Inequality and Technology

This is a start at a theory of inequality. It is a theory. It simplifies a lot in a effort to explain. It is intended to complement Piketty by giving an explanation for why r > g and may be so for a long time. The break from neoclassical economics is to assume that labor is not a homogeneous input, but otherwise the rest is conventional economics.

Neoclassical economics asserts that in equilibrium labor is paid its marginal productivity. This may make sense for many non-cognitive tasks, but for cognitive tasks, especially those requiring team effort, I argue this falls apart. To lay the foundation, I first have to explain Halstead Length.

One of the mysteries of computer software is that some humans are simply much, much better at it than others. Think more than one, even two, orders of magnitude better. Thirty years ago, a professor at Purdue, Maurice Halstead, attempted to understand why. He developed a large number of heuristics to measure capability.

The most important he named Halstead Length. In his model of the brain, human memory is organized into chunks. When you have a chunk open, you instantly know everything in that chunk and visualize the interactions. On average he found you can have seven chunks open at one time. He created an arbitrary scale in which an average person had chunks of size 250, which he found to be about 50 lines of Fortran software.

When he did the same measurement on great developers, however, he found that their Halstead Lengths were 65,000 or so. No other metric of brain capacity varies by anything like that. Like any human attribute, Halstead Length is going to follow a distribution and these very long lengths are going to appear in only the right tail of a distribution. Maybe 0.5%.

Let me explain why this all matters with a few pictures. Assume this image describes the problem you need to solve:

It is a complicated image with lots of detail. Assume you are a person with a capacity for seven chunks each of size 250. Then what you can understand of this image at one time looks like this:

Not very interesting or exciting. Given enough time you can understand it all, of course, but seeing broad patterns and interactions is challenging.

Now go to the extreme and assume you have seven chunks of 65,000. Then the problem looks like this:

You still cannot see it all, but if the problem were a bit smaller you could, and a team of two or three people can see it all. Broad patterns and interactions are much more apparent.

One solution is to reduce the level of detail to make the broad patterns and interactions more visible, but in this case doing so in a way that would let a 7.250 person see it all gives you this:

This is not very useful.

Labor is not a homogeneous input, and I argue that there are increasing returns to Halstead Length. The gains are far more than linear. Halstead Length applies to almost any cognitive activity: to anything where you have to navigate through complex, diffuse information. Greater composers, writers, artists, lawyers, doctors, scientists,… Their supreme talent is to make the complex simple by giving the rest of us a roadmap. Indeed, even managing people is easier the greater the Halstead Length. It is unprovable, but I suspect that no other field though has the same nonlinearity as software.

Not only do larger Halstead Lengths allow you to identity broad patterns and interactions, but they also enable you to populate your chunks with rich data structures ala Knuth that make the contents even more accessible and actionable.

In cognitive tasks, longer Halstead Lengths enable greater productivity, but that productivity varies by task. Most importantly, for tasks involving more than one person, productivity is also affected by the average and variance of the team. Firms which can assemble teams consisting entirely of high talent people are able to get even higher productivity from their employees. However, since this productivity requires the team, there can be an equilibrium in which firms pay above market, below value (AMBV) wages to its workers and pocket the difference.

The wages are above market because other firms realize less value and offer less so the market wage is lower. The firm is a monopsonist, however, and can pay below the marginal value. Obviously, there is room for negotiation. Employees can opt out by trying to create their own teams. We know this as a startup funded by venture capital, but the economics are the same, although they mean that what the statistics call a return on capital is often actually a return to labor. Many small businesses reflect a similar thread.

This is the model for investment banking, for management consulting and for the big technology companies and the many upstarts attempting to join them. The market franchise they have is on the supply side as much as it may be on the demand side: Is it a violation of antitrust law to have a dominating position in any labor market? Interesting question. Antitrust law lags reality.

Software continues to eat the world, so the scope that high-Halstead-Length-teams can address is seemingly expanding without limit. Since these firms can all pay AMBV wages, other firms are increasingly faced with limited labor pools to staff critical functions. Increasingly, U.S. public companies are listing talent as a critical risk factor in their 10-K filings. And for good reason.

We will have inequality because there are higher returns to people with high Halstead Lengths. Moreover, these returns increase as these people align and increase as technology transforms more industries. Halstead Length is not apparent like height, but a high Halstead Length is no different an attribute. You cannot retrain someone 5 feet 6 inches tall to be 7 feet tall. As the percentage of tasks where Halstead Length provides an advantage increases as it will as software eats the world, the amount of inequality will also increase.

Because financial services recognized this decades ago, holders of capital have been able to earn above market returns so r > g. We have been able to pay more to those who help divide the economic pie than to those who grow it.

What do we do about this? I am not sure. I have argued that Halstead Length is like Ricardian land, and at least some of this income should be treated as rent. I offered an excise tax of 10% on incomes over $5 million, 20% on incomes over $50 million and 30% on incomes over $500 million. I still think this is a reasonable proposal.

Should antitrust law apply to labor markets? I just don’t know how to make this actionable. A common belief in the computer industry used to be that at any one time there are only in the order of 10,000 great software developers in the world. Though this seems small, they may create half or more of all software, though millions may build on it. In the mid-1990s Microsoft may have had more than half of them, as may Google today. Again, unknown and unknowable. Their strategies though were similar: if you find great talent, hire it. Who cares what they do as long as they are not doing it for a competitor. The idea of monopolizing a labor market was not covered in my graduate school training.

This is an early draft. Much more thought required.