A U.S. Bureau of the Census study now says the citizen question is likely to harm an accurate count:
Understanding the Quality of Alternative Citizenship Data Sources for the 2020 Census
J. David Brown, Misty L. Heggeness, Suzanne M. Dorinski, Lawrence Warren, Moises Yi
This paper examines the quality of citizenship data in self-reported survey responses compared to administrative records and evaluates options for constructing an accurate count of resident U.S. citizens. Person-level discrepancies between survey-collected citizenship data and administrative records are more pervasive than previously reported in studies comparing survey and administrative data aggregates. Our results imply that survey-sourced citizenship data produce significantly lower estimates of the noncitizen share of the population than would be produced from currently available administrative records; both the survey-sourced and administrative data have shortcomings that could contribute to this difference. Our evidence is consistent with noncitizen respondents misreporting their own citizenship status and failing to report that of other household members. At the same time, currently available administrative records may miss some naturalizations and capture others with a delay. The evidence in this paper also suggests that adding a citizenship question to the 2020 Census would lead to lower self-response rates in households potentially containing noncitizens, resulting in higher fieldwork costs and a lower-quality population count.
J. David Brown & Misty L. Heggeness & Suzanne M. Dorinski & Lawrence Warren & Moises Yi, 2018. "Understanding the Quality of Alternative Citizenship Data Sources for the 2020 Census," Working Papers 18-38, Center for Economic Studies, U.S. Census Bureau.