Broken Symmetry

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

Geanakoplos and Farmer observe:

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

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

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

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

Thouhts on Nick Paumgarten's "The Secret Cycle"

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

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

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

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

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

What should the FTC and SEC do first to help consumers?

The answer is redesign financial statements. Don't leave it to the FASB, which is like letting the foxes guard the henhouse.

The occasion for this reflection came today as Christine Varney announced a series of workshops aimed at improving the Merger Guidelines. Lots of interesting hints in this speech. I was particularly interested in this topic:

[W]e are interested in your views on the use of more direct evidence that is not strictly based on inferences drawn from increases in market concentration. There are several categories of such evidence worth exploring: (1) evidence of the actual, post-merger competitive effects of consummated mergers, (2) evidence of "natural experiments" obtained by looking across different geographic markets, time periods, customer categories, or similar product markets; (3) evidence of the firms' post-merger plans; (4) evidence of customer views of post-merger competition; (5) historical evidence of actual head-to-head competition between the merging firms; and (6) historical evidence of actual or attempted coordination in the industry. Although the Agencies routinely rely heavily on these kinds of evidence to assess competitive effects, the Guidelines address their relevance only in passing and only secondarily, after the relevant market is defined and concentration in that market is measured. Courts also regularly rely on this type of evidence in assessing competitive effects.28 We are interested in views on whether we should adjust the Guidelines to address explicitly what kinds of direct evidence are pertinent and how they should be weighed.

Is it too much to ask that the FTC and the SEC coordinate on this? Recall that Goldman Sachs CEO Lloyd Blankfein recently suggested reforming the accounting rules to require all exposure to flow through to financial statements. Not only might these kinds of reforms benefit the SEC in enforcing its rules, it would give the FTC a better source of data -- at least for public companies -- on which to base econometric analyses of substitutability, for example. Needless to say, investors and ultimately consumers would benefit from having better information too.

Long time readers of Broken Symmetry may recall earlier posts (here, here, and here, for example) on how financial statement report only snapshots in time and time-averages of sales and costs of sales. These were all that was needed when buying and selling patterns changed only annually, or at fastest quarterly. To handle more rapid changes, you have to increase the sampling rate. What we need is a time-series of balance sheet accounts, or income/cash-flow statements on shorter intervals.

Having better designed financial statements would benefit consumers far more overall than even perfectly clear merger guidelines or perfectly efficient SEC enforcement.

How hard would it be for economists from the FTC to sit down with economists from the SEC and hammer out a set of economic data that should be required from public companies but that isn't in the financial statements now? To make it palatable politically, they could offer to get rid of Sarbanes-Oxley hassles in exchange for more information. Have a time-delay of the release of real-time balance sheet info to deal with the trade secret issues.

Why Inventory Turnover Rates Matter to Managers, Owners, and Investors

From the always illuminating Joe Ponzio:

Everything else being equal, the 10% margin business with one inventory turn is no better or worse than the 2% margin business with five turns a year.

In fact, as Joe explains in the rest of his post, the company doing five turns a year is often in better shape. If you want an analogy, it's like the difference between two cars, both of which can carry you 100 miles on 9 gallons of gasoline, but one of which does so at 5000 rpm the whole way while the other does so at 1000 rpm. Same fuel efficiency, but you'll pick the car with more torque every time. You can accelerate or slow down much quicker with the 5000 rpm machine.

Sometimes inventory turnover rates are reported as part of financial statements, usually in the notes. An inventory turnover rate is a frequency -- i.e., given a unit of inventory the turnover rate is in units # / time. Repeatedly on this blog I have suggested that financial statements should report frequencies for each balance sheet account. Such frequencies are called "turnover rates" when the accounts in question are inventory accounts.

Note that accountants usually order balance sheet accounts from short-term to longer-term liquidity. That's a convention, not a measurement. Wouldn't it be nice to have actual numbers for each account?

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.

How Economics Can Become Scientific

The MIT Technology Review blog today reviews a "paper describ[ing] a survey taken by graduate students at seven top-ranking economics programs" on answers to questions, including the following:

• Is neoclassical economics relevant?
• Do economists agree on fundamental issues?
• Can fiscal policy be an effective stabilizer?
• Should the Fed maintain a constant growth rate of the money supply?

The results are mixed. Not a surprise since even among economists the answers to these questions are mixed! But the title of the post raises a large question, which I'd like to answer using systems theory -- i.e., the theory of how highly integrated social networks self-organize. Systems theory has been a central theme for this blog.

If we understand the question in terms of systems, then we can answer in layers the question, "Is economics a science?" These categories are linked to the three generalized components that make "the system of economics":

1. The domain of rules and procedures that make up economic theory;
2. the field of recognized experts who act as gatekeepers to the domain; and
3. the stream of data in the form of observations or measurements used to falsify the domain.

The high-level answer is that economics is a science if it has active components of domain, field, and data. Economics is not only dismal, but dead if none of these is changing. But so long as each of these three have some time-dependence, the difference between economics and other sciences is a difference in degree, not kind.

But on closer inspection, there are indeed apparent problems with these components for economics that do not exist for other sciences. The biggest problem seems to be that at least until about ten or twenty years ago, there was no stream of data on individual or group behavior that could be used to falsify the domain of neoclassical theory that developed around WWII. In other words, there have been few new experiments or new kinds of data sets since neoclassical theory was developed. The field has become somewhat retrenched as it has labored at refining its theories using the same sets of data over and over again.

There are exceptions, of course. I'm in the middle of reading Vernon Smith's Rationality in Economics, in which he describes the interesting ways that actual behavior deviates from neoclassical predictions in actual experiments and field studies. And Smith is not laboring in obscurity, of course. He won a Nobel for his efforts in this regard. But in general, the "science" of economics seems to have been limited by a lack of data. There simply has not been an experimental or observational mechanism for the field to reach consensus on what hypotheses have been falsified.

In perhaps not-so-humble fashion for a non-economist, I would like to propose that experiments and observations of the average time period between individual acts of consumption or production is exactly the kind of data that economists could use to falsify models of individual or group behavior. The fact that such observations have not been made in the past is no accident, for they were generally too expensive to be collected before the Internet became widely available. (Csikszentmihalyi's Experience Sampling Method is a notable exception.)

Journal entries themselves encode the information that is necessary for managers, investors, and owners of corporations to see the frequency spectrum of activity within a firm that provides a unique signature of the firm's activities. Time-averaged measures of costs are not the only variables important to the health of a corporation. Profit is a function of sales and costs of sales over time.

Economics could become more scientific by statistical observations of individual and group behavior over time.

The Identification Problem and Revealed Preferences

Mankiw and Sumner put a gloss on the textbook explanation of the identification problem, which for the uninitiated is explained well-enough by the wikipedia entry here.

But even after reading what Mankiw and Sumner (and by the way, I love Sumner's fearless curiosity), I'm not particularly happy. This is what non-social scientists would call a mess! No wonder there has been a gradual shift within the economics field toward more direct measurements that avoid the most serious identification problems.

Here are a few observations from a non-economist trained in measurement theory by physicists:

The reason the identification problem is so difficult is because revealed preferences for the supply schedule and demand schedule cannot be measured simultaneously for the same population.

You have to measure one, then the other. Meanwhile you have to assume that neither schedule has shifted. Fat chance these days.

Why not start with a more direct measure of supply and demand and avoid the identification problem altogether? Look at the frequency distribution of buying and selling. Price is only a measure of short-term supply and demand -- hence stable only when the frequency distributions are stationary (i.e., when the system is "ergodic").

Acoustically driven programmable liquid motion using resonance cavities

From Sean M. Langelier, Dustin S. Chang, Ramsey I. Zeitoun and Mark A. Burns:

Performance and utility of microfluidic systems are often overshadowed by the difficulties and costs associated with operation and control. As a step toward the development of a more efficient platform for microfluidic control, we present a distributed pressure generation scheme whereby independently tunable pressure sources can be simultaneously controlled by using a single acoustic source. We demonstrate how this scheme can be used to perform precise droplet positioning as well as merging, splitting, and sorting within open microfluidic networks.

Via Technology Transfer Tactics

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.

Utility is Not a Monotonic Function

From Gretchen Rubin's Happiness blog, interviewee Karen Leland offers the following thoughts about happiness:

[I]t's not a constant condition, and it's not supposed to be. The amount of happiness I experience ebbs and flows and that's ok. Sometimes I'm super-joyful, sometimes content and sometimes down. It's a cycle, and it all changes.

Sorry economic theorists, homotheticity is an artifact of large averages.

Another Reason Why Regulators Should We Looking at the Frequency Spectrum

From Zero Hedge via Abnormal Returns:

The three HFT horsemen are C, BAC and CIT. These three stocks traded 860 million shares today which is 10% of all US Equity volume. Think about that: 3 stocks in a universe of over 5000 U.S. stocks represented 10% of the volume. How could this be? Look at the intraday chart of all three of these stocks and you will see a something in common: an early morning move followed by a flatline with a very tight range (around .05). Meanwhile, while these stocks were flatlining the market was heading higher. The S&P 500 gained around 10 points in the afternoon (or 1%) but these 3 stocks did not move. There was a constant bid to these stocks yet anytime they wanted to lift there seemed to be a constant offer just a few pennies higher. This is what HFT looks like. The HFT’s made a killing in these 3 names today – in addition to the .01-.02 spread, they collected about .005/share in liquidity rebates. Not a bad day for a supercomputer.

The linked discussion explains how this is illegal "churning" or "painting the tape" under current regulations. The anomalies that signal this kind of trading are more easily observed when you look at the frequency spectrum of buying and selling, but very difficult to see looking only at time series.

Joseph Stiglitz on Sustainable Capitalism

From Adbusters:

A healthy economy involves using our time efficiently and getting enjoyment out of our time. Spending two hours commuting is not a good use of anybody’s time. There are many ways in which we are very inefficient. We have not thought through efficient land management. I was in a meeting recently in France where in the central city they were talking about how to redesign the whole city to make it environmentally more efficient, to make sure there is less waste, that the energy that is put out is captured and used and reused. So there are lots of things we can do to increase our overall efficiency.

I couldn't have said it better myself:

Creative capitalism can stand for the idea of a capitalism that respects and promotes profit that is sustainable in view of the rhythms of life. Both profit and time can be measured quantitatively. By building institutions that measure and are accountable for how they handle both, we can build better institutions.

As resource constraints become more important per capita, the measuring and managing of the frequency spectrum of human activities over time and space must become more important.

Weighing in on the EMH Debate: Does Behavioral Analysis Resolve the Problems?

See comments from the Economist, DeLong, Yglesias, and Hansen.

The problem with EMH is with its interpretation of the principle of revealed preferences. Unfortunately, the same problematic interpretation often applies to behavioral critiques of EMH. Here's an excerpt from an article I have forthcoming in Intellectual Asset Management:

There are two catches to using preferences "revealed" by market prices to measure individual preferences. The first catch is that one has to watch over a period of time to see the preferences revealed, which means assuming that the preferences do not change during the period of observation. The second catch is that in practice, no large data sets have recorded the revealed preferences of individuals. Only aggregate data, such as consumer price indexes and average household spending over several decades, has been available. Taken together, these catches mean that empirical tests of the rational hypothesis take as a given that preferences do not change in time and that only information about the average preferences of a group is necessary to measure and predict individual preferences.

But preferences do change over time. New books are written, new paintings are painted, new inventions are conceived and reduced to practice. Moreover, no actual person may exist who embodies the average preferences of a large group. Especially if there are outliers, the average preferences of the group may be quite different from the preferences of most individuals within the group.

Unfortunately, many advocates of “behavioral economics” and “bounded rationality” seem to have made the same mistake as the EMH by interpreting the rational hypothesis as a hypothesis about individual behavior. Although it is true that individual behavior often deviates predictably from what might (mistakenly) be called “rational” given certain individual preferences, observations of individual psychology cannot usually provide a proper test of the rational hypothesis. In practice, it has been difficult to verify clear violations of the rational hypothesis. There is often an argument over whether what might be called irrational behavior results instead from rational preferences specific to a particular time and place. For example, although it might seem irrational for a group to demand higher payment for a good already owned than the same group would be willing to pay for the same good not owned, this asymmetry might be explained as rational in view of the consumer surplus in ownership for the group. Because the mechanism traditional economic theory uses to measure preferences is the observation of group behavior, arguments about whether the behavior of a particular group is rational or irrational can quickly devolve into circularity.

This is not to say, of course, that psychology offers no insight to economics. In fact it seems quite likely now that evolutionary psychology and neurology will offer insights into the origins and explanation of observed group behavior. Such insights are not as relevant, however, to the problem of measuring and managing large groups over long periods of time. Systems theory takes a different approach to rehabilitating economic theory.

So the answer is not really. Theories of psychology are very useful and important for business people and leaders in general. But they are not the kind of theories designed to address large-scale, long-term behavior of groups. This is what economics and rational expectations theory has done for the past few decades. It has failed us because behavior that was once uncorrelated, and hence gaussian, has become more interdependent, and hence fat-tailed.

The way forward for us is to recognize that rational expectations are correct only at certain limits, namely, of ergodicity and uniformity in individual preferences. Rational expectations theory is a mean-field approximation. But when we have more granular data about individual dynamics, there's no reason for us to be content with mean-field approximations. Micro and macro theorists need to build nonequilibrium statistical models that are capable of producing both the gaussian and the fat-tailed dynamics that are observable in real markets. Systems theory represents the set of mathematical models that are most narrowly tailored to this goal.

What do Music and Quantum Mechanics Have in Common?

Time and frequency are a Fourier pair:

The key to using music to teach modern physics, in my mind, is harmonic analysis. Harmonic analysis is nothing other than Fourier analysis, a tool which is highly valued in physics and engineering. It is not widely known by the non-scientist, yet it is easy to explain in the musical context—when someone looks at a graphic equalizer on their stereo they are looking at a real-time Fourier amplitude analysis of the music that is being played. One can explain how the synthesis of harmonics affects the timbre of musical sound—how the coefficients in a Fourier series can describe different real functions. A very simple example is the comparison between the organ pipe and the piano string. The ‘stopped’ organ pipe has only odd-numbered harmonics and the piano has all harmonics. (Because the ‘stopped’ organ pipe has a pressure node at one end and a pressure antinode at the other, whereas a string has nodes at both ends.) The different symmetry of the boundary conditions accounts for a major aspect of the difference in the timbre of the organ and the piano.

That's from The birth of the blues: how physics underlies music by J.M. Gibson. Via Physics and Physicists

If you're a regular Broken Symmetry reader, then you should know already that it is not only music that can be understood better with Fourier Analysis, but any time-series that can be decomposed into ocillations of different frequency, including cash-flows. The balance sheet is sort of like the graphic equalizer, except that the frequency of the accounts is not rigorously ordered in terms of liquidity. If it were, then the analogy would be complete.

Goldratt, Lean, Flow, and Financial Statements

Over at Evolving Excellence, Bill Waddell writes about how Lean Theory and Eli Goldratt's Theory of Constraints are part and parcel:

That focus on flow is at the very heart of excellent manufacturing - not merely finding tidbits of waste and eliminating it. The final step in the logical thought progression is that the most fertile ground in the effort to accelerate the flow of products across the fixed costs within the value stream is to know what is limitingthe flow - and that is where Eli Goldratt comes in. He said that an hour saved at the bottleneck (constraint) is an hour saved for the system (in lean terms, an hour saved for everything within the value stream). An hour saved anywhere else is a mirage.

Both theories focus on the frequency spectrum of activities within the firm rather than a time-averaged picture of costs. That's why lean is such a pain for cost accounting, which is based on time-averaged measurement of costs.

As mentioned in an earlier post here, what Goldratt calls "throughput" could also be called flow. Both are quantities per unit time.

If balance sheets included frequency-averages (i.e., turnover rates) for each account, would accountants be able to move assets or liabilities on and off the accounts without there being a trace on the financial statements? Right now, an asset moved on and off the balance sheet betwen the period of financial statements may not show up in the income statement or cashflow. These are time-average pictures of income and cash, and by definition an asset moved on and off within the period of time produces no net effect on the time-average.

We have blinded ourselves by excluding information about flow from our financial statements.

Posner on the Procyclicality of Leverage

From his Atlantic Correspondents blog:

The solution is to require the bank to reduce its debt-equity ratio during booms. Banks will resist this solution because it will reduce their profits. Not that banks are indifferent to risk, but they are less sensitive to it than the regulatory authorities are (or should be) because to an individual bank the systemic component of risk is an "external" cost, as economists say. That is, it is a cost imposed on persons and firms with which the bank has no contractual relations (think of the millions of persons who have lost their jobs in this depression, without having been employed by or had any other contractual relation with any financial firm), rather than only felt by the firm that incurs it.

This idea of gearing banks' capital requirements to the different phases of the business cycle makes a lot of sense. It should be called "anticyclical" rather than "procyclical" since it would tent to counteract the volatility of the bank balance sheet accounts by gearing down leverage on upswings in the business cycle and gearing up leverage during downswings. The idea parallels Taylor's Rule, which is based on the similar observation about the effect of expansion and contraction in the money supply. In both cases, a countercyclical expansion or contraction (of the reserve requirements in the first instance or the money supply in the second) tends to damp the response that other institutions would make to a relatively quick increase or decrease in cash-flow or lending.

But the difficulty is in identifying the right variables to use in calibrating the change in reserve requirements. In the case of Taylor's Rule, one can simply add up M1, M2, &c. I assume this can be done almost daily now since everything is electronic. Why shouldn't fiscal policy be recalibrated daily if the data is there?

In the case of reserve requirements, I don't think bank balance sheet data is reliable enough because of the discretion CFOs have in moving things on and off balance sheet. But in principle, that discretion would be considerably weakened should CFOs be required to report all balance sheet data to the Fed on a daily basis in the same way that M1, M2, &c. are reported daily.

Although this proposal would be very unpopular with the industry as a whole, the new regulatory equilibrium would tend to favor the banks with the strongest balance sheets all along. But to call a bluff you've got to have some skin in the game.

Who has the leverage with VC-backed real-time startups?

The new wave of VC investment in Internet-based startups focuses on "real-time" applications.

Long time readers of BS should know that I am quite enthusiastic, overall, about this development.

But on my way in this morning, I was thinking again of Fourier transforms. The goal of thinner and thinner slices toward the present time comes at a cost of wider frequency.

So who will be the biggest winners because of real-time startups?

Of course, if IRR expectations are reasonable, then everything will turnout just fine. Only they can't be with 2x what's coming out going in the last few years running.

I see a few bandwidth owners tenting their fingers and laughing maniacallly at this fortuitous development.

Time-Frequency Distributions and the Characteristic Time-Scale of Economic Equilibria

Over the weekend, it sort of dawned on me that in looking at Google Insights trends (see, e.g., here), what one is really looking at is a time-frequency distribution.

Over some time period that Google does not specify, Google bins the numbers of searches made in geographical regions, normalizes the number of searches by the total volume of searches within the region, and then rescales the results so that the peak value within the time-window displayed is set equal 100, and other values proportional to percentages of that peak.

As a consequence of the normalization and rescaling it is impossible to put units of frequency on the y-axis in Google Insights charts. The information needed to put units of frequency on the y-axis would be destroyed by either step independently, but is long gone after both.

But even without units of frequency, we can make some qualitative analysis of what these Google Insights tell us about the frequency of demand for particular goods.

For example, when one observes seasonal variations in Google Insights charts, that's equivalent to observing an increase in the frequency of demand. I can't tell you exactly how much faster because only Google knows that. But I can tell you that if Google Insights shows a seasonal variation in searching for your product, then you either need to have inventory in storage or your production cycle has got to speed up to match. The shortages or surpluses that result from the mismatches in the frequency of demand and frequency of supply cause prices to fluctuate; market price signals thus perform a frequency and phase locking function.

Time-frequency distributions are used by engineers, chemists, and physicists to study how the frequency content of a time-varying signal changes in time. Within an economy, variations in the time-frequency distribution of demand show that there are different characteristic frequencies to demand for a particular good. As a result, there is no single economic equilibrium, which is valid at every time-scale. Rather, equilibrium price will depend on the the time-scale over which supply and demand are observed. Supply and demand have to be orchestrated within a hiearchy of longer and longer time-scales in order to avoid systematic errors in frequency and phase-locking.

Synchronized Flow in Your Brain

From the NYT:

When something bright or novel flashes, it tends to automatically win the competition for the brain’s attention, but that involuntary bottom-up impulse can be voluntarily overridden through a top-down process that Dr. Desimone calls “biased competition.” He and colleagues have found that neurons in the prefrontal cortex — the brain’s planning center — start oscillating in unison and send signals directing the visual cortex to heed something else.

These oscillations, called gamma waves, are created by neurons’ firing on and off at the same time — a feat of neural coordination a bit like getting strangers in one section of a stadium to start clapping in unison, thereby sending a signal that induces people on the other side of the stadium to clap along. But these signals can have trouble getting through in a noisy environment.

The Transactions Costs of Frequency and Phase Mismatch

From today's WSJ:

The recession has exposed a harsh side effect of the supply-chain system. Because modern industry rewards suppliers with the leanest inventories and fastest reaction times, when economic crisis struck, tech companies up and down the line contracted as sharply as possible in hopes of being the ones to survive.

Forced to guess at demand for their products in a plummeting market, everyone hit the brakes, hard. An examination of the electronics supply chain -- from retailers all the way back to makers of factory machinery -- shows that, at almost every stage, companies were flying blind as they cut.

Paradoxically, the sudden drop in demand was amplified up the supply chain because (1) the response to new information at each stage in the supply chain was so fast, and (2) the delay as information was transmitted at each link up the supply chain. Had each link been slower to respond or had information about the frequency of demand been shared more quickly up the chain, then there would have been less amplification. Note that unless these frequencies are better matched, then we can expect surpluses to show up again within a few months.

Information about demand and responses to that information need to be frequency locked or oscillations will result.

Internet Traffic Periodicities and Oscillations by Reginald D. Smith

Available here:

User traffic driven periodicities were the first known and most easily recognized. The first discovered and most well-known periodicity is the 24 hour diurnal cycle and its companion cycle of 12 hours. These cycles have been known for decades and reported as early as 1980 and again in 1991 as well as in many subsequent studies. This obviously refers to the 24 hour work-day and its 12-hour second harmonic as well as activity from around the globe. The other major periodicity from human behavior is the week with a period of 7 days and a second harmonic at 3.5 days and barely perceptible third harmonic at 2.3 days.

How the Structure of a Network Affects Synchronization

From a paper by Arenas, Dıaz-Guilera, and Perez-Vicente available here:

Each subnetwork synchronizes independently before the network as a whole synchronizes.

Frequency Matching Supply to Demand: What CEOs Could Learn from Surfers

In any market, demand comes in waves. There are two reasons for this: (1) Each consumer who is part of the demand takes a period of time to consume; and (2) After consuming, each consumer is going to wait a period of time before consuming again, if at all. In mathematical terms, for a given population of consumers, there is a frequency distribution characterizing the average period between acts of consumption. (A frequency is simply the reciprocal of the period of time between acts of consumption.)

Of course, if you're looking at a large enough market, or averaging over a long-enough period of time, these frequency distributions might not be obvious. Rather, the quantity of goods in demand within each period of time may appear steady. Demand often appears steady because for many goods the frequency distribution of consumption is stationary (i.e., the frequency distribution itself doesn't change in time) and the phase (i.e., the amount of time between two acts of consumption by different consumers) is uncorrelated. But this stationarity and asynchronicity is often dependent upon the time-scale or size of the population measured.

For example, if one looks at the worldwide demand for oranges in the last 90 days, demand might appear steady as it does here. But if one looks at the worldwide demand for oranges over the past 5 years, then the periodicity in demand because obvious. See here. Oranges are in season in the winter, and demand for oranges has over time synchronized with orange season. Some of you are wondering about why the southern hemisphere doesn't erase this periodicity in demand. It does, partly. Go look at New Zealand and Australia and see how the demand in these countries spikes in the middle of the year. The southern hemisphere simply has a smaller population!

If you work in marketing, especially at a consumer Internet company, probably none of this is surprising to you. You see waves of customer interest come and go all the time. What do you try to do in response to those waves?

The same thing that surfers do when a swell approaches shore. You try to position yourself close to where the wave is going to peak -- or before it if possible -- and then match your momentum to the wave so that it picks you up, and carries you with it.

In physics terms, by frequency matching (the momentum of a wave is mathematically equivalent to a spatial frequency), you maximize the amount of energy that can be exchanged between the wave and you. If you don't paddle hard enough, in the right direction, at the right time, or in the right spot, then you'll simply be left behind. By contrast, if you can match the momentum closely enough, then you will resonate with the wave -- the wave will push you forward as you push back on the wave. Momentum-matching results in far more fun.

What happens if you paddle too fast? If you paddle way too fast, you'll paddle right over the wave in front of you. For anybody who has actually surfed before, this is hard to imagine because in practice nobody paddles that fast. But the point to see is that if you paddle too fast, then you'll end up oscillating faster than the waves of demand -- overshooting and undershooting with too much or too little inventory when the waves of demand arrive.

Too fast, oscillation. Too slow, left behind. Just right means you catch the wave, and your supply grows at the same rate as the wave of demand. This rate of growth is both efficient and sustainable since, by definition, it matches demand.

The mathematical formalism is equivalent to that used by electrical engineers in describing the waves of voltage and current in a circuit. Momentum-matching the surf, frequency-matching demand, and impedance-matching an input signal are all the same phenomenon as far as the formalism is concerned.

What role do market prices play in matching supply to demand? Market prices are a mechanism for active impedance matching. When the frequency of demand is steady in time, then market prices synchronize the phase of supply and demand cycles. When both the frequency and phase of demand are non-stationary, market price signals synchronize both. I will have more to say about this, but the synchronization of supply and demand at large scales can be a cause of either incredible stability or bubbles and crashes. That's what control theory is for figuring out.

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.

Time, Symmetry, and Accounting

There are many things I love about this article. It's focusing attention on the right problems.

But is it really necessary to introduce gauge theory as a potential solution? Part of the reason why neoclassical theory has hung around so long is because it presents relatively easy mental models for economists and lawyers to use in forecasting group behavior. Not only is gauge theory hard, but some of the best techniques we have for understanding dynamics at the level of individual firms and markets are not gauge invariant. Here I'm thinking in particular of the Fourier transform.

Last year I blogged a bit about how Fourier transforms can and should be applied to the time-series of balance sheet and income statement accounts.

The most useful paragraph of Smolin's article, on my view, is the observation that "the observables of economics are accounting and other records." The reason is because with Smolin's critique of neoclassical assumptions in mind, we have a sound basis for reforming accounting rules. Time and frequency are incompatible observables for the managers of a corporation. Optimizing one means losing track of the other beyond some diffraction limit set by the granularity of the time between financial statements. Folks this is what lean accounting and management advocates have been telling us for years. Will this crisis be the occasion for sensible reform?

I am all for applying state-of-the-art math to economics. But we have to be modest both about the scope of such models and about the capacity of individuals who regulate such markets to grasp the models. I can explain Fourier transforms to an interested, educated audience. Gauge theory, not so much. Why not start with the easier problem and work up to the harder one?

See here also for a discussion of how discrete Fourier transforms of revenues and expenses can help reveal where new capital expenditures are most likely to increase profitability.