Broken Symmetry

What are the Existing Best Models for Business Cycles?

Readers:

Can anybody tell me what models academic economists right now consider the best for explaining business cycles?

Applying Control Theory to the Subprime Mortgage Supply Cycle

In an earlier post, I explained how transactions costs, liquidity, money supply, and scarcity can be modeled as the resistance, inductance, capacitance, and voltage of an RLC circuit.

To show how well this works, let's apply some actual numbers to the supply cycle for subprime mortgages.

An "Ohm's law" must hold whereby price (voltage) = transactions cost (resistance) times current (transactions / unit of time).  Set price equal to $100,000, a good order of magnitude estimate for the price of real property acquired through a subprime mortgage.  Set current equal to the number of sales per day, a good order of magnitude estimate to start with is 100 / day.  If they obey an Ohm's law, transactions costs then will take units of $ / sale.  So with V and I set at $100,000 and 100 sales / day, R = $1,000 / sale.

So assume to begin with that

V = $100,000
I = 100 sales / day
R = $1,000 / sale (because R = V / I)

Because of MBS, CDOs, and CDO^2s, the liquidity in the subprime market was actually much broader than ever before.  How many orders of magnitude is hard to say.  But I'll guess that the rebundling and sale of mortgages increased the scale of supply by a few orders of magnitude, but also increased the number of days / sale as the bundling, rebundling, etc. takes longer to accomplish than a simple mortgage.  If it takes 100 days to do the bundling, but by doing so you get up to $10,000,000 scale, the measure of liquidity becomes:

L = (100 day / sale) / ($10,000,000 sale) = 1 x 10^(-5) days / $

Money supply (capacitance) should be measured in units of days / $ -- i.e., the number of days that each $ loaned from an external supply spends in the market before being paid back.  This is hard to estimate.  I'm going to guess that about $1,000,000,000 of the entire money supply (on average) was locked up mortgages, MBSs, CDOs, or CDO^2s.  And banks were probably holding onto these funds for at least 100 days before they came back to the Fed.  Of course the government kept messing with money supply by increasing and decreasing the cost of lending, but I'm ignoring that.  I'll repeat, however, that if the money supply obeyed something like Taylor's rules, we'd have a way more determinate system.

C = ($1,000,000,000 * 100 days) = 1x10^11 $-days

Solving the differential equations for the frequency of the resonant peak for this cycle, we find that:

Resonant frequency = 1 / square root (L * C) = 1 / sqr ( 1x10^-5 days / $ * 1x10^11 $-days ) = 0.001 cycles / day.

In other words, according to these estimates of liquidity and money supply, we can predict a peak in the subprime mortgage market to occur about once every three years.  And that's rougly how long it seems to have taken for us to reach a peak once bundling of mortgages started.

Beyond Econ 101: Modelling Supply and Demand Cycles as Coupled, Damped, Driven Harmonic Oscillators

The supply and demand curve (x) taught in introductory economics represents the aggregate state of the supply and demand for a particular good or service at a moment in time.

In the real world, supply and demand do not rise or fall with gentle de-accelerations or accelerations.  Rather, with demand held constant, as supply passes a certain price point, suppliers will stop producing the good or service, and begin producing a substitute that can be supplied at lower cost.  Similarly, with supply held constant, when demand reaches its peak of zero marginal gains from increased purchase, demand will begin to fall as consumers begin to substitute lower cost substitutes.

The result is an oscillation in supply and demand.  When one is held constant, the other will oscillate with frequency and magnitude dependent on the relative scarcity of the good, liquidity in the market for the good, external money supply (i.e., capital available for reallocation from other markets), and the rebundling of supply or demand units, which will have an amplifying effect on the price signal.  Transactions costs can be modeled as resistance.

In the real world, supply and demand can seldom be approximated as decoupled from one another (and therefore constant with respect to one another).  The coupling of real supply and demand cycles is better approximated as two coupled, damped, driven harmonic oscillators.  The strength of the coupling will be a function of the "stray impedance" of the market, which arises from any coupling between the independent elements of the "circuits."  Usually, however, transactions costs are the mechanism for coupling.  Beyond a certain threshold, transactions costs will grow nonlinearly, and introduce the effects of non-linear coupling into the system.

The mathematical model is simple.  Undergraduate physics majors could work out the dynamics on paper. The static (x) model drops out by measuring each cycle at a moment in time.

Here are a few predictions from the model.  When the coupling between the oscillators is weak, they'll simply superpose linearly -- i.e., one frequency will simply constructively and destructively interfere with the other.  I.e., the supply cycle will run smoothly regardless of whether demand is blowing up or stagnant; and vice-versa.  When the coupling is strong, however, non-linear effects emerge.  The frequency of the two cycles will "beat" and to produce "envelope frequency" = supply frequency + demand frequency, modulated at "beat frequency" = supply frequency - demand frequency.

If somebody can point me to where in the economic literature this model has been discussed, I would appreciate it.

How To Improve Price Signals

The intrinsic economic value of a good or service is ultimately a function of the value that everybody in society places on that good or service.  Value is a function of scarcity.

Market prices, however, are often a function of only the value estimated by the parties to a transaction at a moment in time (i.e., the value placed on the good or service by the buyer and seller at the time of transaction).

Price could be modeled as a Taylor expansion of terms, each term reflecting the addition of more people to the approximation of price.

Current market prices are linear approximations because market transactions are bilateral (i.e., two-body problems).

For price to more accurately reflect the intrinsic value of a good or service, higher-order terms must be included in the expansion (three-body, four-body, etc.)

Physicists and physical chemists who study non-equilibrium statistical mechanics know how to do these calculations with small molecules.  You need them to model phase transitions, i.e., dynamic changes in physical state (such as melting or evaporation).

Most of the time, markets behave as simiple harmonic oscillators (i.e., linearly), and the difference between price and value is small.  This is the business cycle.

Occasionally, however, the higher-order terms in the expansion can dominate, producing a stagnant or bubble market (i.e., an overdamped or underdamped harmonic oscillator).

Berkshire-Hathaway has produced critically damped harmonic oscillations by making a habit of giving negative feedback, thereby damping the upward effect of valuations to a level that stabilizes oscillation.

Libertarians need to understand better the relationship between market price and externalities.  Government should not be the only entity that forces buyers and sellers (through taxes) to take into account the long-term, low-probability effects that each transaction will have on non-parties.

Again, Berkshire-Hathaway has forged a new path by selling 20-year term puts on the market.  Selling insurance on long-term, low-probability events is one way to limit the need for taxation and public regulation.

The difficulty is always in finding people who can accurately calibrate the coefficients in the price expansion.

UPDATE: Bernanke understands this.

Whom does the Constitution say IP is For?

"To promote the progress of science and useful arts, by securing for limited times to authors and inventors the exclusive right to their respective writings and discoveries;"

I'll be in attendance at the Law & Econ of Innovation Conference tomorrow.  Come say hello if you're there too.

Editorial Note: Cross-Posts to Patent Prospector

Due to non-overlapping audience interest, I will for the time being no longer be cross-posting patent-related posts to Patent Prospector.  For the time being at least, Broken Symmetry will be the exclusive venue for all of my commentary, including patent-related commentary.  I will continue to enjoy reading the commentary from Gary and Jordan at Patent Prospector.

I consider blogging a collaborative enterprise.  Please let me know in a comment or email if there are topics that you would like to hear more (or less) about.

Our Blind Spot for Inventors ...and How Universities Can Remove It

United States Secretary of Commerce Carlos M. Gutierrez, among other things, is in charge of the Patent and Trademark Office.  Yesterday the San Jose Mercury News published this piece by Gutierrez identifying three specific areas for Congress to focus on in considering patent reform:

• Damages Apportionment
• Post-Grant Review
• Patent Application Quality

In two previous posts, I have blogged about Damages Apportionment.  Lately, I have been working through a very good paper by J. Gregory Sidak, which gives some convincing responses to the Lemley and Shapiro arguments that damages apportionment is a necessary response to the problem of Cournot complements.  In a nutshell, asymmetric bargaining power between patent owners and groups of potential licensees may more than make up for the inefficiencies of negotiating with multiple complementary input suppliers. 

This is a complex problem, and it makes sense for us to be very careful about making changes in this area of the law.  Nobody really knows how damages apportionment will prospectively affect the value of patents.  Nonetheless it seems reasonably certain that implementation of damages apportionment would effect a net redistribution of wealth from inventors to licensees.

Post-grant review, by driving up the cost of the patenting process, is also likely to favor large applicants over small ones, especially independent inventors.

Improving patent quality is probably the only reform item proposed by Gutierrez that does not definitively cut against smaller entities and independent inventors.  This is because the quality problem in terms of raw numbers must be more the fault of large entities than small.  My personal experience suggests that startup companies put far more resources into putting together good patent applications than the larger, publicly-traded corporations that are often interested more in having a huge portfolio for defensive/cross-licensing problems with other large publicly traded corporations.

In all of these discussions of patent reform, who's looking out for the dispersed group of small entities and inventors?  Only the universities that are the home for many of these inventors have the resources to get a chair at the table in negotiating patent reform.
 

What the PTO will look like in a few years?

The NYT on Sunday carried this article on the USA National Innovation Marketplace, founded by inventor Doug Hall.

First, this is more evidence of how the shortage of patent lawyers is forcing inventors in many technical fields to find new ways to attract private funding.  I discussed other consequences of the shortage in an earlier post on Stranded R&D.

Second, I wonder: How much more effective would the National Innovation Marketplace be if we had patent lawyers draft a set of claims, and put that up with the other materials offered on the website?

Isn't that what the PTO should look like in an era in which the costs of offering multimedia and social networking services through a website have dropped so low that even teenagers can launch new companies?

UPDATE: On a conference call today (5/13/8) I hear from Patent Commissioner John Doll (a fellow former p-chem grad student!) that the PTO is working on a social network for Examiners.  Why not offer a social network for both inventors and Examiners?  Why not work with Planet Eureka, which has already built one?  The idea of software engineers hired by the PTO reinventing this particular wheel is particularly troubling to me.

Summing Up: Feathering the Nest for Inventors

Sensible patent reform should focus on feathering the nest for inventors in the United States.  There is nothing more important to our long-term prospects within the global economy.  To summarize the posts made this week:

IP is a limited exclusive right to an inventor's time, not a limited exclusive right to a thing.  I.e., IP is Not an Asset.  Lawyers, business people, and politicians should consider how the patent law will affect the activities of inventors.  A plugged R&D pipeline can lead to Stranded R&D and an exodus of inventors from the United States.  We would promote the progress of arts and sciences better by building legal and financial institutions that recognized the benefit of a division of labor between inventing ideas and building things.  This is What Adam Smith taught the Founding Fathers.

Editorial Note: Broken Symmetry and the Lollapalooza Effect

When I was in graduate school at the University of Chicago I took a graduate level physics course on non-equilibrium statistical mechanics.  I struggled in that course.  There were some kids in there that were just off the charts.  I ended up with what one might call a "gentleman's B."  But I did spend quite a bit of time thinking about and visualizing what was happening in the systems we studied in that course.  A few years later, when I started learning about the economic analysis of law, I started thinking about how, with lots of simplifying assumptions, markets could be modeled as physical systems.  And this got me to thinking about how non-equilibrium statistical mechanics might have some interesting applications to the study of economics.

Earlier this year, I started reading Charlie Munger, another ex-physicist who has spent some time thinking about markets.  I read about what he describes as the "lollapalooza effect," which sometimes occurs in markets, and realized that it was basically a description of spontaneous symmetry breaking.

To see the connection, you have to make a lot of simplifying assumptions about how people behave.  Charlie's strength as an investor is probably due to his ability to sense inarticulately when his simplifying assumptions are strong enough to be trusted and when they should be kept under watch.  But here's how one physicist has come to visualize the lollapalooza effect of broken symmetry:

People can be modeled as particles in a potential.  The contours of the potential are determined by the opportunity costs of engaging in various activities (driving, working, playing, everything).  So you have a manifold that includes a variety of local equilibria corresponding to various states of the world.  It gets messy fast determining the shape of these contours because the contours of the manifold (i.e., the opportunity costs of various activities) are themselves a function of the previous activities of the particles.

There's enough energy (capital) in the system to keep the particles bouncing around in one local equilibrium, but not enough for many (or any) of them to bounce out into a new equilibrium.  But every once in a while, there's a perturbation to the system (an exogenous shock), which drives enough of the particles into a particular direction at a high enough energy to move them into a new local equlibrium in which they have different and new local symmetries.  Local symmetry just means what you would see if you were an ant in the particle's position on the manifold.  If the particles can store information and communicate (this is where we completely lose the physicists if we haven't lost them already), they've now got a larger map of their system.

Scale invariance (a tool used by physicists to describe transitions between equilibria) occurs in political or economic revolutions when so much energy gets added to the system that local symmetries are no longer important.  The particles just bounce around so fast that they don't even notice the contours. Once things settle down, they'll tend to settle into new and different local equlibrium.  But it's often difficult to predict with certainty which local equilibria the particles will fall into. Revolutions are messy and difficult to control.  The exception might be for a catalyzed phase transition in which one particle or small group of particles act as "seed crystals," so that everybody ends up moving with them into a new local equilibrium.

Firms and even governments are spontaneously self-assembled organizations of particles that result from the symmetries of particular local equilibria given the amount of energy (capital) available to sustain the organization.  Just like water can take the form of a solid, liquid, or vapor given the amount of energy (measured as a temperature distribution) and its interactions with surrounding molecules (including other water molecules), people will self-assemble into different kinds of private and public institutions in order to minimize the amount of capital required to sustain their assembly.

Incidentally, the concept of allocative efficiency in economics (i.e., the principle of maximizing utility over the manifold for every particle) corresponds pretty closely to the extremization of hamiltonians and lagrangians in physics.  But the transactions costs of engaging in social and economic transactions between particles are dissipative forces (i.e., stickiness to the manifold) that have to be assumed away to do the calculations and find the most efficient equations of motion (i.e., institutional design).  So it's no surprise that the Coase Theorem has to assume away transactions costs in order to say that the default local equilibrium assigned by government doesn't matter.