Broken Symmetry

Utility is Local and Ephemeral

From a commencement address by Ben Bernanke:

Your sense of how well off you are economically depends a great deal on your expectations and aspirations, which in turn are largely formed by the community in which you live.

Via Tyler Cowen. Not new to readers of B.S., but encouraging to see also is the reference to Csikszentmihalyi's theory of flow:

Another factor in happiness, perhaps less obvious, is based on the concept of "flow."12 When you are working, studying, or pursuing a hobby, do you sometimes become so engrossed in what you are doing that you totally lose track of time? That feeling is called flow. If you never have that feeling, you should find some new activities--whether work or hobbies.

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.

Quick Illustration of Rotational Symmetry

From the Built on Facts blog:

Why do mirrors reflect right and left, but not up and down?

After a conversation with a friend over the weekend about this, it occurred to me that this is actually a pretty good way to illustrate how broken symmetries may be hard to spot. You can click through to read the answer in the comments at Built on Facts.

As my friend pointed out, there is also a neurological component to this explanation. We know that our brains are pretty good at inversion -- the lens in our eyes is an inversion center, but we don't see everything upside down and backward. So why don't our brains simply undo the effects of a reflection in a mirror?

The answer is that they can. If you spend enough time studying organic chemistry, for example, you get pretty darn good at distinguishing right from left-handed symmetry. And when you look in a mirror, what you're seeing is actually your enantiomer. The trick is that most of us aren't a close enough study of our appearance to immediately notice the change in handedness. Most of the time, we assume we are looking at a 180 degree rotation of ourselves.

But when we see the reflection of an object without rotational symmetry -- such as English text -- our brain's rotation strategy runs into a snag. We read text from left to right and from top to bottom -- i.e., with z axis pointing out of the page. In a mirror, the same text reads from left to right and from top to bottom, but with z-axis pointing into the page. There's no rotation that will get you into that space.

Conor Clarke Interviews Thomas Schelling

At his Atlantic Correspondents blog:

I think rational expectations can lead to several alternative equilibrium situations, depending on what people choose to expect. If people expect the price of coffee to go up, they will make it go up. And if people expect the price of coffee to go down, it will go down. And the rational expectations model doesn't necessarily tell you what external ingredient beings to sway opinion in one direction or another.

Last year I wrote up a discussion of Schelling's classic explanation of how rationality is only a special case of symmetries in expectations here: Bounded Rationality or Broken Symmetry?

Non-convexities in Production

From The Economics of Non-Convex Ecosystems: Introduction by Partha Dasgupta and Karl-Goran Maler:

The price mechanism is especially problematic in economic systems characterised by positive feedback processes. We now know that in such environments it may prove impossible to decentralise an efficient allocation of resources by means exclusively of prices. Efficient mechanisms would typically involve additional social contrivances, such as (Pigouvian) taxes and subsidies, quantity controls, social norms of behaviour, and so forth. This was proved formally in a justly famous article by Starrett (1972), who showed that for certain types of non-convexities associated with environmental pollution, a competitive price equilibrium simply does not exist: markets for pollution would be unable to equate demands to supplies.

The discussion in Section 4 demonstrates a link between gauge theory in physics and non-convexity theory in economics. Dasgupta and Maler "without rigorous justification" associate investment I with the time-derivative of capital stock K. Using the language of gauge theory, one would say that K is a "conserved current." When local symmetries of the system are broken over time or across space, such currents are no-longer conserved.

Bleg for Economists: Empirical Tests of the Rational Hypothesis

Folks, aside from the lab experiments (which I know produced mixed results), what empirical evidence do we have of the validity of the rational hypothesis? As best I can tell, the last work done in this regard were the nonparametric tests of WARP by Varian and Bronars in the 1980s.

Those studies, of course, were of aggregates of household consumption over long time periods. Has anybody tested the rational hypothesis against revealed preferences outside a laboratory by tracking individual consumer behavior?

The question comes to this: Is there a data set for a large population that tracks the time-series of acts of consumption for each individual in the population over some period of time?

If the rational hypothesis is applied to predict how individuals will behave, then it should be based on empirical data about individual behavior, should it not? Where is that data?

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.

More on Group Selection Theory

From the Independent:

In his study, published in the journal Science, Dr Bowles takes on the proponents of the selfish-gene theory of human evolution by suggesting that natural selection worked on groups of people co-operating together, rather than just individuals.

See also earlier posts from Broken Symmetry relating group selection theory to Tribal Leadership and Executive Compensation.

Entropy in Highly Correlated Systems: Market Equilibrium as Stable Synchronized Flow

The review article linked to the post on Tsallis entropy provides an excellent introduction to this generalization of Boltzmann-Gibb (BG) statistics. In particular, section 2.2 explains how BG statistics obtain at certain limits of the generalized q-statistics (a/k/a Tsallis entropy). What are these limits?

First, BG statistics apply at the limit of independence. So, for example, in a series of N binary events, Tsallis entropy is approximately 2^[N(1-q)]-1/(1-q), and if the events are independent, q = 1 and this reduces to the BG entropy 2^N. This limit is not all that surprising.

Second, BG statistics also apply at the limit of perfect correlation. So, for example, if events are correlated at all scales in accordance with some power law N^r, then the Tsallis entropy is approximately N^[r(1-q)]-1/(1-q). If and when q takes on the value q* = 1 - 1/r, then again BG statistics obtain, albeit to a different set (of rescaled) microscopic variables.

That is really surprising. What that means is that we might see normal (i.e., gaussian statistics) apply even to highly correlated "equilibrium" states. One can't help wondering whether, in fact, that is exactly what we are calling a market equilibrium.

Statistics are all well and good, but what is going on at the micro level to produce these statistics? Tsallis talks in very general terms about "multi-fractal" states. What's that mean? Sounds cool at least, doesn't it?

The paper from Zanette and Kuperman I posted on Friday provides some interesting clues about how microscopic dynamics go from uncorrelated to correlated through a phase transition. The figure posted shows how the number of clusters with different phase characteristics is maximized during phase transitions, and that the process of going from uncorrelated to correlated states involves "cross sync" of spatially dispersed clusters during the phase transition.

Read in conjunction with the papers on Tsallis entropy, I think a picture of how the micro dynamics change with the macro statistics starts to emerge. In particular, we should see Levy statistics during phase transitions, and Gaussian statistics in periods of relatively good syncrhonization/high correlation.

It's a new way to model markets, but the math is all there, folks. Look at the statistics for price shifts within a window to see if they're gaussian or levy distributed. If gaussian, then buyers and sellers are either acting completely independently of one-another (possible, but unlikely) or counterparties are acting synchronously in accordance with share perfectly antisymmetric expectations of future value/revenue (more likely). If levy, then the perfectly antisymmetric synchronized flow among buyers and sellers has broken out into multiple cross-synced clusters.

Is there a way to prevent the market from crashing precipitously at unpredictable intervals? I don't know, but I would think that keeping the market constantly in a phase transition would be a more stable mode of operation -- less susceptible to systemic failures -- than a mode of perfectly correlated expectations.

Cross Synchronized Clusters in an Axelrod-inspired Model

From M. N. Kuperman and D.H. Zanette:

[T]he segregation of oscillators into clusters is not necessarily associated with the synchronization of all the individual phases. In particular, two oscillators may belong to the same synchronized cluster with respect to some of their phases -- which, in the asymptotic state, adopt identical values -- but to different clusters with respect to the other phases. This phenomenon, which we have called cross synchronization, discloses a highly complex form of collective organization, consisting of coherent clusters mixed with respect to the internal variables which specify the individual states. It is interesting to note that Axelrod's model does not exhibit a regime corresponding to cross synchronization. This kind of regime would however make sense as a possible distribution of cultural divrsity over a real population, in the form of partially overlapping cultural domains.

Available here.

What the picture shows is that during phase transitions, spatially local regions within a network may be described by dynamics that share similiarities with multiple spatially far regions elsewhere in the network. By analogy to Axelrod's model, cultural diversity is maximized during phase transitions through a mechanism whereby most local cultures share some but not all traits with many other spatially distant local clusters.

The model has direct implications for those with a normative goal of increasing diversity within a population.

Tyler Cowen on Fischer Black and Correlated Risk

The key question about the current financial crisis is how so many investors could have mispriced risk in the same way and at the same time. This article looks at the work of Fischer Black for insight into this problem. In particular, Black considered why the “law of large numbers” does not always apply to expectations in a market setting. Black’s hypothesis that a financial crisis can arise from extreme bad luck is more plausible than is usually realized. In this view, such factors as the real estate market are of secondary importance for understanding the economic crisis, and the financial side of the crisis may have roots in the real economy as a whole.

Download available here.

Fama and French on Active Investing

Here's an excerpt from their latest post:

Suppose we define a passive investor as anyone whose portfolio of U.S. equities is the cap-weight market portfolio described above. Likewise, define an active investor as anyone whose portfolio of U.S. equities is the not the cap-weight market portfolio. It is nevertheless true that the aggregate portfolio of active investors (with each investor's portfolio weighted by that investor's share of the total value of the U.S. equities held by active investors) has to be the market portfolio. Since the aggregate portfolio of all investors (active plus passive) is the market portfolio and the aggregate for all passive investors is the market portfolio,the aggregate for all active investors must be the market portfolio...

It is, of course, possible that individual active investors add value. But if they do, it's at the expense of other active investors.

Was anybody confused about this? This post of theirs bothers me less than some others because I think it's true that some people who trade fail to consider how transactions costs will add up over time. Especially if you consider the compound interest on transactions costs, you have to be confident that your information and understanding is much better than average before trading.

But their logic doesn't address the more interesting question, which is whether there are individual active investors who consistently take money from their dumber active investor peers.

Tsallis Entropy

I'm speechless.

Strongly ergodic/mixing phenomena are ubiquitous in Nature; essentially, they are driven by microscopic interactions which are short-ranged in spacetime (short-range forces, short-range memory, nonfractal boundary conditions); their basic geometry tends to be continuous, Euclidean-like; their thermodynamics is extensive; their central laws (energy distribution at equilibrium, time-relaxation towards equilibrium) are exponentials; and their thermostatistical foundation is Boltzmann-Gibbs statistics (i.e., q = 1). But weakly ergodic/mixing phenomena also are ubiquitous in Nature (e.g., biological, socio-economical, human cognitive phenomena, etc); essentially, they are driven by microscopic interactions which are long-ranged in space and time (long-range forces, nonmarkovian memory, fractal boundary conditions); their basic geometry tends to be discrete, multifractal-like; their thermodynamics is nonextensive; their central laws (energy distribution at equilibrium, time-relaxation towards equilibrium) are power-laws; and the thermostatistical foundation of (at least some of) them (hopefully) is the q != 1 statistics.

Review here.

Kadanoff on Phase Transitions

Kadanoff has been doing work on renormalization group and nonequilibrium statistical mechanics from the beginning:

This paper Looks at the early theory of phase transitions. It considers a group of related concepts derived from condensed matter and statistical physics. The key technical ideas here go under the names of "singularity", "order parameter", "mean field theory", and "variational method". In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor, "steam", come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in a some statistical variable of the system. The discontinuous property is called the order parameter. Each phase transitions has its own order parameter that range over a tremendous variety of physical properties. These properties include the density of a liquid gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when that jump approaches zero. This note is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of this phenomenon.

Via Physics and Physicists.

Kadanoff makes an interesting epistemological point here. From the mathematical fact that no phase transition can occur within a finite system, he argues that "we must conclude that phase transitions and the definitions of different thermodynamic phases are the result of a process of extrapolating the real behavior of a theory of large bodies, to its infinite conclusion." Thus, the "extrapolation and simplifying ... suggests that at least this part of theoretical physics is not a simple result of the direct examination of nature but rather of the human imagination applied to an extrapolation of that examination."

I don't necessarily disagree with this point. I have noted elsewhere that our theories form part of a feedback loop with the stream of stimulus to our brains and our actions within the universe here. I do want to point out, however, that there is another possibility, which remains (unfortunately) inaccessible to scientific inquiry -- namely, that every seeming finite system is woven together into a fabric that is infinite.

Economists should take note of how the form of Kadanoff's argument here is so similar to the form of justification offered by economists for model-making. It's not that we believe our models are reality; it's that our models help us to perceive things about reality that would otherwise remain inaccessible to our senses -- at least until we learn how to use them better.

Organic Economics

Since the Arrow-Debreu-McKenzie model was introduced to economics in the 1950s, changes over time have been given less consideration in economic models. See, for example, this statement about changes in market prices by Eugene Fama. The efficient-market hypothesis implies that at any given moment an equilibrium market price exists, and (here's where the flow of time drops out of the picture) that the current price at any given moment is most likely the equilibrium price. Unless you have some information that nobody else in the market has, then you're probably making a mistake by guessing that most people are either underestimating or overestimating the value of a particular good. There are exceptions, of course, but in general economists and policymakers (including judges and lawmakers) think about (or at least did think about prior to this recession) economic equilibrium as static —- a perfect allocation of people and things that the market maintains more or less constantly.

Is there a more realistic way to model an economy? How about as an hierarchical social network? The social network must be hierarchical because smaller markets (i.e., smaller subnetworks) are usually connected to larger markets (i.e., bigger networks) such that there is nesting and overlap among them through the mechanism of cross-elasticity in demand.

Already, our model of the economy is of networks within networks. But the hierarchy goes deeper still. Each individual within an economy has his or her own neural network, which orders decisionmaking and behavior. In principle at least, we could identify subnetworks within an economy by looking to see whether particular individuals share substantially similar neural networks. Similar brain structure and dynamics are probably a physical (and biological) manifestation of consensus in belief and perception about past, present, and future within a subnetwork. Market equilibrium could be identified as the state of the system in which neural networks are matched in structure and dynamics so that the flow of goods through the economy is stable over a period of measurement. Such stability would be manifest in a market price that fluctuates only within the range of transactions costs.

From time to time, however, an individual within a subnetwork might make a new connection in his or her neural network. The new connection would arise from a new structural or dynamical pattern within that individual's neural network. Such a new pattern might be induced directly by exposure to new sensory information or statistically random variations in the individual's neural network, or indirectly from exposure to a new pattern communicated by another outside the subnetwork. In any case, the result would be a modification to the preexisting structure and dynamics of that individual's neural network.

An individual with a new pattern in mind (literally) might then attempt to reproduce the new pattern in the subnetwork of individuals who share (now similar, but not the same) neural network structure and dynamics. Through communication, the new pattern is either recognized, thereby rerouting every neural network in the subnetwork (albeit, through feedback loops, probably with some refinements), not recognized at all because too great a variation from preexisting patterns to be communicated, or rejected as inconsistent with important preexisting accepted patterns. Although a ridiculously difficult problem to solve mathematically, whether a new pattern would be accepted or rejected by the subnetwork could in principle be characterized using control theory to analyze the stability of the system including the new pattern within its preexisting environment. In practice, it's probably necessary to carry out the experiment to know.

The iteration of such a process eventually results in an increasingly sophisticated neural network shared among the subnetwork, with more and more specialized ability to recognize and explain more and more complex information over time. Interconnections among subnetworks, although difficult to achieve, might be expected to produce large returns to the individuals who are capable of matching the patterns in otherwise disconnected subnetworks.

To understand the new insights that such a model would give us in understanding economics, consider how individuals within the network of an economy include both entrepreneurs and customers. A successful entrepreneur, in practice, is one who is able to anticipate what patterns are going to be accepted by the neural networks of customers. Within this organic model of economics, capitalism is a game in which entrepreneurs conduct experiments in order to discover what patterns of behavior (i.e., what neural networks of prospective customers) will adapt by accepting a new pattern offered as an alternative to a preexisting pattern of behavior used to live with time-evolving resource constraints. Correct predictions are rewarded by the mass of individuals that adopts a new pattern of behavior. Incorrect predictions -- or inappropriately timed predictions -- generally disappear without a trace.

Not coincidentially, this game of capitalism provides a social parallel to the flow experience described by Mihalyi Csikszentmiahlyi as optimal to individual psychology. The same basic rules of the game apply both at the level of neural networks and at the level of networks of individuals within an economy. Because of how neural networks constitute economic networks, it should not surprise us to see that similar mathematical structure and dynamics apply to both. Consumer internet marketing professionals probably already know more about how neural networks work than do many neurologists!

Neoclassical theory offers zero insight into any of these dynamics.

Transitions to Synchronization on a Lattice Obey the Same Power Law as Directed Percolation

From F. Ginelli, R. Livi, A. Politi, and A. Torcini's paper On the relationship between directed percolation and the synchronization transition in spatially extended systems:

In this paper we have expounded a partially rigorous argument to show why the synchronization transition in spatially extended systems may belong to the DP universality class....

The crucial difficulty to determine the universality class for the synchronization transition is that the order parameter (the difference field) can be arbitrarily small. This casts doubts about the very definition of the zero-difference field as a truly absorbing state. In fact, in a previous paper [15], it was speculated that the DP scaling behaviour might be restricted to a finite range. The analysis carried on in this paper clarifies that the synchronization transition genuinely belongs to DP universality class...

In other words, the structure of a network of synchronized oscillators and the structure of a percolating flow in a weak field are the same in their critical state.

It's just speculation, but could the reason that these systems share critical structure be because they also share dynamics? Perhaps there are vortices that form during directed percolation whose angular momentum corresponds to the frequency and phase of syncrhonized oscillators on a lattice?

What Could Kin Selection Theory and Negligence Law Possibly Have in Common?

The same equation has been applied in both. See David Sloan Wilson's description of W.D. Hamilton's discovery of kin selection theory:

Hamilton became world famous for explaining how altruism can evolve according to the rule br - c >0, where b is the benefit that the altruist gives a recipient, c is the cost to the altruist, and r is the chance that the recipient shares the same altruistic gene through a common ancestor.

And compare with Judge Learned Hand's definition of negligence in United States v. Carroll Towing:

Since there are occasions when every vessel will break from her moorings, and since, if she does, she becomes a menace to those about her; the owner’s duty, as in other similar situations, to provide against resulting injuries is a function of three variables: (1) The probability that she will break away; (2) the gravity of the resulting injury, if she does; (3) the burden of adequate precautions. Possibly it serves to bring this notion into relief to state it in algebraic terms: if the probability be called P; the injury, L; and the burden, B; liability depends upon whether B is less than L multiplied by P: i.e., whether B < PL.

Make sure to read all of Wilson's blog post. Hamilton later expanded his theory. Note that Hand's formula has been indicated as a foundation of law and economics by Judge Posner.

Spontaneously Broken Continuous Symmetries in the Preference Functions of Economic Actors

Suppose we model an economy as a network of individual actors. Each actor is a node in the network. Each has a bundle of goods and a preference function associated with it. Consumption and production activities result in a transformation of the bundle. Exchanges result in a flow of goods through the network.

To a good approximation, at any given moment in time if we looked at the preferences for a particular good at each node, we might observe a continuous symmetry -- i.e., the relative preference for the good at each node might be approximately the same throughout the nework.

Now imagine that we watch what happens over time if we permit for a change in preferences to result from a (for now assume exogenous) new transormation discovered at a particular node. Suppose, for example, that one node in the network discovers a way to make a similar quality good using fewer inputs. At that node, the preferences for the particular good produced are going to diminish relative to other goods because the same (or similar good) can be produced at lower opportunity cost.

And now suppose that other nodes in the network can somehow (via mirror neurons or language) learn about this new means for producing the good so that both the knowledge and the change in preferences can propagate through the network.

Such propagation is arguably an example of the spontaneous breaking of a continuous symmetry in preferences. The observable result would be an oscillation -- a goldstone mode.

In general, not all continuous symmetries can be spontaneously broken to result in a goldstone mode. Under the Mermin-Wagner Theorem, continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions less than or equal to 2. (Isn't this an explanation for why a one-dimensional series of price changes does not have a finite average?) But apparently, so long as the nodes in our network can interact in more than two dimensions (which they can since our preferences, in general, can have as many dimensions as there are goods), then there can be goldstone modes.

Let's take this a step further by imagining that instead of each node being connected only to a neighborhood of other nodes, each node is connected to all other nodes -- i.e., that our network is all-to-all. How might this be accomplished? By designating a central place for exchange -- a market. Now when a new preference is discovered, regardless of whether the new preference is communicated to any other node directly, the new preference will be reflected by a new kind of exchange in the market, which is observable (by construction) by all nodes in the network.

How will propagation of this new preference take place in an all-to-all network? It depends on whether the new transformation that resulted in the new preference can be "reverse-engineeered" by observing the new exchange alone. If so, then the new preference may be adopted instaneously, and a new equilibrium reached within the time needed for the new kinds of exchanges to be completed (although this will depend on the frequency of previous consumption, production, and exchange activities). If not, then the market mechanism will not result in a global approach to the new equilibrium. Rather, alternative mechanisms for communicating the new transformation will be required.

In addition, the time required for frequency and phase matching a new exchange within the framework of existing exchanges among the nodes should not be overlooked. Especially if the new transformation occurs at low-frequency, it might be a long time before the network transitions to the new mode of operating through the necessary exchanges required.

Letter Comment to the FTC on the Evolving IP Marketplace

Here are a few excerpts:

According to systems theory, innovation emerges from iterated cycles in which data, theory, and the people who collect data and form theory constitute feedback loops, which evolve over time. Each cycle manifests as the gathering and exchange of information among a network of experts who act as gatekeepers to a set of symbolic rules and procedures. Following the terminology of Mihaly Csikszentmihalyi, I call the network of experts a “field,” and the set of symbolic rules and procedures a “domain.” To give examples, topology, physical chemistry, and constitutional law are domains. Each of these domains is associated, respectively, with the fields of mathematicians who specialize in topology; academic and practicing physical chemists; and academics, practicing lawyers, and judges who work on constitutional law.

From the point of view of an economist, the most important difference between systems theory and neoclassical theory may be that systems theory permits for economic actors (the field) to have preference functions (the domain) that evolve over time. As a result, although neoclassical theory is still a useful model of economic activity when changes in preferences are small within the window of time in which economic activity is observed, more generally no stable equilibrium may be reached because preferences may change during the period of observation. In addition, because systems theory need not assume that economic actors know how their preferences have or will change over time, an assumption that actors will try to match their allocation of resources to their preferences can be called “rational” only in a weak sense. Under systems theory, whether an economic actor will engage in an activity of consumption, production, or exchange is a function of: (1) their history of preferences; (2) their history of consumption, production, and exchanges with others; and (3) the frequency of their exchanges with others. Whereas within neoclassical theory institutions are designed to promote allocative efficiency, within systems theory institutions are designed to promote the discovery of information about preferences, and thereby the synchronization and frequency-matching of consumption and production activities through exchange and cooperation.

For example, the systems theory makes explicit the spatial and temporal dynamics underlying the knowledge problem described by F.A. Hayek in “The Use of Knowledge in Society.” With the systems theory in mind, we can identify the function of markets with their facilitation of the exchange of information and coordination of economic activity independent of central planning. This is in stark contrast with neoclassical theory, which often identifies the function of markets with the maximization of aggregate utility based on an assumption of stable preferences — a function that cannot be carried out by a central planner beyond a small scale. The systems theory therefore identifies markets as a mechanism for rewarding information exchange and cooperation, thereby facilitating economic growth.

Download Letter Comment to FTC on the Evolving IP Marketplace (Final)

Robert H. Frank's "Nonpositional Goods" are the Gauge Bosons of Local Symmetries in Economics

In "Positional Externalities Cause Large and Preventable Welfare Losses," Robert H. Frank notes how so-called "positional goods" may effect a redistribution of wealth in society by drawing resources into their creation that might be more efficiently allocated to other goods.

Earlier posts here and here considered the relevance of gauge theory to neoclassical economic models and concluded that invariances such as the Coase Theorem and the Miller-Modigliani theorem are conservation laws that are linked by Noether's Theorem to important symmetries in the neoclassical model.

I've been chewing this over for a while. An important question raised here is "What are transactions costs?" Somebody unfamiliar with the Coase Theorem or New Institutional Economics might naively believe the category limited to brokers' or attorneys' fees. They are not. Coase understood these costs to include, for example, the costs of searching for and identifying potential counterparties in addition to such fees. In fact, a major project for research within the field of New Institutional Economics seems to be getting precise in categorizing transactions costs.

On my view, the difficulty with categorizing transactions costs can be traced back to the fact that one person's "costs" are another person's revenue. In other words, transactions costs are deeply interwined with the symmetries or asymmetries in the bundle of goods and preferences held by potential counterparties.

Physicists have developed a very useful tool for categorizing particles based on the symmetries of the fields through which particles interact. This is gauge theory, of which Yang-Mills theory, which gives us the Standard Model, is the most well-established.

But before Yang-Mills theory there was Weyl's classical field theory. Classical field theory in physics actually bears much in common with neoclassical theory in economics. Both theories assume that symmetries in key variables are global. In neoclassical theory, if the value of some currency is inflated, then it may seem to each individual like they are richer, but because the currency value is inflated for everybody, buying power -- the value of the currency -- is the same.

By contrast, Yang-Mills (and in general any non-abelian gauge field) Theory permits for some symmetries to exist only locally. Many interesting consequences flow from the fact that global symmetries may be broken. One is path-dependence: The order in which interactions take place in Yang-Mills Theory matters to the ultimate configuration of the system. In fact, as Yang himself put it, when global symmetries are broken, "local symmetries dictate interactions".

Analogy to Yang-Mills Theory might bear fruit for economists. In particular, the methodology of categorizing interactions through local symmetry breaking could be very useful in formulating a more precise theory of transactions costs.

I will have more to say about this over time. For now, let me observe simply that most goods are produced and exchanged in discrete units. In physics terms, this means that the field of value in these goods is quantized. According to neoclassical economic theorists, this quantization shouldn't matter because goods can be exchanged indefinitely until the closest match to equilibrium is achieved.

That isn't what happens in practice, of course. To wit, what Robert H. Frank calls "nonpositional goods" are the analogs to gauge bosons of non-abelian gauge theory. Because the field of values for a good is quantized and because only local symmetries are conserved for the good, the lowest energy eqilibrium may never be reached.

But identifying "transactions costs" as the gauge bosons that result from local symmetry breaking is probably a useful insight in itself considering how difficult it has been to be precise about transactions costs in the past.

Why is our System of Executive Compensation so Broken?

Robert H. Frank has an answer:

When the strength of positional concerns differs across domains, the resulting conflict between individual and social welfare is structurally identical to the one inherent in a military arms race. To illustrate, consider rival nations faced with deciding how to apportion available resources between domestic consumption and military armaments. Each country’s valuations are typically more context-dependent in the armaments domain than in the domain of domestic consumption. After all, having lower domestic consumption than one’s rival might entail psychological discomfort, but being less well armed could spell the end of political independence. The familiar result is a mutual escalation of expenditure on armaments that does not enhance security for either nation. Because the extra spending comes at the expense of domestic consumption, its overall effect is to reduce welfare. Note that if each country’s valuations were equally context-sensitive in the two domains, there would be no arms race, for in that case the attraction of having more arms than one’s rival would be exactly offset by the penalties of having lower relative consumption.

So long as CEO pay performance is determined by what other CEOs are getting paid rather than by how much value the company creates during the CEO's tenure, CEO pay will be a positional good in Frank's terms, which draws value away from employees, customers, and investors.

How could CEO pay become less positional? By giving other stakeholders (but especially investors) more transparency into the cash-flows in and out of the firm. Boards and shareholders are forced to compete with other boards and shareholders because those measurements of CEO performance are right now more reliable than more direct measurements of company growth.

Levy or Inhomogeneous Poisson Process?

Mankiw comments:

Stock prices are approximately brownian motion, which means they are everywhere continuous but nowhere differentiable. In plainer English, "continuous" means that stock prices an instant from now, or an instant ago, are close to where they are now. But "not differentiable" means that the direction they move over the next instant is not necessarily close to the the direction they were heading over the last instant. A roller coaster with that property would be quite a ride.

And in reply, ironman says:

Since at least January 2008, stock prices moved away from approximating Brownian motion to instead follow more of a Lévy Flight.

And I ask, are we sure that the rate of price changes has been stationary over this period of time? It's not a Levy process unless the rate is stationary.

On my view, an inhomogeneous Poisson process is more likely at work in market prices. The reason is because market prices have to synchronize two different frequency distributions -- one for supply, one for demand.

Market Prices Synchronize Flows

Suppose for a moment that you had never heard of economics or the rational hypothesis but nonetheless had to explain the phenomena of market prices with reference to neither. Where might you start?

I would start by observing what is exchanged. Price is only a measure in some currency of what is exchanged. Let's make it concrete: if someone pays $1 to someone else for a peanut butter and jelly sandwich, then the price is either $1 or 1 PB&J. The definition of buyer and seller is arbitrary, thus so is the unit of price.

Why is there an exchange? Because at the moment in time of the exchange, each party wants something that their counterparty has more than something else currently owned. Alice is hungry and Bob wants the $1 more than the PB&J.

Does this make Alice and Bob rational? No. All it means is that Alice was hungry and Bob was not! Suppose Alice and Bob don't complete their transaction at this moment in time, but rather at an earlier or later moment in time. Suppose it's breakfast rather than lunch time. Will Alice pay $1 for the PB&J? No. She just had breakfast, and anyway she doesn't like peanut butter for breakfast. Now suppose it's dinner rather than lunch. Yes. Alice is hungry because she skipped lunch. She prefers steak, of course. But she's famished so PB&J will do. Bob, on the other hand, might decide at dinner time that $1 is no longer a fair price. Now he's hungry too, and maybe he can't afford to buy or make himself dinner with only $1 from Alice.

This all may seem like a silly exercise to you, but really it's not. What it shows is that price varies in time as preferences vary in time. Preferences are not static, although they may appear to be so if we look at a large enough group over a long enough time.

What are Alice and Bob doing then? They are cooperating. Alice happens to have an extra dollar left over from her sale of a sweater she knitted. Bob has an extra PB&J because he bought too many ingredients. Alice and Bob are meeting each others' needs -- creating wealth in Smith's parlance.

Let's try to generalize from Alice and Bob. Let's say later Charlie shows up and wants a PB&J for a $1. He saw Alice eating hers and wanted one too. Will Bob sell him a PB&J for a $1? That depends. Does Bob have another PB&J to sell? Obviously, Charlie is out of luck if the answer is no. But maybe Charlie is willing to pay more than $1. If so, then Bob might be able to buy more ingredients (if necessary) or spend more time making another PB&J for Charlie.

Why did the price go up? The answer is not scarcity alone! It was not the existing supply and demand alone that determined whether a transaction took place, or if so, at what price. It was scarcity AND the time required for Bob to make the sandwich. If the sandwich wasn't already prepared, then there might be no deal if Bob didn't have the time to make a sandwich right then, or if Charlie couldn't or wouldn't wait for the sandwich to be made.

Asymmetries in both time and goods on both sides of the trade determine whether a transaction will occur, and at what price. But over time periods much longer than the average period of time between transactions, it is the asymmetries in time that matter most in determining price -- money and goods equilibrate because cycles of consumption or production eventually synchronize.

It is in this sense that market prices synchronize the activities of market actors, whose rhythms are otherwise set by hard wired biological needs.

But if price is a function of the frequency and synchronization of complementary activities, then what need is there to add to our theory a hypothesis that market actors seek always to maximize their share of the value of a transaction?

For an earlier post on this topic, see here.

Broken Symmetries at Ford Redux

I have learned not to talk my book because it makes it harder to change my mind. But at this point, I am comfortable with the risk of that with Ford.

Back in April of 2008, I wrote the following:

In the automotive industry, Ford has one of the strongest brand names in the world. But for the past ten years, it has been dogged by persistent problems, driving its market value close to $10 billion at one point earlier this year. What are we to make of Ford's long-term prospects in the automotive market? Here are a few factors relevant to Ford's durable competitive advantage I have been considering:

• Product Quality: the newest quality ratings from J.D. Powers and Consumer Reports put Ford quality in striking distance of its Japanese competition
• Brand Identity: Ford has a brand name that is very differentiated from that of its Japanese competition, and probably in a favorable way from the perspective of customers in the emerging markets of Europe, South America, Asia, and India
• Economies of Scale: Mullaly is implementing at Ford the same scale advantages that have been practiced at Toyota for some time: centralizing worldwide design and production, narrowing the number of models and brands to the core few that offer the highest margins.

It's possible that GM and Chrysler will catch-up eventually, but Ford appears to have a good head start on its American competition in these regards. And it's selling at under $20 billion despite doing almost $200 million in sales annually, and a well-capitalized balance sheet.

This investment, together with another I made in regional department store Gottschalks, has been a wondeful lesson for me in the importance of competitive advantage. I bought a slug of both companies in mid-2007 after studying Benjamin Graham. Both companies were trading even then at a large discount to their book value.

Shortly thereafter I started reading Warren Buffett's annual reports and Charlie Munger, and I went back and looked at these investments. My analysis of Ford is given above. My analysis of Gottschalks, not so great. Gottschalks was what Buffett would call a cigar-butt stock. While I held onto both, I kept buying Ford through 2008 and early 2009. I thought Ford was a bargain after Kirk Kerkorian had to get out because he borrowed too much to get in last year. That decline in price had nothing to do with the value of the stock. On the other hand, it looks like I won't get my puff out of Gottschalks.

I won't be answering questions about how Ford should be valued now. I want to be free to change my mind on this one. But I can tell you that it is higher than what it selling at today. The factors cited above spell compound growth.

How Liquidity Constraints Alone Can Produce Price Bubbles

This post requires readers to have some background in mathematics, and complex analysis in particular. The point is to give a very succinct and precise explanation for how and why price bubbles can result without any assumption of rationality or irrationality. Bubbles can result from liquidity constraints alone.

For purposes of the argument, I make the following definitions of key variables:

Let q be defined as the discrete time-varying quantity that represents the volume of transactions that can occur within a market within a particular window in time. If it helps, think of q as a measure of aggregate current inventories. Let's set units of volume as dollars (although any fungible good might work). Then the units of q are dollars per unit time ($/day, for example). The derivative dq/dt thus specifies how the dollar volume per unit time is changing.

Let c be defined as the bid-ask spread in volume -- i.e., as the difference in dollars between the volume of goods offered for sale and the quantity of goods asked for purchase at a given moment in time. This bid-ask spread can be read off the markets in real-time. For purposes of this argument, we will assume that it does not vary much in time relative to q -- i.e., that dc/dt << dq/dt.

Here comes the key assumption for my argument:

Assume market price p is proportional at each moment in time to the volume available for transactions and inversely proportional to the bid-ask spread, i.e., that:

p = q / c

If we assume also that the total number of transactions that occur within the market within the time window within which q is measured is a conserved quantity (i.e., that inventory q is not created or destroyed within the relevant time frame), then we can define the "current" of transactions as:

i = -dq/dt

Now let L be defined as the amount of time it takes to complete a transaction at a given price level within a unit of time, so that:

p = -L di/dt

Finally, assume that some transactions costs R exist, but do not vary much on the relevant time-scale. Then p = i R.

Electrical engineers and physicists will recognize this as the model used for an LC circuit. I've even chosen the notation to be the same to avoid confusion in applying the model

These quantities together constitute a partial differential equation (PDE) that can be solved for p. The easiest way to do that is to treat p, q, and i as complex variables with a magnitude and time-varying phase. Then after a Laplace transform of the PDE, the complex transfer function is found by algebra:

H(s) = R / [R + (sL - 1/sC)]

H(s) peaks when its denominator gets closest to zero, i.e., when:

sL - 1/sC = 0

Or when s = 1 / sqt(LC)

What this means is that for a given volume of inventory (take, for example, the money supply M1), there is a characteristic frequency for fluctuations in price, which is determined by the liquidity variables L and c. Let's say that somehow the price could be changed exogenously (for example, by increasing or decreasing M1 with interest rates). When the period of time required for a cycle of increase and decrease matches 1/sqt(LC), then price will peak. So long as L and c can accommodate the dramatic fluctuations in p, everything will be fine. But sometimes the system will blow up. For example, the market may not be able to accommodate the total inventory available for sale (i.e., c may break down) or the price of the transaction may require additional transactions costs in time or money (R or L may go nonlinear).

Something like this just happened in the U.S.