CHINA has enjoyed (and suffered) more than its fair share of social mobility in recent decades. Between 1981 and 2005, over 600m Chinese moved out of poverty, according to Shaohua Chen and Martin Ravallion of the World Bank. Some Chinese of modest means became fabulously rich. But not all social mobility was upwards. From 1949 to the end of the 1960s, China's communists uprooted landlords, expropriated capitalists, and banished bourgeois intellectuals to the hinterlands. Through collectivisation, socialisation and rustication, they dismantled the traditional mechanisms (land, capital, schooling) by which the well-to-do pass on their advantages to their offspring.

Some of those mechanisms may now be back in operation, however. Inequality in China has, of course, risen sharply in the past 30 years. A few scholars are now documenting its transmission from one generation to the next. In a 2010 paper, for example, Yingqiang Zhang of Beijing Jiaotong University and Tor Eriksson of Aarhus University, Business and Social Sciences, in Denmark looked at the offspring of thousands of households included in a longitudinal survey of nine provinces from 1989 to 2006. The offspring experienced diverging fortunes over the years, roughly in line with national trends. This rising inequality might not be worrying if it reflected an increasingly dynamic, meritocratic society, rewarding greater effort or ability. But the authors estimate that 63% of this inequality in outcomes was due to inequality of opportunity.

Inequality of opportunity is not easy to measure, or even to define. Economists tend to worry when some people are barred from making their full contribution to society, while other people reap disproportionate rewards, taking more from the national product than they add to it. That is not just unfair; it is inefficient.

Philosophers go further. They feel people should be rewarded or punished only for the things they can choose, such as effort, and not for circumstances outside their control. Those circumstances include obvious inherited privileges, such as wealth and social connections. But the definition can extend further, to include many things we normally associate with merit, such as talent. We do not, after all, get to choose our talents, so why should we be rewarded for them, beyond perhaps what is necessary to make us put those talents to good use?

In their 2010 paper, Messrs Zhang and Eriksson take account of a number of circumstances beyond the individual's control, including the income, education and employer of a person's parents; as well as that person's place of birth and gender. They find that having richer parents helped a person's prospects (a 10% increment in parental income was reflected in a 4.5% income boost for their offspring) and having parents who were employed by the state helped a lot. Parental education, on the other hand, was no help whatsoever. In these provinces, where your parent works matters more than where he went to school.

Not every parental influence can be observed, distinguished and measured, however. So in a recent working paper, the two authors look at an alternative indicator: namely, the correlation between one brother's income and another's. This fraternal comparison is a good "omnibus" measure of the weight of family and community influence, according to Mr Eriksson. Two children brought up by the same people, under the same roof, in the same neighbourhood, will share many of the same circumstances of birth and background. If these things matter greatly in a society, they will govern the life chances of both brothers, resulting in a tight correlation in their incomes. If, on the other hand, family background matters little, the fraternal correlation will be low.

In a 2000 paper co-authored by Mr Eriksson, he and his colleagues found that the correlation was much higher in the US (0.43) than in the Nordic countries (0.14 to 0.26). In China, the correlation is higher still: 0.57. To put that in context, the authors argue that knowing what a person's brother earns gives you a a better guide to a Chinese person's income than economists are normally able to obtain from knowing how many years of schooling and work experience a person has under his belt.

There is, however, one big obstacle to calculating brother correlations in China. Thanks to the one-child policy, few young, urban Chinese have siblings. The author's estimate of 0.57, therefore, applies only to rural China. In China's cities, inequality of opportunity takes a rather different form: the second-born are denied the opportunity to exist.