Inequality and mobility
2008-07-14 · Original WordPress address
Kenworthy has stopped making sense. Thoma and Talking Heads fans rejoice.
Kenworthy's argument is that growing income inequality is bad IF intragenerational income mobility hasn't increased too. He shows charts showing mobility hasn't increased and then... presto... badness.
This is wrong. Totally wrong.
Suppose last year there was two possible incomes, 50% of people earn $0 and the rest earn $1. Suppose this year the possible earnings are $0 and $10 (OMG a rise in inequality!). Some proportion n of the people earning $0 last year now make $10 and some people that were earning $1 now are earning $0. Same sort of thing happens next year... inequality grows even higher so that the top earners make $100, the lowest $0 and people move between groups
Given Kenworthy's endorsement of Friedman's views of inequality, I assume he agrees the best measure of income inequality is inequality of lifetime earnings. So if I was earning $0 last year decade, I could expect to earn n * $10 this year decade and 2*n* (1 - n) * $100 next year decade. At n=40%, which is about the parametrization that fits the data, this would be $52 for my expected lifetime earnings.
Now here's the point: with a constant n, i.e. a constant fraction of people moving into the high income group, increases in inequality translate to increases in my expected lifetime income. To see this, just add zeros to the high income this year decade and next and then do the math.
How could that be a bad thing?