Broken Symmetry

Buried and a Bleg: Vector Analysis on a Lattice?

I'm buried for the next few days at work.

I have a few posts in the hopper for once I'm back online. In the meantime, here's a bleg for readers with some math and maybe physics or chemistry training:

Can you do vector calculus on a lattice? Suppose that instead of continuum in space, you can only translate between nodes in a network -- a lattice. Further suppose that directed edges between nodes can appear and disappear over some time interval associated with transfer of some quantity between nodes. Can we treat the scalar field of quantities at each node using the same vector calculus that would apply to a continuous scalar field? For example, can we define gradient, curl, and divergence?

The model I have in mind for a simple economy is of nodes representing actors. For each node, there is a vector representing that node's allocation of resources within the economy along with a time-dependent preference vector, which produces a scalar utility for each node when multiplied with the resource vector.

The set of exchanges that occur between nodes over time constitute a network, which evolves to maximize utility locally. Some exchanges, however, might increase utility locally at the same time that they decrease utility for the universe of nodes over all. We might call the difference between the gain in local utility and the loss in overall utility an "externality." Notice that if we cutoff our analysis of the impact on utility with the two nodes that are part of an exchange, then there can be no externalities.

Local asymmetries in preferences or resources will dictate what types of exchanges occur within this model.

There is a lot more that could be done with this type of application

http://omegle.com/

What happens when an immutable force meets an immovable object?

Too funny:

George Soros claims (in his op-ed in the Wall Street Journal) that the Efficient Market Hypothesis is invalid, because prices in financial markets "always provide a biased view of the future, and that distortions of prices in financial markets may affect the underlying reality." Thoughts?

EFF: All the evidence I know says that market predictions are unbiased. It's understandable, however, that hedge fund managers are immune to this evidence since it's a threat to their existence

But it really helps point out a semantics game that's being played. When Fama talks about "efficient," he doesn't mean "perfectly efficient," just the best on average over long periods of time. I still haven't seen a convincing response from Fama to the data in Buffett's "Super Investors of Graham and Doddsville." There are certainly some investors who consistently outperform the market. Fama may win in the end to the extent that many of these will have so much money thrown at them that their returns will inevitably regress to the mean.

The measure of the skill of an investor is a function of both their returns and the scale at which they can sustainably achieve those returns. Intellectually, it's actually pretty easy to beat the market investing your own money if you're sufficiently cleareyed. The hard part is the emotional part -- the being patient and sitting on your hands when the crowd is headed the other way.

Who are the customers for a venture capitalist?

The answer is not entrepreneurs, as much as they'd like you think so. Neither is it the public who buys IPOs nor the public companies that often acquire startups from a VC's portfolio. The answer is the limited partners who give their money to the VC to invest.

This central fact has been overlooked by some entrepreneurs. Thanks in part to the work of people like Nivi at Venture Hacks and Fred Wilson at Union Square, that is changing. Expectations for entrepreneurs are coming into line with the expectations of VCs and their customers. This is absolutely crucial to the long-term survival of venture capital!

But as always in life, things are more complex than the most correct answer can summarize. What makes VCs profitable for investors, after all, is in part a function of how good their relationships are with both entrepreneurs (on the entrance side) and investment banks or established companies (on the exit side).

I have been wondering about something for a long time, and I hope that this post will generate some feedback from those experienced in venture capital. It seems to me that most VCs get the part about being entrepreneur friendly. Although some VCs in practice are surely more entrepreneur friendly than others, to some extent when somebody calls a VC "founder friendly" or "founder unfriendly" this may reflect the dynamics of a given deal rather than the bigger picture. The sample is too small to say.

What I have not observed, however, is a VC marketing and broadcasting to LPs their connections and relationships with investment bankers or established public companies. Why not? Why are these stakeholders in the VC market kept in the wings?

There is a practical point to this question, which is that most established companies are getting less innovation through venture capital-backed startups than they could if these relationships were cultivated, and more feedback were flowing from these large company "customers" back to the startups who will probably be acquired by the same large companies since the IPO market is closed for the foreseeable future.

Readers, what do you think? Please email or leave comments below.

UPDATE (7/7/9): I noticed recently that Fred Wilson a few years ago did a post about how, in fact, his view is that entrepreneurs are his customers and limited partners his shareholders. That model has much to recommend it, but I'm not sure that the incentive structure created by the LLC/serial LP model is consistent with it. A different legal structure would make more sense if that were the intent. But maybe it's just the tax issues and other restrictions on transfer of LP interests that prevents the different legal structure.

Also, I eventually answered my own question by reflecting on the limited leverage that startups have in negotiating with one or two potential acquirers without a healthy IPO market available. I agree with Ben Graham that IPOs are not for individual investors. But startups need an IPO market to get a fair price for their work from potential acquirers.

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

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

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

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

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

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

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

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

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

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

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

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

Why is our System of Executive Compensation so Broken?

Robert H. Frank has an answer:

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

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

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

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.

Periodicity in Everything: Magnesium and Beer Edition

Demand for magnesium should be fairly smooth right? Magnesium is used in alloys of steel and aluminum. It's not the sexiest of commodities.

Well demand for magnesium fluctuates in weekly cycles in the U.S. Fewer people want magnesium on Saturday.

What do people want on weekends instead? How about beer?

Blogging and Scholarship

In general, it seems the academic community is warming up to the idea of blogs as complementary to scholarship. The benefits are obvious enough -- blogs can potentially reach a wider audience and provide feedback on new ideas quicker than the traditional system of private correspondence, conferences, and peer reviewed publication.

There are certain fields -- mathematics, sociology, literature, poetry, philosophy -- for which these benefits seem decisive. Although a scholar in these fields will still want to publish in addition to blogging, once a critical mass of scholars in these fields are publishing their work online, the community within the field will increasingly find the Internet to be a more convenient medium for exchanging ideas. Each scholar has control over their own printing press. Going from expression to wide publication takes zero time rather than months or years.

There are other academic fields, however, for which the benefits seem less decisive. These fields include, for example, experimental physics, engineering, and medicine. These fields, by comparison, are driven more strongly by new empirical results. Empirical studies are time consuming, and take months or years to complete. The time scale of reporting cannot be shorter than the time scale of information gathering.

By the way, neither group of fields is entirely empirical or theoretical. It's just that, on balance, the first group is more theoretical and the second, more empirical. The two groups need each other, and the growth of both fields will be limited by how much information (both data and theory) is shared between them.

In terms of raw numbers, I think the off-line population of the second group is actually much larger than the first group because the second group is generally the group that society calls upon to assist in solving its problems. This is the academic group that has the most direct impact on the rest of society, and its number bears that out. By contrast, the first group (of theorists) probably has a more lasting impact on the way that academia evolves independent of society. The big successes in the first group percolate out of academia through the second group, and eventually change society as a whole. Marx changed the face of the world with his ideas. The Wright Brothers changed the face of transportation. Both theory and practice were necessary to both; but their day to day lives looked quite different, and their influence on society over time reflects those differences.

At the moment, it seems that the first group is going to grow much faster than the second group into the blogosphere. Over the short run, this isn't a big deal. There are still plenty of sources of data available online. The problem is that many of these sources are journalists from newspapers and magazines that are on the verge of bankruptcy. Moreover, very few of these sources of data are put together using the careful methodology that one might find in a typical empirical study by an economist or sociologist, for example. In effect, the Internet is crammed with lots of theorists analyzing a tiny amount of data that is from comparatively unreliable sources. The Internet is a bit like our consciousness in that sense.

What can we do to bring more data online, and keep it organized but accessible? The people who specialize in gathering data now have little incentive to put it onto the Internet when the existing mechanisms for sharing that information are just as good or better, and make it easier to predict whether and how recognition and reward will be distributed tot he gatherers?

People rave about the importance of openness on the Internet. But already I'm beginning to see that the evolution of property rights will be no different on the Internet than it was on any frontier of the past. To encourage people to share valuable goods with others, we have to define and enforce property rights a contracts. Attribution rights to content distributed over the Internet is going to become more and more important as larger and larger portions of the population move online. If we want to make the highest quality content available at the lowest cost to users, then exclusive rights and privately adaptable rules for allocating them are going to be necessary.

Else the owners of the most valuable content are simply going to keep it offline.

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.

Levy or Inhomogeneous Poisson Process?

Mankiw comments:

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

And in reply, ironman says:

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

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

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

Market Prices Synchronize Flows

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

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

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

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

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

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

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

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

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

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

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

For an earlier post on this topic, see here.

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.

Periodicity or Rationality?

From today's WSJ:

Optimism regarding industrial metals rests on similarly fragile foundations. Bellwether copper is up 43% since late February. This head fake comes courtesy of China cannily stockpiling inventories of raw materials like copper and iron ore even as demand contracts virtually everywhere else.

Stockpiling, however, isn't consumption. The surge in Chinese imports hasn't been matched by increases in industrial production, suggesting metals are going into warehouses, not factories.

The actions of the Chinese could be explained as rational in response to their forecasted needs. Alternatively, we could just note the amount of commodities flowing into China per unit time and how that amount changes in time. Does it matter whether the latter is explained as a rational choice?

Broken Symmetries at Ford Redux

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

Back in April of 2008, I wrote the following:

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

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

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

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

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

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

Where's the Exit for Venture-Backed Startups?

From Alan Patricof in the NYT:

The sum and substance of all of these developments is that the minimum economic level to bring a company public today is at least a $50 million offering at a $250 million market value. With realism back in the market and a return to rational metrics, like multiples of revenues and, better yet, profits, venture capitalists have had to face the hard reality that it is highly unlikely that taking a company from start-up to a point where it can justify this type of market capitalization in a three-, five- and even seven-year time frame is realistic, except in a limited number of situations.

For these reasons, I believe that the paradigm has changed for the venture business. We can no longer realistically expect the same kinds of absolute returns that were achieved in the past through a quick turnaround from start-up to liquidity through an I.P.O. Rather, I believe that most of the companies that venture capitalists are funding today will find an exit through merger or acquisition. And if we expect to achieve a return in a reasonable time frame of three to five years, we are probably looking at a sale price of $20 million to $100 million. This is the valuation range where most young companies are being acquired.

Clearing Bottlenecks in the Innovation Pipeline

From the Tech Transfer Tactics blog:

The scenario is not at all uncommon for TTOs: Resources are never adequate to actively work every invention file, and faculty IP that doesn’t get the attention a researcher wants creates a dilemma for the university. Though the innovations involved may be valuable, if they are dormant too long a decision must be made — either move them to the front burner or give them back to the inventor and give up any claim to future revenues. But what happens if the TTO decides it wants to keep ownership while the inventor, frustrated by a lack of progress, wants the IP signed over?

Click through and read the caveats on the standard "release." Why shouldn't university tech transfer offices behave more like the Federal government does when notified under Bayh-Dole?

Group Learning is Unstable Without Feedback

Via Overcoming Bias I found this paper on "inductive biases in cultural learning." In the study, one person was asked to estimate the height and width of a successive series of boxes. Together, the series of height and width coordinates constitute a one-dimensional function. As shown in column (i) in the Figure, four different functions (a), (b), (c), and (d) were selected.

After the first person had estimated the function by looking at the series of boxes (column i), a next person was shown a series of boxes with dimensions equal to the first person's estimate of the height and width (column ii). Then a third person did the same thing using the second person's estimates (column iii). Basically, a sophisticated game of "telephone." But look at what happens when the function of height and width varies from the very simplest function of y=x (i.e., square):

Without direct access to the information, except for the square, estimates of the funciton radically departed from the original measurements after four iterations, and then converged after that to a square.

Sort of gives new meaning to the idea of the square as a platonic form, no? But there are all sorts of interesting implications here. What a brilliant experiment.

Meaningful Patent Reform: Lessons from the Peer Review System

What if patent reform were about bringing the patent system more into line with its constitutional goal of "promoting the progress"? What would such patent reforms look like?

Innovation occurs in a feedback loop. Each domain of knowledge is embodied as theory in the minds of a field of scientists or engineers. The domain evolves as the field of experts accepts or rejects contributions to the domain. An individual who learns the domain and has enough contributions to the domain accepted eventually becomes recognized as an expert. Both the domain and the field evolve over time.

The peer review process for scientific literature is an example of an institution that is designed to govern innovation within a domain. In the case of peer review, the goal is to ensure that very little false theory makes it into the literature. Knowledge in domains governed by peer review is considered more reliable because the institution of peer review permits some good contributions to be rejected erroneously in order to avoid bad contributions. In this sense, peer review might be considered a conservative model for promoting innovation.

Notice, however, that the institution of peer review is subject to a serious flaw. Namely, peer review by itself does not specify or provide an institutional mechanism for deciding what members of the field of experts should have the power to accept or reject new contributions. Academic politics ensue.

The patent system, by contrast, is founded upon a more liberal approach to promoting innovation. Under the patent system, the rewards for an innovation are ultimately determined not by a subset of experts in a given field, and not even by a consensus among the entire field. The rewards of the patent system are determined by whether people who are probably not experts at all are willing to pay for the innovation.

The patent system is also more aggressive than the peer review system in the sense that there is not as much concern with false positives. Under the patent system, inventors are encouraged to disclose their work early and often. In fact, it's safer to file a patent application before the invention is reduced to practice because a sale or public use of the invention can trigger a loss of rights.

To be sure, the PTO examines applications for compliance with both formal requirements and substantive law. These examinations include opinions from Examiners (skilled in the relevant domain) on the substantive issues of enablement, novelty, nonobviousness, utility, and so on. But nobody would confuse a patent examination with peer review.

As many people have pointed out in the past, we don't really want the peer review system for patents since many applications are a complete boondoggle -- they're either worthless because there are already better solutions to the same problem or not enough better to justify the additional cost for the average customer. In the case of patents, there is less of a need to filter out the bad disclosures because the claims to such technology are worthless anyway (plus or minus the transactions costs of litigation).

Because under the patent system the market helps perform the function of filtering contributions, the focus of the PTO and of patent examination should be almost entirely upon the requirements of Section 112 -- i.e., upon the requirements of specific, clear claims that are supported by a comprehensive and clear disclosure.

Notice that this is already how the patent system functions with respect to drugs. If you want to market or sell a new drug, you can look it up in the Orange Book and see whether somebody has already patented it. Examiners in this domain are also sticklers for enablement, requiring multiple examples when the enablement is in question. There aren't many successful challenges to infringement or validity in the drug domain.

In improving disclosures and claims, there are several ways in which the patent system might be improved by reflection upon comparison to and constrast with the system of peer review. By comparison, the peer review system is better at enforcing a social norm among scholars that prior publications must be read and cited as part of any offering of a purportedly new contribution. Scholars who fail to comply risk being labeled dilettantes or cranks. These norms are quite effective at reducing the amount of redundant work in the academy.

From a social perspective, time and money are wasted whenever more than one company invests in producing the exact same invention. Multiple inventions cannot always be avoided -- sometimes new tools or information will suddenly make multiple inventions inenvitable. But at least the norm should be that engineers and scientists should consult the literature before spending time and money (either theirs or another's) on inventing.

There are two ways that the patent system could put teeth into this requirement. First, inventors ought to be required to conduct a prior art search and explain how their work is different from the prior art. That's the quid pro quo for the second -- that the penalties for infringers who independently invent should be higher. Yes, you read that right -- higher.

The conventional wisdom among many in patent law right now is that independent invention should be a defense to patent infrigement because the patents offered no contribution to the infringer's independent work. The conventional wisdom is not wrong in that under our current system, patents indeed offer no benefits to the independent inventor as a source of knowledge. What the conventional wisdom ignores is that society loses out whenever two or more companies spend money inventing the same thing. The patent system (with some reforms) is uniquely well-suited to avoid that waste.

There is another meaningful patent reform that is revealed by contrasting the patent system with the peer review system. The patent system, unlike the peer review system, can provide the benefit of market prices to help in identifying valuable contributions. Paradoxically, that information is not available to the public. Whereas the PTO could be a clearinghouse for information about the market value of inventions, it is instead merely a recording office. Disclosing the details of transactions involving patents should be part of the quid pro quo for patenting. Market price is the most compact indicator of the value of an invention to society, and both buyers and sellers would benefit from that information being public.

Market prices are not a perfect indicator of the value of a contribution. (See the debate over FAS 157 and mark-to-market accounting.) But they're much better than any alternative now available. Liquidity in patent rights is not going to improve significantly until price information is readily available to any (even casually) interested buyer because without that information being public, the transactions costs will always be a function of the legal fees associated with doing diligence on a portfolio. These legal fees right now are redundantly incurred by potential buyers.

Under the current system, the PTO is nothing more than a quick and dirty peer review. Given the dysfunctions that result, it's understandable that experts in fields that find nothing valuable in patent disclosures would feel cheated by patentee-inventors who fail to convince investors and business people to help them commercialize an invention. It's much easier to convince an Examiner to issue a patent on an idea than it is to start a company and bring it to customers. On the other hand, patentee-inventors have a right to complain about infringers who are breaking the law.

Unfortunately, given the direction that reform seems headed, it seems likely that we are moving towards a system in which patents are irrelevant to most fields. Inventors have no incentive to disclose; companies have no incentive to read their disclosures. The point of this post is to explain that it doesn't have to be that way. Just as the peer review sysetm provides the incentive of recognition, the patent sysetm could provide the incentives of reward. No grant administration committee can compete with the market in putting an accurate price tag on new inventions.

As a final note, it seems to me that property rights and their occasional inefficiencies (in the form of holdups) are a necessary evil in encouraging incumbents to spend the time and money reviewing published patent applications and issued patents to avoid redundant R&D expenditures. The economies of scale to litigating damages are too steep for small entities to get a seat at the bargaining table. Without the big stick of an injunction, what incentive do would-be infringers have to review patents?

I want to emphasize on the other hand that small entities and independent inventors who cannot make their inventions relevant to incumbents through better disclosures and careful distinctions from the prior art should not expect to get anything for their work. Work that cannot be easily incorporated into product development may be beautiful in some poetic or mathematical sense. But the patent system has nothing to say about beauty except to the extent that it increases profits.

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.

Happy 100th Birthday Silicon Valley! Thanks, Steve Blank.

Just in case readers of this blog have not already discovered Steve Blank, please go and read his posts on the Secret History of Silicon Valley here. These are off the charts as far as blog posts go.

I always had been curious about how Silicon Valley, a place I had lived and worked in, came to be. And throughout my career as an entrepreneur I kept asking questions of my VC investors and friends; Where did entrepreneurship come from? How did Silicon Valley start? Why here? Why now? How did this culture of “make it happen” emerge, etc. And the answer came back much as it did in my past jobs; Who cares, get back to work.

After I retired, Jerry Engel, director of the Lester Center on Entrepreneurship, at U.C. Berkeley Haas Business School was courageous enough to give me a forum teach the Customer Development Methodology. As I was researching my class text, I thought it would be simple enough to read up on a few histories of the valley and finally get my questions about the genesis of entrepreneurship answered.

Negative Interest Rates: Time to Bring in the Toilet Plunger?

See proposals by Mankiw here and here.

This is a fantastic idea. Basically, since the Fed sets only positive or zero targets, what we have now is a system in which the Fed can only flush money down the toilet (by raising rates) or sit on it and let things marinate (by holding the rates steady). Had the Fed raised rates as the housing and mortgage bubble inflated, it would have a third option now, but it didn't so now we're plugged.

Letting the Fed set negative targets, in effect, gives the Fed a plunger to back the plugged toilets (i.e., the banks that won't lend) with negative pressure: "Either lend or pay me back!"

I think this is a brilliant plan to get the pipes flowing smoothly again.

The Equity Premium is Not So Mysterious

From Liquidity and Price Discovery by Maureen O'Hara, available here:

In this context, liquidity is akin to a tax or a cost borne by investors. It seems to me that if these costs are large enough, they should negatively affect asset prices because of their effect on net asset returns.6 In the same vein, reducing these costs through, for example, the introduction of a more efficient trading mechanism should have an immediate positive effect on an asset’s value.7 The microstructure of the market influences these liquidity costs, and so if the effects are large enough, microstructure and liquidity affect asset returns.

Donald T. Campbell on Multiple Inventions

From Evolutionary Epistemology available here:

A major empirical achievement of the sociology of science is the evidence of the ubiquity of simultaneous invention. If many scientists are trying variations on the same corpus of current scientific knowledge, and if their trials are being edited by the same stable external reality, then the selected variants are apt to be similar, the same discovery encountered independently by numerous workers. This process is no more mysterious than that all of a set of blind rats, each starting with quite different patterns of initial responses, learn the same maze pattern, under the maze's common editorship of the varied response repertoires. Their learning is actually their independent invention or discovery of the same response pattern.

Sociologists could have just checked with the Patent & Trademark Office, where multiple simultaneous inventions have been a way of life since way before Darwin.

But is Campbell right here about there being no difference between blind rats in a maze and inventors tackling the same problem? Maybe. But doesn't the "pattern of initial responses" matter in terms of how fast a particular rat runs the maze? And if some rats run mazes faster than others, then don't we want to reward those rats?

In fact, the "initial pattern of responses" of an experienced inventor may take on the characteristics we more typically associate with artistic or mathematical genius after a lifetime of inventing. But who will devote a lifetime to inventing without inventions being protectible as property? Rats in a maze indeed.

What midlevel managers used to do when R&D was vertically integrated?

From Tech Transfer Tactics:

Smith, who shifted jobs a year ago to her refocused position, says that one of the first things she did was create a physical engagement map for one aerospace company that shows all of the places on the campus that they touch. The company’s representatives were surprised to see that they are working with the Latin American studies department, optical sciences, material sciences, the business college, electrical and computer engineering, as well as aerospace. “It was very important to show them the map,” Smith says. “They are a decentralized company and didn’t have their finger on the pulse of all of their relationships with the university."