Median earnings and selection bias

Ezra Klein (link) cited a particularly revealing graphic from the Hamilton Project. And I found this via Washington's blog (link).

The gist of the story is that most reports citing median annual earnings of US workers fail to disclose a severe selection bias: the number reflects the median of full-time wage earners.

The number cited is the black line in the chart to the left.

The more realistic number is the gray line, which includes part-timers, and the unemployed.

If you want to know what's the plight of 25-64 year old (i.e. fit to work) men in the States over time, looking at the black line is like judging a fruit vendor by looking at the fruits displayed on top of the pile.

Removing part-timers and the unemployed is  naughty because those are precisely the ones who would drag down the average. This is clearly shown in the chart, where the gray line is everywhere beneath the black line.

***

The other feature of interest in this analysis is the "plummeting" of the median. The median is the mid-point of a distribution: half the men earn above that amount, and half earn below that the median earnings. It is not a number that is easy to manipulate (especially when the data have been adjusted for inflation).

If someone who's earning $25K (below median) becomes unemployed, this event has no impact on the median because earning $0 also is a below-median number. To move the number down significantly, we need big shifts from above-median to below-median.

Let's pick out 1997 when the median earnings of all men peaked at about $40,000. The median then declined over the next 10 years or so to $33,000 or so. This means that instead of 50% earning less than $40K, we now have a higher than 50% of men earning less than $40K. This keeps getting worse over time. One percentage point represents 800,000 people as there are some 80 million men between 25 and 64.

The fact that the full-time median has stayed flat implies that it's the bottom that has fallen out. (There is an additional chart cited by Klein that showed that the average full-time earnings have soared in the same period, and that is possible because the median would not move if we suddenly doubled the earnings of the top 1%; such a policy would result in a drastic increase in the average earnings.)

When the median number is changing as drastically as is portrayed here, we are looking at a crisis.

 

 

Comments

[Jonathan]

Kaiser check out some of the work by Rich Burkhauser on this. He has been discussing biases in this sort of measure for some time now.

[jrkrideau]

If someone who's earning $25K (below median) becomes unemployed, this event has no impact on the median because earning $0 also is a below-median number.

Maybe I am not getting the context here but would this not actually raise the median?
R code

df1 <- c(25,10,12,15,19,57,68,72,100,120,85)
median(df1)

df2 <- df1[-1]
median(df2)

[Jeffrey]

The median is the midpoint of the data set. Because $25k and $0 are both on the same side of the midpoint, movements from one of these levels to the other one will not affect the median.

[NB]

"The fact that the full-time median has stayed flat implies that it's the bottom that has fallen out.
...
When the median number is changing as drastically as is portrayed here, we are looking at a crisis."

That is too big of a jump. Part time male workers have a declining median wage, yes, but there could be other elements at play. As more women enter ther workforce and households more commonly have multiple incomes (starting right about where the part time decline is in the 70s) you would expect to see declines in part time wages because competition just increased for the same jobs. Now with more families relying more on multiple incomes the individual earner's income doesn't need to be as high.

Is there still a problem, yes. But this doesn't necessarily imply an income crisis, there are a lot of other labor market features that tie in here.