ACS: How do errors in birthyr average to zero?


This is a follow-up to my recent question “Is the cutoff for age in the ACS 1st of April”. (Sorry, I don’t know how to link my two questions.) I want to use the ACS for recent years. Currently, I am trying to determine date of birth of individuals as precisely as possible. The problem with using the ACS is that it is administered throughout the year (as compared to a specific day like the census) and therefore the information on survey year, birth year and birth quarter do not uniquely determine the year of birth. However, what I don’t understand is, how errors in the calculated birth year (survey year minus age at the time of the survey) cancel out throughout the year, as it says in the IPUMS-USA data description (section “comparability”).

In my understanding, for those born in the 1st quarter, the birth year is calculated correctly whenever the survey date was after 1st of March. For those born in the 2nd quarter, the birth year is calculated correctly whenever the survey data was after 1st of July, and so on. So in my understanding, with the survey date being unknonw, the expected error in the calculated birth year is larger, the higher the quarter of birth. Also, the birth year is never underestimated but sometimes overestimated (namely for everybody whose birthday is after the survey date). All in all, I don’t see how errors averaged across the census year can be close to zero, I’d rather say the average error is clearly positive. Where is my mistake? Thank you for any thought on this!


Your reasoning is correct here. Assuming a uniform distribution of surveys and births across the year, the average error should be somewhere between zero and one. The documentation on the BIRTHYR variable isn’t very clear, but it ultimately depends on how “close to zero” is interpreted. Clearly the error won’t be zero, but it won’t be greater than 1 year either. We will adjust the wording on the comparability tab to reflect this nuance.


Thank you very much for your answers to this and to my other post, Jeff!