Looking for ways to estimate average household sizes based on their incomes (US census data)

Question

The US census provides the population of households within a given area (say, census tract) making a certain amount of money per year (ACS T056). So if I were to be tasked to determine the population for a given census tract living inside households making between $35,000 and $40,000 a year, the best way I currently know how to estimate that would be to multiply the average household size (ACS T021) for that area by the respective number of households making $35,000 to $39,999 (T056_008).

The problem with this is that average household size probably varies with respect to that house's income. For my native state of South Carolina, in 2015 the Average Household Size value for census block groups varies between 1.2 people per household and 5 people per household with an average of 2.66. Has anyone determined a better way than just using the average household size to refine their population estimates that are based on total household numbers?

Some ideas:

• maybe I should just plug a constant estimated household size like 2.58 that represents the entire United States
• maybe I could find determine on some macro level the impact that income has on household sizes and apply multipliers to respective income segments (very apprehensive of this -- could backfire terribly)
• maybe there are some overlooked ACS columns that could help me better estimate household sizes based on income segments (my hope)
• maybe household size does not correlate with income at all, in which case I would be better off using my original method of using the local average household size column (T021) or my 2.58 people/household number.

Answer 1

Multiplying by a single number would be a fairly silly exercise, as households differ by size with income, so your estimate will likely be fairly far off the target. I would probably start by developing a cross-tabulation of income categories and household sizes for a reasonably small area (PUMA in which that tract is sitting from public use data, say), so that say 25% of HHs in that income range are 1 person, 35% are 2 persons, etc.; and then apply that table to compute the total population of interest.

Keep also in mind that income information in ACS is fairly lousy (as income information always is in the U.S., where people believe in that number being their great personal private treasure). About a quarter of that data is made-up, see https://www.census.gov/acs/www/methodology/sample-size-and-data-quality/item-allocation-rates/. This is by far the worst item, and nonresponse on it is trending up. I would definitely not care for the difference between $35K and $40K in light of this; it would be a fairly spurious, false precision if you focus on that number.

Nearly anything at the tract level will have large standard errors, especially if you have income bands of $5000 in which may be 5% to 10% of population would be falling. For a census tract of the typical size of 4,000 people, that's 400 people in the population, and probably about 20 in the sample. So your fair standard error will be a half of your estimate.

As always, a good resource to ask more detailed questions on ACS is its data community, https://acsdatacommunity.prb.org/.