the money supply was infinite or zero. In that sense at least, the comment about infinite money supply and hyperinflation being correlated is still consistent with the model. The diagram simply doesn't show how interest rates might depend upon money supply (or vice versa).

But we can develop a more complete answer by peaking back at the condensed matter system that inspired the 1D Ising Model. How does the strength of the magnetic field affect temperature? It is important, in this context, to remember that "temperature" is actually a number assigned to a distribution of energy in the system that has a particular shape. Whether an increase or decrease in the strength of a magnetic field will affect the shape of the distribution depends on the details of the microscopic dynamics. With too much or too little energy available to the system, a change in the magnetic field isn't going to have a big influence on the microdynamics, and hence the temperature will be insensitive to the magnetic field at these extremes.

Translating back into economic terms, this means that when individual decisions about savings and consumption are either perfectly independent or perfectly correlated (conditions which correspond to very high and very low total energy in the system), then a change in interest rates isn't going to have a big influence on money supply.

And does that not seem to be the case in fact?