I am working on refining and publicizing the Yost Index, which is a composite index incorporating information from 7 ACS tables (poverty, education, home value, income, employment, mortgage, and rent). It has been around since the early 2000s and does a good job of reducing the complexity of SES information in health studies where SES is an important confounder but not the primary focus of inquiry. It has been calculated for the nation and by state, at the block group and census tract level, and for a variety of years.
I have recently been asked me to compute the margin of error for the index. That was not the request exactly - it was more in the form of a challenge: "aren't the MOEs for your variables so massive that what you are doing is not workable?" I disagree - for many of these variables the MOEs are typically around 10-20% of the estimate. One way to respond is to compute the MOEs and let the users decide if they are massive or not. However, I am not sure the best way to do this across 7 tables. It seems that the errors would not be independent - for a given census tract, if income is underestimated, then poverty would be likely to be overestimated.
I started to put together a worked example of weird/unexpected results when applying the Census MOE formulas, but the Census beat me to it. They write:
"Users should note that this method for calculating the MOE and SE for aggregated count data is an approximation, and caution is warranted because this method does not consider the correlation or covariance between the component estimates. This method may result in an overestimate or underestimate of the derived estimate's SE depending on whether the component estimates are highly correlated in either a positive or negative direction. As a result, the approximated SE may not match the result from a direct calculation of the SE that does include a measure of covariance"
In another document, they work through some examples. Their examples show widely differing MOEs despite being relatively simple cases, far simpler than what I am trying to do.
Their first example gives three ways of calculating the SE for the number of males below poverty level in Wyoming with results ranging from 1,649-1,852 versus an actual SE of 2,012.
The second example give two ways of calculating the SE for the number of males in the US with results of 20,589 and 67,413 versus an actual SE of 16,583.
The third example gives two ways of calculating the SE for the number of people over 65 in the US with results of 45,552 and 103,620 versus an actual SE of 12,577.
So I think I have reached a dead end, and the best I can do is calculate exact MOEs from the PUMS data at the PUMA level.