Scot Sumner find poorly decomposed data

He is looking at reviews from a new book about social mobility. Evidently the book talks about why some children do not move up from poverty. One of the book reviews posted this bubble chart. It shows your chance of being rich if you were poor before, and visa versa. The numbers in the bubble gives you the probability you stay where you are.

Scott notices the mobility in the middle quintiles, the rows at the 2nd, 3rd and 4th quintiles show a lot of mobility. If you were rich or poor, you are likely to end up in the middle. Why is that? Its the middle class. Most activity takes place in the middle class, that is where the economy is most divergent and has the most second derivative; the most spare liquidity compared to the economic activities at that level.  In other words, the economy is optimized around the middle class.

This is poor decomposition because the quintiles are linear and not weighted by total volatility. At least two of the quintiles need to be combined, they are equally significant. The real social mobility issue is mainly about the dirt poor and the filthy rich.   But over all, I agree with Scott, this does not show much immobility over a few generations, but a few generations is a long time, a hundred years of more.

The second derivative makes us wide band, so our lives are not volatile, we have options. The poor and filthy rich will be volatile, more signifant. The middle three are important, but not as significant toward the outcome. The second derivatives are the partial transactions, any element a and b do not make a probability in one step, they queue up.  Set combinatorics are paced.