How hot labor markets can lead to misleading median comparisons.

September 10th, 2019 at 3:07 pm

The Census income and earnings data sometimes have a confusing characteristic that is not uncommon in these sorts of data, especially in periods of tight labor markets, as was 2018. The issue has to do with changes in medians from one year to the next.

For example, the data that came out this morning showed that for both men and women full-time, full-year workers, real annual earnings rose 3.4 and 3.3 percent, respectively, 2017-18. But for all ft/fy workers, combining both genders, earnings fell 0.6 percent. The decline was statistically insignificant, but jeez–that’s confusing, right? Why would earnings fall, overall, in a year with a clearly solid job market, especially when both genders did pretty well?

A number have folks have asked me about this today–a similar dynamic is in the data for median household income: the real median went up  significantly last year for the two household types–family and non-family (individual) households–but not for all households (i.e., it rose slightly, by 0.9 percent, but the change was insignificant).

One way this often occurs, especially in hotter labor markets, is that the composition of workers or families change in ways that can make it hard to figure out what’s up and what’s down. Consider the first two columns below, arrayed from lowest to highest, assuming no change in the composition of people or HHs in the data. The median goes up in ways that we expect in positive economies.

No comp change                   Comp change

Year 1 Year 2 Year 1 Year 2
1 2 1 1
2 3 2 1
3 4 3 2
4 5 4 3
5 6 5 4

Numbers in bold italics are medians.

But now look at columns 3 and especially 4. What happens there, relative to column 2, is that two people with very low incomes or earnings enter the distribution. Imagine, for example, that these two “1’s” were sitting it out on the sidelines of the labor market, but got pulled in, hoping to take advantage of the tight conditions. This shifts everybody else up that year such that median slips from 4 to 3. A comparison of the two years would suggest no change at all in incomes and earnings. In fact, the number of ft/fy women grew more than twice that of men last year (0.7 million men vs. 1.6 million women).

At any rate, I suspect something like this is going on in these data.

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