Is inequality approaching a tipping point?

As with my last post, I'm trying to catch up here in linking to my recent Bloomberg pieces. This is my last one from two weeks ago. Given all the recent discussion of rising inequality, I wanted to point to a really fascinating paper from about 15 years ago that almost no one (in economics, at least) seems to know about. The paper looks at a very general model of how wealth flows around in an economy, and points to the existence of a surprising phase transition or tipping point in how wealth ends up being distributed. It shows that, beyond a certain threshold (see text below), the usual effect of wealth concentration (a small fraction of people owning a significant fraction of all wealth) becomes much worse: wealth "condenses" into the hands of just a few individuals (or, in the model, they might also be firms), not merely into the hands of a small fraction of the population.

Are we approaching such a point? I've mentioned some evidence in the article that we might be. But the important thing, I believe, is that we have good reason to expect that such a threshold really does exist. We are likely getting closer to it, although we may still have a ways to go. 

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We know that inequality is on the rise around the world: The richest 1 percent command almost half the planet’s household wealth, while the poorest half have less than 1 percent. We know a lot less about why this is happening, and where it might lead.

Some argue that technological advancement drives income disproportionately to those with the right knowledge and skills. Others point to the explosive growth in the financial sector. Liberals worry that extreme inequality will tear society apart. Conservatives argue that the wealth of the rich inspires others to succeed.

What if we could shed all our political prejudices and take a more scientific approach, setting up an experimental world where we could test our thinking about what drives inequality? Crazy as the idea might sound, it has actually been done. The results are worth pondering.
Imagine a world like our own, only greatly simplified. Everyone has equal talent and starts out with the same wealth. Each person can gain or lose wealth by interacting and exchanging goods and services with others, or by making investments that earn uncertain returns over time.

More than a decade ago some scientists set up such a world, in a computer, and used it to run simulations examining fundamental aspects of wealth dynamics. They found several surprising things.

First, inequality was unavoidable: A small fraction of individuals (say 20 percent) always came to possess a large fraction (say 80 percent) of the total wealth. This happened because some individuals were luckier than others. By chance alone, some peoples’ investments paid off many times in a row. The more wealth they had, the more they could invest, making bigger future gains even more likely.

For those who worry about the corrosive effects of wealth inequality on social cohesion and democracy, the idea that it follows almost inexorably from the most basic features of modern economies might be unnerving. But there it is. A small fraction owning most of everything is just as natural as having mountains on a planet with plate tectonics.

Suppose we reach into this experimental world and, by adjusting tax incentives or other means, boost the role of financial investment relative to simple economic exchange. What happens then? The distribution of wealth becomes more unequal: The wealth share of the top 20 percent goes from, say, 80 percent to 90 percent.

If you keep boosting the role of finance and investment, something surprising happens. Inequality doesn’t just keep growing in a gradual and continuous way. Rather, the economy crosses an abrupt tipping point. Suddenly, a few individuals end up owning everything.

This would be a profoundly different world. It’s one thing to have much of the wealth belonging to a small fraction of the population -- 1 percent is still about 70 million people. It’s entirely another if a small number of people -- say, five or eight -- hold most of the wealth. With such a chasm between the poor and rich, the idea that a person could go from one group to the other in a lifetime, or even in a number of generations, becomes absurd. The sheer numbers make the probability vanishingly small.

Are we headed toward such a world? Well, data from Bloomberg and the bank Credit Suisse suggest that the planet’s 138 richest people currently command more wealth than the roughly 3.5 billion who make up the poorest half of the population. Of course, nobody can say whether that means we’ve reached a tipping point or are nearing one.

Experimental worlds are useful in that they exploit the power of computation to examine the likely consequences of complex interactions that would otherwise overwhelm our analytical skills. We can get at least a little insight into what might happen, what we ought to expect.

Our experimental world suggests that today’s vast wealth inequality probably isn’t the result of any economic conspiracy, or of vast differences in human skills. It’s more likely the banal outcome of a fairly mechanical process -- one that, unless we find some way to alter its course, could easily carry us into a place where most of us would rather not be.

Inequality, chemistry and crime

My latest column in Bloomberg (published Sunday night in the US, I think) looks a little at the link between socioeconomic inequality and crime. That there is such a link has been established rather convincingly by statistical analyses across many nations spanning decades. This was all laid out convincingly in the 2009 book The Spirit Level by Richard Wilkinson and Kate Pickett. See also this short TED talk by Wilkinson which covers the main points very clearly.

But I also referred (rather vaguely) in my column to two other lines of research that deserve some discussion. One is an idea in criminology known as "routine activity theory" which has increasingly become a branch of applied computational social science. In effect, it views crime as a kind of natural social chemistry taking place between potential offenders and targets, and has a good track record in accounting for empirical patterns of crimes of all kinds by considering simple factors such as patterns of human movement on streets, of street lighting, of building architecture and so on. It more or less gives up on thinking about the deep psychology of crime and its motivation. In general, this perspective asserts, you tend to get more crime where you have more targets coming together more frequently with more potential offenders, just as you get more chemical reactions whenever potential reactant molecules come into contact more frequently. I've written about this a little before in New Scientist (a copy of that article is on the web here).

The empirical success of routine activity theory is sometimes taken as evidence that factors such as poverty and social inequality don't matter in crime, as the theory doesn't explicitly consider such factors. This is a serious misunderstanding. After all, the theory focuses on the factors that bring together potential or motivated offenders with potential targets, and doesn't attempt to explore the factors that might give a person the motivation to commit crime in the first place. Here the analogy to chemistry is again constructive, I think. In chemistry, reactants coming together isn't enough. They generally need sufficient energy (or a catalyst) to help them overcome an energy barrier (caused by repulsive forces between molecules) before they can react. It's entirely plausible to think of prevailing social norms as a kind of energy barrier to the commission of crimes, as these forces tend to persuade people to avoid crime. In general, we should expect high levels of trust and strong social norms to suppress and discourage crime, much as a lowering the temperature of a chemical solution makes reactions go more slowly. (Low temperature increases the effective size of energy barriers to reaction, which must be overcome by collisions between molecules; these are stronger at higher temperatures.)

Analogies aside, the point is that routine activity theory actually fits together quite well with the existence of larger social factors that influence overall probabilities of crime. The factors considered in the theory can determine detailed patterns of crime, even as the larger global factors influence overall rates. The work considered by Wilkinson and Pickett strongly suggests that social inequality is one of the most important global factors encouraging crime (and other measures of social dysfunction).

The second body of work I wanted to add a little detail on looks at what creates high levels of inequality in the first place. On the drivers of inequality, of course, there is a huge literature in social science and economics and I don't pretend to be an expert on it. However, there is an interesting perspective motivated by physics that I think should be much more widely known. This paper from several years ago by Jean-Philippe Bouchaud and Marc Mezard analyses a very simple model of an economy and shows that a high level of economic inequality is a more or less generic and unavoidable outcome. It is something to be expected on mathematical grounds alone. The basic idea is to model an economy as a system in which wealth flows around among people by two fundamentally different processes. First, it flows between individuals when they make exchanges or trades, through contracts, employment, sales and so on. Second, wealth also accrues to individuals (or departs from them) on account of investments in instruments yielding uncertain returns. Importantly, the second factor contributes an element to individual wealth that involves a random multiplicative factor -- random because investments are uncertain, and multiplicative because, quite sensibly, the wealthier invest more than the poorer, and typically more in direct proportion to their wealth. The poor partake very weakly in this multiplicative channel to wealth growth, while the wealthy participate progressively more strongly.

Bouchaud and Mezard showed that the inevitable outcome in such a basic system is that a large fraction of the total wealth in the economy ends up being held by a small faction of the population. This is the case even if every individual is considered to have the same inherent money making skills. (The authors, of course, do not believe this to be the case; but making this assumption makes it possible to explore how natural economic dynamics can drive large wealth disparities even in the absence of any differences in skill.) It's the multiplicative nature of the returns on investments that makes it happen. This pattern in the distribution of wealth holds in every nation and was known long ago, being first described by Italian economist Vilfredo Pareto. This paper gave to my knowledge the first really fundamental explanation of why this pattern holds everywhere. Since then a number of works have taken this approach much further.

However, the universal form of this distribution does not preclude the possibility of some societies being more unequal than others. You can have a society in which the top 5% hold 90% of the wealth, or in which that same top 5% holds 99.9% of the wealth. Such variations are driven by the relative strength of multiplicative returns on investment versus the flows in an economy that might act to reduce inequality. Obviously, taxation is one mechanism that leads to a redistribution of wealth from richer to poorer and one should expect, in a broad brush way, that lower taxes should tend to associate with higher levels of wealth inequality.

I strongly recommend this paper -- it's short and you can skip over some of the mathematical detail -- as it shows how some very important global economic realities may have quite simple underlying causes. The bigger problem, of course, is learning then how to craft real world policies so as to keep inequality within bounds, avoiding the many kinds of social dysfunction it clearly seems to give rise to.