### Monday, June 22, 2009

## Born of high means

Let's suppose that everybody gets their income by random chance. Suppose that random chance is approximated by a draw of one ball from a bag. The bag contains balls that are one of five colors, and these correspond to five income levels (let's say $20,000, $40,000, $60,000, $80,000 and $100,000.)

There are parents and children. Let's suppose that the children's draws of balls are independent of the parents. If Mom draws a $20,000 ball, what are the odds that Junior will draw something better? It would be 4/5, or 80%. If Mom draws a $40,000 ball, there's a 20% chance Junior ends up worse off, 20% chance Junior is the same, and 60% chance he's better off. Etc. For those children whose parents drew the $100k ball, 20% will do as well, no more. Spread the balls out over more categories than five, and you'd get finer gradations, but the logic is the same. Be born to a higher-income person, and there's a higher chance your income will be less, if income is randomly distributed.

Now look at the two strands of data Russ Roberts extracts from a recent Pew study on generational income mobility. At the bottom end of the income distribution we get a result that would appear to be pretty well drawn from random chance. It looks like race matters; you can speculate all you want about it, I don't have much to add based on the graphs except that the ratio of black to white income rises from 44% to 53%. It's better in relative terms, but I couldn't argue with you if you said it wasn't "better enough". But I'm more interested in the top quintile. 44% of those whose parents where in the upper fifth of the income distribution exceed their parents' income; on average, their income is 2% less than their parents'. And on my random draw exercise, you'd expect no more than 10% to be better off rather than 44%.

So for those at the bottom, your children are likely to do better off, though no more so than if all incomes were drawn randomly. For the rich, there's some persistence over generations. Inherited traits do matter, be it height or brains or beauty. If you think 44% is too many, how do you do something about it without killing the incentive of the most productive to work on their children's behalf?

And, more importantly: Would this "chance distribution" story in my first two paragraphs be anybody's idea of what the "right" amount of generational income mobility is? If not, what is? (For more, see Mueller, Tollison and Willett [1974].)

There are parents and children. Let's suppose that the children's draws of balls are independent of the parents. If Mom draws a $20,000 ball, what are the odds that Junior will draw something better? It would be 4/5, or 80%. If Mom draws a $40,000 ball, there's a 20% chance Junior ends up worse off, 20% chance Junior is the same, and 60% chance he's better off. Etc. For those children whose parents drew the $100k ball, 20% will do as well, no more. Spread the balls out over more categories than five, and you'd get finer gradations, but the logic is the same. Be born to a higher-income person, and there's a higher chance your income will be less, if income is randomly distributed.

Now look at the two strands of data Russ Roberts extracts from a recent Pew study on generational income mobility. At the bottom end of the income distribution we get a result that would appear to be pretty well drawn from random chance. It looks like race matters; you can speculate all you want about it, I don't have much to add based on the graphs except that the ratio of black to white income rises from 44% to 53%. It's better in relative terms, but I couldn't argue with you if you said it wasn't "better enough". But I'm more interested in the top quintile. 44% of those whose parents where in the upper fifth of the income distribution exceed their parents' income; on average, their income is 2% less than their parents'. And on my random draw exercise, you'd expect no more than 10% to be better off rather than 44%.

So for those at the bottom, your children are likely to do better off, though no more so than if all incomes were drawn randomly. For the rich, there's some persistence over generations. Inherited traits do matter, be it height or brains or beauty. If you think 44% is too many, how do you do something about it without killing the incentive of the most productive to work on their children's behalf?

And, more importantly: Would this "chance distribution" story in my first two paragraphs be anybody's idea of what the "right" amount of generational income mobility is? If not, what is? (For more, see Mueller, Tollison and Willett [1974].)

Labels: economics