Inequality by country

In the previous post, I produced an oversimplified model that showed why inequality in income is inevitable, and that raises the question, can something be done to modify that, and if so, is it desirable to do so? To answer that sort of question, first we should look at where the inequality is, because different countries have different economic policies. First, there has to be a measure of inequality, and economists have created something called a Gini index to measure this. This registers a country using values between 0 (everyone has exactly the same wealth) to 1 (one person has the lot). The journal Science produced maps to compare countries. The US had a Gini index of 0.4 in 2010. What does that mean? Apparently, the top 1% controlled nearly 20% of US income, but the 99% is also unevenly spread, as my crude model would have predicted. In 2012, the top 20% of Americans enjoyed over 50% of the US income, up from 43% in 1967, and this is presumably due to very many more higher incomes for the tech-savvy graduates of Silicon Valley and similar places. Thus this increase is in part due to more investment in education, and that does not seem wrong, at least to me. The middle 20% received about 14% of all income, and the bottom 20% about 3% of the income. That should not be a total surprise to those who followed the logic of my crude model.

Now, if we look at other countries, we see some odd results. One of the more common results in the Science article was “no data”. However, the countries with most equality tended to be Scandinavian countries, parts of the old Soviet Union (some “Stans”, Belorus and Ukraine) and some of the old “Iron Curtain” countries, such as what was Czechoslovakia, Hungary, and one or two others. The most uneven country was South Africa, with some African and South American countries running fairly close behind.

What can we conclude from that? The extreme value for South Africa probably lies in the historical tying up of the mineral resources such as gold and diamonds by a few hands. The second point is that for historical reasons there is more than one society there, and while efforts are being made to integrate these and give more opportunities to those previously deprived, in fairness there is only a limit to what can be done in a short time. Whether that limit has been reached is another matter. Equality does not depend on wealth, but probably more on social policy, thus Scandinavia has plenty of wealth, particularly Norway, but the money has been mainly put aside by the government, thanks to royalties on oil production and very progressive taxation. Similarly, many of the countries in South and Central America have been plagued by right wing governments, including dictatorships, and these are centres for much greater inequality.

This suggests at least two points. The first is that inequality is the greatest the further the society is away from general near equality. In other words, as my model suggests, the more time there is to develop free of external influences, the greater the inequality. The second is that the more progressive the taxation, the more equal the society. Unfortunately, that is not a free ride, as it often leads to a transference of wealth, when the rich simply pack up their bags and go to somewhere with a more friendly taxation policy. What to do about inequality, if anything, is quite a difficult question to answer.

Inequality in Society

By now, just about everyone will have heard about Thomas Piketty, who has claimed that the world inequality is getting worse and inevitably it will get much worse, on the grounds that wealth generates wealth. He has been attacked from various quarters, usually on relatively irrelevant details, for example that some of the data in his statistics are not quite right, but so far nobody has provided a knockout blow. Now, in

a recent edition of Science, where a number of articles addressed this issue of inequality of income in the world, one particular item took my attention: it arose from some physicists who argued such inequality is natural and arises from considerations similar to those of the second law of thermodynamics. Very specifically, they consider the statistical origin of entropy, and argue that a distribution of wealth where everyone has the same is just one of very many distributions, so it is extremely improbable when one considers how wealth evolves. 

One way to illustrate the concept is to construct a simple model, and this is instructive (in my opinion, anyway) because it also shows something about models. Consider a game with these rules. There are 128 participants, and they play in rounds, and every round the players earn one credit. At the end of the round they may spend any of what they have, or they can save. If they get four credits, on the next round they get a bonus credit (return on investment) and they also have the choice of borrowing a further four credits. To further simplify, assume there is a fifty per cent chance of taking a specific option from the choice of two, and if the option is to spend, the choices of how much is evenly divided amongst the options. Now, watch how this game evolves.

At the end of round 1, each player has 1 credit, and half elect to spend it, which gives 64 with 1 credit and 64 on zero. Following round two, half of the first 64 continue to save, and half of those who choose to spend use one credit and the other half both credits. So we now have 32 with two credits, 48 with 1 credit and 48 with none. The reader can keep this going for himself, but it soon becomes apparent that 8 soon reach the 4 credit mark, at which point they get their bonus, then two will further invest, and of these, 1 will take the option of borrowing, and that one gains two each round, even though by borrowing he effectively has to repay at some stage. So, after five rounds, out of 128 originals, 1 has got ahead of everyone else, and only one other is close behind.


The analogy with entropy is as follows. In statistical thermodynamics, the entropy of a state is proportional to the logarithm of the number of ways of forming it, and the more ways, the higher the entropy. The second law says a system tries to maximize entropy. There is only one way to get to maximum wealth, while there are many ways to get a low wealth.

You may protest that this game is too crude, and you would be right, but it shows something about models. The first point about models is you have to get all the equations (a numerical statement of the rules) down and you have to accurately fix all the constants and functions. In this example, all earnings are in units of 1 (a constant) but in practice, it will be a distribution. Similarly with investment returns, and there are a number of other problems. Nevertheless, this simple model gives a qualitative result that matches reality: the distribution of wealth will always be unequal because different people make different decisions on what to do with what they earn, and the effects become very pronounced quite quickly. What this model has really done is not to predict social behavior, but rather to show the effects of a proposition, and that is where models are strong.