# Inequality and mobility

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?

## 5 thoughts on “Inequality and mobility”

1. swong says:

Stupid question? I’m not really versed in the inequality debate among economists. The word seems to have a highly technical meaning outside of its common usage.

What’s the churn like between the n and not n groups? If you were modeling this programatically, would you randomly select your n pool fresh at the beginning of each year? Or would you just do some mixing at the interface between n and not n?

2. n characterizes the churn between groups. If you’re poor one year, you have a 100*n% chance of becoming rich the next year.

Actually, I said in the post n=40% is about right for the real data, but that’s not true because my example is year to year. n=40% is right for the decade by decade churn. Forty percent of poor people become rich people every ten years.

Also, in my example there are no young poor families or immigrants taking the old poor families’ places at the bottom. I assumed all the new rich supplanted old rich that have become poor. Of course, reality has new young families and new immigrant families so in reality expected lifetime income is even higher. This means reality is more rosey than my example, but I was trying to make it hard on myself.

3. Anna says:

Why do you base your view on an unrealistic example?

If you look at Lane Kenworthy’s example from the real world it is obvious that the poorest ones in the US have lost the most from increasing inequality – they have more or less stayed within their percentile while this percentile has received a decreasing share of the pie.

4. >> “Why do you base your view on an unrealistic example?”

He’s an economist[1]! Duh!

[1] Although he does teach non-economics classes, a crime for which he’s on The Watchlist.

ðŸ™‚

5. Anna, take another look at Kenworthy’s data. The bottom 20%tile have the highest mobility. Nearly 50% of this group make it to a higher income group within a decade.

This makes sense because this group is mostly young people starting their careers.