Tyler Cowen, among many others, is intrigued by a study by Raj Chetty and others showing downward mobility of black males.
My view, which I came to in the process of reading Gregory Clark’s study of long-term heritability of income, is that inter-generational income has a large heritable component and a large random component. Over several generations, the random component washes out. But for the difference across a single generation, the random component matters.
This model suggests that when someone’s income is far above (below) the heritable component, it will revert to the mean. Children will do worse than parents who have enjoyed a positive shock and they will do better than parents who have suffered a negative shock.
If the shocks to income were normally distributed, then mean reversion would not produce any systematic pattern of children falling below parents or rising above them. So you would not expect the Chetty result in that case.
But what if the random component is not normally distributed? Suppose that what you observe in one generation are a few really large shocks on the up side, with a lot of smaller negative shocks on the down side. The next generation will then have some apparent big losers and a lot of apparent small winners. Depending on how you sort the data (Chetty appears to be looking at measures of income based on rank rather than absolute level), Chetty’s result could be an artifact of the random component. It might be that if he were to measure incomes three or four generations apart, the apparent downward mobility would disappear.