Numbers, Facts and Trends Shaping Your World

As Growth Stalls, Unauthorized Immigrant Population Becomes More Settled

Appendix C: Methodology


The estimates presented in this report for the unauthorized immigrant population are based on a residual estimation methodology that compares a demographic estimate of the number of immigrants residing legally in the country with the total number of immigrants as measured by a survey—either the American Community Survey (ACS) or the March Supplement to the Current Population Survey (CPS); the difference is assumed to be the number of unauthorized immigrants in the survey, a number that is later adjusted for omissions from the survey (see below). The basic estimate is:


The legal resident immigrant population is estimated by applying demographic methods to counts of legal admissions covering the period from 1980 to 2012 obtained from the Department of Homeland Security’s Office of Immigration Statistics and its predecessor at the Immigration and Naturalization Service, with projections to 2013. The initial estimates are calculated separately for age-gender groups in six states (California, Florida, Illinois, New Jersey, New York and Texas) and the balance of the country; within these areas the estimates are further subdivided into immigrant populations from 35 countries or groups of countries by period of arrival in the United States. Variants of the residual method have been widely used and are generally accepted as the best current estimates (Baker and Rytina, 2014; Hoefer, Rytina and Baker, 2012; Warren and Warren, 2013). See also Passel, Cohn and Gonzalez-Barrera (2013), Passel and Cohn (2008) and Passel (2007) for more details. The overall population estimates presented in this report are the residual totals, adjusted for survey omissions for these six states and the balance of the country, subdivided for Mexican immigrants and other groups of immigrants (balance of Latin America, south and east Asia, rest of world) depending on sample size and state.

Once the residual estimates have been produced, individual foreign-born respondents in the survey are assigned a specific status (one option being unauthorized immigrant) based on the individual’s demographic, social, economic, geographic and family characteristics. These status assignments are the basis for the characteristics reported here (including, for example, specific countries of birth, detailed state estimates, duration of residence and presence of children). A final step in the weighting-estimation process involves developing final state-level estimates that take into account trends over time in the estimates. For this report, additional status assignments involving Temporary Protected Status (TPS) and Deferred Action for Childhood Arrivals (DACA) were done for the 2012 ACS only. Later reports will focus on more detailed information on the countries and regions of origin of the immigrants, estimates for all states and major metropolitan areas, and various demographic, social and economic characteristics of the unauthorized and legal immigrant populations.

Data Sources and Survey Weights

The American Community Survey is an ongoing survey conducted by the U.S. Census Bureau. The survey collects detailed information on a broad range of topics, including country of birth, year of immigration and citizenship—the information required for the residual estimates. The ACS has a continuous collection design with monthly samples of about 250,000; the nominal annual sample size was about 2.9 million households for 2005-2009 with about 1.9 million included in the final sample. The initial sample was expanded to almost 3.3 million addresses for 2011 and over 3.5 million for 2012; the final sample included more than 2.1 million address in 2011 and almost 2.4 million in 2012. (

For this report, public use samples of individual survey records from the ACS are tabulated to provide the data used in the estimation process. The public use file is a representative 1% sample of the entire U.S. (including about 3 million individual records for each year 2005-2012) obtained from the Integrated Public Use Microdata Series or IPUMS (Ruggles et al., 2010). The ACS began full-scale operation in 2005 covering only the household population; since 2006 it has covered the entire U.S. population. ACS data are released by the Census Bureau in September for the previous year.

The other survey data source used for residual estimates comes from March Supplements to the Current Population Survey. The CPS is a monthly survey currently of about 55,000 households conducted jointly by the U.S. Bureau of Labor Statistics and the Census Bureau. Since 2001, the March supplement sample has been expanded to about 80,000 households; before then, the expanded March Supplement sample included about 50,000 households. The CPS universe covers the civilian noninstitutional population. The CPS was redesigned in 1994 and, for the first time, included the information required for the residual estimates (i.e., country of birth, date of immigration and citizenship). Some limitations of the initial March Supplement redesign of the CPS as implemented in 1994 preclude its use in making these estimates, so the first CPS-based estimates are for March 1995. CPS data are released by the Census Bureau in September for the previous March. The most recent March CPS data were for 2013.

Population figures from both the ACS and CPS are based on the Census Bureau’s official population estimates for the nation, states and smaller areas through a weighting process that ensures the survey figures agree with pre-specified national population totals by age, sex, race and Hispanic origin. At the sub-national level, the two surveys differ in their target populations. The March CPS data agree with state-level totals by age, sex and race and are based on a process that imposes other conditions on weights for couples (U.S. Census Bureau, 2006). The ACS weights use estimates for much smaller geographic areas that are summed to state totals ( – especially Chapter 11).

The population estimates for the surveys are based on the latest available figures at the time the survey weights are estimated. This process produces the best estimates available at the time of the survey, but it does not guarantee that a time series produced across multiple surveys is consistent or accurate. Significant discontinuities can be introduced when the Census Bureau changes its population estimation methods, as it did several times early in the 2000s and in 2007 and 2008 (Passel and Cohn, 2010), or when the entire estimates series is recalibrated to take into account the results of a new census.

The estimates shown for unauthorized immigrants and the underlying survey data are derived from ACS IPUMS 1% samples for 2005-2012 and March CPS public use files for 1995-2013, which have been reweighted to take into account population estimates consistent with the 1990 Census, the 2000 Census, the 2010 Census and the most recent population estimates. The population estimates used to reweight the March 2011 CPS come from the Census Bureau’s Vintage 2011 population estimates (; they are consistent with the 2010 Census and the estimates used to weight the March 2012-2013 CPS. The population estimates used to reweight the CPS for March 2001 through March 2010 are the Census Bureau’s intercensal population estimates for the 2000s (; these population estimates use demographic components of population change for 2000-2010 and are consistent with both the 2000 and 2010 censuses. Similarly, the population estimates used to reweight the CPS for March 1995 through March 2000 are the intercensal population estimates for the 1990s, which are consistent with the 1990 and 2000 censuses. The ACS data for 2010-2012 do not require reweighting as they are weighted to recent population estimates based on the 2010 Census. For the 2005-2009 ACS, the reweighting uses the same intercensal population estimates as used for the CPS.7 The reweighting methodology for both the ACS and CPS follows, to the extent possible, the methods used by the Census Bureau in producing the sample weights that equal the population totals. See Passel, Cohn and Gonzalez-Barrera 2013 for more details on weighting and adjustments for survey undercoverage.

Because of the much larger sample size in the ACS (3.1 million sample cases in 2012 including more than 350,000 foreign-born cases) than the March CPS (203,000 sample cases in 2013 with about 26,000 foreign-born), the ACS-based estimates should be considered more accurate than the CPS-based estimates. In this publication, we have replaced the previous CPS-based estimate for 2012 with the new ACS-based estimate. The CPS-based estimate for 2013 should be considered preliminary as it will be replaced with an ACS-based estimate when the 2013 ACS data become available.

Status Assignments—Legal and Unauthorized Immigrants

Individual respondents are assigned a status as a legal or unauthorized immigrant based on the individual’s demographic, social, economic and geographic characteristics so the resulting number of immigrants in various categories agrees with the totals from the residual estimates. The assignment procedure employs a variety of methods, assumptions and data sources.

First, all immigrants entering the U.S. before 1980 are assumed to be legal immigrants. Then, the data are corrected for known over-reporting of naturalized citizenship on the part of recently arrived immigrants (Passel et al. 1997) and all remaining naturalized citizens from countries other than Mexico and those in Central America are assigned as legal. Persons entering the U.S. as refugees are identified on the basis of country of birth and year of immigration to align with known admissions of refugees and asylees (persons granted asylum). Then, individuals holding certain kinds of temporary visas (including students, diplomats and “high-tech guest workers”) are identified in the survey and each is assigned a specific legal temporary migration status using information on country of birth, date of entry, occupation, education and certain family characteristics. Finally, some individuals are assigned as legal immigrants because they are in certain occupations (e.g., police officer, lawyer, military occupation, federal job) that require legal status or because they are receiving public benefits (e.g., welfare or food stamps) that are limited to legal immigrants. As result of these steps, the foreign-born population is divided between individuals with “definitely legal” status (including long-term residents, naturalized citizens, refugees and asylees, legal temporary migrants, and some legal permanent residents) and a group of “potentially unauthorized” migrants.

The number of potentially unauthorized migrants typically exceeds the estimated number of unauthorized migrants (from the residual estimates) by 15-35%. So, to have a result consistent with the residual estimate of legal and unauthorized immigrants, probabilistic methods are employed to assign legal or unauthorized status to these potentially unauthorized individuals. This last step also involves a check to ensure that the legal statuses of family members are consistent; for example, all family members entering the country at the same time are assumed to have the same legal status. The entire process requires several iterations to produce estimates that agree with the demographically derived population totals. At the end, the final estimates agree with the residual estimates for the six individual states noted earlier and for the balance of the country; for Mexican-born and other legal and unauthorized immigrants in each area; and for children, working-age men and working-age women within each category. Finally, the survey weights for the foreign-born are adjusted upward so the tabulated figures agree with the analytic, demographic estimates of the total number of legal and unauthorized migrants developed in the very first step.

For this report, two additional status groups have been assigned to persons initially assigned as unauthorized immigrants: (1) DACA approval or persons approved under the Deferred Action for Childhood Arrivals criteria; and (2) Temporary Protected Status. Under the DACA standards, an unauthorized immigrant must meet a number of specific criteria (U.S. Citizenship and Immigration Services, 2012

  1. Arrived in the U.S. before age 16 and were under age 31 as of June 15, 2012;
  2. Continuously resided in the U.S. Since June 15, 2007;
  3. Physically present in the U.S. on June 15, 2012;
  4. Enrolled in school, have a high school diploma or a GED or have been honorably discharged from the military or the Coast Guard at the time of application;
  5. Not been convicted of a felony, a significant misdemeanor offense. or three or more other misdemeanors, and do not present a threat to national security or public safety.

Using information from the 2012 ACS on year of arrival in the U.S., educational attainment, and veteran status, we determine whether persons assigned as unauthorized immigrants meet criteria (1)-(4). If they do so, they are identified as potential DACA applications. From this pool, we selected enough ACS respondents to represent the 580,000 DACA requests received by DHS as of September 2013 and approximate their characteristics (e.g., age by country of origin, age by gender, age by marital status and state of residence). See the tables at %20for%20Childhood%20Arrivals/USCIS-DACA-Characteristics-Data-2014-7-10.pdf.

Temporary Protected Status (TPS) is primarily a function of an individual’s country of birth and date of arrival. As of calendar 2013, approximately 420,000 persons had been granted TPS.8 We selected ACS respondents previously designated as unauthorized immigrants to represent the TPS population based on country of birth and year of arrival:

El Salvador 270,650 Arrived before 2001
Honduras 83,349 Arrived before 1999
Haiti 58,037 Arrived before 2011
Nicaragua 4,275 Arrived before 1999
Syria 2,475 Arrived before 2013
Sudan 514 Arrived before 2005
Somalia 378 Arrived before 2012

Other Methodological Issues

Rounding of Estimates. All state- and national-level estimates for unauthorized immigrant populations are presented as rounded numbers to avoid the appearance of unwarranted precision in the estimates. Estimates less than 100,000 are rounded to the nearest 5,000; estimates in the range of 100,000-250,000 to the nearest 10,000; estimates smaller than 1 million to the nearest 25,000; estimates of 1-10 million are rounded to the nearest 50,000; and estimates larger than that to the nearest 100,000. Unrounded numbers are used for statistical significance tests, in plotting charts and in computations of differences and percentages.

Duration of Residence. The reference date for the ACS is July 1 of the survey year (e.g., July 1, 2010 for the 2010 ACS). However, data are collected throughout the year and the date when individual information was collected is not available in the public use data. It is not possible to determine the exact duration of residence in the U.S. for each respondent, only the year of arrival in the U.S. In computing the distribution of duration of residence and the median duration of residence, we assumed that, on average, the ACS respondents arriving in a given year spent half of that year in the U.S. and, further, that respondents spent half of the survey year in the U.S. So, for example, in the 2012 ACS, the number of immigrants who had been in the U.S. for less than 10 years was estimated as those who reported arriving in 2003-2012 (which represents persons in the U.S. for less than 9.5 years) plus half of those arriving in 2002. The median duration of residence was computed from tabulations of immigrants by calendar year of arrival. For the CPS, period of immigration is reported in two-year intervals (e.g., immigrants arriving in 1998-1999); for computing distributions and medians, we assumed that the arrivals were evenly distributed across the period.

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  1. For the 2005, the ACS included only the household population; it did not cover the group quarters population. To make the data for the 2005 ACS comparable with 2006 and later, we augmented the ACS by adding records to represent the group quarter population by borrowing records from the 2006 ACS. (See Passel, Cohn and Gonzalez-Barrera 2013.)
  2. Table entitled, “Existing Grants of Temporary Protected Status” supplied by DHS.

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