United States Government Accountability Office

GAO Report to the Subcommittee on 

Terrorism, Technology and Homeland 

Security, Committee on the Judiciary, 

U.S. Senate 

ESTIMATING THE 

UNDOCUMENTED 

POPULATION 

A “Grouped Answers” 

Approach to 

Surveying ForeignBorn Respondents 

September 2006 

 

GAO-06-775 
What GAO Found

United States Government Accountability Office

Why GAO Did This Study

Highlights

Accountability Integrity Reliability

September 2006

ESTIMATING THE UNDOCUMENTED 

POPULATION

A “Grouped Answers” Approach to 

Surveying Foreign-Born Respondents 

Highlights of GAO-06-775, a report to the 

Subcommittee on Terrorism, Technology 

and Homeland Security, Committee on the 

Judiciary, U.S. Senate 

As greater numbers of foreign-born 

persons enter, live, and work in the 

United States, policymakers need

more information—particularly on 

the undocumented population, its

size, characteristics, costs, and 

contributions. This report reviews 

the ongoing development of a

potential method for obtaining 

such information: the “grouped 

answers” approach. In 1998, GAO

devised the approach and 

recommended further study. In

response, the Census Bureau tested

respondent acceptance and 

recently reported results. 

GAO answers four questions. 

(1) Is the grouped answers

approach acceptable for use in a

national survey of the foreign-born? 

(2) What further research may be

needed? (3) How large a survey is 

needed? (4) Are any ongoing 

surveys appropriate for inserting a 

grouped answers question series

(to avoid the cost of a new survey)? 

For this study, GAO consulted an

independent statistician and other

experts, performed test 

calculations, obtained documents,

and interviewed officials and staff 

at federal agencies. 

The Census Bureau and DHS 

agreed with the main findings of 

this report. DHHS agreed that the 

National Survey of Drug Use and

Health is not an appropriate survey

for inserting a grouped answers 

question series. 

What GAO Recommends

The grouped answers approach is designed to ask foreign-born respondents 

about their immigration status in a personal-interview survey. Immigration 

statuses are grouped in Boxes A, B, and C on two different flash cards—with the 

undocumented status in Box B. Respondents are asked to pick the box that 

includes their current status and are told, “If it’s in Box B, we don’t want to 

know which specific category applies to you.” 

A random half of respondents are shown the card on the left of the figure (Card 

1), resulting in estimates of the percentage of the foreign-born population who 

are in each box of that card. The other half of the respondents are shown the 

card on the right, resulting in corresponding estimates for slightly different 

boxes. (No one sees both cards.) The percentage undocumented is estimated 

by subtraction: The percentage of the foreign-born who are in Box B of one card 

minus the percentage who are in Box A of the other card. 

Immigration Status Cards 1 and 2 

Student, work, 

business or tourist visa

(did not violate admi”ssion 

period limit or other conditions)

Undocumented

Do not have a currently valid, 

official document such as

an I-94 with an unexpired 

period of admission issued 

to me by the U.S. government

Refugee or asylee

(approved, not 

applicant)

TPS*, parolee, or some 

other category

Not in Box A or Box B

*Temporary Protected Status

 

Legal permanent resident

with a valid and official 

green card issued to me by 

the U.S. government

United States

citizen

Student, work, 

business or tourist visa

I am not in violation of

admission period limits

or work restrictions

Currently 

“undocumented”

Right now, I do not have 

a currently valid, legal U.S.

immigration status

Refugee or asylee

(approved, not 

applicant)

TPS*, parolee, or some 

other category

Not in Box A or Box B

*Temporary Protected Status

 

United States

citizen

Box

Box

Box

Legal permanent

resident

with a valid and official 

green card issued to me 

by the U.S. government

Sources: GAO; Corel Draw (flag and suitcase); DHS (resident alien cards). (The actual size of each card is 8-1/2" by 11.")

Student, work, 

business or tourist visa

(did not violate admission 

\period limit or other conditions)

Undocumented

Do not have a currently valid, 

official dcoument such as

an I-94 with an unexpired 

period of admission issued 

to me by the U.S. government

Refugee or asylee

(approved, not 

applicant)

TPS*, parolee, or some 

other category

Not in Box A or Box B

*Temporary Protected Status

 

United States

citizen

Legal permanent

resident

with a valid and official 

green card issued to me by 

the U.S. government

Card 1 Card 2

Student, work, 

business or tourist visa

(did not violate admission 

period limit or other conditions)

Undocumented

Do not have a currently valid, 

official document such as

an I-94 with an unexpired 

period of admission issued 

to me by the U.S. government

Refugee or asylee

(approved, not 

applicant)

Legal permanent resident

with a valid and official 

green card issued to me by 

the U.S. government

United States

citizen

Student, work, 

business or tourist visa

I am not in violation of

admission period limits

or work restrictions

Currently 

“undocumented”

Right now, I do not have 

a currently valid, legal U.S.

immigration status

Refugee or asylee

(approved, not 

applicant)

TPS*, parolee, or some 

other category

Not in Box A or Box B

*Temporary Protected Status

 

Legal permanent resident

with a valid and official 

green card issued to me 

by the U.S. government

United States

citizen

Box

Box

Box

The grouped answers approach is acceptable to many experts and immigrant 

advocates—with certain conditions, such as (for some advocates) private sector

data collection. 

Most respondents tested did not object to picking a box. Research is needed to 

assess issues such as whether respondents pick the correct box. A sizable 

survey—roughly 6,000 or more respondents—would be needed for 95 percent 

confidence and a margin of error of (plus or minus) 3 percentage points. The 

ongoing surveys that GAO identified are not appropriate for collecting data on

immigration status. (For example, one survey takes names and Social Security

numbers, which might affect acceptance of immigration status questions.) 

Whether further research or implementation in a new survey would be justified 

depends on how policymakers weigh the need for such information against 

potential costs and the uncertainties of future research.

GAO makes no new

recommendations in this report. 

www.gao.gov/cgi-bin/getrpt?GAO-06-775.

To view the full product, including the scope 

and methodology, click on the link above. 

For more information, contact Nancy R. 

Kingsbury at (202) 512-2700 or 

kingsburyn@gao.gov. 
Contents 

Letter 1

Results in Brief 5

Background 7

Experts Seem to Accept “Grouped Answers” Questions If Fielded 

by a Private Sector Organization 27 

Various Tests Are or May Be Needed 34 

Some 6,000 Foreign-Born Respondents Are Needed for 

“Reasonably Precise” Estimates of the Undocumented 40 

The Most Efficient Field Strategy Does Not Seem Feasible 45 

Observations 53

Agency Comments 56 

Appendix I Scope and Methodology 60 

Appendix II Estimating Characteristics, Costs, and 

Contributions of the Undocumented Population 64 

Appendix III A Review of Census Bureau and GAO Reports on 

the Field Test of the Grouped Answer Method 68 

Appendix IV A Brief Examination of Responses Observed while 

Testing an Indirect Method for Obtaining Sensitive 

Information 73 

Appendix V The Issue of Informed Consent 82 

Appendix VI A Note on Variances and “Mirror Image” Estimates 84 

Appendix VII Comments from the Department of Commerce 86 

Page i GAO-06-775 Estimating the Undocumented Population
Appendix VIII Comments from the Department of Homeland 

Security 89 

Appendix IX Comments from the Department of Health and Human 

Services 90 

Appendix X GAO Contact and Staff Acknowledgments 92 

Bibliography 93 

Tables 

Table 1: Approximate Number of Foreign-Born Respondents 

Needed to Estimate Percentage Undocumented within 

2, 3, or 4 Percentage Points at 90 Percent Confidence 

Level, Using Two-Card Grouped Answers Data 43 

Table 2: Approximate Number of Foreign-Born Respondents 

Needed to Estimate Percentage Undocumented, within 

 2, 3, or 4 Percentage Points, at 95 Percent Confidence 

Level, Using Two-Card Grouped Answers Data 43 

Table 3: Survey Appropriateness: Whether Surveys Meet Criteria 

Based on the Grouped Answers Design 50 

Table 4: Survey Appropriateness: Whether Surveys Meet Table 3 

(Design Based) Criteria and Additional Criteria Based on 

Immigrant Advocates’ Views 52 

Table 5: Experts GAO Consulted on Immigration Issues or 

Immigration Studies 60 

Page ii GAO-06-775 Estimating the Undocumented Population
Figures 

Figure 1: Immigration Status Card 1, Grouped Answers 8 

Figure 2: Immigration Status Card 2 11 

Figure 3: Cards 1 and 2 Compared 13 

Figure 4: SIPP Flash Card 21 

Figure 5: Training Card 1 23 

Figure 6: Training Card 2 24 

Figure 7: Immigration Status Card Tested in GSS 25 

Abbreviations 

ACS American Community Survey 

BLS Bureau of Labor Statistics 

CASI Computer Assisted Self Interview 

CPS Current Population Survey 

DHS Department of Homeland Security 

GSS General Social Survey 

HHS Department of Health and Human Services 

INS Immigration and Naturalization Service 

NAWS National Agricultural Workers Survey 

NCHS National Center for Health Statistics 

NHIS National Health Interview Survey 

NORC National Opinion Research Center 

NRC National Research Council 

NSDUH National Survey on Drug Use and Health 

NSF National Science Foundation 

OMB Office of Management and Budget 

SAMHSA Substance Abuse and Mental Health Services Administration 

SIPP Survey of Income and Program Participation 

This is a work of the U.S. government and is not subject to copyright protection in the 

United States. It may be reproduced and distributed in its entirety without further 

permission from GAO. However, because this work may contain copyrighted images or 

other material, permission from the copyright holder may be necessary if you wish to 

reproduce this material separately. 

Page iii GAO-06-775 Estimating the Undocumented Population
United States Government Accountability Office

Washington, DC 20548 

September 29, 2006 

The Honorable Jon Kyl

Chairman 

The Honorable Dianne Feinstein 

Ranking Minority Member 

Subcommittee on Terrorism, Technology 

 and Homeland Security 

Committee on the Judiciary 

United States Senate 

As greater numbers of foreign-born persons enter, live, and work in the 

United States, policymakers and the general public increasingly place high

priority on issues involving immigrants. Because separate policies, laws, 

and programs apply to different immigration statuses, valid and reliable 

information is needed for populations defined by immigration status. 

However, government statistics generally do not include such information. 

The information most difficult to obtain concerns the size, characteristics, 

costs, and contributions of the population referred to in this report as 

undocumented or currently undocumented.1

 Such information is needed 

because, for example, large numbers of undocumented persons arrive 

each year, and the Census Bureau has realized that information on the size 

of the undocumented population would help estimate the size of the total

U.S. population, especially for years between decennial censuses.2

 More 

 1

Our previous reports and those of other government agencies have sometimes used the

terms undocumented, illegal aliens, illegal immigrants, unauthorized immigrants, and 

not legally present. We use undocumented here, because this report concerns a technique

for surveying the foreign-born and an ongoing federally funded survey uses this term as a

response category when asking about legal status. We define undocumented as foreignborn persons who are illegally present in the United States. Foreign-born persons (that is, 

persons not born as U.S. citizens) were born outside the United States to parents who were

both not U.S. citizens at the time of the birth.

2

Most recently, the Census Bureau has stated that among its “enhancement priorities” to 

“improve estimates of net international migration” are efforts to research ways of 

estimating “international migrants by migrant status (legal migrants, temporary migrants, 

quasi-legal migrants, unauthorized migrants, and emigrants)” with the overall purpose of

producing annual estimates of the U.S. population. (“The U.S. Census Bureau’s Intercensal 

Population Estimates and Projections Program: Basic Underlying Principles,” paper

distributed by the Census Bureau at its conference on Population Estimates: Meeting User 

Needs, Alexandria, Virginia, July 19, 2006.) 

Page 1 GAO-06-775 Estimating the Undocumented Population
generally, information about the undocumented population—and about

changes in that population—can contribute to policy-related planning and 

evaluation efforts. 

As you know, in 1998, we devised an approach to surveying foreign-born 

respondents about their immigration status.3

 This self-report, personalinterview approach groups answers so that no respondent is ever asked 

whether he, she, or anyone else is undocumented. In fact, no individual 

respondent is ever categorized as undocumented. Logically, however, 

grouped answers data can provide indirect estimates of the undocumented 

population. Generally, grouped answers questions on immigration status 

would be asked as part of a larger survey that includes direct questions on 

demographic characteristics and employment and might include questions 

on school attendance, use of medical facilities, and so forth; some surveys 

also ask specific questions that can help estimate taxes paid. Potentially, 

combining the answers to such questions with grouped answers data can

provide further information on the characteristics, costs, and 

contributions of the undocumented population. 

We reported the first results of preliminary tests of the grouped answers 

approach, primarily with Hispanic farmworkers, in 1998 and 1999; the 

majority of the preliminary test interviews were fielded by Aguirre 

International of Burlingame, California.4

 We also recommended that the 

Immigration and Naturalization Service (INS) and the Census Bureau 

further develop and test the method. In response, the Census Bureau 

contracted for a test as part of the 2004 General Social Survey (GSS), 

which is fielded by the National Opinion Research Center (NORC) at the 

University of Chicago, with “core funding” provided by a grant from the 

 3

GAO, Immigration Statistics: Information Gaps, Quality Issues Limit Utility of Federal 

Data to Policymakers, GAO/GGD-98-164 (Washington, D.C.: July 31, 1998), and Survey

Methodology: An Innovative Technique for Estimating Sensitive Survey Items, 

GAO/GGD-00-30 (Washington, D.C.: November 1999).

4

See GAO/GGD-98-164 and GAO/GGD-00-30. 

Page 2 GAO-06-775 Estimating the Undocumented Population
National Science Foundation (NSF).5

 The Census Bureau’s analysis of the 

2004 GSS data became available in 2006. 

In this report, we respond to your request that we review the ongoing 

development of the grouped answers approach and related issues. We 

address four questions: (1) Is the grouped answers approach “acceptable”

for use in a national survey of the foreign-born population?6

 (2) What kinds 

of further research are or may be needed, based on the results of tests 

conducted thus far and expert opinion? (3) How large a survey is needed

to provide “reasonably precise” estimates of the undocumented 

population, using grouped answers data? (4) Are there appropriate 

ongoing surveys in which the grouped answers question series might 

eventually be inserted (thus avoiding the costs of fielding a new survey)? 

To answer these questions, we 

• consulted private sector experts in immigration issues and studies, 

including immigrant advocates, immigration researchers, and

others;7

 5

The GSS is a long-standing series of nationally representative personal-interview selfreport surveys, each consisting of a “core” question series and additional “modules.” The 

funding for fielding the core question series is provided by a grant from NSF. The modules

are question series added through grants from and contracts with a variety of sources. The 

Census Bureau contracted for a grouped answers module in the 2004 GSS. The bulk of the

funding for that Census–GSS contract had been provided to the Census Bureau by the 

Department of Homeland Security (DHS). This test of the grouped answers approach was

in response to our earlier recommendation in GAO/GGD-98-164. 

6

The acceptability of the grouped answers approach for use in a national survey is defined 

here primarily in terms of (1) the responses of immigrant advocates when the grouped 

answers approach is explained to them (that is, objecting versus not objecting to or

accepting the method) and (2) respondents’ tendency to pick a box when the grouped 

answers immigration status question is posed to them (rather than their refusing or saying

that they “don’t know”). The opinions of other experts—for example, those who have 

conducted studies of immigrants—are also relevant, as are interviewer judgments about 

respondent reactions. 

7

In all, we consulted over 20 private sector immigration experts (listed in appendix I, table

5). Because of the importance of immigrant advocates’ views on the issues in surveying

immigrants, table 5 identifies the experts representing immigrant advocate organizations. 

For purposes of this report, we define immigrant advocate organizations as those whose 

purpose includes representing the immigrants’ point of view. More generally, in reporting

the views of the experts we consulted, we recognize that in some cases other 

knowledgeable persons might have differing views. 

Page 3 GAO-06-775 Estimating the Undocumented Population
• consulted an independent statistical expert, Dr. Alan Zaslavsky, and 

other experts in statistics and surveys;8

• reanalyzed the data from the 2004 GSS test and subjected both our 

analysis and the Census Bureau’s analysis to review by the 

independent statistical expert; 

• performed test calculations, using specific assumptions; and 

• identified ongoing surveys that might be candidates for 

piggybacking the grouped answers question series, gathered

documents on those surveys, and met with officials and staff at the 

federal agencies that conduct or sponsor them.9

We also met with other relevant federal agencies.10 Appendix I describes 

our methodology and the scope of our work in more detail. We conducted 

our work in accordance with generally accepted government auditing 

standards between July 2005 and September 2006. 

 8

Alan Zaslavsky is Professor of Statistics, Department of Health Care Policy, Harvard

Medical School, Boston, Massachusetts. We selected Dr. Zaslavsky because he (1) is

independent with respect to the method we discuss; (2) is a noted statistician who has 

received many awards, has advised multiple executive agencies on the design and analysis 

of large-scale surveys, and serves on the National Research Council’s (NRC) Committee for 

National Statistics at the National Academy of Sciences; and (3) has developed innovative 

statistical approaches. We also sought the advice of two other noted statisticians who had 

advised us in earlier work on this method (Dr. Fritz Scheuren and Dr. Mary Grace Kovar of

NORC at the University of Chicago) and GAO colleagues with expertise in statistics. 

9

We talked with four agencies sponsoring or conducting these surveys: the Census Bureau

in the Department of Commerce, the Bureau of Labor Statistics (BLS) in the Department of

Labor, and the National Center for Health Statistics (NCHS) and the Substance Abuse and 

Mental Health Services Administration (SAMHSA) in the Department of Health and Human 

Services (HHS). Survey-related staff at these agencies provided information on the specific 

surveys. Additionally, we deemed some staff at these agencies to be experts in statistics 

and survey research. 

10These included the Statistical and Science Policy Branch of the Office of Information and 

Regulatory Affairs in the Office of Management and Budget (OMB), the Employment and 

Training Administration in the Department of Labor (DOL), and the Office of Immigration 

Statistics within the Policy Directorate and the Research and Evaluation Division, Office of 

Policy and Strategy, U.S. Citizenship and Immigration Services in the Department of

Homeland Security (DHS). 

Page 4 GAO-06-775 Estimating the Undocumented Population
Acceptance of the grouped answers approach appears to be high among 

immigrant advocates and respondents. The advocates we interviewed 

generally accepted the approach—with provisos such as fielding by a 

university or other private sector organization, appropriate data protection 

(including protections against government misuse), and high-quality 

survey procedures. The independent statistician, reviewing the Census 

Bureau’s analysis and our reanalysis of the 2004 GSS test of respondent 

acceptance, concluded that the grouped answers approach is “generally

usable” for surveys interviewing foreign-born respondents in their homes.11

Results in Brief 

Based on the results of the GSS test and on consultations and interviews 

with varied experts, further work is or may be needed to 

• Expand knowledge about respondent acceptance. For example, 

the 2004 GSS test did not cover persons who are “linguistically 

isolated” in the sense that no member of their household age 14 or 

older speaks English “very well”.12 

• Test the accuracy of responses or respondents’ intent to answer 

accurately.13 To date, no tests of response accuracy, or the intent to 

answer accurately, have been conducted, although a number of 

relevant designs can be identified. 

Thousands of foreign-born respondents would be needed to obtain 

“reasonably precise” grouped answers estimates of the undocumented 

 11Our reanalysis differed from the Census Bureau’s in that we eliminated 19 GSS cases that 

we deemed ineligible because, for example, interviewing took place over the telephone

rather than in person, as required by the grouped answers approach; we found that 6 

respondents of more than 200 failed to provide usable, specific answers. 

12The GSS allowed bilingual household members to help respondents with limited English 

skills. Our earlier testing with farmworkers was conducted in Spanish, but no testing has 

covered linguistically isolated non-Hispanic respondents. About 4 percent of the foreignborn population both (1) does not speak Spanish and (2) is linguistically isolated (that is, 

is part of a household in which no member age 14 or older speaks English “very well”).

Although this may seem a small percentage, it is possible that non-Hispanic undocumented 

persons are concentrated in this group. 

13The distinction between accurate responses and the intent to answer accurately is 

necessary because some respondents may mistakenly think that they are, for example, in 

a legal status. 

Page 5 GAO-06-775 Estimating the Undocumented Population
population.14 Our calculations and work with statisticians showed that 

while many factors are involved and it is not possible to guarantee a 

specific level of precision, roughly 6,000 interviews would be likely to be

sufficient to support estimates of the size of the undocumented population

and major subgroups within it (especially high-risk subgroups, defined by 

characteristics such as age 18 to 40, recently arrived, employed15). 

Quantitative estimates are also possible; for example, major program costs 

associated with the undocumented population may also be estimated, 

given appropriate program data. 

None of the ongoing, large-scale national surveys we identified appear to 

be appropriate for piggybacking the grouped answers question series. One 

self-report personal interview survey is fielded by a private sector 

organization (under a contract with a Department of Health and Human 

Services (HHS) agency); however, that survey focuses on the use of illegal 

drugs, and we believe that direct questions on drug use might heighten the 

sensitivity of the questions on immigration status. We believe other 

ongoing surveys to be inappropriate; for example, one asks other sensitive

questions (on HIV status) and takes respondents’ names and Social 

Security numbers. Additionally, the Census Bureau fields these surveys. 

Whether further research or a new survey would be justified depends on 

issues such as how policymakers weigh the need for such information 

against potential costs. 

We received comments on a draft of this report from the Department of 

Commerce (Census Bureau), the Department of Homeland Security 

(DHS), and the Department of Health and Human Services (DHHS). The 

Census Bureau and DHS generally agreed with the main findings of the 

report, and DHHS agreed that the National Survey of Drug Use and Health

would not be appropriate for “piggy-backing” the grouped answers 

question series. These agencies also provided other technical comments 

(see appendices VII, VIII, and IX). 

 14We define “reasonably precise” as a 90 percent or 95 percent confidence interval spanning

plus or minus 2 to 4 percentage points. A 90 percent or 95 percent confidence interval is the 

interval within which the parameter in question would be expected to fall 90 percent or 95

percent of the time, if the sampling and interval estimation procedures were repeated in an

infinite number of trials. 

15In many cases, the method would not be suitable for low-risk subgroups. (High-risk and 

low-risk refer to subgroups with above-average and below-average percentages of 

undocumented persons, respectively.) 

Page 6 GAO-06-775 Estimating the Undocumented Population
Survey questions about sensitive topics carry a “threat” for some 

respondents, because they fear that a truthful answer could result in some 

degree of negative consequence (at a minimum, social disapproval). The 

grouped answers approach is designed to reduce this threat when asking 

about immigration status. 

Background 

Grouped Answers Reduce 

“Question Threat” and 

Allow Indirect Estimates 

of the Undocumented 

Three key points about the grouped answers approach are that 

1. no respondent is ever asked whether he or she, or anyone else, is 

undocumented; 

2. two pieces of information are separately provided by two subsamples 

of respondents (completely different people—no one is shown both 

immigration status cards); and 

3. taking the two pieces of information together—like two different 

pieces of a puzzle—allows indirect estimation of the undocumented 

population, but no individual respondent (and no piece of data on an 

individual respondent) is ever categorized as undocumented.

We discuss each point in some detail.16 

1. No respondent is ever asked whether he or she is in the

undocumented category. Unlike questions that ask respondents to 

choose among specific answer categories, the grouped answers approach 

combines answer categories in sets or “boxes,” as shown in figure 1. 

 16The grouped answers approach derives from (1) the residual method described by Henry 

S. Schryock and Jacob S. Siegel and Associates, The Methods and Materials of 

Demography (Washington, D.C.: U.S. Government Printing Office, 1980), and Robert

Warren and Jeffrey S. Passel, “A Count of the Uncountable: Estimates of Undocumented 

Aliens Counted in the 1980 Census,” Demography, 24:3 (1987): 375–93, and (2) earlier 

indirect survey-based techniques, such as “randomized response” (see Stanley Warner, “A 

Survey Technique for Eliminating Evasive Answer Bias,” Journal of the American 

Statistical Association, 60 (1965): 63–69, and Bernard Greenberg and others, “The

Unrelated Questions Randomized Response Model: Theoretical Framework,” Journal of 

the American Statistical Association, 64 (1969): 520–39. 

Page 7 GAO-06-775 Estimating the Undocumented Population
Figure 1: Immigration Status Card 1, Grouped Answers 

Student, work, 

business or tourist visa

I am not in violation of

admission period limits

or work restrictions

Currently 

“undocumented”

Right now, I do not have 

a currently valid, legal U. S. 

immigration status

Refugee or asylee

(approved, not 

applicant)

TPS*, parolee, or some 

other category

Not in Box A or Box B

*Temporary Protected Status

 

United States

citizen

Legal permanent

resident

with a valid and official 

green card issued to me 

by the U.S. government

Sources: GAO; Corel Draw (flag and suitcase); DHS (resident alien cards). (The actual size of the card is 8-1/2" by 11.")

Page 8 GAO-06-775 Estimating the Undocumented Population
Box B includes the sensitive answer category-—currently 

“undocumented”—along with other categories that are nonsensitive.17 

Each respondent is asked to “pick the Box”—Box A, Box B, or Box C—

that contains the specific answer category that applies to him or her. 

Respondents are told, in effect: If the specific category that applies to you 

is in Box B, we don’t want to know which one it is, because right now we 

are focusing on Box A categories.18 

By using the boxes, the interview avoids “zeroing in” on the sensitive 

answer. The specific categories shown in the boxes in figure 1 are grouped 

so that 

• one would expect many respondents who are here legally, as well 

as those who are undocumented, to choose Box B,19 and 

• there is virtually no possibility of anyone deducing which specific 

category within Box B applies to any individual respondent. 

2. Two pieces of information are provided separately by two 

subsamples of respondents (no one is shown both immigration 

status cards). Respondents are divided into two subsamples, based on 

randomization procedures or rotation (alternation) procedures conducted 

outside the interview process. (For example, a rotation procedure might 

specify that within an interviewing area, every other household will be 

designated as subsample 1 or subsample 2.) 

 17Note that Box B in figure 1 uses the term currently “undocumented”—with quotation 

marks around undocumented. We believe this wording may help communicate with 

undocumented respondents who either (1) had a legal status in the past (for example, 

entered with a temporary visa but have now overstayed and thus lost their legal status) or

(2) are likely to acquire a legal status in the near future (for example, entered illegally and 

applied for legal status but have not yet received it). Potentially, the quotation marks might 

help communicate with respondents who have some kind of document (for example, a

“matricula card” issued by the Mexican government) but who do not have a valid legal 

immigration status that allows U.S. residence. 

18In the test with Hispanic farmworkers, interviewers explained: “Because we’re using the

boxes—we WON’T ‘zero in’ on anything somebody might not want to tell us.”

19In future, changes in percentages of foreign-born in various statuses might warrant 

changes in groupings across the boxes. Additionally, the specific legal statuses defined by

law might change, requiring a change in the legal statuses shown on the cards. 

Page 9 GAO-06-775 Estimating the Undocumented Population
This “split sample” procedure has been used routinely for many surveys 

over the years. As applied to the grouped answers approach, the two 

subsamples are shown alternative flash cards. Immigration Status Card 1, 

described above, represents one way to group immigration statuses in 

three boxes. A second immigration status flash card (Immigration Status

Card 2, shown in figure 2) groups the same statuses differently. 

Page 10 GAO-06-775 Estimating the Undocumented Population
Figure 2: Immigration Status Card 2 

Sources: GAO; Corel Draw (flag and suitcase); DHS (resident alien cards). (The actual size of the card is 8-1/2" by 11.")

Student, work, 

business or tourist visa

I am not in violation of

admission period limits

or work restrictions

Currently 

“undocumented”

Right now, I do not have 

a currently valid, legal U. S. 

immigration status

Refugee or asylee

(approved, not 

applicant)

TPS*, parolee, or some 

other category

Not in Box A or Box B

*Temporary Protected Status

 

Legal permanent resident

with a valid and official 

green card issued to me 

by the U.S. government

United States

citizen

The alternative immigration-status cards can be thought of as “mirror 

images” in that 

• the two nonsensitive legal statuses in Box A of Card 1 appear in Box 

B of Card 2 and 

• the two nonsensitive legal statuses in Box B of Card 1 appear in Box 

A of Card 2. 

However, the undocumented status always appears in Box B. 

Page 11 GAO-06-775 Estimating the Undocumented Population
Interviewers ask survey respondents in subsample 1 about immigration 

status with respect to Card 1. They ask survey respondents in subsample 

2 (completely different persons) about immigration status with respect to

Card 2. Each respondent is shown one and only one immigration-status 

flash card. There are no highly unusual or complicated interviewing 

procedures.20

Because the two subsamples of respondents are drawn randomly or by 

rotation, each subsample represents the foreign-born population and, if 

sufficiently large, can provide “reasonably precise” estimates of the 

percentages of the foreign-born population in the boxes on one of the 

alternative cards. 

Incidentally, a respondent picking a box that does not include the sensitive 

answer—for example, a respondent picking Box A or Box C in figure 1—

can be asked follow-up questions that pinpoint the specific answer 

category that applies to him or her. Thus, direct information is obtained on 

all legal immigration statuses. The data on some of the legal categories can 

be compared to administrative data to check the reasonableness of 

responses. Additionally, these data provide estimates of legal statuses, 

which are useful when, for example, policymakers review legislation on 

the numbers of foreign-born persons who may be admitted to this country 

under specific legal status programs. 

3. No individual respondent is ever categorized as undocumented, 

but indirect estimates of the undocumented population can be

made. Using two slightly different pieces of information provided by the

two different subsamples allows indirect estimation of the size of the 

currently undocumented population—by simple subtraction. 

The only difference between Box B of Card 1 and Box A of Card 2 is the 

inclusion of the currently “undocumented” category in Box B of Card 1. 

Figure 3 shows both cards together for easy comparison. 

 20Unlike some other indirect estimation techniques, the grouped answers approach does

not require unusual stratagems as part of the survey interview, such as asking respondents

to make a secret random selection of a question. 

Page 12 GAO-06-775 Estimating the Undocumented Population
Figure 3: Cards 1 and 2 Compared

Student, work, 

business or tourist visa

I am not in violation of

admission period limits

or work restrictions

United States

citizen

Currently 

“undocumented”

Right now, I do not have 

a currently valid, legal U.S.

immigration status

Refugee or asylee

(approved, not 

applicant)

Legal permanent

resident

with a valid and official 

green card issued to me 

by the U.S. government

TPS*, parolee, or some 

other category

Not in Box A or Box B

*Temporary Protected Status

 

TPS*, parolee, or some 

other category

Not in Box A or Box B

*Temporary Protected Status

 

Refugee or asylee

(approved, not 

applicant)

Legal permanent resident

with a valid and official 

green card issued to me 

by the U.S. government

Student, work, 

business or tourist visa

I am not in violation of

admission period limits

or work restrictions

Currently 

“undocumented”

Right now, I do not have 

a currently valid, legal U.S.

immigration status

United States

citizen

Subsample 1, Card 1 Subsample 2, Card 2

Sources: GAO; Corel Draw (flag and suitcase); DHS (resident alien cards). (The actual size of each card is 8-1/2" by 11.")

Thus, the percentage of the foreign-born population who are currently 

undocumented can be estimated as follows: 

• Start with the percentage of subsample 1 respondents who report 

that they are in Box B of Card 1 (hypothetical figure: 62 percent of 

subsample 1). 

Page 13 GAO-06-775 Estimating the Undocumented Population
• Subtract from this the percentage of subsample 2 who say they are 

in Box A on Card 2 (hypothetical figure: 33 percent of subsample 2). 

 

• Observe the difference (29 percent, based on the hypothetical 

figures); this represents an estimate of the percentage of the 

foreign-born population who are undocumented.

Alternatively, a “mirror-image” estimate could be calculated, using Box B 

of Card 2 and Box A of Card 1.21 

To estimate the numerical size of the undocumented population, a 

grouped answers estimate of the percentage of the foreign-born who are 

undocumented would be combined with a census figure. For example, the 

2000 census counted 31 million foreign-born, and the Census Bureau 

issued an updated estimate of 35.7 million for 2005. The procedure would 

be to simply multiply the percent undocumented (based on the grouped 

answers data and the subtraction procedure) by a census count or an 

updated estimate for the year in question. 

These procedures ensure that no respondents—and no data on any 

specific respondent—are ever separated out or categorized as 

undocumented, not even during the analytic process of making indirect, 

group-level estimates. 

To further ensure reduction of “question threat,” the grouped answers 

question series begins with flash cards that ask about nonsensitive topics 

and familiarize respondents with the 3-box approach. For each 

nonsensitive-topic card, interviewers ask the respondent which box 

applies to him or her, saying: If it’s Box B, we do not want to know which 

specific category applies to you. 

In this way, most respondents should understand the grouped answers 

approach before seeing the immigration-status card. 

 21The result of the subtraction would be the same, either way—assuming that the same 

percentage of subsample 1 and subsample 2 chose Box C.

Page 14 GAO-06-775 Estimating the Undocumented Population
To help ensure accurate responses, respondents who choose Box A can be

asked a series of clarifying questions.

22 (No follow-up questions are 

addressed to anyone choosing Box B.) The questions for Box A 

respondents are designed to prompt them to, essentially, reclassify 

themselves in Box B, if that is appropriate.23

The grouped answers question series can potentially be applied in a largescale general population survey, where the questions on immigration 

status would be added for the foreign-born respondents—provided that an 

appropriate survey can be identified. If a new survey of the general 

foreign-born population were planned, it would involve selecting a general 

sample of households and then screening out the households that do not

include one or more foreign-born persons. 

Finally, we note that while the initial version of the grouped answers 

approach involved three alternative flash cards (and was termed the 

“three-card method”), we recently devised the version described here, 

which uses two cards rather than three. The two-card method is simpler, is 

easier to understand, and provides more precise estimates. All cards are

alike in that they feature three boxes in which specific answer categories 

are grouped.

Characteristics, Costs, and 

Contributions Can 

Potentially Be Estimated 

Generally, grouped answers questions on immigration status would be 

asked as part of a larger survey that includes direct questions on 

demographic characteristics and employment and might include questions 

on school attendance, use of medical facilities, and so forth; some surveys 

also ask specific questions that can help estimate taxes paid. Potentially, 

combining the answers to such questions with grouped answers data can

be used to provide further information on the characteristics, costs, and 

contributions of the undocumented population. 

 22For example, in the test with Hispanic farmworkers, respondents who picked Box A and 

said they were legal permanent residents (they had a green card) were asked (1) under 

which program they had applied for a green card (Family Unity, employer, and so forth), 

(2) whether they had received the card (or had applied but not yet received it), (3) how 

they received it (in person or by mail), and (4) whether they had then applied for U.S. 

citizenship—and if so, whether they had received citizenship. 

23If a respondent decides to reclassify himself or herself in Box B, on the basis of follow-up 

questions, survey procedures can record only the Box B classification—and delete the 

original Box A classification, as well as any answers to Box A follow-up questions. This

prevents retention of any detailed immigration-status material on respondents in Box B.

Page 15 GAO-06-775 Estimating the Undocumented Population
For example, the numbers of undocumented persons in major subgroups 

—such as demographic or employment status subgroups—can be 

estimated, provided that the sample of foreign-born persons interviewed is 

sufficiently large. 

Grouped answers data collected from adult respondents can also be used

to estimate the number of children in various immigration statuses, 

including undocumented—provided that an additional question is asked.24

Additionally, when combined with separate quantitative data (for example, 

data on program costs per individual), grouped answers data can be used 

to estimate quantitative information (such as program costs) for the 

undocumented population as a whole—or, again, depending on sample 

size, for specific subgroups. 

The procedures for deriving these more complex indirect estimates are 

described in appendix II. No grouped answers respondent is ever 

categorized as undocumented. 

Statistical Information Is 

Needed on the 

Undocumented Population 

The foreign-born population of the United States is large and growing— 

as is the undocumented population within it. Congressional policymakers, 

the U.S. Commission on Immigration Reform, and the National Research 

Council’s (NRC) Committee on National Statistics have indicated a need 

for statistical information on the undocumented population, including its 

size, characteristics, costs, and contributions. 

The Census Bureau estimates that as of 2005, foreign-born residents (both 

legally present and undocumented) numbered 35.7 million and accounted

for at least one-tenth of all persons residing in each of 15 states and the 

District of Columbia.25 These figures represent substantial increases over 

the prior 15 years. For example, in 1990 the foreign-born population 

totaled fewer than 20 million; only 3 states had a population more than 

 24The additional question would ask for the number of foreign-born children in the

household who are in each box of the same immigration status card that the adult 

respondent used to report which box he or she is in. However, this questioning approach

has not been tested. 

25The 15 states and their percentages of foreign-born residents in 2005 were Arizona, 14.5; 

California, 27.2; Colorado, 10.1; Connecticut, 12.5; Florida, 18.5; Hawaii, 17.2; Illinois, 13.6; 

Maryland, 11.7; Massachusetts, 14.4; Nevada, 17.4; New Jersey, 19.5; New York, 21.4; 

Rhode Island, 12.6; Texas, 15.9; Washington, 12.2. The percentage in the District of 

Columbia was 13.1.

Page 16 GAO-06-775 Estimating the Undocumented Population
one-tenth foreign-born. One result is that as the Department of Labor has

testified, foreign-born workers now constitute almost 15 percent of the 

U.S. labor force, and the numbers of such workers are growing.26

A new paper from the Department of Homeland Security (DHS) puts the 

“unauthorized” immigrant population at 10.5 million as of January 2005 

and indicates that if recent trends continued, the figure for January 2006 

would be 11 million.27 The Pew Hispanic Center’s indirect estimate of the

undocumented population as of 2006 is 11.5 million to 12 million. These 

estimates represent roughly one-third of the entire foreign-born 

population.28 DHS has variously estimated the size of the undocumented 

population as of January 2000 as 7 million and 8.5 million.

29 Government 

and other estimates for 1990 numbered only 3.5 million.30 

These various indirect estimates of the undocumented population are 

based on the “residual method.” Residual estimation (1) starts with a 

census count or survey estimate of the number of foreign-born residents 

who have not become U.S. citizens and (2) subtracts out estimated 

numbers of legally present individuals in various categories, based on 

administrative data and assumptions (because censuses and surveys do 

not ask about legal status). The remainder, or residual, represents an 

indirect estimate of the size of the undocumented population. 

To illustrate the role of administrative data and assumptions, residual 

estimates draw on counts of the number of new green cards issued each

 26Statement of Ronald Bird, Chief Economist, Office of the Assistant Secretary for Policy, 

U.S. Department of Labor, before the Committee on the Judiciary, U.S. Senate, July 5, 2006. 

27Michael Hoefer, Nancy Rytina, and Christopher Campbell, Estimates of the Unauthorized 

Immigrant Population Residing in the United States: January 2005 (Washington, D.C.:

Department of Homeland Security, Office of Immigration Statistics, August 2006). 

28Jeffrey S. Passel, "The Size and Characteristics of the Unauthorized Migrant Population in

the U.S.: Estimates Based on the March 2005 Current Population Survey,” Research Report

(Washington, D.C.: Pew Hispanic Center, Mar. 7, 2006). 

29The first figure is from U.S. Immigration and Naturalization Service, Office of Policy and 

Planning, Estimates of the Unauthorized Immigrant Population Residing in the United 

States: 1990 to 2000 (Washington, D.C.: January 2003); the second is from Hoefer, Rytina,

and Campbell. 

30While different estimates are based on different definitions of undocumented, and there

are questions about data reliability, it seems clear that the population of undocumented 

foreign-born persons is large and has increased rapidly. 

Page 17 GAO-06-775 Estimating the Undocumented Population
year. But they also require assumptions to account for emigration and 

deaths among those who received green cards in earlier years. 

A recent DHS paper providing residual estimates of the undocumented 

population includes ranges of estimates based on alternative assumptions 

made for two key components.31 For example, “by lowering or raising the 

emigration rates 20 percent . . . the estimated unauthorized immigrant 

population would range from 10.0 million to 11.0 million.”32 The DHS paper

also lists assumptions that were not subjected to alternative specifications. 

We believe the DHS paper represents an advance because, up to now, 

analysts producing residual estimates have generally not made public 

statements regarding the precision of the estimates. (Some critics have,

however, indicated that residual estimates are likely to lack precision.33) 

While the residual approach has been used to profile the undocumented 

population on two characteristics—age and country of birth—it is limited

with respect to estimating (1) current geographic location and (2) current 

employment and benefit use. The reason is that current characteristics of 

legally present persons are not maintained in administrative records; 

analysts must therefore rely largely on assumptions .

34 In contrast, the 

grouped answers method does allow for the possibility of estimating 

current characteristics based on current self-reports. 

During the mid-1990s, the U.S. Commission on Immigration Reform 

determined that better statistical “information on legal status and type of 

immigrant [is] crucial” to assessing immigration policy. Indeed, the 

 31The alternative assumptions were made for levels of (1) American Community Survey 

(ACS) undercounting of “unauthorized” immigrants and (2) emigration from the United 

States on the part of legal immigrants counted as having been “admitted” between 1980 and 

2004. 

32Hoefer, Rytina, and Campbell, p. 6.

33See Kenneth Hill, “Estimates of Legal and Unauthorized Foreign-Born Population for the

United States and Selected States Based on Census 2000,” presentation at the U.S. Census 

Bureau Conference, Immigration Statistics: Methodology and Data Quality, Alexandria, 

Virginia, February 13–14, 2006. A similar point was made by Jacob S. Siegel and David A.

Swanson, The Methods and Materials of Demography, 2nd ed. (San Diego, Calif.: Elsevier 

Academic Press, 2004), p. 479.

34Administrative records on where legal immigrants live are based on their residence (or

intended residence) at the time when legal permanent resident status was attained; these 

records have not been subsequently updated. There are no administrative records on

current activities of legal permanent residents, such as employment.

Page 18 GAO-06-775 Estimating the Undocumented Population
Commission called for a variety of improvements in estimates of the costs 

and benefits associated with undocumented immigration.35 NRC’s 

Committee on National Statistics further emphasized the need for better 

information on costs, especially state and local costs.36 (If successfully 

fielded, the grouped answers method might help provide general 

information on such costs—and, potentially, specific information for large 

states such as California. Sample size limitations would be likely to 

prohibit separate analyses for specific local areas, small states, and states

with low percentages of foreign-born or undocumented.) 

Over the years, we have received numerous congressional requests related

to estimating costs associated with the undocumented population.37

Recent Census Bureau research and conferences reflect the realization 

that undocumented immigration is a key component of current population 

growth and that there is a resultant need for information on this group.38

Additionally, some of the immigrant advocates we interviewed expressed 

an interest in being able to better describe the contributions of the 

undocumented population. 

Surveys Are a Key 

Information Source 

Various national surveys ask foreign-born respondents to provide 

information about themselves and, in some cases, other persons in their 

households. While such surveys provide a wealth of information on a wide

variety of areas, including some sensitive topics, national surveys 

generally do not ask about current immigration status—with the exception 

of a question on U.S. citizenship, which is included in several surveys. 

 35See U.S. Commission on Immigration Reform, U.S. Immigration Policy: Restoring 

Credibility: 1994 Report to Congress (Washington, D.C.: U.S. Government Printing Office, 

1994), pp. 179–86. 

36NRC, Committee on National Statistics, Local Fiscal Effects of Illegal Immigration: 

Report of a Workshop (Washington, D.C.: National Academy Press, 1996), p. 1-2. 

37See, for example, GAO, Illegal Alien Schoolchildren: Issues in Estimating State-by-State 

Costs, GAO-04-733 (Washington, D.C.: June 23, 2004), and Undocumented Aliens: 

Questions Persist about Their Impact on Hospitals’ Uncompensated Care Costs, 

GAO-04-472 (Washington, D.C.: May 21, 2004). For a more general discussion, see 

GAO/GGD-98-164, ch. 2, “Policy-Related Information Needs.” 

38Census Bureau staff told us that this research includes J. Gregory Robinson, 

“Memorandum for Donna Kostanich,” DSSD A.C.E. Revision II Memorandum Series No.

PP-36, U.S. Bureau of the Census, Washington, D.C., December 31, 2002. 

Page 19 GAO-06-775 Estimating the Undocumented Population
As we reported earlier, it is believed that direct questions on immigration 

status “are very sensitive, and negative reactions to them could affect the 

accuracy of responses to other questions on [a] survey.”39 Two surveys that 

have asked respondents directly about immigration status for several 

years are 

• the National Agricultural Workers Survey (NAWS), an ongoing annual

cross-sectional self-report survey of farmworkers, fielded by Aguirre 

International, a private sector firm under contract to the Department of 

Labor, since 1988,40 and 

• the Survey of Income and Program Participation (SIPP), a longitudinal 

panel survey of the general population, conducted by the Census Bureau, 

which has asked immigration status questions since 1996. 

Of the two, SIPP is the more relevant, because its immigration status 

questions have been administered to a sample of the general foreign-born 

population. 

SIPP has asked an adult respondent-informant from each household to 

provide information about himself or herself and about others in his or her 

household, including which immigration-status category applied to each 

person when he or she came to this country. Answers are facilitated by a 

flash card that lists major legal immigration statuses (see fig. 4).41 A further 

question asks whether each person obtained a green card after arriving in

this country. The SIPP questions come close to asking about—but do not 

actually allow an estimate of—the number of foreign-born U.S. residents 

 39GAO/GGD-98-164, p. 3. 

40While NAWS data collections are fielded annually, results are generally reported every 

other year. See U.S. Department of Labor, Findings from the National Agricultural 

Workers Survey (NAWS) 2000–2002: A Demographic and Employment Profile of United

States Farm Workers. Research Report 9 (Washington, D.C.: March 2005). 

41The SIPP flash card has neither an undocumented category nor an “other status not

listed” category. However, persons reported to have an immigration status not on the SIPP 

card—which would logically include undocumented persons as well as a small number of

persons in various minor legal immigration categories—are tallied separately. 

Page 20 GAO-06-775 Estimating the Undocumented Population
who are currently undocumented.42 According to the Census Bureau, SIPP 

is now scheduled to be “reengineered,” but the full outlines of the revised 

effort have not been set.

Figure 4: SIPP Flash Card

Source: U.S. Bureau of the Census. (The actual size of the card is 8-1/2" by 11.")

CARD U

IMMIGRATION STATUS AT TIME OF ENTRY

1 – Immediate relative or family-sponsored

 permanent resident

2 – Employment-based permanent resident

3 – Other permanent resident

4 – Granted refugee status or granted asylum

5 – Non-immigrant (e.g., diplomatic, student,

business, or tourist visa)

SIPP-24204 (1-16-2004)

U

 42Although NAWS and SIPP have received OMB clearance (under the Paperwork Reduction

Act), and although no special field problems have emerged, it is difficult to say whether 

field problems might arise in future. Reasons include question-threat and related problems 

depending, in part, on contextual factors, such as current levels of immigration 

enforcement in the nonborder areas of the United States, and the perceived relevance of 

the question to the survey. 

Page 21 GAO-06-775 Estimating the Undocumented Population
In the middle to late 1990s, the grouped answers question series was 

subjected to preliminary development and testing with Hispanic 

respondents, including interviews with farmworkers conducted by Aguirre 

International, under contract to GAO.43 In these tests, every respondent 

picked a box.44 However, these interviews were not conducted under 

conditions of a typical large-scale survey in which interviewers initiate 

contact with respondents in their homes.45

To further test respondents’ acceptance of the grouped answers approach, 

the Census Bureau created a question module with 3-box flash cards and 

contracted for it to be added to the 2004 GSS. When presenting the survey

to respondents, interviewers explained that NORC of the University of 

Chicago fielded the GSS survey, with “core funding” from an NSF grant.46

The Census Bureau’s question module included cards from the three-card 

version of the grouped answers approach—which features only one 

immigration status category in Box A. The cards used were 

The Grouped Answers 

Approach Has Been Tested 

in Surveys Fielded by 

Private Sector 

Organizations 

• the two training cards shown in figures 5 and 647 and 

• the immigration status card shown in figure 7.48 

 43The contract specified that Aguirre would provide GAO data on actual responses that had 

been “stripped of person-identifiers and related information.”

44Additionally, GAO conducted cognitive interviews focused on testing the appropriateness 

of the icons used on the cards (see GAO/GGD-00-30, pp. 44-45). Cognitive interviewing 

focuses on the mental processes of the respondent while he or she is answering a survey 

question. The goals are to find out what each respondent thinks the question is asking, 

what the specific words or phrases (or icons on a card) mean to him or her, and how he or

she formulates an answer. Typically, cognitive interviewing is an iterative process in which 

the findings or problems identified in each set of interviews are used to modify the 

questions to be tested in the next set of interviews. 

45GAO/GGD-98-164 and GAO/GGD-00-30. 

46The GSS consists of a “core” question series and additional “modules.” The funding for

fielding the core question series is provided by a grant from NSF. The modules are question 

series added through a variety of grants and contracts. 

47An expert reviewer of a draft of this report noted that the housing types on the training

card shown in figure 5 are not all mutually exclusive; that is, a single family house can be 

located on a farm. 

48These cards were initially subjected to 1997–98 developmental tests conducted with more 

than 100 Hispanic immigrants who were farmworkers or in other situations such as

applying for aid at a legal clinic specializing in immigration cases—such that a fair number 

of those interviewed seemed relatively likely to be undocumented. See GAO/GGD-00-30 

and GAO/GGD-98-164. 

Page 22 GAO-06-775 Estimating the Undocumented Population
Figure 5: Training Card 1 

B

C

A

Other type of dwelling 

(specify)

Farm

Single-family

house

Hut, shack

or other

nonstandard

dwelling

Apartment

building

Sources: GAO; Dominican Republic (illustrations). (The actual size of the card is 8-1/2” by 11.”)

Page 23 GAO-06-775 Estimating the Undocumented Population
Figure 6: Training Card 2 

B

C

A

Other type of

transportation

Boat

Train

Walking

car, truck, or 

bus 

Airplane

Source: GAO. (The actual size of the card is 8-1/2” by 11.”)

Page 24 GAO-06-775 Estimating the Undocumented Population
Figure 7: Immigration Status Card Tested in GSS 

Training card 1 shows different types of houses arranged in three boxes. 

Respondents are asked to indicate the type of house they lived in when in

their home country—by picking a box. They are told that if the answer is 

in Box B, we don’t need to know which specific type applies to them, 

because right now we are focusing on Box A. 

Training card 2 shows different modes of transportation, again arranged in

three boxes. Respondents are asked to indicate the mode of transportation 

they used the most recent time they traveled from their home country to 

Sources: GAO; Corel Draw (flag and suitcase); DHS (resident alien cards). (The actual size of the card is 8-1/2" by 11.")

Student, work, or 

tourist visa

Undocumented

I do not have my own valid

official green card

Refugee or asylee

Without a green card

Some other category

Not in Box A or Box B

 

Legal permanent resident

With a valid and official green 

card issued to me by the 

U.S. government

United States

citizen

Page 25 GAO-06-775 Estimating the Undocumented Population
the United States—again by picking a box. They are again told that if it’s in

Box B, we don’t need to know which specific mode applies. 

Additionally, the GSS–Census Bureau module asked interviewers to 

(1) judge respondents’ understanding of the 3-box format, (2) observe 

whether respondents objected or “kept silent for a while” when presented 

with the immigration status card, and (3) record any comments that 

respondents made about the cards. As the Census Bureau has noted, the 

module was a partial test because only one immigration status card was 

tested. 

Data and documentation from this field test became available in late 2005.

A Census Bureau analysis of these data (completed in 2006 and 

reproduced in full in appendix IV), indicates that of 237 foreign-born 

respondents, 216 (roughly 90 percent) chose a box, 4 gave other answers, 

and 17 refused or said “don’t know.” The Census Bureau took this “as an 

indication that most foreign-born who are asked about their migrant status 

in this format would understand the question, know the answer, and 

answer willingly.” 

Further, the Census Bureau paper stated that 

• the “overwhelming majority of foreign-born respondents” picked a 

box on the immigration status card without—according to 

interviewers—any objection, hesitation, or periods of silence; 

• while some interviewers did not give a judgment or were confused 

about rating respondents’ understanding, about 80 percent of 

respondents were coded as understanding and about 10 percent as 

not;49 and 

• some respondents’ comments, written in by interviewers, indicated 

that although the GSS is a “personal interview” survey, telephone 

interviews had been substituted, in some cases, and this meant that 

respondents could not see the cards—making the use of the 3-box 

format difficult. 

The Census Bureau’s paper highlighted various limitations of the 2004 

GSS test, including (1) testing only one immigration status card, 

 49The Census Bureau’s paper said that field representatives reported that the remaining 

respondents were in doubt and may not have understood. 

Page 26 GAO-06-775 Estimating the Undocumented Population
(2) underrepresenting Hispanics, and (3) in some instances interviewing 

over the telephone (instead of in person), so that respondents did not see 

the flash cards.50

The acceptability of the grouped answers approach appears to be high, 

when implemented in surveys fielded by a university or private sector 

organization. Many immigration experts, including advocates, accepted 

the grouped answers approach, although some conditioned their 

acceptance on a quality implementation in a survey fielded by a university 

or other private sector organization. An independent statistical expert 

believed that the grouped answers approach would be generally usable 

with survey respondents. 

Some of the researchers and advocates we contacted were extremely 

enthusiastic about the potential for new data. No one objected to 

statistical, policy-relevant information being developed on the size, 

characteristics, costs, and contributions of the undocumented population.

Overall, the immigration experts we contacted (listed in appendix I, table

5) accepted the grouped-answers question approach—although advocates 

sometimes conditioned their acceptance on, for example, the questions 

being asked in a survey fielded by a university or private sector 

organization—with data protections built in. Many also offered 

suggestions for maximizing cooperation by foreign-born respondents or 

ideas about how advocacy organizations might help. 

Some advocates indicated that a key condition of their support would be 

that (1) the grouped answers question on immigration status be asked by a 

university or private sector organization and (2) identifiable data (that is, 

respondents’ answers linked to personal identifiers) be maintained by that 

organization. Two advocate organizations specifically stated that they 

“could not endorse,” or implied they would not support, the grouped 

answers approach, assuming the data were collected and maintained by, in 

one case, the Census Bureau and, in the other case, the government. Many 

other immigration experts and advocates preferred that grouped answers 

Experts Seem to 

Accept “Grouped 

Answers” Questions If 

Fielded by a Private 

Sector Organization 

Keys to Acceptance Are 

Fielding by a Private 

Sector Organization, Data 

Protections, and Quality 

Implementation 

 50The Census Bureau’s paper also noted that the nonresponse rate for the GSS overall (that

is, averaged across a combination of U.S.-born and foreign-born persons selected for the

sample) was 29.6 percent. (Persons who are selected for interview but not interviewed may 

be either native-born or foreign-born; because they were never asked and never reported

where they were born, a specific response rate for the foreign-born cannot be calculated.)

Page 27 GAO-06-775 Estimating the Undocumented Population
data on immigration status be collected by a university or other reputable 

private sector organization pledged to protect the data. 

The immigration advocates said that private sector fielding of a grouped 

answers survey and protection of such data from nonstatistical uses that 

might harm immigrants were key issues because 

• Some foreign-born persons are from countries with repressive 

regimes and thus have more fear of (less trust in) government than 

the typical U.S.-born person. 

• Despite current law protecting individual data from disclosure, 

some persons believe that information collected by a government 

agency such as the Census Bureau is routinely shared (or that in 

some circumstances it might be shared) across government 

agencies. Further, one advocate pointed out that the Congress could 

change the current law, eliminating that protection. (Although the 

grouped answers approach does not identify anyone as 

undocumented, it does provide some information regarding each 

respondent’s immigration status.) 

• Extremely large-scale data collections—notably, the American 

Community Survey (ACS)—can yield estimates for areas small 

enough that if the data were publicly available, they could be used 

for nonstatistical, nonpolicy purposes. Some advocates referred to 

the World War II use of census data to identify the areas where 

specific numbers of persons of Japanese origin or descent resided. 

They also pointed out that Census Bureau data on ethnicity—

including counts of Arab Americans—are publicly available by zip 

code. (The Census Bureau, unlike other government agencies and 

private sector survey organizations, is associated with extremely 

large-scale data collections, and some persons may not fully 

differentiate Census Bureau data collection efforts of different 

sizes.) 

• Hostility to or lack of trust in the Census Bureau might result in 

potentially lower response rates for foreign-born persons, based on 

the World War II experience of the Japanese or a more recent 

incident in which Census Bureau staff helped a DHS enforcement 

Page 28 GAO-06-775 Estimating the Undocumented Population
unit access publicly available data on ethnicity by zip code. 51, DHS 

stated that it did not use these data and had not requested the 

information by zip code.52 The Census Bureau clarified its position 

on providing help to others requesting publicly available data.53

Various advocates saw the issues listed above as linked to their own 

acceptance, as well as to respondent acceptance, of a survey. Linking 

these issues to respondent acceptance of a survey was, in some cases, 

echoed by other immigration experts we consulted.54 Some immigrant 

advocates and other immigration experts counseled us that if there were 

an increase in enforcement efforts in the interior of the United States (as 

opposed to border-crossing areas), foreign-born respondents’ acceptance 

of the grouped answers questions would be likely to decrease—at least, if

the questions were asked in a survey fielded by the government. 

One advocate expressly stated a preference for a grouped answers survey 

with funding by a nongovernment entity, such as a foundation. We 

discussed with a number of immigrant advocates who objected to a 

government-fielded survey the possibility of a survey fielded by a private 

 51See Samia El-Badry and David A. Swanson, “Providing Special Census Tabulations to 

Government Security Agencies in the United States: The Case of Arab-Americans,” paper 

presented at the 25th International Population Conference of the International Union for 

the Scientific Study of Population, Tours, France, July 18–23, 2005. One advocate was 

particularly concerned about the possibility that lower respondent cooperation might have

resulted from these incidents and, if so, might have led to underrepresentation of these

communities in Census Bureau data. Additionally, one advocate questioned whether local

estimates of the undocumented might, in future, facilitate possible efforts to base 

apportionment on population counts that do not include undocumented residents. We note 

that most large-scale personal-interview surveys do not include sufficient numbers of

foreign-born respondents to allow indirect grouped answers estimates of undocumented

persons for small geographic areas, such as zip codes.

52See “U.S. Customs and Border Protection Statement on Census Data,” Department of

Homeland Security, Press Office, Washington, D.C., August 13, 2004. 

53Charles Louis Kincannon, Director, “Procedures for Providing Assistance to Requestors

for Special Data Products Known as Special Tabulations and Extracts,” memorandum to

Associate Directors, Division Chiefs, Bureau of the Census, Washington, D.C., August 26, 

2004. 

54It might be noted that SIPP officials told us that when the Census Bureau conducted the 

SIPP survey and asked about immigration status, interviewers did not experience field 

problems. However, SIPP asks about immigration status at the time when respondents 

came to this country (and one other question); SIPP stopped short of a specific question on

current undocumented status—and the SIPP data do not allow indirect estimation of the

number who are currently undocumented. 

Page 29 GAO-06-775 Estimating the Undocumented Population
sector organization with government funding. In some cases, we 

specifically referred to one or both of the following surveys, which 

(1) have been conducted for many years without inappropriate data 

disclosures and (2) ask direct sensitive questions: 

• the National Survey on Drug Use and Health (NSDUH), fielded by RTI 

International under a contract from HHS’s Substance Abuse and Mental 

Health Services Administration (SAMHSA), and 

• the National Agricultural Workers Survey (NAWS), fielded by Aguirre 

International, under a contract from the Department of Labor.

55

The advocates’ response was generally to accept the concept of 

government funding of a university’s or private sector survey 

organization’s field work, provided that appropriate protections of the 

data were built into the funding agreement. 

GAO’s contract with Aguirre International for early testing of the grouped 

answers approach with farmworker respondents specified that data on

respondents’ answers would be “stripped of person-identifiers and related 

information.” Additionally, the GSS “core funding” grant with NSF and its 

contractual arrangements with sponsors of question modules—such as the 

grouped-answers question insert contracted for by the Census Bureau— 

do not involve the transfer of any data other than publicly available data, 

stripped of identifiers, and limited so as to avoid the possibility of 

“deductive disclosure” with respect to respondent identities or local 

areas.56 

Various advocates said that their acceptance was also contingent on 

factors such as 

1. high-quality data, including coverage of persons who have limited 

English proficiency, with special attempts to reach those who are 

linguistically isolated (that is, members of households in which no one 

 55These two examples involve agencies that are viewed neutrally by the immigrant 

advocates we talked with. (Agencies that are viewed negatively by some immigrant 

advocates are DHS and the Census Bureau.) 

56GSS receives funding for its core questions through a grant from NSF. GSS interviewers 

and advance letters told respondents about the NSF sponsorship. Additionally, respondents 

were told that one purpose of the survey was to inform government officials.

Page 30 GAO-06-775 Estimating the Undocumented Population
14 or older speaks English “very well”) and to overcome other 

potential barriers (such as cultural differences); 

2. appropriate presentation of the survey, including an appropriate 

explanation of its purpose and how respondents were selected for 

interview; and 

3. transparency—that is, keeping the immigrant community informed 

about or involved in the development and progress of the survey. 

One advocate specifically said that her organization’s support would be 

contingent on both (1) the development of more information on 

respondent acceptance within the Asian community—particularly among 

Asians who have limited English proficiency or are linguistically isolated—

and (2) a survey implementation that is planned to adequately

communicate with Asian respondents, including those who are 

linguistically isolated or have little education.57 Although one-fourth of the 

2004 GSS test respondents were Asian, the test was conducted in English 

(allowing help from bilingual household members), and no other tests 

have included linguistically isolated Asians.58 

Advocates and other experts made several suggestions for maximizing 

respondent cooperation with a survey using the grouped answers question 

series—that is, maximizing response rates for such a survey as well as 

maximizing authentic participation. 

Advocates suggested that the survey (1) avoid taking names or Social 

Security numbers,59 (2) hire interviewers who speak the respondents’ 

home-country language, (3) let respondents know why the questions are 

being asked and how their households came to be selected, (4) conduct 

Advocates and Experts 

Suggest Ways to Maximize 

Respondent Cooperation 

and Offer Their Assistance 

 57This would mean communication that takes account of cultural as well as language 

concerns. 

58The 2004 GSS was limited to respondents who either were fluent in English or were

helped by a household member who was fluent in English; some persons with limited 

English proficiency are likely to have been reached. The preliminary testing and 

development of the grouped answers approach offered a choice of Spanish or English 

interviews. However, linguistically isolated non-Hispanics have not yet been included in

any test. 

59Later in this report, we describe potential ways of testing whether respondents “pick the

correct box”—ways that do not require routine collection of respondent names and Social 

Security numbers as part of the main survey. 

Page 31 GAO-06-775 Estimating the Undocumented Population
public relations efforts, (5) obtain the support of opinion leaders, 

(6) select a survey group from a well-known and trusted university to 

collect the data, and (7) ask respondents about their contributions to the 

American economy through, for example, working and paying taxes. 

Additionally, survey experts suggested 

• using audio–Computer Assisted Self Interview (audio-CASI),60 

• carefully explaining to respondents how anonymity of response is 

protected, and 

• paying respondents $25 or $30 for participating in the interview. 

Survey experts viewed these elements as key ways of boosting response 

rates or encouraging authentic responses to sensitive questions. For 

example, NAWS, which uses respondent incentives, achieves extremely 

high response rates within cooperating farms—97 percent in 2002, with a 

$20 payment to farmworkers selected. 

Some immigrant advocates also offered suggestions for how their 

organizations or other advocates might help the effort to develop and field

the grouped answers approach, including 

1. providing contacts at local organizations to help with arrangements for 

future research, 

2. developing or reviewing Box A follow-up questions, and 

3. serving on an advisory board with other representatives from 

immigrant communities.61 

 60CASI, or Computer Assisted Self Interview, means that the respondent himself or herself 

uses a laptop to view the questions and flash cards and to indicate his or her answers. 

Audio-CASI adds earphones so that questions and instructions can be spoken to the

respondent while he or she views the questions on the screen. Audio-CASI programming

can be completed in any one of several languages. Experts told us that studies have shown 

increased reporting of sensitive items when audio-CASI is used. 

61Two advocates mentioned positively the transparency that the Census Bureau works 

toward through outreach to immigrant-advocate organizations. This outreach includes

explanation of data collection goals and policies. 

Page 32 GAO-06-775 Estimating the Undocumented Population
As we report above, the Census Bureau’s recent analysis of the 2004 GSS 

grouped answers data concluded that the “overwhelming majority of 

foreign-born respondents” picked a box without objection, hesitation, or 

silence. The Census Bureau reported, more specifically, that roughly 

90 percent (216 of 237 respondents) chose a box, 4 gave other answers, 

and 17 refused to answer or said “don’t know.” 

Our subsequent analysis excluded 19 of the 237 respondents in the Census

Bureau analysis because

GSS Data and Independent 

Statistical Consultant 

Review Show “General 

Usability” of the Grouped 

Answers Approach 

• 4 were not foreign-born (for example, 1 had been born abroad to 

parents who had, by the time he was born, become naturalized U.S. 

citizens); 

• 1 was not classifiable as either foreign-born or not foreign-born 

(because he did not know whether his parents were born in the 

United States); 

• 4 others were known to have been interviewed on the telephone, 

based on written-in interviewers’ comments recorded in the 

computer file (for example, one wrote that the respondent could 

not see the cards because the interview was on the telephone); and 

• 10 others were subsequently found to have been interviewed on the 

telephone, based on a special GSS hand check of the interview 

forms for respondents who had refused or said “don’t know,” 

which was carried out in response to our request. 62 

As a result, in our analysis we found that only 6 personally interviewed 

foreign-born GSS respondents refused or said “don’t know.” 63 One of the 

6 was an 18-year-old Mexican who told the interviewer that he did not 

know whether or not he was a legal immigrant. Additionally, we found that 

the 4 respondents who gave “other answers” had provided usable 

 62GSS Director Tom Smith graciously arranged for a hand check of interviews coded refusal 

or “don’t know,” thus providing key information to us in time for this report. (Specific 

mode-of-interview data for all 2004 GSS respondents will not be available until the end of

2006.) The GSS Director also said that, overall, about 10 percent of the 2004 GSS interviews 

were conducted over the telephone. 

63Similar numbers refused or said “don’t know” on the two 3-box training cards. 

Specifically, 8 respondents refused or said “don’t know” on the housing card, 6 on the 

transportation card. 

Page 33 GAO-06-775 Estimating the Undocumented Population
information (for example, one called out that he had a student visa) and 

thus could be recoded into an appropriate box. 

After reviewing the two analyses of the GSS test data—the one that the 

Census Bureau performed and the other we performed—Dr. Zaslavsky 

concluded that 

The test confirms the general usability of the [grouped-answers approach] with subjects

similar to the target population for its potential large-scale use—that is, foreign-born

members of the general population. Out of about 218 respondents meeting eligibility 

criteria and who were most likely administered the cards in person (possibly including a 

few who had telephone interviews but responded without problems), only 9 did not

respond by checking one of the 3 boxes. Of these, 3 provided verbal information that

allowed coding of a box, and 6 declined to answer the question altogether. Furthermore,

several of these [6] raised similar difficulties with other 3-box questions on nonsensitive 

topics (type of house where born, mode of transportation to enter United States), 

suggesting that the difficulties with the question format were at least in part related to the

format and not to the particular content of the answers. Thus, indications were that there

would not be a systematic bias due to respondents whose immigration status is more 

sensitive being unwilling to address the 3-box format. 

Dr. Zaslavsky emphasized the importance of minimizing or completely 

avoiding telephone interviews when using the grouped answers 

approach—or, alternatively, providing advance copies of the cards to 

respondents before interviewing over the telephone.64 (Dr. Zaslavsky’s 

written review is presented in full in appendix III.) 

The findings on respondent acceptance—that is, the GSS test—raised 

some unanswered questions about acceptance that experts said should be 

addressed. Additionally, the experts said that one or more tests of 

response validity are needed to determine whether respondents “pick the 

correct box” versus systematically avoiding Box B. 

Various Tests Are or 

May Be Needed 

 64Alternatively, we believe that it might be possible to estimate the bias incurred by 

including a small number of telephone interviews in the analysis (or by eliminating them 

from the analysis). 

Page 34 GAO-06-775 Estimating the Undocumented Population
The independent reviewer of the GSS analyses (Dr. Zaslavsky) concluded 

that 

four issues should be addressed in future field tests:

(a) Equivalent acceptability of all forms of the response card, 

(b) Usability with special populations including those with low literacy, the

linguistically isolated, and concentrated immigrant populations, 

(c) Methods that avoid telephone interviews, or reduce bias and nonresponse due to

use of the telephone, 

(d) Use of follow-up questions to improve the accuracy of box choices. 

As the independent expert explained with respect to point (b), GSS 

undercoverage of the foreign-born population occurred at least in part 

because interviews were conducted only in English, although household 

members could help respondents with limited English.65 Various 

colleagues and experts we talked with supported points (a) through (d). 

We further note that points (a) and (c) were covered or touched on in the 

Census Bureau’s paper reporting its analysis of the 2004 GSS data. In our 

discussions with Census Bureau staff, they also mentioned that further 

tests of acceptance should include (d) follow-up questions for Box A 

respondents. 

Additionally, some advocates and an immigration researcher suggested 

improving the cards, which might minimize the potential for “don’t know” 

or inaccurate answers. A survey expert suggested using focus groups to 

further explore respondent perceptions of the cards—and to potentially 

improve them.66 

Earlier testing covered a key portion of the populations (Hispanic 

farmworkers) cited in (b) above, was conducted in Spanish, and included

Questions for Further 

Research Were Suggested 

by the GSS Test 

 65Questions were asked and answers were apparently given in English. 

66The pretesting and cognitive testing conducted on the cards so far has been limited to 

certain groups of Hispanics. We believe that testing with other groups, potentially including

focus group testing, could be important before large-scale implementation. It also might be

appropriate to change specific categories and definitions of statuses on the cards, 

depending on future changes in laws.

Page 35 GAO-06-775 Estimating the Undocumented Population
Box A follow-up questions as recommended in (d) above.67 In those 

interviews, every respondent picked a box. However, 

1. No language other than Spanish or English has been used in testing; 

thus, as one immigrant advocate pointed out, no testing has focused on 

linguistically isolated Asians (those living in households in which no 

adult member speaks English). 

2. The interviews with Hispanic farmworkers were not conducted under 

typical conditions of a household survey. 

3. Only one immigration status card was tested with Hispanic 

farmworkers and in the GSS. 

Therefore, we agree that the acceptance-testing issues the experts raised 

should be considered in assessing the grouped answers approach. 

Several experts told us that tests of respondent accuracy—or at least 

respondents’ intent to respond accurately—should be conducted. These 

experts emphasized that grouped answers data would not be useful if 

substantial numbers of respondents were to systematically avoid picking 

Box B (that is, to not pick the box with the undocumented category). 

However, one immigration study expert believed that if a response validity

study involved lengthy delays, fielding a grouped answers survey should 

proceed in advance of a validity study. 

We agree with the experts’ position that tests are needed to determine 

whether respondents systematically avoid Box B (even after Box A followup check questions). Tests of response validity would ideally be conducted 

with the methods of encouraging truthful answers that experts mentioned, 

such as (1) explaining why the survey is being conducted, how the 

respondent was selected, and how the anonymity of answers is ensured, 

and (2) using audio-CASI and, if appropriate, paying respondents for 

participating in the interview. And, as the Census Bureau pointed out, such 

a study should include the full grouped answers question series, including 

follow-up questions, and it should test both Card 1 and Card 2. Even if 

small numbers of respondents were to respond inaccurately, it would be 

helpful to estimate this and adjust for any resulting bias. 

Studies Should Test 

Whether Respondents Pick 

the Correct Box 

 67In fact, a key part of the earlier testing focused on the development of icons to help 

respondents with limited literacy. 

Page 36 GAO-06-775 Estimating the Undocumented Population
We discussed various approaches to conducting validity studies with 

immigration experts, including immigrant advocates, and with agencies 

conducting surveys. In reviewing these approaches, we found that 

response validity tests vary according to whether they are conducted 

before, during, or after a survey is fielded. 

Before a large-scale survey is conducted. The grouped answers 

question series could be asked of a special sample of respondents for 

whom the answers are known, in advance, by study investigators on an 

individual-respondent basis. Such knowledge might be based, for example,

on information that recent applicants for green cards have submitted to 

DHS.68 “Firewalls” could be used to prevent survey information from being 

given to DHS.We discussed this approach with DHS; however, experts 

criticized a DHS-based validity study on both methodological and public

relations grounds.69 An alternative source of data on individuals’ 

immigration statuses might avoid these problems, but no alternative 

source has yet been identified. 

Before or as part of a large-scale survey. In either situation (that is, in

a presurvey study or as part of a survey), respondents could be asked if 

they would be willing to participate in special validity-test activities in 

return for a payment of, say, $25 or $30 for each activity. Later, after 

interviewing had been completed in a given location—not as part of the 

interview process—a sample of respondents who chose Box A (that is, 

those who claimed to be here legally) could be asked to 

• participate in a focus group in which respondents would discuss 

how they felt answering the grouped answers questions when the 

interviewer came to their house and, also, could possibly be asked 

to fill out a “secret ballot” indicating whether they had answered 

authentically in the earlier home interview; 

• give permission for a record check and provide information that 

could subsequently be used in a record check (for example, their 

 68NCHS has suggested that some kind of validity test at the individual level is needed. 

Interviewing persons whose status is known in advance is a classic approach. 

69One expert scoffed at a validity test limited to persons whose immigration status is

known to DHS. An immigrant advocate pointed to the issues that arose when the Census 

Bureau helped DHS obtain publicly available information on ethnicity by zip code; she

indicated that a public relations problem could result even if only carefully crafted, 

carefully protected sharing of information took place. 

Page 37 GAO-06-775 Estimating the Undocumented Population
name, date of birth, and Social Security number) and permission to 

check these data with the Social Security Administration;70 or 

• show his or her documentation (for example, green card) to a 

documents expert.71 

These checks would logically be focused on Box A respondents, for most 

of whom such checks would be less threatening. We believe that it is 

reasonable to assume that most respondents who chose Box B picked the 

correct box. Further, because the survey interview states that there are no

more questions on immigration if the respondent picks Box B, pursuing 

follow-up validity checks might be deemed inappropriate for Box B 

respondents.72

After data are collected. With a large-scale survey, it would be possible 

to conduct comparative analyses after the data were collected. We provide 

three examples.73

1. Grouped answers estimates of the percentage undocumented could be 

compared for (a) all foreign-born versus (b) high-risk groups, such as 

those who arrived in the United States within the past 5 or 10 years. 

The expectation would be that with valid responses, a higher estimate 

 70One immigrant advocacy organization pointed out that it would be important in such a

study to protect the data so that the agency checking records (in this instance, the Social 

Security Administration) could not discover information about any identifiable respondent. 

Protective approaches might include (1) using code numbers and a “third party” model and 

(2) adding numerous “fake” cases to the checklist and notifying the agency that this was

being done. (See GAO, Record Linkage and Privacy: Issues in Creating New Federal

Research and Statistical Information. GAO-01-126SP (Washington, D.C.: April 2001).) 

71The ideas for these approaches are an outgrowth of our discussions concerning NSDUH 

with SAMSHA. The NSDUH project officer said that as part of that survey (which is fielded 

by RTI International in Research Triangle Park, N.C., under a contract with SAMHSA), a

sample of respondents were offered $25 for a hair sample and $25 for a urine sample. 

Ninety percent of those offered the incentive payments provided one or both samples. 

72It would be important to craft such a study so that respondents would not be tempted to

distort information in order to receive payment. One immigrant advocate suggested asking 

“what other experience federal agencies have had with paying a select group of

respondents to participate in a validity test” to determine “whether the payment approach

is considered scientifically sound.” One way of addressing this concern might be to offer all 

or some Box B respondents a “minimal threat” follow-up opportunity, such as participating 

in a focus group, which could also be associated with a payment. 

73Other possible comparative analyses might also be useful. DHS suggested comparisons to

results from the Latin American Migration Project and the New Immigrant Survey. 

Page 38 GAO-06-775 Estimating the Undocumented Population
of the percentage undocumented would be obtained for those who 

arrived more recently—because, for example, persons who had arrived 

recently were not here during the amnesty in the late 1980s.74

2. Comparisons could be made of (a) Box A estimates of specific legal 

statuses and the approximate dates received—notably, the numbers of 

persons claiming to have received valid green cards in 1990 or more 

recently—with (b) publicly available DHS reports of the numbers of 

green cards issued from 1990 to the survey date.

75

3. Analysts could compare (a) grouped answers estimates of the number 

undocumented overall to (b) estimates of total undocumented

obtained by the residual method.76 

Wherever possible, Card 1 and Card 2 should be tested separately for 

accuracy of response. 

The advantage of conducting a validity study in advance of a survey is that

if significant problems surface, adjustments in the approach can be made. 

Or if the problems are substantial and cannot be easily corrected—and if

the anticipated survey were to be fielded mostly or only to collect grouped 

answers data—then that survey could be postponed or canceled. However, 

the results of validity tests conducted during or after a survey can be used 

to interpret the data and, potentially, to adjust estimates if it appears that, 

for example, 5 to 10 percent of undocumented respondents had 

erroneously claimed to be in Box A of Card 1. As one expert noted, 

 74This is a version of the standard “known groups” validity test—an approach that NCHS

suggested using if it is not possible to conduct individual checks. 

75An expert in immigration studies suggested this test. As DHS’s comments indicate, such a 

test would involve adjusting the DHS figures on, for example, the number of green cards 

issued in specific years to account for subsequent return-migration and mortality, as well 

as taking account of survey undercoverage. For information on adjustments needed in

comparisons involving green cards, see Nancy F. Rytina, Estimates of the Legal Permanent 

Resident Population and Population Eligible to Naturalize in 2004 (Washington, D.C.: 

Department of Homeland Security, Office of Immigration Statistics, February, 2006), p. 3,

table 2. For an analogous comparison for U.S. citizenship, see Jeffrey S. Passel, Rebecca L. 

Clark, and Michael Fix, “Naturalization and Other Current Issues in U.S. Immigration: 

Intersections of Data and Policy,” in Proceedings of the Social Statistics Section of the 

American Statistical Association: 1997 (Alexandria, Va.: American Statistical Association, 

1997). 

76This test was suggested by another expert in immigration studies. Residual estimates are 

based primarily on comparing (1) administrative data on the number of legal immigrants 

with (2) census counts or survey estimates of the number of foreign-born residents who

have not become U.S. citizens. 

Page 39 GAO-06-775 Estimating the Undocumented Population
conducting an advance study does not preclude conducting a subsequent 

study during or after the survey. 

Although several factors are involved, and it is not possible to guarantee a 

specific level of precision in advance, we estimate that roughly 

6,000 foreign-born respondents, or more, would be needed for a grouped

answers survey.77 As we explain below, this is based on (1) a precision 

requirement (that is, a 95 percent confidence interval consisting of plus or 

minus 3 percentage points), (2) assumptions about the sampling design of 

the survey in which the questions are asked, and (3) the assumption that 

approximately 30 percent of the foreign-born population is currently 

undocumented. 

An indirect grouped answers estimate of the undocumented population 

generally requires interviews with more foreign-born respondents than a 

corresponding hypothetical direct estimate would—assuming it were 

possible to ask such questions directly in a major national survey. One 

key reason is that the main sample of foreign-born respondents must 

be divided into two subsamples. Half the respondents answer each 

immigration status card. On this basis alone, one would have to double the 

sample size required for a direct estimate based on a question asked of all 

respondents. Further, the estimate of undocumented, which is achieved by 

subtraction, combines two separate estimates, each characterized by some 

degree of uncertainty.78 

Determining the number of respondents required for a “reasonably 

precise” estimate of the percentage of the foreign-born population who are 

undocumented involves three key factors: 

Some 6,000 ForeignBorn Respondents 

Are Needed for 

“Reasonably Precise” 

Estimates of the 

Undocumented 

 77A sample of foreign-born is contained within a general sample of the household 

population. As we explain in a later section of this report, an efficient way to survey the 

foreign-born is by piggybacking on an existing, ongoing large-scale survey of the total 

household population, which includes foreign-born persons—if an appropriate ongoing

survey can be identified. A higher-cost alternative would be to identify a new sample of the 

total household population and screen (by mini-interviews conducted by telephone or in 

person or both) for households that contain one or more foreign-born persons.

78The size of the error associated with a grouped answers estimate relative to a direct 

estimate depends on the distribution of immigration statuses. Assuming that 33.3 percent 

of foreign-born persons are in the undocumented category, 33.3 percent are in the set of 

legal statuses in Card 1, Box A, and 33.3 percent are in the set in Card 2, Box A, we would 

expect the error associated with a grouped answers estimate of the percentage 

undocumented to be twice that associated with a corresponding direct estimate. 

Page 40 GAO-06-775 Estimating the Undocumented Population
1. specification of a precision level—that is, choice of a 90 percent or 

95 percent confidence level and an interval defined by plus or minus 

2, 3, or 4 percentage points; 

2. information on (or assumptions about) the sampling design for the 

main survey and for subsamples 1 and 2; and 

3. to the extent possible, consideration of the likely distribution of the 

foreign-born population across immigration status categories,

including the various legal categories and the undocumented 

category.

79 

With respect to the first factor involved in determining sample size, some 

agencies—for example, the Census Bureau and the Bureau of Labor 

Statistics (BLS)—use the 90 percent confidence level. Other agencies use

the 95 percent level. 

With respect to the second factor, the sampling design of a large-scale, 

nationally representative, personal-interview survey is based on 

probabilistic area sampling rather than simple random sampling of 

individuals. This often reduces the precision of estimates (relative to 

simple random sampling).80 The reason is that persons selected for 

interview are clustered in a limited number of areas or neighborhoods 

(and residents of a particular neighborhood may tend to be similar). It is 

possible that the design for selecting subsamples 1 and 2 could increase

precision; however, it is not possible to predict by how much.81 

 79If there is no information on the distribution of immigration status, then a potentially very 

large sample size would be estimated, based on a “worst case scenario” distribution.

However, if there is information, this may allow a given level of precision to be attained 

with a smaller sample.

80To illustrate how this occurs in practice, referring to the National Health Interview Survey

(NHIS), NCHS told us that an estimate of the percentage of persons who are foreign-born, 

18 to 39 years old, and U.S. citizens is characterized by a variance that is roughly 1.6 times 

the variance that would be associated with a corresponding estimate based on simple 

random sampling. (In theory, a complex sampling design could reduce the variance rather

than increasing it.) 

81The independent statistical consultant (Dr. Zaslavsky) advised us that rotating the use of

immigration status cards 1 and 2 in every other household interviewed (balancing the use 

of alternative cards within areas or clusters) might increase precision. The logic is that 

because some areas are defined by factors such as income and ethnicity—which might be

related to immigration status—rotation would help ensure balance on these factors. 

Page 41 GAO-06-775 Estimating the Undocumented Population
With respect to the third factor, existing residual estimates point to a fairly 

even 3-way split between three main categories—undocumented, U.S. 

citizen, and legal permanent resident. However, there is some uncertainty

associated with these estimates, the distribution may vary across 

subgroups, and the percentages may change in future.82 Therefore, a range 

of distributions is relevant. 

Taking each of these factors into account (to the extent possible) and 

using conservative assumptions, we estimated the approximate numbers 

of respondents required for indirect estimates of the undocumented 

population that are “reasonably precise.” 

Table 1 shows required sample sizes for the 90 percent confidence level, 

table 2 for the 95 percent level, with precision at plus or minus 2, 3, and 

4 percentage points. In estimating these required sample sizes, we made 

conservative assumptions and specified a range of possibilities for the 

distribution with respect to the undocumented category. 

To identify a single, rough figure for the sample size needed for reasonably

precise estimates, we focused on 

1. the 95 percent level, which is more certain and, we believe, preferable; 

2. the 30 percent column, because a current residual estimate of the 

undocumented population is in this range; and 

3. the middle row (for plus or minus 3 percentage points), which is a 

midpoint within the area of “reasonable precision” as defined above. 

With this focus, we estimate that roughly 6,000 or more respondents would 

be required.83

 82For example, it is possible that new immigration laws would allow large numbers of

currently undocumented persons to legalize their status. 

83We believe these are reasonable choices but we realize that others might focus on, for 

example, more precise estimation (plus or minus 2 percentage points). 

Page 42 GAO-06-775 Estimating the Undocumented Population
Table 1: Approximate Number of Foreign-Born Respondents Needed to Estimate Percentage Undocumented within 2, 3, or 4

Percentage Points at 90 Percent Confidence Level, Using Two-Card Grouped Answers Data

Percent undocumented foreign-born (range of possibilities) Estimate within 2, 3, or 4 

percentage points 10% 30% 50% 70% 90%

2 10,700 9,900 8,100 5,500 2,100

3 4,800 4,400 3,600 2,500 900

4 2,700 2,500 2,000 1,400 500

Source: GAO analysis.

Note: Estimated numbers of respondents were calculated assuming that (1) foreign-born persons 

who are not undocumented are evenly split between the legal statuses in Box A, Card 1, and Box A, 

Card 2 (a conservative assumption in that it maximizes the required number of respondents), 

(2) sample selection design for the main survey and for subsamples 1 and 2 increases the variance of 

an estimate of undocumented by 1.6 (which does not build in potential reductions in variance that 

might occur with a careful design for the selection of subsamples 1 and 2); and (3) for simplicity, no 

respondents choose Box C. 

 

Table 2: Approximate Number of Foreign-Born Respondents Needed to Estimate Percentage Undocumented, within 2, 3, or 4

Percentage Points, at 95 Percent Confidence Level, Using Two-Card Grouped Answers Data

Percent undocumented foreign-born (range of possibilities) Estimate within 2, 3, or 4 

percentage points 10% 30% 50% 70% 90%

2 15,200 14,000 11,500 7,800 2,900

3 6,800 6,200a5,100 3,500 1,300

4 3,800 3,500 2,900 2,000 700

Source: GAO analysis.

Note: Estimated numbers of respondents were calculated assuming that (1) foreign-born persons 

who are not undocumented are evenly split between the legal statuses in Box A, Card 1, and Box A, 

Card 2 (a conservative assumption in that it maximizes the required number of respondents), 

(2) sample selection design for the main survey and for subsamples 1 and 2 increases the variance of 

an estimate of undocumented by 1.6 (which does not build in potential reductions in variance that 

might occur with a careful design for the selection of subsamples 1 and 2); and (3) for simplicity, no 

respondents choose Box C. 

a

This is the approximate number of foreign-born respondents needed for an overall estimate of the 

percentage undocumented with a confidence interval of plus or minus 3 percentage points at the 

(preferred) 95% confidence level, assuming that 30% of the foreign-born are undocumented. 

High-risk subgroups—subgroups with higher percentages of 

undocumented (such as adults 18 to 44 and persons who arrived in the 

United States within the past 10 years)—would require fewer respondents 

for the same level of precision, as illustrated in the tables’ middle and right 

columns. For example, if about 70 percent of a subgroup were 

undocumented, a survey with about 3,500 respondents in that subgroup

would produce an estimate of the percentage of the subgroup that is 

Page 43 GAO-06-775 Estimating the Undocumented Population
undocumented, correct to within approximately plus or minus 

3 percentage points at the 95 percent confidence level. 

Low precision could obtain for smaller subgroups in which there are 

relatively few undocumented persons (for example, 10 percent or less), 

particularly if—as assumed in tables 1 and 2—there is an even split of 

legally present foreign-born persons across the Box A categories of 

immigration status cards 1 and 2.84

The independent statistician we consulted indicated that if more than one 

grouped answers survey is conducted, combining data across two or more 

surveys could help provide larger numbers of respondents for subgroup 

analysis. For example, if a large-scale survey were conducted annually,

analysts could combine 2 or 3 years of data to obtain more precise 

estimates. (One caveat is that combining data from multiple survey years 

reduces the time-specificity associated with the resulting estimate.) 

Finally, we note that to estimate the numerical size of the undocumented 

population, 

• A grouped answers estimate of the percentage of the foreign-born who 

are undocumented would be combined with a census count of the 

foreign-born or an updated estimate. For example, the 2000 census 

counted 31 million foreign-born persons, and the Census Bureau later 

issued an updated estimate of 35.7 million for 2005. 

• The specific procedure would be to multiply the percentage

undocumented (based on the grouped answers data and the 

subtraction procedure) by a census count or an updated estimate of the 

foreign-born population for the year in question. 

The precision of the resulting estimate of the numerical size of the 

undocumented population would be affected by (1) the precision of the 

grouped answers percentage estimate, which is closely related to sample 

size, as described above, and (2) any bias in the census count or updated 

estimate of the foreign-born population.85 The precision of the grouped 

 84However, if the percentage undocumented overall were to sharply decrease, it might be 

appropriate to change the groupings on the cards to mitigate this factor.

85Such bias might arise from problems in accurately covering the foreign-born population. 

An additional caveat is that coverage of the undocumented may be lower than coverage of

other foreign-born persons. We examined coverage issues in GAO/GGD-98-164. 

Page 44 GAO-06-775 Estimating the Undocumented Population
answers percentage is taken into account by using a percentage range 

(for example, the estimate plus or minus 3 percentage points) when 

multiplying. Although the amount of bias in a census count or updated 

estimate is unknown, we believe that any such bias would have a 

proportional impact on the calculated numerical estimate of the 

undocumented population.86 

To illustrate the proportional impact, we assume that a census count for 

total foreign-born is 5 percent too low. Using that count in the 

multiplication process would cause the resulting estimate of the size of the 

undocumented population to be 5 percent lower than it should be.87 The 

situation is analogous for subgroups.88 

Overall, it seems clear that reasonably precise grouped answers estimates 

of the undocumented population and its characteristics require large-scale 

data collection efforts but not impossibly large ones. 

A low-cost field strategy would be to insert the new question series in an 

existing, nationally representative, large-scale survey—that is, to pose the 

grouped answers questions to the foreign-born respondents already being 

interviewed. However, based on our review of on-going large-scale 

surveys, the insertion strategy does not seem feasible. Specifically, we 

identified four potentially relevant surveys but none met criteria based on

the grouped answers design and other criteria based on immigrant 

advocates’ concerns. 

The Most Efficient 

Field Strategy Does 

Not Seem Feasible 

 86This assumes that the census count or updated estimate is a constant.

87Suppose hypothetically that an updated estimate for some future year estimates the 

foreign-born population as 40 million and that a grouped answers estimate of the

percentage of foreign-born who are undocumented is 30 percent. Multiplying 40 million by 

30 percent would yield an estimate of 12 million undocumented (hypothetical data). 

Further suppose that the true size of the foreign-born population, in that future year, were 

actually 42 million. Multiplying 42 million by 30 percent would yield 12.6 million— 

a result just 5 percent higher than 12 million. 

88In contrast, analysts have pointed to a potentially disproportionate, magnifying impact of 

bias in census counts (or error in updated estimates of the size) of the foreign-born 

population on residual estimates of the number who are undocumented. See Kenneth Hill, 

“Estimates of Legal and Unauthorized Foreign-Born Population for the United States and

Selected States Based on Census 2000,” presentation at the U.S. Census Bureau 

Conference, Immigration Statistics: Methodology and Data Quality, Alexandria, Virginia, 

February 13–14, 2006. Siegel and Swanson (p. 479) make a similar point. 

Page 45 GAO-06-775 Estimating the Undocumented Population
The dollar costs associated with inserting a grouped answers module are 

difficult to calculate in advance because many factors are involved. 

However, to suggest the “ball park” within which the cost of a grouped 

answers insert might be categorized, if an insertion were possible, we 

present the following two examples. 

• The GSS test, in which a grouped answers question module was 

inserted, cost approximately $100 per interview (more than 

200 interviews were conducted). On average, the question series took 

3.25 minutes. Logically, per-interview costs are likely to be higher in 

relatively small surveys than in larger surveys with thousands of 

foreign-born respondents. 

• For the much larger Current Population Survey (CPS), with interviews 

covering native-born and foreign-born persons in more than 

50,000 households, the Census Bureau and BLS told us that “an average 

10-minute supplement cost $500,000 in 2005.”89 This implies $10 per 

interview at the 50,000 level, but per-interview costs might be higher 

when the question series applied to only a portion of the respondents. 

Additional costs might apply for flash cards and foreign-language 

interviews. BLS noted that still other costs would apply for advance 

testing and subsequent analyses requested by the customer. 

A more costly option would be to ask the grouped answers question series 

in a follow-back survey of foreign-born respondents identified in 

interviewing for an existing survey. (In-person self-report interviews can 

cost $400 to $600 each.) More costly still would be the development of a 

new, personal-interview survey of a representative sample of the foreignborn population devoted to migration issues; the main reason is that there 

would be additional costs in “screening out” households without foreignborn persons. 

We identified four potentially relevant ongoing large-scale surveys. All 

have prerequisites and processes for accepting (or not accepting) new 

questions. We also developed six criteria for assessing the appropriateness 

of each survey as a potential vehicle for fielding the grouped answers 

approach. Three criteria are based on design requirements, and three are 

based on the views of immigrant advocates. We found that no ongoing 

large-scale survey met all criteria. 

 89More than 6,000 of these households included one or more foreign-born persons. 

Page 46 GAO-06-775 Estimating the Undocumented Population
We identified four nationally representative, ongoing large-scale surveys in 

which respondents are or could be personally interviewed.90 Three of these 

conduct most or all interviews in person: 

1. the Current Population Survey (CPS), sponsored by BLS and the 

Census Bureau and fielded by Census; 

Four Ongoing Large-Scale 

Data Collections 

Sometimes Accept 

Additional Questions 

2. the National Health Interview Survey (NHIS), sponsored by the 

National Center for Health Statistics (NCHS) and fielded by the Census 

Bureau; and

3. the National Survey on Drug Use and Health (NSDUH), sponsored by 

SAMHSA and fielded by RTI International, a private sector contractor. 

The fourth survey is the American Community Survey (ACS), a much 

larger survey fielded by the Census Bureau and using “mixed mode” data 

collection. The majority of the data are based on mailed questionnaires or 

telephone interviews, with the remaining data based on personal 

interviews. In addition, there is one personal-interview follow-back survey 

that uses the ACS frame and data to draw its sample.91 Other follow-back 

surveys might eventually be possible. 

For any of these four surveys, inserting a new question or set of questions 

(or fielding a “follow-back” survey based on respondents’ answers in the 

main survey) requires approvals by the Office of Management and Budget

(OMB), the agencies that sponsor or field the surveys, and in cases in 

which data are collected by a private sector organization, the 

organization’s institutional review board. 

The prerequisites for an ongoing survey’s accepting new questions 

typically include low anticipated item nonresponse, pretesting and pilot

 90A fifth survey, SIPP, a large-scale in-person survey, is scheduled to be “reengineered” to

provide an “effective alternative to the current SIPP.” It is anticipated that administrative 

data will be combined with survey data, although the exact directions that the revised 

effort will take are not yet known. (We defined large-scale as 50,000 or more interviews,

including native-born and foreign-born respondents. The foreign-born represent about 

12 percent of the national population, implying that a survey of 50,000 U.S. residents could 

be expected to collect data on roughly 6,000 foreign-born persons.) 

91This follow-back survey concerns alcohol use and alcoholism; it is sponsored by the 

National Institute of Alcohol Abuse and Alcoholism. OMB told us that, in part because ACS 

is a new survey, very few other follow-up efforts, if any, are likely to be approved in the

next few years.

Page 47 GAO-06-775 Estimating the Undocumented Population
testing (including debriefing of respondents and interviewers) that 

indicate a minimum of problems, review by stakeholders to determine 

acceptability, and tests that indicate no effect on either survey response 

rates or answers to the main survey’s existing questions.92 Another 

prerequisite would be the expectation of response validity.93 

Additionally, multiple agencies mentioned a need for prior “cognitive 

interviewing,” compatibility with existing items (so that there is no need to

change existing items), and no significant increase in “respondent burden”

(by, for example, substantially lengthening the interview).94 

Agencies sponsoring or conducting large-scale surveys varied on the 

perceived relevance of immigration to the main topic of their survey. For 

example, BLS noted that some of its customers would be interested in data 

on immigration status by employment status (among the foreign-born), 

and the Census Bureau has indicated the relevance of undocumented 

immigration to population estimation. But some other agencies saw little 

relevance to the large-scale surveys they sponsored or conducted. 

Resistance to including a grouped answers question series might occur 

where an agency perceives little or no benefit to its survey or its 

customers. 

Additionally, one agency raised the issue of informed consent, which we 

discuss in appendix V. 

 92For example, with respect to possible impacts on answers to main-survey questions, 

SAMHSA (which sponsors the NSDUH) indicated a concern that asking about immigration 

status might make respondents less likely to provide honest answers to questions about

illegal behaviors such as drug use (potentially because of fear of such actions as 

deportation). 

93As we discussed in a previous section, experts told us that it is important to demonstrate 

that respondents, especially undocumented respondents, “pick the correct box”—or at 

least to demonstrate that they intend to pick the correct box (rather than avoiding Box B).

94Cognitive interviewing focuses on the mental processes of the respondent while he or she

is answering a survey question. The goals are to find out what each respondent thinks the 

question is asking, what the specific words or phrases (or icons on a card) mean to him or

her, and how he or she formulates an answer. Typically, cognitive interviewing is an 

iterative process in which the findings or problems identified in each set of interviews are 

used to modify the questions to be tested in the next set of interviews.

Page 48 GAO-06-775 Estimating the Undocumented Population
Based on the design of the grouped answers approach, as tested to date, 

two criteria for an appropriate survey are (1) personal interviews in which 

respondents can view the 3-box cards and (2) a self-report format in which 

questions ask the respondents about their own status (rather than asking 

one adult member of a household to report information on others). A third 

criterion is that the host survey not include highly sensitive direct 

questions that could affect foreign-born respondents’ acceptance of the 

grouped answers questions.95 We based these criteria on the results of the 

GSS test, our knowledge of the grouped answers approach, and general

logic. 

No Ongoing Large-Scale 

Data Collection Met Our 

Criteria 

As shown in table 3, one of the surveys we reviewed (the CPS) does not 

meet the self-report criterion; that is, it accepts proxy responses. Two 

other surveys (the NHIS and NSDUH) do not meet the criterion of an 

absence of highly sensitive questions, since they include questions on HIV 

status (NHIS) and the use of illegal drugs (NSDUH). Conducting a followback survey based on ACS would meet all three criteria.96

 95For example, if a respondent had already admitted engaging in a behavior related to 

illegal activity, he or she might be less likely to accurately answer a question on 

immigration status. Of course, if future testing were to indicate that a particular type of

sensitive item did not affect immigration responses, this criterion would be dropped. 

96The ACS is a mixed-mode rather than a solely personal-interview survey. It gathers 

information on all members of a household based, in some cases, on a single adult 

respondent-informant rather than randomly selecting one or more respondents in each 

household and asking them to provide information about themselves. However, one followback personal interview survey has based its sample selection on the ACS frame and its 

data. We further note that if a follow-back survey based on the CPS could be conducted, 

then—provided that the follow-back was designed for self-report personal interviews—it 

would meet the criteria in table 3. 

Page 49 GAO-06-775 Estimating the Undocumented Population
Table 3: Survey Appropriateness: Whether Surveys Meet Criteria Based on the Grouped Answers Design

Three design-based criteria

Survey 

type Specific survey

1. Are the data gathered in

personal interviews?

2. Are all respondents 

selected to self-report? 

3. Are direct questions not

highly sensitive?

Current Population Survey 

(CPS) 

YES. Mostly, for in-person 

waves; 16% of foreign-born 

interviewed by telephone, in

the in-person waves.a

No. An adult respondent 

reports on self and provides 

proxy responses for others 

in his or her household. Inperson data for 6,744 

households with 1 or more 

foreign-born members 

(2006). 

YES, not highly sensitive.

b

National Health Interview

Survey (NHIS)

YES. Mostly; 17% of 

foreign-born sample adults 

interviewed by telephone.

YES. For some questions, 

but not all, 4,829 foreignborn adults self-report 

(2004). 

No. There are direct 

questions on HIV, other 

STDs.c

Ongoing 

survey

National Survey of Drug Use 

and Health (NSDUH)

YES. All interviewed in 

person. 

YES. 7,364 foreign-born age 

12 and older and 4,934 

foreign-born age 18+ selfreport (2004). 

No. There are direct 

questions on respondent’s 

use and sale of drugs like

marijuana and cocaine. 

Potential 

follow-back 

survey

Potential American 

Community Survey (ACS) 

follow-back survey, by the 

Census Bureau—on all or a 

sample of all foreign-born on 

whom ACS data were 

collected 

YES. A follow-back could 

specify personal 

interviews only. (ACS is 

mixed mode, mostly mail.) 

YES. A follow-back could 

specify self-report only. 

(ACS data include both selfreport data and proxy data 

in which one member of a 

household provides 

responses for others.) 

YES, not highly sensitive. 

Source: GAO analysis.

 aThe CPS includes successive data collections or “waves” to update data over time, at selected 

households. In some waves, interviews are conducted in person; in others, by telephone. 

b

Based on the core CPS questionnaire. (Different modules or supplements may be added in particular 

survey years or CPS waves.) 

c

HIV refers to human immunodeficiency virus. STDs refers to sexually transmitted diseases.

The views of immigrant advocates, which were echoed by some other 

experts, suggested three additional criteria for a candidate “host” survey: 

1. data collection by a university or private sector organization,

2. no request for the respondent’s name or Social Security number, and 

3. protection from possible release of grouped answers survey data for 

small geographic areas (to guard against estimates of the 

undocumented for such areas). 

Page 50 GAO-06-775 Estimating the Undocumented Population
The experts based their views on (1) methodological grounds (foreignborn respondents would be more likely to cooperate, and to respond 

truthfully, if all or some of these criteria were met) and (2) concerns about 

privacy protections at the individual or group levels.97 These criteria are 

potentially important, in part because the success of a self-report 

approach hinges on the cooperation of individual immigrants and, most 

likely, also on the support of opinion leaders in immigrant communities.98

With respect to the first criterion above, we note that with the exception of 

initial GAO pretests, all tests of the grouped answers approach have 

involved data collection by a university or private sector organization. 

Without further tests, we do not know whether acceptance would be 

equally high in a government-fielded survey. 

As shown in table 4, an ACS follow-back would potentially not meet any

of the three criteria based on immigrant advocates’ views. Only one survey 

(NSDUH) met all three criteria based on immigrant advocates’ views—and 

because of its sensitive questions on drug use, that survey did not meet the 

design-based table 3 criteria. 

 97With respect to the individual level, Census Bureau staff told us that they are extremely 

careful not to disclose information, that such disclosure is prohibited by law, and that the

Census Bureau explains this to respondents. However, they also said that some 

respondents erroneously believe that all government agencies share information with one 

another or might do so under certain circumstances. 

98We note that the relevance of the criteria in table 4 would likely be heightened if interior 

enforcement efforts (that is, those conducted away from border areas) were to sharply 

increase. 

Page 51 GAO-06-775 Estimating the Undocumented Population
Table 4: Survey Appropriateness: Whether Surveys Meet Table 3 (Design Based) Criteria and Additional Criteria Based on 

Immigrant Advocates’ Views 

Three additional criteria based on immigrant advocates’ views 

Survey type Specific survey

Meets all table 3 

(design based) 

criteria

1. Does a 

nongovernment 

organization conduct 

field work?

2. Are interviews 

anonymous (that is, 

no names or Social

Security numbers are 

taken)?

3. Is sample too small 

for reliable small-area 

estimates of

undocumented?a

Current Population 

Survey (CPS)

No. No. The Census

Bureau conducts field 

work.b

No. Takes names. YES.

National Health

Interview Survey

(NHIS)

No. No. The Census

Bureau conducts field 

work.c

No. Takes both names 

and Social Security

numbers.

YES. 

Ongoing 

survey

National Survey of 

Drug Use and Health

(NSDUH)

No. YES. YES. YES. 

Potential 

follow-back

Potential American 

Community Survey

(ACS) follow-back

survey by the Census 

Bureau—on all or a 

sample of foreign-born 

on whom data were 

collected

YES. No. Only the Census 

Bureau can conduct 

field work.

No. Takes names in the 

initial survey, and a 

follow-back would be

based on knowing each 

person’s identity.

Potentially, no. A followback might be 

extremely large. (Also, 

small-area releases are 

not prohibited by law or 

policy.)

Source: GAO analysis.

Note: Table 3 criteria are personal interviews; respondent reports on himself or herself; no highly 

sensitive direct questions.

a

For this report, we define “small area” as below the county level. 

b

For CPS, only the Census Bureau can conduct a follow-back. 

c

For NHIS, a follow-back by a private sector organization might be possible. 

In conclusion, we did not find a large-scale survey that would be an 

appropriate vehicle for “piggybacking” the grouped answers question 

series. 

Page 52 GAO-06-775 Estimating the Undocumented Population
For more than a decade, the Congress has recognized the need to obtain 

reliable information on the immigration status of foreign-born persons 

living in the United States—particularly, information on the 

undocumented population—to inform decisions about changing 

immigration law and policy, evaluate such changes and their effects, and 

administer relevant federal programs. 

Until now, reliable data on the undocumented population have seemed 

impossible to collect. Because of the “question threat” associated with 

directly asking about immigration status, the conventional wisdom was 

that foreign-born respondents in a large-scale national survey would not 

accept such questions—or would not answer them authentically. 

Using the grouped answers approach to ask about immigration status 

seems promising because it reduces question threat and is statistically 

logical. Additionally, this report has established that 

Observations 

Testing So Far Affirms 

That the Grouped Answers 

Approach Is Promising 

• The grouped answers approach is acceptable to most foreign-born 

respondents tested (thus far) in surveys fielded by private sector 

organizations; it is also acceptable—with some conditions, such as private 

sector fielding of the survey—to the immigrant advocates and other 

experts we consulted. 

• A variety of research designs are available to help check whether 

respondents choose (or intend to choose) the correct box. 

• The grouped answers approach requires a fairly large number of personal 

interviews with foreign-born persons (we estimate 6,000) to achieve 

reasonably precise indirect estimates of the undocumented population 

overall and within high-risk subgroups. 

However, the most cost-efficient method of fielding a grouped answers 

question series—piggybacking on an existing survey—does not seem 

feasible. Rather, fielding the grouped answers approach would require a 

new survey focused on the foreign-born. This raises two new questions 

about “next steps”—and the answers depend, in large part, on policymaker 

judgments, as described below. 

Page 53 GAO-06-775 Estimating the Undocumented Population
Question 1: Are the costs of a new survey justified by information 

needs? DHS stated (in its comments on a draft of this report) that the 

“information on immigration status and the characteristics of those 

immigrants potentially available through this method would be useful for 

evaluating immigration programs and policies.” The Census Bureau has 

indicated that information on the undocumented would help estimate the 

total population in intercensal years. And an expert reviewer emphasized 

that a new survey of the foreign-born would be likely to help estimate the 

total population.99 

Additionally, policymakers might deem a new survey of the foreign-born to

be desirable for other reasons than obtaining grouped answers data. 

Notably, an immigration expert who reviewed a draft of this report 

pointed out that a survey focused on the foreign-born might provide more 

in-depth, higher-quality data on that population than existing surveys that 

cover both the U.S.-born and foreign born populations. For example, more 

general surveys, such as the ACS and CPS (1) ask a more limited set of 

migration questions than is possible in a survey focused on the foreignborn, (2) are not designed with a primary goal of maximizing participation 

by the foreign-born (for example, are not conducted by private sector 

organizations), and (3) as DHS pointed out in comments on a draft of this

report, may not be designed to cover persons who are only temporarily 

linked to sampled households, because such persons may have arrived

only recently in the United States and are temporarily staying with 

relatives.100 

A new survey aimed at obtaining grouped answers data on immigration 

status would require roughly 6,000 (or more) personal, self-report 

interviews with foreign-born adults. Other in-person, self-report interviews 

in large-scale surveys have cost $400 to $600 each. A major additional cost 

Two New Questions about 

“Next Steps” 

 99This expert reviewer told us: “One of the biggest issues surrounding immigration is the

scale of in- and out-migration. The failure to understand this process is one of the biggest 

reasons that the population estimates were so far off at the time of the 2000 census. A 

survey devoted to the foreign-born could be especially helpful in ensuring that we have the 

best weights [information on population] possible, particularly if the survey could

accurately estimate illegal aliens.” 

100The ACS defines residence in a household as living there for 2 months (either completed 

or ongoing). For a discussion of other quality issues in the ACS, see Steven A. Camarota 

and Jeffrey Capizzano, “Assessing the Quality of Data Collected on the Foreign Born: An 

Evaluation of the American Community Survey (ACS): Pilot and Full Study Findings,” 

Immigration Studies White Papers, Sabre Systems Inc., April 2004. 

http://www.sabresys.com/whitepapers/CIS_whitepaper.pdf (Sept. 6, 2006). 

Page 54 GAO-06-775 Estimating the Undocumented Population
would be obtaining a representative sample of foreign-born persons; this 

would likely require a much larger survey of the general population in 

which “mini-interviews” would screen for households with one or more 

foreign-born individuals. 

We did not study the likely costs of such a data collection or options for 

reducing costs. However, survey costs can be estimated (based on, for 

example, the experience of survey organizations), and policymakers can, 

in future, weigh those costs against the information need—keeping in 

mind the results of research on the grouped answers approach, to date, 

and experts’ opinions on research needed. 

Question 2: What further tests of the grouped answers method, if 

any, should be conducted before planning and fielding a new 

survey? On one hand, advance testing could 

• assess response validity (that is, whether respondents pick—or intend 

to pick—the correct box) before committing funds for a survey and in 

time to allow adjustments to the question series; 

• further delineate respondent acceptance and explore the impact on 

acceptance of factors such as government funding—or funding by a 

particular agency—in order to inform decisions about whether or how 

to conduct a survey;101 and 

• as suggested in DHS’s comments on a draft of this report, help 

determine the cost of a full-scale survey.102

On the other hand, extensive advance testing would likely delay the 

survey--and may not be needed because 

 101Potentially, the prospects for private sector funding could be explored. One question 

would be whether it is possible to identify a willing private sector source that is not aligned 

with a particular perspective on immigration issues. 

102Alternatively, survey costs can be estimated—albeit more roughly—on the basis of the

experience of survey organizations. 

Page 55 GAO-06-775 Estimating the Undocumented Population
• response validity could be assessed—and respondent acceptance could 

be further delineated—concurrently with or subsequent to the survey 

rather than in advance,103

• the need for advance testing of response validity would be lessened if 

policymakers see a need for more or better survey data on the foreignborn additional to the need for grouped answers data on immigration 

status (see discussion in question 1, above); 

• the value of advance testing would be lessened if changes in 

immigration law and policy occurred between the time of an advance

test and the main survey, because such changes could affect the 

context in which the survey questions are asked and, hence, change the 

operant levels of acceptance and validity; and 

• survey costs can be estimated—albeit more roughly—on the basis of 

the experience of survey organizations. 

Given the arguments for and against advance testing, it seems appropriate

for these to be weighed by policymakers. 

We provided a draft of this report to and received comments from the 

Department of Commerce, the Department of Homeland Security, and the 

Department of Health and Human Services (see appendices VII, VIII, and 

IX, respectively). The Office of Management and Budget provided only 

technical comments, and the Department of Labor did not comment. 

The Census Bureau agreed with the report’s discussion of 

Agency Comments 

• the grouped answers method, including its strengths and 

limitations; 

• the Census Bureau-GSS evaluation, including the conclusions of the 

independent consultant (Alan Zaslavsky); and 

• the need for a “validity study” to determine whether the grouped 

answers method can “generate accurate estimates” of the 

undocumented population. 

 103 Validity tests conducted concurrent with the survey and follow-on checks that compare 

survey results against (adjusted) administrative information would seem to be appropriate, 

if a survey is, in fact, fielded. 

Page 56 GAO-06-775 Estimating the Undocumented Population
The Census Bureau also provided technical comments, which we used to 

clarify the report, as appropriate. 

The Department of Homeland Security stated that the kinds of information 

that the grouped answers approach would provide, if successfully 

implemented, would be useful for evaluating immigration programs and 

policies. DHS further called for pilot testing by GAO to assess the 

reliability of data collection and to help estimate the costs of an eventual 

survey.104 As we indicate in the “observations” section of this report, two 

key decisions for policymakers concern 

• whether to invest in a new survey and 

• whether substantial testing is required in advance of planning and 

fielding a survey. 

We believe that depending on the answers to these questions, another 

issue—one we cannot address in this report—would concern identifying 

the most appropriate agency for conducting or overseeing (1) tests of the 

grouped answers and (2) an eventual survey of the foreign-born 

population. However, we believe that conducting or overseeing such tests 

or surveys is a management responsibility and, accordingly, is not 

consistent with GAO’s role or authorities. DHS made other technical 

comments which we incorporated in the report where appropriate.105 

 

The Department of Health and Human Services (HHS) agreed that the 

NSDUH would not be an appropriate vehicle for a grouped answers 

question series. Commenting on a draft of this report, HHS said that the 

report should include more information on variance calculations and on 

 104DHS suggested that the pilot testing be conducted within a limited geographic area. 

105For example, DHS pointed to the issue of an existing survey (the American Community 

Survey) defining residence in a household as living there for 2 months (either completed or 

ongoing). DHS said this would likely exclude some unauthorized and temporary migrants

and indicated that, if a new survey needs to be conducted, it should be designed to cover all

foreign-born persons residing here. 

Page 57 GAO-06-775 Estimating the Undocumented Population
“mirror-image” estimates.106 Therefore, we (1) added a footnote illustrating 

the variance costs of a grouped answers estimate relative to a 

corresponding direct estimate and (2) developed appendix VI, which gives

the formula for calculating the variance of a grouped answers estimate and 

discusses “mirror image” estimates. 

Additionally, HHS said that interviewers should more accurately 

communicate with respondents when presenting the three-box cards. We 

believe that the text of appendix V on informed consent, based on our 

earlier discussions with privacy experts at the Census Bureau, deals with 

this issue appropriately. As we state in appendix V, it would be possible to

explain to respondents that “there will be other interviews in which other

respondents will be asked about some of the Box B categories or 

statuses.” Finally, HHS made other, technical comments, which we 

incorporated in the report, as appropriate. 

The Office of Management and Budget provided technical comments. In 

addition, our discussions with OMB prompted us to re-order some of the 

points in the “observations” section of the report. 

The Department of Labor informed us that it had no substantive or 

technical comments on the draft of the report. 

We are sending copies of this report to the Director of the Census Bureau, 

Secretary of Homeland Security, Secretary of Health and Human Services, 

Secretary of Labor, Director of the Office of Management and Budget, and 

to others who are interested. We will also provide copies to others on 

request. In addition, the report will be available at no charge on GAO’s 

Web site at http://www.gao.gov. 

 106A grouped answers estimate of the percentage of the foreign born who are

undocumented can be defined as the percentage of subsample 1 who are in Box B, Card 1,

minus the percentage of subsample 2 who are in Box A, Card 2. Alternatively, a grouped 

answers estimate could be defined as the percentage of subsample 2 who are in Box B,

Card 2, minus the percentage of subsample 1 who are in Box A, Card 1. If both calculations 

are performed and two estimates are derived, they might be termed “mirror image” 

estimates. 

Page 58 GAO-06-775 Estimating the Undocumented Population
If you or your staff have any questions regarding this report, please call me 

at (202) 512-2700. Contact points for our Offices of Congressional 

Relations and Public Affairs may be found on the last page of this report. 

Other key contributors to this assignment were Judith A. Droitcour, 

Assistant Director, Eric M. Larson, and Penny Pickett. Statistical support 

was provided by Sid Schwartz, Mark Ramage, and Anna Maria Ortiz. 

Nancy R. Kingsbury, Managing Director 

Applied Research and Methods

Page 59 GAO-06-775 Estimating the Undocumented Population
Appendix I: Scope and Methodology Appendix I: Scope and Methodology 

To gain insight into the acceptability of the grouped answers approach, we

discussed the approach with numerous experts in immigration studies and 

immigration issues, including immigrant advocates. Table 5 lists the 

experts we met with and their organizations. 

Table 5: Experts GAO Consulted on Immigration Issues or Immigration Studies

Name and title Organization 

Steven A. Camarota, Director of Research Center for Immigration Studies

Robert Deasy, Director, Liaison and Information 

Crystal Williams, Deputy Director 

American Immigration Lawyers Associationa

J. Traci Hong, Director of Immigration Program 

Terry M. Ao, Director of Census and Voting Programs 

Asian American Justice Centera 

Guillermina Jasso, Professor of Sociology New York University 

Benjamin E. Johnson, Director of Policy, Immigration Policy Center American Immigration Law Foundationa

John L. (Jack) Martin, Director, Special Projects 

Julie Kirchner, Deputy Director of Government Relations 

Federation for American Immigration Reform

Douglas S. Massey, Professor of Sociology and Public Affairs Princeton University 

Mary Rose Oakar, President 

Thomas A. Albert, Director of Government Relations 

Leila Laoudji, Deputy Director of Legal Advocacy 

Kareem W. Shora, Director, Legal Department and Policy 

American-Arab Anti-Discrimination Committeea

Demetrios G. Papademetriou, President Migration Policy Institute 

Jeffrey S. Passel, Senior Research Associate Pew Hispanic Center 

Eric Rodriguez, Director, Policy Analysis Center 

Michele L. Waslin, Director, Immigration Policy Research

National Council of La Razaa

Helen Hatab Samhan, Executive Director Arab American Institute Foundationa

James J. Zogby, President 

Rebecca Abou-Chedid, Government Relations and Policy Analyst 

Nidal M. Ibrahim, Executive Director 

Arab American Institutea

Source: GAO.

Note: Other immigration experts we briefly consulted with by telephone or e-mail or in conversations 

at an immigration conference included George Borjas, Professor of Economics and Public Policy, 

Harvard University; Georges Lemaitre, Directorate for Employment, Labour, and Social Affairs, 

Organisation for Economic Co-operation and Development, Paris, France; Enrico Marcelli, Assistant 

Professor of Economics, University of Massachusetts at Boston; Randall J. Olson, Director, Center 

for Human Resource Research, The Ohio State University; and Michael S. Teitelbaum, Vice 

President, Alfred P. Sloan Foundation, New York. 

a

Organization advocating for immigrants or expressly dedicated to representing their views. We call 

such organizations immigrant advocates, although some may not, for example, lobby for legislation. 

Page 60 GAO-06-775 Estimating the Undocumented Population
Appendix I: Scope and Methodology 

To ensure that we identified immigration experts from varied perspectives, 

we consulted Demetrios G. Papademetriou, who is among the immigration

experts listed in table 5, and Michael S. Teitelbaum, Vice President of the 

Alfred J. Sloan Foundation. With respect to immigrant advocates, we 

sought to include advocates who represented (1) immigrants in general, 

without respect to ethnicity; (2) Hispanic immigrants, as these are the 

largest group of foreign-born residents; (3) Asian American immigrants, as 

these are also a large group; and (4) Arab American immigrants, as these 

have been the target of interior (that is, nonborder) enforcement efforts in 

recent years. 

To determine what the 2004 General Social Survey (GSS) test indicated 

about the acceptability of grouped answers questions to foreign-born 

respondents and its “generally usability” in large-scale surveys, we 

obtained the Census Bureau’s report of its analysis of those data, and we 

assessed the reliability of the GSS data through a comparison of answers 

to interrelated questions. Then we 

• submitted the Census Bureau’s report of its analysis to Dr. Alan 

Zaslavsky, an independent expert, for review; 

• developed our own analysis of the GSS data and submitted our paper 

describing that analysis to the same expert;1

 and 

• summarized the expert’s conclusions and appended his report and the 

Census Bureau’s report (reproduced in appendixes III and IV), as well 

summarizing our conclusions.2

We used these procedures to ensure independence, given that the GSS test

was based on our earlier recommendation that the Census Bureau and the 

 1

The independent review considered the Census Bureau and GAO analyses of the GSS data

in terms of (1) their overall reasonableness and thoroughness, given the general objective 

(describing respondents’ acceptance and understanding), (2) key points of difference 

(if any) between the two analyses or differences in conclusions, (3) whether the analyses 

raised unanswered questions that should be addressed, and (4) whether the conclusions

appeared to be justified. The reviewer was also free to comment on other aspects of the

analyses. 

2

We believe this report independently addresses respondent acceptability because we 

(1) focus on the results of the GSS test (rather than critiquing the Census Bureau’s work),

(2) report how the method performed rather than subjectively assessing its merit, and 

(3) relied on an independent expert. 

Page 61 GAO-06-775 Estimating the Undocumented Population
Appendix I: Scope and Methodology 

Department of Homeland Security (DHS) test the grouped answers 

approach.3

To describe additional research that might be needed, we outlined the 

grouped answers approach and reviewed the main conclusions of the GSS 

test in meetings with the immigration experts listed in table 5 and with 

private sector statisticians.4

 Additionally, we discussed the approach with 

various federal officials and staff at agencies responsible for fielding largescale surveys.5

To assess the precision of indirect estimates, we addressed questions to 

Dr. Zaslavsky, developed illustrative tables showing hypothetical 

calculations under specified assumptions, and subjected those tables to 

review. 

To identify and describe candidate surveys for piggybacking the grouped 

answers question series, we set minimum criteria for consideration 

(nationally representative, mainly or only in-person interviews, and data 

on at least 50,000 persons overall, including native-born and foreign-born). 

Then we identified surveys that met those criteria, collected documents 

concerning the surveys, and interviewed officials and staff at federal 

agencies that sponsored or conducted those surveys. We also talked with 

experts in immigration about additional key criteria for selecting an 

appropriate survey. 

The scope of our work had several limitations. We did not attempt to 

collect new data from foreign-born respondents in a survey, focus group, 

or other format. We did not assess census or survey coverage of the 

 3

DHS contributed to the funding of the Census Bureau’s contract with the National Opinion 

Research Center (NORC) for the insertion of a module (question series) into the GSS. 

4

We consulted with Alan Zaslavsky, Fritz Scheuren, and Mary Grace Kovar.

5

In our earlier work, we consulted with numerous other private sector experts on 

immigration and statistics. For those experts, see GAO/GGD-00-30, p. 29. 

Page 62 GAO-06-775 Estimating the Undocumented Population
Appendix I: Scope and Methodology 

foreign-born or undocumented populations.6 We did not assess 

nonresponse rates among foreign-born or undocumented persons selected 

for interview. We did not review alternative methods of obtaining 

estimates of the undocumented. 

While we consulted a number of private sector experts and sought to 

include a range of perspectives, other experts may have other views. 

Finally, we do not know to what extent the broad range of persons who 

compose immigrant communities share the views of the immigrant 

advocates we spoke with. 

 6

In 1998, we recommended that the Commissioner of the Immigration and Naturalization 

Service (INS) and the Director of the Census Bureau “devise a plan of joint research for 

evaluating the quality of census and survey data on the foreign-born,” based on our 

discussion of the need to evaluate coverage and possible methods for doing so (see 

GAO/GGD-98-164). This recommendation is still open. In 2002, Census Bureau staff 

assumed that 15 to 20 percent of the undocumented were not enumerated in the 1990

census and stated the belief that coverage of this group improved in the 2000 census. 

(See Joseph Costanzo and others, “Evaluating Components of International Migration: 

The Residual Foreign-Born,” Population Division Working Paper 61, U.S. Census Bureau,

Washington, D.C., June 2002, p. 22.) However, the Census Bureau has not quantitatively 

estimated the coverage of either the foreign-born population overall or the undocumented

population. 

Page 63 GAO-06-775 Estimating the Undocumented Population
Appendix II: Es

Costs, and Co

Undo

timating Characteristics, 

ntributions of the 

cumented Population 

Page 64 GAO-06-775

Appendix II: Estimating Characteristics, 

Costs, and Contributions of the 

Undocumented Population 

Logically, grouped answers data can be used to estimate subgroups of the 

undocumented population, using the following procedures: 

1. isolate survey data for (a) the subsample 1 respondents who are in the 

desired subgroup, based on a demographic or other question asked in 

the survey (for example, if the survey included a question on each 

respondent’s employment, data could be isolated for foreign-born who 

are employed), and (b) subsample 2 respondents in that subgroup; 

2. calculate (a) the percentage of the subsample 1 subgroup respondents 

who are in each box of immigration status card 1 and (b) the 

percentage of subsample 2 subgroup respondents who are in each box 

of immigration status card 2; and 

3. carry out the subtraction procedure (percentage in Box B, Card 1, 

minus percentage in Box A, Card 2), thus estimating the percentage of 

the subgroup who are undocumented. 

 

The resulting percentage can be multiplied by a census count or an 

updated estimate of the foreign-born persons who are in the subgroup (for 

example, multiply the estimate of the percentage of employed foreign-born 

who are undocumented by the census count or updated estimate of the 

number of employed foreign-born). 

These steps can be repeated to indirectly estimate the size of the 

undocumented population within various subgroups defined by activity, 

demographics, and other characteristics (such as those with or without 

health insurance) that are asked about in the survey. Without an extremely 

large survey, it would be difficult or impossible to derive reliable estimates 

for subgroups with few foreign-born persons or few undocumented 

persons. Ongoing surveys conducted annually have sometimes combined 

2 or 3 years of data in order to provide more reliable estimates of lowprevalence groups; however, there is a loss of time-specificity.

Program cost data are sometimes available on an average per-person 

basis, and surveys sometimes ask about benefit use. In such cases, the 

total costs of a program associated with a certain group can be estimated.

Program costs associated with the undocumented population might be 

estimated by either (1) multiplying the estimated numbers of 

undocumented persons receiving benefits by average program costs or 

(2) performing the following procedures: 

Key Characteristics 

Can Be Estimated 

Some Program Costs 

Can Be Estimated 

 Estimating the Undocumented Population
Appendix II: Estimating Characteristics, 

Costs, and Contributions of the 

Undocumented Population 

1. Isolate survey data for all foreign-born subsample 1 respondents who 

said they were in Box B of Card 1 and estimate each individual 

respondent’s program cost.1 Then aggregate the individual costs to 

estimate the total program cost (potentially, millions or billions of 

dollars) associated with the population of foreign-born persons defined 

by the group of immigration statuses in Box B, Card 1. 

2. Isolate data for all foreign-born subsample 2 respondents who said they 

were in Box A of Card 2 and, as above, estimate each individual 

respondent’s program costs, aggregating these to estimate the total 

program costs associated with the population of foreign-born persons 

defined by the immigration statuses in Box A, Card 2 (again, potentially 

millions or billions of dollars). 

3. Because the only difference between the immigration statuses in Box 

B, Card 1, and Box A, Card 2, is the inclusion of the undocumented 

status in Box B, Card 1, start with the total program cost estimate for 

all Box B, Card 1, respondents and subtract the corresponding cost 

estimate for Box A, Card 2, respondents. 

The result of the subtraction procedure represents an indirect estimate of 

program costs associated with the undocumented population. A more 

precise cost estimate can be obtained by calculating an additional “mirror 

image” cost estimate—this time, starting with costs estimated for 

respondents in Box B of Card 2 and subtracting costs associated with 

respondents in Box A of Card 1. The two “mirror image” estimates could 

then be averaged. 

The key limitations on such procedures are sample size and the 

representation of key subgroups—for example, foreign-born respondents 

residing in small states and local areas. Thus, for example, it is possible 

that state-level costs associated with undocumented persons might be 

estimated with reasonable precision for a large state or city with many 

foreign-born persons and a relatively high percentage of undocumented 

(potentially, California or New York City) but not for many smaller states 

 1

Estimation of program costs associated with an individual respondent (or those in very

refined subgroups) is sometimes calculated based on a combination of (1) answers to 

specific questions (such as whether the person is attending public school in the school 

district where he or she lives or how many emergency room visits he or she made) and 

(2) separately available information on program costs per individual (for example, the perpupil costs of public education in specific school districts or the per-visit costs of 

emergency room care). 

Page 65 GAO-06-775 Estimating the Undocumented Population
Appendix II: Estimating Characteristics, 

Costs, and Contributions of the 

Undocumented Population 

or areas, unless very large samples (or samples focused on selected areas 

of interest) were drawn. Further work could explore the ways that 

complex analyses could be conducted to help delineate costs. 

Contributions can be conceptualized as contributions to the economy 

through work or, potentially, through taxes paid. Such contributions might 

be estimated by combining grouped answers data with other survey 

questions to estimate relevant subgroups, such as employed 

undocumented persons. In complex analyses, these data could potentially

be combined with other data to help estimate taxes paid. 

Logically, other quantitative estimates might be obtained through 

procedures similar to those outlined above for estimating program costs. 

For example, the numbers of children in various immigration statuses 

might be estimated by asking an adult respondent how many foreign-born 

children (or how many foreign-born school-age children) reside in the 

household and then—using the 3-box card assigned to the adult 

respondent—asking how many of these children are in Box A, Box B, and 

Box C.2

 We note that, thus far, testing has not asked respondents to report 

children’s immigration status with the grouped answers approach. 

If subsamples 1 and 2 are sufficiently large, it might also be possible to 

estimate the portion of the undocumented population represented by 

• “overstays” who were legally admitted to this country for a specific 

authorized period of time but remained here after that period 

expired (without a timely application for extension of stay or

change of status)3

 and 

Contributions Might 

Be Estimated 

Logically, Estimates 

Can Be Made of 

Undocumented 

Children 

Other Estimates May 

Be Possible 

 2

Potentially, based on the location of the responding household, state and local per-pupil 

school costs could be obtained. Totaling state and local school costs for foreign-born

children in each box would be followed by a group-level subtraction. In this way, the costs

of schooling undocumented immigrant children could be estimated—nationally and 

potentially for key states—without ever categorizing any child as undocumented and

without ever estimating the number of undocumented children in any school district. 

3

See GAO, Overstay Tracking: A Key Component of Homeland Security and a Layered

Defense, GAO-04-82 (Washington, D.C.: May 21, 2004). 

Page 66 GAO-06-775 Estimating the Undocumented Population
Appendix II: Estimating Characteristics, 

Costs, and Contributions of the 

Undocumented Population 

• currently undocumented persons who are applicants for legal 

status and are waiting for DHS to approve (or disapprove) their 

application. 

To estimate overstays would require a separate question on whether the 

respondent had entered the country on a temporary visa. 4 To estimate 

undocumented persons with pending applications would require a 

separate question concerning pending applications for any form of legal 

status (including, for example, applications for U.S. citizenship as well as 

applications for legal permanent resident status and other legal statuses). 

The precision of such estimates would depend on factors such as sample 

size, the percentages of foreign-born who came in on temporary visas or 

who have pending applications of some kind, and the numbers of 

undocumented persons within these groups. 

 4

See Judith A. Droitcour and Eric M. Larson, “An Innovative Technique for Asking Sensitive 

Questions: The Three-Card Method,” Bulletin de Mèthodologie Sociologique, 75 (July 2002): 

5–23. 

Page 67 GAO-06-775 Estimating the Undocumented Population
Appendix III: A Review of Census Bureau and

GAO Reports on the Field Test of the Appendix III: A Review of Census Bureau and Grouped Answer Method 

GAO Reports on the Field Test of the 

Grouped Answer Method 

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Appendix III: A Review of Census Bureau and

GAO Reports on the Field Test of the 

Grouped Answer Method 

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Appendix III: A Review of Census Bureau and

GAO Reports on the Field Test of the 

Grouped Answer Method 

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Appendix III: A Review of Census Bureau and

GAO Reports on the Field Test of the 

Grouped Answer Method 

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Appendix III: A Review of Census Bureau and

GAO Reports on the Field Test of the 

Grouped Answer Method 

Page 72 GAO-06-775 Estimating the Undocumented Population
Appendix IV: A Brief Examination of 

Responses Observed while Testing an Indirect Appendix IV Method for Obtaining Sensitive Information : A Brief Examination of 

Responses Observed while Testing an 

Indirect Method for Obtaining Sensitive 

Information 

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Appendix IV: A Brief Examination of 

Responses Observed while Testing an Indirect 

Method for Obtaining Sensitive Information 

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Appendix IV: A Brief Examination of 

Responses Observed while Testing an Indirect 

Method for Obtaining Sensitive Information 

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Appendix IV: A Brief Examination of 

Responses Observed while Testing an Indirect 

Method for Obtaining Sensitive Information 

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Appendix IV: A Brief Examination of 

Responses Observed while Testing an Indirect 

Method for Obtaining Sensitive Information 

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Appendix IV: A Brief Examination of 

Responses Observed while Testing an Indirect 

Method for Obtaining Sensitive Information 

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Appendix IV: A Brief Examination of 

Responses Observed while Testing an Indirect 

Method for Obtaining Sensitive Information 

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Appendix IV: A Brief Examination of 

Responses Observed while Testing an Indirect 

Method for Obtaining Sensitive Information 

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Appendix IV: A Brief Examination of 

Responses Observed while Testing an Indirect 

Method for Obtaining Sensitive Information 

Page 81 GAO-06-775 Estimating the Undocumented Population
Appendix V: The Issue of Informed Consent Appendix V: The Issue of Informed Consent 

Appropriately informing each respondent about what information he or 

she is being asked to provide is a key issue. On one hand, the grouped 

answers approach logically conveys to each respondent exactly what he or

she is being asked to reveal about himself or herself; no one we spoke with 

suggested otherwise. On the other hand, the grouped answers question 

series does not indicate that the respondent is being asked to participate 

in an effort that will result in estimates of all immigration statuses. 

Therefore, a statement is needed to convey this information. 

Officials and staff at the National Center for Health Statistics (NCHS) were 

particularly concerned about this issue and believed that failing to 

adequately address informed consent issues could be considered 

unethical.1

Privacy protection specialists at the Census Bureau said that

• An introductory statement before the first immigration-related 

question might be phrased, “The next questions are geared to

helping us know more about immigration and the role that it plays in 

American life.” 

• When each respondent is shown the 3-box training cards, it would 

be possible to explain to him or her that—while the survey does not 

ask, and does not want to know, the specifics of which Box B 

category applies to him or her—there will be other interviews in 

which other respondents will be asked about some of the Box B 

categories or statuses.2

 

• Just before showing each respondent the immigration status card, it 

should be stated—and, in fact, interviewers stated in the test with 

Hispanic farmworkers—that “Using the boxes allows us to obtain 

the information we need, without asking you to give us information 

that you might not want to.” Further: “Because we’re using the 

boxes, we WON’T ‘zero in’ on anything somebody might not want to 

tell us.”3

 1

None of the immigration experts we interviewed raised this issue, however. 

2

Thus far, testing has included only one immigration status card, so test interviewers have 

not told respondents that other respondents will be providing information on some of the 

Box B statuses. 

3

See GAO/GGD-00-30. 

Page 82 GAO-06-775 Estimating the Undocumented Population
Appendix V: The Issue of Informed Consent 

• It may also be possible to explain that the study’s goal is to allow 

researchers to broadly estimate all categories or statuses on the card 

for the population of immigrants—but to indicate that this will be 

done without ever asking questions that “zero in” on something that 

some respondents might not want to disclose in an interview. 

• Neither the estimation method (that is, the two cards) nor the 

specific policy relevance of immigration-status estimates would have

to be described to all respondents.However, interviewer statements 

should be provided for responding to respondents who have doubts 

or questions. 

Page 83 GAO-06-775 Estimating the Undocumented Population
Appendix VI: A Note on Variances and “Mirror Appendix VI: A Note on V Image” Estimates

ariances and 

“Mirror Image” Estimates 

The statistical expression and variance of a grouped answers estimate is 

as follows, with the starting point being the percentage or proportion of 

subsample 1 who are in Box B, Card 1, and the procedure being to 

subtract from this the proportion of subsample 2 who are in Box A, Card 2 

(with cards and boxes as defined as in figure 3): 1

Grouped answers estimate = p1 – p2. 

where 

 p1

 = the proportion of subsample 1 in Box B, Card 1 

 p2

 = the proportion of subsample 2 in Box A, Card 2 

Variance (p1

 – p2) = [(p1q1/n1) + (p2q2/n2)] 

where 

 q1

 = 1 – p1 = the proportion of subsample 1 not in Box B, Card 1 

 q2

 = 1 – p2 = the proportion of subsample 2 not in Box A, Card 2

 n1

 and n2 = numbers of respondents in subsamples 1 and 2, 

 respectively. 

The immigration status cards in figure 3 are designed so that Boxes A and 

B include all major immigration statuses. This design ensures that, on each 

card, the Box B categories apply to the largest possible number of legally 

present respondents. In designing the cards this way, we reasoned that 

this should reduce the question threat associated with choosing Box B. 

As a result, few respondents are expected to choose Box C (“some other 

category not in Box A or Box B”). For example, in the 2004 GSS test, only 

one foreign-born respondent of more than 200 chose Box C. Therefore, we 

believe that for purposes of illustrative variance calculations, it is 

reasonable to assume that no one chooses Box C. Under this assumption,

the two mirror-image estimates of the percentage of the foreign-born who 

are undocumented would necessarily be exactly the same, as explained 

below. 

Assuming that no respondent chooses Box C, then 

 q1

 = 1 – p1 = the proportion of subsample 1 in Box A, Card 1 

 q2

 = 1 – p2 = the proportion of subsample 2 in Box B, Card 2 

 1

For simplicity, the discussion in this appendix assumes simple random sampling, for both 

the main sample and the selection of the two subsamples. 

Page 84 GAO-06-775 Estimating the Undocumented Population
Appendix VI: A Note on Variances and “Mirror 

Image” Estimates

The alternative, mirror-image estimate can then be defined as follows: 

Mirror-image estimate = q2

 – q1

As indicated above, q1 and q2 are defined in terms of p1 and p2. Using 

algebraic substitution, we have: 

 p1

 – p2 = (1– q1) – (1– q2) = 1 – 1 – q1 + q2 = q2 – q1 

In other words, under the assumption that no one chooses Box C, the 

mirror-image estimates of the percentage undocumented are, by definition, 

identical. Thus, no precision gain follows from combining them.2

 No 

additional information is provided by a second, mirror-image estimate. 

In contrast, quantitative indirect estimates are based on a combination of 

(1) grouped answers data and (2) additional, separate quantitative data or

estimates (for example, per-person estimates of emergency-visit costs 

based on respondent reports of number of emergency room visits in the 

past year and other information from hospitals on per-visit costs). If the 

quantitative data are tallied or totaled for individuals in each box of each 

card, the result is four different figures, none of which can be derived from 

the others. (There are different respondents in each box, and each would 

have separately reported how many emergency room visits, for example, 

he or she made in the past year.) Thus, for quantitative estimates of this 

type, calculating two independent mirror-image estimates, and averaging 

them, may yield a more precise result. 

 2

Logically, if very few persons choose Box C, the precision gains from combining the

mirror-image estimates (which would necessarily be very similar to each other) would be 

very small. 

Page 85 GAO-06-775 Estimating the Undocumented Population
Appendix VII: Comments from the Appendix VII: Comments from the Department of Commerce 

Department of Commerce 

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Appendix VII: Comments from the 

Department of Commerce 

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Appendix VII: Comments from the 

Department of Commerce 

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Appendix VIII: Comments from the Department of Appendix VIII: Comments from the Homeland Security

Department of Homeland Security 

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Appendix IX: Comments from the Department 

of Health and Human Services Appendix IX: Comments from the 

Department of Health and Human Services 

Page 90 GAO-06-775 Estimating the Undocumented Population
Appendix IX: Comments from the Department 

of Health and Human Services 

Page 91 GAO-06-775 Estimating the Undocumented Population
Appendix X: 

A

GAO Contact and Staff 

cknowledgments 

Page 92 GAO-06-775

Appendix X: GAO Contact and Staff 

Acknowledgments 

Nancy R. Kingsbury, (202) 512-2700 or kingsburyn@gao.gov. 

Key GAO staff contributing to this report include Judith A. Droitcour, 

Eric M. Larson, and Penny Pickett. Statistical support was provided by 

Sid Schwartz, Mark Ramage, and Anna Maria Ortiz. 

GAO Contact 

Staff 

Acknowledgments 

 Estimating the Undocumented Population
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