Thursday, June 26, 2014

Rise and Fall

In a column last week, Greg Mankiw said "According to a recent study, if your income is at the 98th percentile of the income distribution — that is, you earn more than 98 percent of the population — the best guess is that your children, when they are adults, will be in the 65th percentile."  Of course, you wouldn't expect those children to do as well as their parents--there's not much room to rise and lot of room to fall--but that was a bigger decline than I would have expected, so I decided to take a closer look.  

 The study refers to people born in 1980-82 and "when they are adults" is age 30.  Of course, 30-year-olds generally earn less than middle-aged people, but the authors of the study say that relative positions have pretty much stabilized by then--that is, we'd see about the same pattern if we came back 20 years later. 

Here is the pattern for people whose parents were in the 60th percentile.

The large number of people in the second percentile (actually about 6% of all 30-year olds) had zero income.  That makes it hard to read, so here is the figure showing just the lower part of the y-axis.  

The most common destination is in the low 70s.  The chances of rising above that level drop off pretty sharply.  But overall, the differences are pretty small:  you could say that people from the 60th percentile are about equally likely to end up at any point in the distribution.

Here is the 80th percentile.  It's a similar basic pattern, although the chances of winding up near the top are higher and the chances of ending near the bottom are lower.

Here is people whose parents were in the 98th percentile.  This looks different--the higher the ranking, the better your chances of getting there.  The most likely destination is the 99th percentile--even higher than the  "percentile" of zero earnings.  

 I haven't calculated the mean percentile--I'll look at this more later--but this seems to give a different picture than Mankiw's summary.


  1. Interesting, I have many questions here:

    1. In the second graph, why is zero income at the second percentile and not the first percentile? Is there a negative income category? And why is there the big gap on the x-axis between the first two percentiles? Also, that looks like about 4% so why do you call it 6%?

    2. So is Mankiw's conclusion basically driven by his definition of the mean or median rather than the mode as "the best guess"?

    3. In his definition, Mankiw seems to be blurring "income" and "earnings." But they're different, no? Is it just that these differences are tiny, even at the 98th percentile?

  2. 1. Yes, the "first percentile" is people with negative income. It's about 0.3 percent, and people whose parents had high incomes are substantially more likely to be there. So I suspect that most of them aren't really people who'd fallen to the bottom, but people who took losses on businesses or investments at that time. The 6% with zero income is of the total--only about 4.5% of people whose parents were at the 60th percentile wound up there. The authors numbered the groups as 1st, 4th, 7th, 8th, etc. percentiles, which is what I used for the x-scale.
    2. The median destination for people whose parents were in the 98th percentile is the 75% percentile. I'd think that's a better summary than the mean in this case, but I'm not really sure how best to interpret the data.
    3. I think he was just being careless. The data count capital gains, which are important near the top.