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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?"

Political context

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.

Bias Correction

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.

Update

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:

G-7 countries:

  • 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"

Other countries:

  • 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
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closed as off-topic by usεr11852, Alexis, Sycorax, gung Mar 27 '18 at 19:01

  • This question does not appear to be about statistics within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ There are plenty of statistical studies of Census under-reporting for populations at risk like homeless and illegal migrants, using for instance capture-recapture. $\endgroup$ – Xi'an Mar 27 '18 at 15:33
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    $\begingroup$ I'd strongly suggest you ask this question again at Politics.SE (or perhaps Skeptics.SE), because ultimately this is a question about political outcomes, not statistical methodology. If your question was "How can potential undercounting be corrected in a census" then @AdamO's answer is excellent, but otherwise this discussion is missing the most relevant aspects of the circumstances. $\endgroup$ – Bryan Krause Mar 27 '18 at 17:54
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    $\begingroup$ I'm voting to close this question as off-topic because this question belongs in the Politics.SE. $\endgroup$ – usεr11852 Mar 27 '18 at 18:06
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    $\begingroup$ I'm voting to close this question as off-topic because it is speculative in nature: asking about evidence of effects from causes that have not yet happened. More context: the other countries do not have the U.S.'s specific history of institutionalize xenophobia and racism. $\endgroup$ – Alexis Mar 27 '18 at 18:09
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    $\begingroup$ I'm voting to close this question as off-topic because questions about the effects of a specific change on a specific survey are subject matter questions for the respective discipline, not statistical questions about surveys, or their analysis, more generally. This belongs somewhere other than Cross Validated. $\endgroup$ – gung Mar 27 '18 at 19:01
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In survey development, changes to instruments often have unforeseen consequences: lies, refusal to answer, and refusal to participate. My assumption given the size, funding, and talent of the US Census is that they did not make this change lightly and have planned to account for it. Conversely, I find the media's general tendency is to exaggerate issues to rouse public interest, even at the cost of not faithfully reporting the truth.

When instruments are developed, the usual process of identifying questions will involve a development cycle of 1) Holding focus groups 2) Performing pilot studies and 3) Using A/B testing. Focus groups are held with stakeholders (the people who want the data) and participants (the people who give the data) to identify reasonable questions that are not overly invasive, time consuming, or difficult to understand. Pilot studies involve administrating the instrument without the intention of calculating reliable statistics, but to determine the feasibility of the methodology. A/B testing administers the new and old (or alternate versions) of the instrument to subsets of the same population. In @Edm's comment on this post, he shows a poignant note from the Census Director(s) complaining that they have not been able to adopt this process.

The US Census uses methodology to account for sensitive questions. They oversample groups who are less likely to respond. Weighting is applied in the Horvitz-Thompson estimator to account for non-response in estimating populations. These two methods, taken together, tend to give precise and unbiased estimators. If non-response is very high, the consequence is not an undercount, but a wide margin of error.

An example of using HT estimation to eliminate non-response bias

Suppose we administer a survey in an urban and rural setting. The urban setting contains (N=500) individuals and the rural (N=50). Suppose rural participants are less likely to respond, so we oversample them at a fraction of 2:1. Altogether we take a SRS of 50 urban people and 10 rural. Suppose non-citizens refuse the citizenship question with p=0.5. If non-citizens are overrepresented in the rural setting, the design would require an even higher fraction than 2:1 to achieve comparable efficiency. Say 0% urban are non-citizen and 50% rural are non-citizen; this requires 4:1. Doing 2:1, expected counts are 0/50 in the urban sample and 2.5/7.5 with 2.5 omitted for incomplete data. This would be a biased estimate. In the urban sample, citizens were 100% likely to respond. That means that the 5/10 who said they were citizens responded with probability 1. The remainder responded with probability 0.5, so the inverse prob weight is 2. The 2.5 missing from the numerator and denominator is multiplied by 2 to make 5. The expected counts become 5/10.

This all of course relies upon being able to reliably calculate those weights.

Lastly the documentation on the US Census survey design is fantastic. Any statistician who is interested in statistical surveys should peruse.

https://www2.census.gov/programs-surveys/acs/methodology/design_and_methodology/acs_design_methodology_ch04_2014.pdf

https://www.census.gov/about/policies/quality/standards/standarda1.html

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    $\begingroup$ Although oversampling and other corrections could correct for changes in response rates, there may be an issue whether incorporating this new question, requested by the US Department of Justice (not initiated by the Census Bureau), at such a late date will allow adequate testing to make such corrections work well. Six former Census Directors have questioned the wisdom of making this late-stage change to the 2020 Census. $\endgroup$ – EdM Mar 27 '18 at 16:46
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    $\begingroup$ "My assumption given the size, funding, and talent of the US Census is that they did not make this change lightly and have planned to account for it" - this assumption misses the political motivations for the change, which did not originate with the census and which critics believe is explicitly to cause undercounting of particular parts of the population. That said, this part of the discussion probably belongs in Politics rather than Stats. $\endgroup$ – Bryan Krause Mar 27 '18 at 17:03
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    $\begingroup$ Countries like Canada and the UK/EU have had much more strict immigration policy than the United States. The US has had a strange system where legal immigration is difficult but illegal immigration has been largely tolerated. This means that there are a substantial number of undocumented immigrants living in the US, many of them for decades. Estimates of the undocumented population in the US are around 3-3.5%. The equivalent percentage for Canada is closer to <0.3%, at least a 10-fold difference. $\endgroup$ – Bryan Krause Mar 27 '18 at 17:21
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    $\begingroup$ Furthermore, undocumented immigrants in the US are highly concentrated in certain states and cities, where the percentage can be much greater than the average. Additionally, many families contain a mixture of documented immigrants or citizens with undocumented immigrants, and they may also be susceptible to under counting. $\endgroup$ – Bryan Krause Mar 27 '18 at 17:22
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    $\begingroup$ @Aksakal That doesn't solve the potential problem in any way. $\endgroup$ – Bryan Krause Mar 27 '18 at 17:49

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