It seems that the US Government is adding back the question about citizenship to the US Census. The question was in the form since 1890, e.g. see #15 "Is the person naturalized?" here. In 2000 Census it was worded as follows: "Is this person a citizen of the United States?"
The media and some politicians characterize this reinstatement of the citizenship question as controversial due to the concerns that it can lead to undercounting the population. I'll try to outline the crux of the problem first. The political issue appears to be not even the absolute bias, but the relative bias across the voting districts. Presumably due to distrust of the government on part of illegal aliens, they may be inclined to not get counted in census. This may lead to undercounting the overall population in raw data in the voting regions where there is relatively large number of illegal aliens, and as a consequence these areas will be relatively less represented in the legislative bodies.
It appears that the question will be introduced upon request from agencies other than Census Bureau, but certainly Census will be tasked with design of the survey and analysis of the collected raw data. Obviously, nobody's going to use the raw data to re-district the area. So, Census will have to deliver their best estimate of the population sizes in US.
What is known about the magnitude of the bias that can be introduced into the estimate of the population when the question about citizenship is introduced into the US Census? How can this bias be corrected by US Census Bureau?
Since the question was in and out of US Census and it was also always present in American Community Surveys, there must be a wealth of data on the impact of the question, biases and ways to correct them. It is a very interesting task for a statistician. I bump into Census folks all the time on conferences and happy hours, and found them to be very dedicated and passionate about their job.
I found secretary of commerce's letter explaining rationale behind the decision to reinstate the citizenship question. The bottom line: US Census Bureau couldn't assert whether this question causes material impact on accuracy of population estimates, there is no empirical evidence of such effect. He outlines the analysis done by the Bureau in a letter. It's a very interesting read.
Citizenship question in other countries
Judging by how many peer countries have the citizenship question in their census form, there clearly is a utility in asking it. Here are some countries with citizenship questions in census surveys:
- Japan, 2010 census form, #5 "Nationality"
- question #22 in the form in a recent UK Census: "what passports do you hold?"
- German survey 2011, household form, #6: "What is (are) your citizenship(s)?"
- French survey form, question #4: "what is your nationality?"
- Canada 2016 survey, #13: "Of what country is this person a citizen?", with options "1: Canada, by birth; 2: Canada, by naturalization; 3: Other country — specify"
- Italy, 2011 form, List A, last column "Citizenship"
- Russian Census of 2010, see #6 in the form
- Ireland's census form, #10: "What is your Nationality?"
- Spain, 2011 form, in basic person information: "¿Cuál es su nacionalidad?"
- Portugal, 2011 form, #9, "Qual é a sua nacionalidade?"
- Turkey, 2007 form, "Nationality" column
- Greece, 2011 form, #7, "Ποιας χώρας είστε υπήκοος" (Which country you are a national)
- China, 2010 census form, seems to have an entirely separate questionnaire for foreigners