GREG MANKIW has followed up on his extremely unconvincing paper dismissing concern over high income inequality with an even less convincing blog post dismissing concern over low income mobility. Mr Mankiw argues that the so-called Great Gatsby curve, which shows that countries with higher income inequality also have lower income mobility, is "not particularly surprising". He offers an analogy: think of nations as chess clubs.

Some clubs have a bunch of players with similar levels of skill at chess. In this case, everyone would have a win-lose record that is close to each other, and a person's club ranking one year would not have a lot of predictive value for his ranking the next. That is, we would have small inequality and substantial mobility. Other clubs are more heterogeneous. They have some masters and some novices. The masters have much better records than the novices, and their better records tend to persist year to year. That is, we would have substantial inequality and little mobility. If we put all these clubs together in a scatterplot, we would get something close to the Great Gatsby curve.

What Mr Mankiw is implying here is that the reason why countries like Germany or Australia have low levels of income inequality, while countries like America and China have high levels of income inequality, is that people in Germany and Australia are more homogenous in their economic abilities than people in America and China. Because they are more homogenous, they are also more likely to show variance in their relative rankings from year to year.

We will leave aside for the moment the question of why one might think that Germans are more homogenous than Americans, which might reflect a familiar kind of prejudice, or why one might think that Chinese are less homogenous than Australians, which would reflect a novel one. The main point here is that Mr Mankiw evidently has no idea why people talk about the Great Gatsby curve. The significance of the curve is that people who want to defend gross inequalities of income in countries like America often argue that income inequality is okay as long as you have income mobility: if today's burger-flipper can become tomorrow's prosperous burgher with a little grit and hard work, society is still fair. The problem with this thesis is the Great Gatsby curve. It shows that the greater the distance in a country between rich and poor, the harder it is to go from poor to rich or vice versa. Countries don't compensate for income inequality through income mobility; they tend to be either fair or unfair on both metrics at the same time. If Mr Mankiw does not find this "surprising", he should wonder why people who defend gross inequalities of income would have resorted to such an implausible argument.

Mr Mankiw then adds a corollary which I can only describe as amazing.

Suppose we combined two clubs, one with mostly masters and one with mostly novices. The new combined club would be more heterogeneous and, therefore, would exhibit more inequality and less mobility than either of the clubs separately. The application of this corollary to the Great Gatsby curve is that if we looked at Europe as a whole, rather than each nation separately, we would find that Europe as a whole has more inequality and less mobility than the individual countries. That is, Germans are richer on average than Greeks, and that difference in income tends to persist from generation to generation. When people look at the Great Gatsby curve, they omit this fact, because the nation is the unit of analysis. But it is not obvious that the political divisions that divide people are the right ones for economic analysis. We combine the persistently rich Connecticut with the persistently poor Mississippi, so why not combine Germany with Greece?

The amazing thing here is that Mr Mankiw seems to have no concept of what argument he's in. Let's put it this way: does Mr Mankiw think that the reason why Germans are persistently richer than Greeks is that Germans are innately smarter or harder-working than Greeks? Seriously? Is "Greeks deserve to be poorer because they have less merit" really the argument he wants to make here? I could almost believe it might be, except that he then goes on to compare the German/Greek divide to the Connecticut/Mississippi divide. Does Mr Mankiw believe that Mississippians are poor because they are innately less smart or hard-working than people in Connecticut? Take a look at the fascinating new study of regional income mobility differences which David Leonhardt reports on today in the New York Times. It's true: Mississippi has much less income mobility than Connecticut. So do Alabama, Georgia, the Carolinas, Ohio and Indiana. Does Mr Mankiw think people in Indiana are innately less smart or hard-working than people in Connecticut? If not, what differences between Indiana and Connecticut account for the disparity?

In his article on income disparity, Mr Mankiw hinted that genetic differences may play a significant role in earning power. I don't think Mr Mankiw believes that Greeks and Mississippians are genetically inferior to Germans and Connecticut...ians. I imagine he would make the reasonable argument that people in Greece and Mississippi have lower earning power because they are less educated, live in lower-productivity economies, and have inferior governance to people in Germany and Connecticut. But this is the whole point of the Great Gatsby curve! In a country like China, if you are born in a farming village in Xinjiang, you are overwhelmingly likely to be poor and remain poor; if you are born in a middle-class family in Shanghai, you may attend one of the world's finest technical universities and become a millionaire. To the extent that wealth in America depends on whether you are born in a poor state like Mississippi or a rich one like Connecticut, we are less like Australia's egalitarian, mobile economy, and more like China's inegalitarian, stratified one.

With his chess-club analogy, Mr Mankiw is trying to make it seem as though the responsibility for income disparities and income immobility in different groups must lie in the abilities of the players. The rules of chess are the same everywhere, so if some groups have wide and persistent disparities between players, it must be because the players' abilities vary widely. Societies, obviously, do not all play by the same rules. The assumption of most people who believe in the logic of statistics would be that if your chess clubs are sufficiently large, say 10m or more, the distribution of the players' innate abilities is probably pretty similar. In that case, if there are differences in the level and persistence of variance, it's probably because the clubs are playing with different rules. The question is whether those rules are fair, or whether they codify unjustifiable privilege.

The argument over the Great Gatsby curve is an argument about whether America's economy is fair. With his Germany/Greece and Mississippi/Connecticut analogy, Mr Mankiw has stumbled on a very convincing point: whether you are rich or poor in Europe or America depends to a great extent not on your own qualities or efforts, but on where you happen to be born. America is not a meritocracy, Mr Mankiw is saying; not only do those born rich tend to stay rich and vice versa, just being born in one state or another makes a huge difference to your lifelong earnings. Amazingly, he seems completely unaware that this is the case he's just made.