Broken Symmetry

How Persuasive Are You?

When you recommend a new product to your friend and she tries it out, is it because you've persuaded her, or because she shares your preferences? If you're like me, you don't generally bother recommending things to people unless you know they happen to share your tastes along some dimension. Yet in principle there are some people out there whose opinions are "influential" -- coaxing otherwise disinterested people to try new things despite having different tastes. In principle, that's part of why professional athletes and celebrities are paid to endorse products. But teasing out exactly how much of the adoption of a new product is due to influence and how much is due to shared characteristics (i.e., "homophily") in the network can be difficult.

One cut at this question is forthcoming in PNAS in an article titled, "Distinguishing Influence Based Contagion from Homophily Driven Diffusion in Dynamic Networks" by Sinan Aral, Lev Muchnik,and Arun Sundararajan (as noted on the OrgTheory blog) (try emailing Aral for a copy):

In the context of product adoption, peer influence is associated with the presence of adopters in one‟s local network... However, identification of causal peer influence effects is complicated by the unobservability problem. Each user either has adopter friends or not, making it impossible to observe whether those with adopter friends ... would have adopted had they not had adopter friends. Homophily in this case creates a selection bias because treatments are not randomly assigned: adopters are more likely to be treated due to similarity with their neighbors. Thus, frequently used methods such as regression analysis, which can only establish correlation, are insufficient. Causal treatment effects can on the other hand be estimated via matched sampling, which controls for confounding factors and overcomes selection bias by comparing observations that have the same likelihood of treatment.

Toward this end we adapt matched sample estimation for use in dynamic networked settings. Conditioning matches on a vector of observable characteristics, behaviors and attributes yields influence estimates that account for the homophily that may make product adoption decisions cluster in the network even if no influence exists. This procedure establishes upper bounds on the degree to which influence (rather than homophily) explains assortative mixing and temporal clustering in networks. Since influence can vary over time, our framework provides estimates of its evolution. We can also assess the marginal influence of having an additional adopter friend for any arbitrary number of friends.

The upshot of this work is that shared characteristics among individuals accounts for almost all of the "viral" spread of new product adoption -- i.e., that preferences are largely fixed within the time-scale of weeks or months after a new product is introduced. There exists, nonetheless, a small group of people who are "influenced" into adopting a new product -- i.e., whom adopt the product through social interactions with other adopters with whom few characteristics are shared.

At least on its face, the work seems to affirm the use of fixed preferences as an approximation in this context. This validates the use of this approximation by economists. It also demonstrates, however, that the approximation is not without exception. Also of interest to economists.

One question I had on considering the work is whether it would be possible to single out the "influenced" and "influencers" in this survey, and determine whether or not such people occupy a position as bridges or "weak-tie" links within the social networks. Along the lines of Granovetter, the idea is that influence here is largely a function of whether or how often individuals come into contact with others with characteristics far different from their own. It would be interesting to know whether these individuals could be identified using this approach, which isolates "influence" from homophily.

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.

Ecological and Constructivist Rationality

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

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

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

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

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

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

Both forms of rationality are necessary to the pleasing result.

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

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

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

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

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

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

Spectral Analysis of Different Economic Groups

The NYT yesterday ran a very cool infographic: How Different Groups Spend Their Day.

Be sure to click on the various groups in the top right and watch how the chart shifts. These shifts vividly show that different socioeconomic groups have different frequency spectra for a given activity of consumption or production. From the chart, all we can infer is the difference in mean among the distributions for various groups. But from the data that made up the chart, we might also be able to see the shape of the distributions -- i.e., how much variance there is within the group in time spent on a given activity each day.

Can you see how tracking the frequency of consumption and production for a given individual or group would be a quantitative way to classify different groups, or even organizations? Notice how people with college and advanced degrees spend many more hours working than people with high school degrees. Notice how people over 65 years spend more than twice as much time watching television as adolescents and young adults.

Oh, and guess what most people without children do with the time that people with children spend on family care? T.V. What a waste.

Thoughts on High-Frequency Trading

I've been thinking about doing a longer post on this topic for a while since it fits so well with the idea of applying Fourier analysis to market regulation. Tyler Cowen blogs about it today:

The correct judgment of efficiency occurs at the system-wide level, not at the level of the individual trading strategy. The short-run story is that private profits exceed social returns but in the longer run the trading activity and liquidity brings increasing social returns and better communication of information.

Especially interesting was the comment from Matt Belcher:

I'm a high-frequency trader so take my comments on that basis. Prior to high-frequency trading and fully-electronic markets, the most trading profits went to the physically largest and most charismatic traders on the trading floors. By being large or gregarious they were more easily able to get the attention of brokers and get filled on their orders first, effectively front-running the other traders on the floor. On the NYSE, the specialist in charge of the book also could also extract profits at will. Since the advent of HFT, profits have moved from these traders to the ones with the best computer scientists. You can argue whether the new market is more efficient or fair, but you can't claim that the old one was somehow perfect and impossible to manipulate.

Putting aside fraud like churning and front-running (i.e., assuming the government is monitoring it!), from a social perspective HFT simply turns the fastest firms into the market makers by giving them a competitive advantage over other market makers in profiting on the spread. One could make a good argument, then, that the investments in HFT are a waste from a social perspective. Given the fact that the frequency of new information about public company stock, for example, becomes available on a time-scale much, much longer than the difference in time-scale between the last generation of market makers and the new generation of HFT market makers, this looks like a classic case of the croupiers on Wall Street taking another cut from the public.

But the argument is not so simple. A key empirical question is whether, in fact, the bid-ask spread has narrowed as a result of HFT. If so, then over a long-enough period of time, it may be that the social benefits of a narrower spread make up for the costs of investing in HFT.

A big picture issue is that the frequency of trading is dependent upon what sorts of information and analysis are done by the trader. If you're going to be day trading, then you ought to have access to HFT technology. If you're buying on fundamentals, then from an IRR perspective, whether you have HFT technology at your disposal will matter only when you're moving around a significant number of the total outstanding shares in a company.

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?

"Computational Social Science"

From David Lazer, Alex Pentland, Lada Adamic, Sinan Aral, Albert-László Barabási, Devon Brewer, Nicholas Christakis, Noshir Contractor, James Fowler, Myron Gutmann, Tony Jebara, Gary King, Michael Macy, Deb Roy, Marshall Van Alstyne:

To date, research on human interactions has relied mainly on one-time, self-reported data on relationships. New technologies, such as video surveillance (1), e-mail, and “smart” name badges, offer a moment-by-moment picture of interactions over extended periods of time, providing information about both the structure and content of relationships. For example, group interactions could be examined through e-mail data, and questions about the temporal dynamics of human communications could be addressed: Do work groups reach a stasis with little change, or do they dramatically change over time (2)? What interaction patterns predict highly productive groups and individuals? Can the diversity of news and content we receive predict our power or performance (3)? Face-to-face group interactions could be assessed over time with “sociometers.” Such electronic devices could be worn to capture physical proximity, location, movement, and other facets of individual behavior and collective interactions.

The data could raise interesting questions about, for example, patterns of proximity and communication within an organization, and flow patterns associated with high individual and group performance (4). We can also learn what a “macro” social network of society looks like (5), and how it evolves over time. Phone companies have records of call patterns among their customers extending over multiple years, and e- Commerce portals such as Google and Yahoo collect instant messaging data on global communication. Do these data paint a comprehensive picture of societal-level communication patterns? In what ways do these interactions affect economic productivity or public health? It is also increasingly easy to track the movements of people (6). Mobile phones allow the large-scale tracing of people’s movements and physical proximities over time (7). Such data may provide useful epidemiological insights: How might a pathogen, such as influenza, driven by physical proximity, spread through a population?

Available here. To model that data, you need a theory of highly integrated, complex dynamical systems. That set of theory is what I refer to as "systems theory" on this blog.

Computational social science is actually not new. Csikszentmihalyi started collecting such data with pagers decades ago using his "Experience Sampling Method" (ESM).

Via Dan Katz at the Computational Legal Studies blog.

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?

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.

The Problem with the Principle of Revealed Preferences and a Suggested Solution

In Chapter 5 of the Foundations of Economic Analysis, Paul Samuelson sets forth what he calls "The Pure Theory of Consumer's Behavior," which he identifies with the analysis of utility. According to Samuelson, many economists "separate economics from sociology upon the basis of rational or irrational behavior, where these terms are defined in the penumbra of utility theory. It would seem extremely important, therefore, to know clearly what is contained in the conventional utility analysis, if only to understand the consequences of denying its validity." (at 90)

What is utility? It is not happiness in Bentham's sense, or welfare in some general sense. Nor is it a physiological or psychological. "Originally great importance was attached to the ability of goods to fill basic biological needs," writes Samuleson, "but in almost every case this view has undergone extreme modification."

Why? Because of "the recognition that a cardinal measure of utility is in any case unnecessary; that only an ordinal preference, involving 'more' or 'less' but not 'how much,' is required for the analysis of consumer's behavior."

This is a weak explanation for why consumer behavior should be considered independent of psychology or biology. Why would biology or psychology demand that preferences be cardinal rather than ordinal when a measure of consumer behavior does not? Samuelson does not say. This makes the fact that evolutionary biology, social psychology, and sociology have made a come back recently less surprising, does it not?

But how does this utility analysis of consumer behavior work then? Starting from the assumption of ordinal preferences, Samuelson postulates the existence of a utility function. To help the reader in visualizing his argument, assume for now that there are only two types of goods or activities, A and B, that a consumer can choose. If we assign the quantity of good or activity A to the x-axis and the quantity of good or activity B to the y-axis, then the utility function would be a set of lines in the x-y plane. None of these lines cross; each represents a set of x,y pairs (or bundles of A and B) which produce the same amount of utility for the consumer. The lines are called "indifference curves."

How does this get us to a theory of consumer behavior? We get there with just two additional assumptions:

The utility analysis rests on the fundamental assumption that the individual confronted with given prices and confined to a given total expenditure selects that combination of goods which is highest on his preference scale.

(at 97) In other words, given a budget, a consumer behaves so as to maximize her utility by selecting the bundle of goods that includes as many of the goods that she ranks highly as possible.

There are two assumptions here. First, that the consumer maximizes utility. Second, that the particular bundle of goods selected reveals that the consumer prefers that bundle over any other.

As one might guess from the title of this post, I see problems with one of these assumptions, and it is not the assumption of maximization. As Richard Feynman has noted, for example, the behavior of many systems (human and non-human) can be described as a constrained extremization. It would be more surprising to find out that consumer behavior does not maximize or minimize some quantity.

The problem is with the principle of revealed preference. What the principle suggests is that the preferences (and hence utility) of a consumer can be measured indirectly (i.e., revealed) by observing what bundle of goods is preferred. The problem is that, by construction, a preference is revealed only when a transaction occurs. Although everybody has experienced an increase and decrease in preferences for particular goods over time (such as hunger and thirst), the principle of revealed preferences gives us no way to measure how preferences evolve in time between transactions. Relatedly and in addition, to make a complete "measurement" of consumer preferences for an entire set of goods, one must assume that the ranking of preferences does not change over time (or at least that it changes in deterministic ways). Otherwise there is no logically coherent way to rank the entire set of preferences.

Why do economists make these assumptions? They assume revealed preferences because there are few obvious alternative methods for measuring preferences. They assume time-independence of preferences because there is no other way to measure the entire preference function. Ultimately, they make both of these assumptions because with them, one can make reasonable forward-looking forecasts about how an economy will change as a result of shifts in supply or demand for a particular good. Reasonable, but not perfect!

There are alternatives for measuring preferences. On this blog a year ago I started writing about one. Consider as an alternative to the ordinal ranking of preferences a cardinal measurement of preferences. The preferences of a consumer for a particular good could be measured by counting how often the consumer consumed the particular good within a specific window of time. This measurement of consumer preference would take units of frequency. So if a consumer ate 5 apples in a day, we would say that the consumer had preference 5 apples per day. If the consumer ate only 1 orange per week, then we would say that the consumer had preference 1/7 oranges per day.

Notice how this alternative method of measuring preferences is consistent with the principle of revealed preferences in the sense that within a particular window of time we can rank preferences for each consumer. Within the window of the one week observed, the consumer preferred apples to oranges. If the preferences of this particular consumer are stable over many weeks, then the preference function observed through revealed preferences will be either almost or exactly the same as the preference function measured directly through frequency of consumption and then ranked. This condition of stability is called "ergodicity" by physicists.

But notice also how this method of measuring preferences provides additional flexibility. In particular, the model permits for us to treat preferences as varying with the time-scale of observation. Over the course of a month, consumers might not have much interest in oranges. But over the course of a year, there may be a more substantial preference for oranges.

In addition, the alternative method of measuring preferences permits us to get more information out of the fact of exchange. Whereas before an exchange was our only source of information about the preferences of the parties to the exchange, now with our independent measurement of preferences we can use the fact of exchange as an additional source of information.

Let's say Charlie sells A to Warren for B. If we know that Charlie uses an A / week and B / day, then we can infer that Charlie probably has either some inventory of B or expects to get access to more B within the next day. The fact of exchange tells us about the model that Charlie and Warren have in mind in forecasting their future needs based on their memory of the history of their preferences. In other words, the fact of exchange in view of measured frequencies of preferences still tells us something about their subjective valuation, but it tells us something more subtle than that Charlie prefers B to A and Warren vice-versa. It tells us how often Charlie and Warren expect to use A and B given their current inventory and history of consumption.

For earlier Broken Symmetry posts on related topics see here and here.

In a nutshell, my suggestion is to replace the principle of revealed preferences with a hypothesis of periodicity. The principle of revealed preferences would still obtain in the limit of ergodicity.

Revisiting Robert Ellickson's Critique of Functionalism

An excerpt from Order Without Law:

[E]arly functionalists had a tendencey to consider a human group as a single organizm whose "health" could be examined. It was then easy for them to surmise that Darwinian evolutionary processes would help favor the survival of socially adaptive norms. In the following passage the libertarian scholar Friedrich Hayek lapsed into this sort of analysis:

It is not only in his knowledge, but also in his aims and values, that man is the creature of civilization: in the last resort, it is the relevance of these individual wishes to the perpetuation of the group or the species that will determine whether they will persist or change. It is, of course, a mistake to believe that we can draw conclusions about what our values ought to be simply because we realized that they are a product of evolution. But we cannot reasonably doubt that these values are created and altered by the same evolutionary forces that have produced our intelligence. All that we can know is that the ultimate decision about what is good or bad will be made not by individual human wisdom, but by the decline of the groups that have adhered to the "wrong" beliefs. [The Constitution of Liberty at 36]

(Before nonlibertarian scholars dismiss these thoughts, they should be aware that both Lon Fuller and Thomas Schelling have also harbored suspiciously functionalist sentiments.) [Citing Fuller's "Human Interaction and the Law," and Schelling's Micromotives and Macrobehavior at 124-133].

The difficulty with this sort of organic analysis is that evolutionary processes, as most biologists understand them, select either genes or individual organisms, not groups, for survival. [Citing Dawkins's Selfish Gene and E.O. Wilson's Sociobiology at 106-129; and noting V.C. Wynne-Edwards's dissent.] Assume, for example, that honesty is a functional norm in the sense that, if all the members of a group were consistently honest, they would each be better off than if everyone were consistently dishonest. Would the Darwinian struggle favor the survival of the groups of honest persons? Not necessarily. A dishonest individual living in an environment surrounded by honest people might especially prosper, surrounded by easy marks. As a result, the Darwinian process would tend to select dishonest people for survival. In short, to support a Panglossian scenario of group evolutionary progress, functionalists could not rely simply on the biological theory of natural selection. Instead, they had to develop theories to explain how social-control systems would evolve within groups to prevent successful invasions by deviants who would subvert group welfare.

The punchline is that group selection theory is now enjoying a resurgence among some evolutionary biologists, notably including E.O. Wilson, whom Ellickson cites in support of the proposition that the theory has been rejected by evolutionary biologists. Wilson and Holldobler recently published, The Superorganism, which lays out a group selection theory for how cooperation evolved among insects.

The other objections to functionalism raised by Ellickson are also moot now in view of the improved theoretical tools for being more 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. Such models help to eliminate much of the conceptual circularity to which Ellickson objects in this passage.

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.

Best Four Sentence Summary of the Crisis and How to Fix It

From Shiller and Akerlof in today's WSJ:

Commercial and savings banks used to have reason to be careful initiating mortgages -- they would most likely hold the debt for years. But banks would increasingly sell the mortgages they initiated to others. And regulation did not adapt to reflect this change in the financial structure. The regulatory failure led to a profound systemic instability in our economy, which accounts for the severity of our economic crisis. Devising new regulatory structures that will allow financial innovation to proceed and yet prevent new such systemic problems is the major challenge to our creative capitalism today.

Tjalling Koopmans on Milton Friedman on Profit Maximization

Here's Milton Friedman:

Let the apparent immediate determinant of business behavior be anything at all -- habitual reaction, random chance, or what not. Whenever this determinant happens to lead to behavior consistent with rational and informed maximization of returns, the business will prosper and acquire resources with which to expand; whenever it does not the business will tend to lose resources and can be kept in existence only by the addtion of resources from outside. The process of natural selection helps to validate the hypothesis [of profit maximization]-- or, rather, given natural selection, acceptance of the hypothesis can be based largely on the judgment that it summarizes appropriately the conditions for survival.

Here's Tjalling Koopmans picking that apart:

Here a postulate about individual behavior is made more plausible by reference to the adverse effects of, and hence the penalty for, departures from the postulated behavior. The reality of the penalty is documented by technological and institutional facts, such as the reproducibility of production processes and the operation of accounting procedures in bankrputcy laws. . . But if this is the basis for our belief in profit maximization, then we should posulate that basis itself and not the profit maximization which it implies in certain circumstances.

Friedman's argument is incomplete for at least two reasons. First, we need an additional explanation as to how or why profit maximization is the relevant selection criterion. There is no a priori reason for this to be true of any institution. Second, we need to know at what level the selection criterion is applied -- i.e., to individual or group performance. The level at which competitive pressure applies will determine the amount of in-group coopearation below that level.

Where does thirst for knowledge fit within our preference functions?

Via Peter Klein at Organizations and Markets I found the recent paper by Paul A. David on the emergence of norms of openness among scientists during the Renaissance, along with an accompanying comment by Kenneth Arrow, which includes these extraordinary passages:

It seems to me that that there is a motive for action not taken account of in standard economic models. It is a motive that operates in a social context and cannot fully be discussed in the terms standard in “methodological individualism.” I refer to what appears to me to be a tendency for individuals to exchange information, to engage in gossip at all levels. There is some form of satisfaction not only in receiving information but also in conveying it. Currently, this is exemplified by the curious phenomenon of Wikepedia, where individuals spend time and effort to convey information without pay and without fame. Probably, there is even an evolutionary basis for this phenomenon, though explanations of social traits (other than those involving kin) on the basis of natural selection have proved to be difficult.

* * * snip * * *

No doubt, consumer demand in the form of practical implications played some role in the acceptance of mathematicians. We all recall the story of Archimedes’ determination of density by weighing in water, and its use in detecting fraud in the making of a royal crown. I have heard no such stories about Euclid or Apollonius of Perga. A major accomplishment of Renaissance mathematicians was the solution of algebraic equations of the third and fourth degree--that is, expressing the solution in terms of repeated taking of roots. But this is and was not a practical way of solving these equations. It was of purely theoretical and, if I may put it so, aesthetic interest, only appreciated by cognoscenti.

Like any modern follower of William of Occam, I hate to multiply causes. The desires for economic success and for reputation are important and basic for the understanding of the growth of scientific knowledge. But I find it hard to understand the developments without the additional desires to acquire and to distribute information, above and beyond the values of economic reward and fame.

What do we consume when we learn new mathematical truths? How might such a good fit within preference function that includes traditional goods? Should we call it a violation of the rational hypothesis if certain groups will forebear traditional goods in order to satiate a thirst for knowledge?

Surowiecki on Positive Feedback Loops

Back in May I blogged a bit about how subprime mortgage securities could be modeled as a positive feedback loop. James Surowiecki picks up the same theme in the latest Financial Page for the New Yorker:

Explanations for the crash often focussed on the hysteria and panic that periodically seem to seize investors. But the madness of crowds wasn’t the whole story. In a healthy market, there are countercyclical forces—mechanisms and institutions that go against the general market trend and encourage diversity of thinking—that make it harder for feedback loops and vicious cycles to take hold. Lately, though, many of these institutions and mechanisms have become procyclical: instead of countering trends, they amplify them.

Are short time horizons reinforced by the media?

I'm not a CFA or registered broker agent, so this isn't investment advice. But have you noticed that at the same time that short-term treasuries have been at historic lows, the long-term treasuries are very low also? Sure, the story about 1, 3 and 6 month t-bills makes for great headlines -- those are dramatic cliffs in mid-September. At the same time, there hasn't been the volatility in the longer-term notes. 30 year notes, for example, are still hanging around 4 percent, where they've been all year.

Which demonstrates quite vividly that nobody really believes that the equity market isn't going to resume a normal, sustainable (8% to 15% depending on how optimistic you are politically) rate of growth over the next 30 years. Yet most investors are not ready to jump into the equity market for the long-term (as the short-term rates ably demonstrate).

Again, I'm not an investment advisor or macroeconomist by training, but the money being used to buy short-term notes will have to go somewhere within the next six-months when those short-term notes expire. Real estate, like all assets whose value isn't fundamentally derived from human capital, doesn't have the growth potential of equity. Debt markets will surely pick up for some high-quality issuers, including the manufacturers of staple commodities. But for long time horizons, equity is looking better and better as 2008 goes on. Besides that, selling equity now means you fail a basic test of investing -- if Warren Buffett is buying, are you buying or selling?

How poorly regulated markets can degrade human character

From John Gray's contribution to a Templeton conversation on the market:

The free market as it existed in mid-Victorian England came about not because the state withdrew from the economy, but rather because state power was used to privatize land that had been under various forms of common ownership, or not owned at all. The laissez-faire economy that existed for a few decades in 19th-century England was made possible by the Enclosure Acts. These laws, enacted by Parliament starting in the second half of the 18th century, displaced farm laborers from the countryside and created the industrial working class that was the free market's human base. But with the extension of democratic voting rights in the late 19th and early 20th century, these workers began to demand that economic activity be subject to various kinds of regulation. The eventual result was the managed market economy that exists in Britain and many other countries today. A historical perspective is useful because it enables us to see that economic systems are living things. In real time, free markets rarely work according to the models constructed by economists. There are booms and bubbles, busts and crashes. It is only in economics textbooks that markets are self-regulating. Against this background, the relation between economics and ethics can be seen more clearly. The traits of character most rewarded by free markets are entrepreneurial boldness, the willingness to speculate and gamble, and the ability to seize or create new opportunities. It is worth noting that these are not the traits most praised by conservative moralists. Prudence, thrift, and the ability to press on patiently in a familiar pattern of life may be admirable qualities, but they do not usually lead to success in the free market.

Markets, like any human institution, are morally neutral. Whether they promote virtue or vices is determined by the rules of the game. Rules that are easily manipulated (because too complex or because compliance is difficult to verify) reward dishonesty. Bad morals hurt morale.

The moral of the story of the Enclosure Acts is that market rules need to accommodate the needs of all stakeholders in a given domain. Demsetzian propertization remained incomplete until labor was included in the bargain. Regulators and owners of IP should be wary of running into the same problem with inventors.

Underappreciated Cause of the Crisis

The same rapid technological advances that are driving the marginal cost of information dissemination and trade execution to zero may also have implications for the incentives faced by information producers. As trading costs fall, the marginal investor may be becoming less experienced, less sophisticated, and less able to derive fundamental security values from raw information. At the same time, the characteristics and business models of publicly traded companies are changing as the economy itself changes. Newly listed firms are far less likely to generate sufficient cash flows in the near term to internally finance the costs of expansion and compensation. A high current stock price becomes a vital cash substitute for these firms. These trends combine to create strong incentives for firms to distort the information they produce to the investor community. We show that, indeed, there is evidence of deterioration in the quality of information that firms supply to investors. This deterioration may slow down the improvements in security markets that technological progress brings about. Moreover, private mechanisms such as litigation and information packaging by financial intermediaries are unlikely to solve the problem of information quality. Investor education and the regulation of information disclosure in particular may therefore play an important role in the development of securities markets in the foreseeable future.

From Technology, Information Production, and Market Efficiency by Shleifer et al.

Here are few interesting charts from the paper:

The units for the y-axis here are percent of average firm assets.  Discretionary accruals are basically adjustments to cash flow permitted under GAAP.

Is there any correlation between how many discretionary accruals are used and future returns?  Yes.

Accounting rules need to be made simpler.  Corporations must be required to report more information, not less.  Intermediaries who process financial statements and other accounting information produced by publicly traded corporations need to be independent of the investment banks or other insitutions that finance publicly traded corporations.

Would you still read Consumer Reports if it were paid for and published by GE, GM, and Dell? 

Mark Sanders explains the Lincoln Conjecture

Via Dane Stangler at Growthology, I found this article connecting Kuhnian paradigm shifts with Schumpeterian creative destruction.  It's a connection with intuitive appeal.  Author Mark Sanders distinguishes "fundamental" from "instrumental" knowledge as sources of new opportunities for entrepreneurs.  "Fundamental" knowledge is knowledge of why things work (e.g., fire is a chemical reaction that requires oxygen and hydrocarbons).  "Instrumental" knowledge is knowledge of how things work (e.g., adding fuel and blowing on fire makes it burn hotter).

There are several interesting insights offered by Prof. Sanders.  But here's the one that caught my eye this morning:

[S]cience and fundamental knowledge are quickly replacing learning by doing and instrumental knowledge as the main source of opportunity for commercial innovation.

He doesn't speculate on why this is so (that's not the point of his article), but it seems easy enough to see that improvements in communication and transportation technology basically eliminated the competitive advantage of instrumental knowledge for entrepreneurs.  Trade secrets could be kept safely for decades in an era before wireless communication and cheap and easy travel.

Could this be part of the explanation for why Abraham Lincoln identified the patent system as the next major stage of human progress?  Despite the transactions costs, we need property rights to extend to intangibles in order to permit decentralized coordination of entrepreneurial activities in an era in which trade secrets no longer provide decent returns on investment.

As an aside, the comparison between Schumpeter and Kuhn is interesting when considered in conjunction with a working paper I have posted on SSRN on how certain doctrines of antitrust and IP (namely, the essential facilities, reverse doctrine of equivalents, and Feist originality doctrines) can be used to switch from property rules to liability rules when dealing with natural monopolies.  I hadn't considered it before, but the more I think about it, the more I like the idea that Schumpeter and Kuhn are both concerned with fundamental ideas that create natural monopolies for a product or idea over the time period between when that product or idea is pioneered and when the next pioneering product or idea comes along.

In general, it strikes me that Schumpeter and Arrow are really describing the same sort of competition, but with Schumpeter emphasizing its temporal aspects and Arrow its spatial.  Put the two together and you get an evolutionary model of competition, messier to model but more accurate as a description.

Dane Stangler at Growthology

I've been a regular reader of the Growthology blog since its launch.  In terms of interests, there probably isn't a better match to my own in the blogosphere.  But I was skeptical when regular bloggers Tim and Bob suggested that guest blogger Dane Stangler might steal their show.  But he's been on fire!  Check out this post on consumption for a taste:

Consumption is often derided as either wasteful or mindless or soul-destroying. (This, by the way, is not a partisan issue: you can locate various criticisms of consumption at any point on the spectrum of American politics.)

Such knocks, however, see only one stage of consumption: the actual purchase of a product or service or its actual use. They usually don't extend (necessarily) to what that consumption gets you. When you "consume" a cell phone, what you're really consuming is connection with other people. When you purchase a better refrigerator, you're consuming the ability to store food for longer periods of time than was available to most humans throughout history, thus raising the ability to improve nutrition. When you buy a drink from Starbucks, you're getting not only the drink itself but also the experience and interaction with others. (One of the original investment bets behind Starbucks, remember, was provision of a "third place" for people to get together.)

Does behavioral law & economics cut against Burkean conservatism?

Cass Sunstein makes the case here.

I agree with his point that the precautionary principle in its strongest form is incoherent.  But following Judge Posner, I would argue that it's the right mood to be in when considering government action.

Google's unprecedented access to information about demand

...is now more open to the public.  I'm going to play around with the site a little and see if I can't use it to illustrate how demand synchronizes in different markets over a certain length of time.

Does encouraging consumption or government spending promote economic growth?

No.  It's efficient allocation of capital through voluntary exchange, and the efficient allocation of human capital through divisions of labor that promote economic growth.

The vulgar Keynesian prescription is to encourage consumption, when a dynamic of precautionary storage takes hold. And in extremis that might be a good idea, because if all everyone does is hoard, it's hard to figure what to invest in, except maybe storage tanks. But it's much better to develop a financial system that actually performs, that identifies fruitful projects and allocates claims fairly. Storage eats wealth, while productive enterprise creates it. People know this. No one "invests" in gold or oil when a financial system is working. They do so when it is broken. Like now.

That's Interfluidity found via Tyler Cowen.

Maybe better accounting theory would help?

How to Observe Utility Functions

By economic hypothesis, every individual has a utility function, which represents the measure of that individual's happiness.  It is tradition in economics is to guess at the shape of individual utility functions by observing the relative preferences of individuals for one set of goods or services or another as demonstrated, for example, by voluntary exchanges.  Thus, profit can be a relatively good approximation of aggregate utility because it provides an indirect measure of utility increases.

But most accounts of utility seem to emphasize goods over activities as the source of utility.  An unorthodox account of utility and preferences might begin instead with an emphasis on the relative preference for one set of activities over another as demonstrated by voluntary exchanges or acts of consumption and acts of production independent of voluntary exchange.  One of the instrumental benefits of such an account of utility is that it leads more naturally to an understanding of how and why utility functions might vary in time.

For example, one conventional way to interpret the aggregate demand function from introductory economics is as a reflection of the aggregate utility enjoyed by consumers of a particular good.  This is a fine interpretation, and it obviously has its instrumental value.  Another way to interpret the same curve, however, is as a measure of the frequency of consumption of that same good within an economy.  Some consumers will tend to consume lots of a particular good, and some little.  Consumers who are consuming at their "natural frequency" (i.e., the reciprocal of the period of time they are generally observed to wait between acts of consumption) will not want to consume more; consumers who are consuming faster or slower than that natural frequency might want to decrease or increase their consumption respectively.  All of these have an impact on how aggregate utility evolves in time.

Another benefit of interpreting demand this way is that it provides an instrumental means for actually measuring demand.  In particular, in many cases, demand for goods will exhibit a Poisson distribution in frequency of consumption.  That's because the natural frequency for consumption (or production) will be randomly distributed in time when you look at a large enough group over a long enough period in time.

All three of the curves shown in the Figure above are Poisson distributions.  Lambda represents the average value of the distribution -- the mean frequency of consumption for the ensemble of people consuming or producing.  The x-axis then measures how often people within the ensemble are consuming or producing in units of reciprocal time (i.e., frequency).  The y-axis measures how many people within the ensemble are consuming or producing at each frequency.  As you can see, the shape of the distribution becomes more peaked as the average value approaches zero.  This is because there is no way to consume less than zero of a particular good.

How are these Poisson distributions connected to supply and demand?  Let's start with supply.  How could we measure aggregate supply?  What if instead of looking at marginal costs we were to count how often a particular good was supplied within an economy -- i.e., the frequency of production?  In that case, we might see Poisson distributions that look just like those shown in the Figure above.  But of course, we don't just want to see the frequency distributions, but the measure of the aggregate supply available at different price levels.  To find that, we just plot the cumulative distribution function that corresponds to the Poisson distributions in production.

These plots are just integral sums of the values of the Poisson distributions from zero up to whatever value is plotted along the x-axis.  These are aggregate supply curves. The y-axis here is normalized, but it could also be measured in units of people.  Assuming that there are only a finite number of people in our society, so that there are opportunity costs associated with engaging in production or consumption in the market we're measuring, then the y-axis could also be measured in units of dollars or whatever currency the market prefers.

If you started with the frequency distributions for demand, and instead of integrating from zero up to the value along the x-axis, you integrated from the value along the x-axis up to infinity, you would see a corresponding set of aggregate demand curves.

If you're interested in reading more, check out the paper excerpt I posted on SSRN.  There are plenty of interesting observations that can be made about these dynamics (for example, notice how the elasticity of the curves increases as the Poisson distribution increases in average frequency).  After puzzling over the dynamics that might be used to model these supply and demand curves for a while, I believe that the best way to think of them is as a network of limit-cycle oscillators -- a model that has been studied in biological systems.