From Jed Kolko, chief economist at Indeed, formerly chief economist at Trulia.

Last week the Census reported large gains in median household income in two different surveys: 5.2% from the Current Population Survey’s March 2016 Annual Social and Economic Supplement (ASEC), and 3.8% from the 2015 American Community Survey (ACS). But these are slippery measures, and several thoughtful responses (here, here, and here) catalogued numerous cautions, including the limitations of these self-reported Census survey data relative to administrative data.

A particularly important concern when interpreting these income gains is whether households are changing. The share of young adults living in their parents’ homes has climbed sharply since 2005 and continues to rise, according to last week’s data release. Their earnings count toward their parents’ household income – so larger households mean higher household incomes, even if individuals’ earnings don’t change. Fortunately, the surveys released last week aren’t just about income; they’re also the definitive sources on households and living arrangements, so we can unpack the change in median household income and assess whether changing household structure had an effect.

Both the ASEC and ACS show a that the number of adults per household was essentially unchanged between 2014 and 2015. (The two surveys actually cover different time periods, but for simplicity I’m calling them 2014-to-2015 changes. See note at end.) The number of adults (18+) per household rose a slight 0.2% in the ACS and was flat in the ASEC. The increase in young adults living at home, noted above, is only part of the broader changes in living arrangements; at the same time as more young adults are living with parents, a rising share of households are single-person. Changes in household size, therefore, explain essentially none of the increase in median household income.

A different factor, however, explains some of the jump in household income. More adults were working in 2015 than in 2014. The number of workers per household increased 1.1% in the ASEC and 0.5% in the ACS: this includes all workers, regardless of how many hours per week or weeks per year they worked. The number of full-time, year-round workers per household increased more: 1.2% in the ASEC and 1.7% in the ACS.

Change, 2014-2015, in: ASEC ACS
adults (18+) per household 0.0% 0.2%
workers (all types, any age) per household 1.1% 0.5%
full-time, year-round workers (any age) per household 1.2% 1.7%
median earnings: full-time, year-round workers 2.9% 2.8%
median income: households (as published) 5.2% 3.8%

Still, the percentage increases in workers per household and full-time, year-round workers per household were smaller than the percentage increases in median household income. That suggests that even after accounting for changing in household size and changes in employment rates, earnings per worker rose. And, in fact, both surveys report that explicitly: median earnings for full-time, year-round workers rose 2.9% in the ASEC and 2.8% in the ACS.

In theory the change in median household income should be pretty close to the sum of the change in earnings per full-time, year-round workers and the change in full-time, year-round workers per household. But they’re not, in either survey. That’s because medians don’t behave as neatly as means do when you try to combine or disaggregate them; it’s also because income encompasses more than work-related earnings (e.g. investment income); and there are margins of error around all of these survey-data estimates.

Despite these caveats, consistent results emerge from the two surveys. Even with the rising share of young adults living with parents, household size was essentially unchanged and therefore does not explain the rise in median household incomes. Both employment rates (especially full-time, year-round employment) and per-worker earnings rose, and the percentage rise in earnings was larger than the percentage rise in employment. Most of the jump in median household income, therefore, appears to be rising earnings, with rising employment playing an important supporting role. The labor market improved for workers on both of these fronts: the rise in median household income is indeed good news.

Methodology notes and data sources:
ASEC: estimates for households, adult population, workers, and full-time year-round workers are based on my calculations from the microdata file and exclude group quarters. The estimate of per-worker earnings is based on the Census PINC05 files. Note that the increase in median earnings for full-time, year-round workers is higher than those for men and women separately as shown in the published report, even when averaged properly; such as the quirky properties of medians. The ASEC was conducted in March 2016, and income refers to the 2015 calendar year.

ACS: estimates for households, adult population, workers, full-time year-round workers, and per-working earnings are from Factfinder tables S2002, S2601A, B23027, and B25002. Adult population excludes group quarters; workers include adults in group quarters (not possible to separate them using the published tables). The ACS was conducted on a rolling basis through 2015, and income refers to the previous twelve months.

Here’s a longer explanation of the differences between the ASEC and the ACS, especially the time periods covered.