January 9, 2012

U.S. Foreign-Born Population: How Much Change from 2009 to 2010?

Appendix B: Methodology

Population data from the American Community Survey (ACS) are tied to the Census Bureau’s official population estimates through a weighting process that is designed so the ACS figures agree with pre-specified population totals by age, sex, race and Hispanic origin for the nation and smaller geographic areas (Census Bureau, 2009). The ACS data also agree with control totals for group quarters populations. Each year, the Census Bureau produces new population estimates, not only for the most recent year but also for every year since the most recent census; these estimates are designated by the year produced as, for example, “Vintage 2009.” Each new ACS is weighted to that year’s vintage of population estimates, but earlier ACS datasets are not reweighted to reflect the newest vintage of estimates.

Comparisons of ACS estimates from one year to another encompass both real underlying population changes and changes in the population estimates used to weight the ACS. For most years, changes in the series of population estimates from one vintage to the next tend to be small—reflecting mainly the incorporation of final data on births, deaths and immigration to replace the preliminary data used the year before. However, the changeover to population data from the 2010 Census from estimates based on the 2000 Census (including Vintage 2009 estimates in the 2009 ACS) has significant effects on measures of change in the foreign-born population (as documented in this report).

Similar issues of inconsistent population weights across time arose with the Census Bureau’s Current Population Survey (CPS) during the 2000-2010 decade. To develop consistent measures of the unauthorized immigrant population across the decade and consistent measures of annual change, the Pew Hispanic Center produced alternative population weights for the CPS and used the reweighted data as a basis for measuring change over time. (See Passel and Cohn, 2010 as well as Kochhar et al., 2010.) The Pew Hispanic revised estimates reported here for the 2009 ACS represent the first step in applying a consistent weighting methodology to ACS data for 2005-2010.

Differences Between Intercensal and Postcensal Population Estimates

The Census Bureau’s Population Estimates Program produces postcensal estimates of the total population for the nation, states, counties and places as well as estimates for age, sex, race/Hispanic groups for the nation, states, and counties. For the 2000-2009 decade, the postcensal estimates represent updates of the 2000 Census. After the results of the 2010 Census became available, the Census Bureau produced an alternative set of intercensal population estimates for the nation, states and counties that are consistent with both the 2000 and 2010 censuses. These intercensal estimates provide a basis for developing consistent population weights for the ACS that can be used to assess year-to-year changes in various population groups, including the foreign-born.

Differences between the intercensal estimates and postcensal estimates (for the 2010 Census) are not large in the context of a total population of 309 million or a foreign-born population of 40 million. However, for year-to-year comparisons as measures of population change, incompatibilities attributable to weighting changes or other methodological changes can be as large as the actual change and can severely distort measures of change over time. For 2009, the intercensal population estimate for the total population is only 235,000, or 0.1% below the vintage 2009 estimate. (See Appendix Table 1.) However, the Hispanic intercensal population estimate exceeds the postcensal population estimate by 908,000, or 1.8%, and the Asian (alone, not Hispanic) intercensal estimate exceeds the postcensal estimate by 675,000, or 4.7%. Almost all of these differences occur among adults. The majority of adults in these two groups are foreign-born, and together account for about two-thirds of all immigrants. Thus, these differences between the population estimates used to weight race groups can lead to notable differences in survey-based estimates of the foreign-born population for 2009.

ACS Weighting

Development of ACS population weights is a complex process that involves postcensal estimates for age-sex-race/Hispanic populations for counties or groups of counties as well as estimates of married couples and group quarters populations (U.S. Census Bureau, 2009). The weighting process uses six race/Hispanic groups—white, black, American Indian and Alaska Native, Asian, Native Hawaiian, and Hispanic.8

For each race/Hispanic group, the population is further divided by sex and into 13 age groups— younger than 5, 5-14, 15-17, 18-19, 20-24, 25-29, 30-34, 35-44, 45-49, 50-54, 55-64, 65-74, 75 and older. If the number of cases in a subgroup within a weighting area is “too small” (fewer than 10) or the adjustment factor for a group (the amount by which its weight is enlarged or reduced) is “extreme” (below 1/3.5 or greater than 3.5), the category is “collapsed” with other groups until the weighting criteria are met. In the collapsing process, race/Hispanic groups are first merged. Then, the age-sex cells are tested within the merged race/Hispanic group. The goals of the collapsing scheme are “to keep children [under 18] together whenever possible by collapsing across sex within the first three age categories. In addition, the collapsing rules keep men age 18-54, women age 18-54, and seniors 55+ together in separate groups by collapsing across age” (U.S. Census Bureau, 2009: pp. 11-13).

ACS weighting is done separately for persons in households, institutional group quarters by type (correctional institutions, juvenile detention facilities, nursing homes, other long-term care facilities), and noninstitutional group quarters (college dormitories, military facilities, other noninstitutional facilities). The weighting for group quarters is done at the state level by type of facility with no demographic controls imposed. The household weighting uses the demographic groups described above subdivided into four groups: householders in married couple or unmarried partner households; spouses or unmarried partners of persons in the first group; householders of other types of households; and the balance of the household population.

Unlike its disclosure practice in weighting the CPS, the Census Bureau does not publish detailed population estimates used in ACS weighting or specify the weighting areas; moreover, in the publicly available ACS microdata, the geographic areas used in weighting do not seem to be identifiable. Thus, it is not possible for data users outside the Census Bureau to replicate the full ACS weighting process. However, in order to produce estimates that can be compared across different years of the ACS, the Pew Hispanic Center has developed revised weights by following the general concepts employed by the Census Bureau in weighting the ACS.

Implementing Revised ACS Weighting

The Pew Hispanic analysis uses a modified weighting process that adjusts the existing ACS weights to produce a consistent set of data that approximates the weights that would have been obtained from a full ACS weighting based on the intercensal population estimates. Integrated Public-Use Microdata Series (IPUMS) datasets are used in this process (Ruggles et al., 2010).9 The reweighting uses population estimates at the state level and is a greatly simplified version of the full ACS weighting. Iterative proportional fitting is used to match control totals based on the intercensal population estimates for three sets of marginal totals:

  1. 1. State-level population totals by age, sex, and race/Hispanic origin using the same breakdowns in the Census Bureau’s weighting process. More stringent cell-size requirements are imposed to minimize changes from the initial ACS weights. Collapsing rules follow the concepts in the Census Bureau weighting.
  2. 2. State-level totals for household, institutional group quarters and noninstitutional group quarters. The broad grouping of group quarters populations is used because more detailed information on group quarters type is not available in the ACS public datasets. No demographic breakdowns are used.
  3. 3. National totals for age, sex, and race/Hispanic origin groups with no collapsing. Ten iterations are performed to ensure convergence on all dimensions of the fitting process. The final adjustment to detailed national totals for age-sex-race groups is not part of the Census Bureau’s procedures but is included to maintain strict consistency of the reweighted data with the intercensal population estimates.

Race Groups. The race groups used in weighting assign all non-Hispanic individuals to one of five specific race groups and require population totals for the same groups. Accordingly, the intercensal population estimates used in the PHC reweighting are “bridged race” estimates released by the CDC (U.S. Centers for Disease Control and Prevention, 2011). These estimates are consistent with the Census Bureau’s intercensal estimates (U.S. Census Bureau, 2011a) but have reassigned estimates of “some other race” and multiple race populations to four specific race groups (white, black, American Indian and Alaska Native, and Asian and Pacific Islander). The Asian and Pacific Islander group in the bridged race estimates is subdivided into Asian and Native Hawaiian using proportions from the intercensal population estimates for the U.S. and for California (the only state with enough sample cases to require a separate control total for Native Hawaiians).

For weighting purposes, individual respondents in the ACS who give multiple responses to the race item or who are classified as some other race are assigned a single race group in accordance with the methods used to develop the bridged race estimates.10 The assignments use the IPUMS probabilities with thresholds selected to bring state totals for individual race groups in line with the bridged race aggregate estimates published by NCHS (Ingram et al., 2003).11 These assigned races are used in reweighting, but the original ACS race item is retained for all other analyses.

Collapsing Rules. To minimize adjustments to the published ACS weights, the collapsing rules for race groups and age-sex groups are much more stringent than the Census Bureau employs in its weighting. If the number of ACS respondents in a state within a race group is less than 100 or the required adjustment factor is less than 0.67 or greater than 1.5, the race group is collapsed with the next smallest non-Hispanic race group.12 For age-sex groups within a race group, the same minimum number of respondents and ranges for the adjustment factor determine whether the group is collapsed. Collapsing rules first attempt to keep children (younger than 18) and adults separate. For children, age groups are first collapsed by combining males and females and then by collapsing age groups. For persons ages 18-54, collapsing is first done for age groups to maintain separate totals for men and women. For ages 55 and older, the rules are the same as for children.

Regions. The estimates of the foreign-born population shown in this report divide the world into regions. “Europe” includes Russia and all the newly independent countries that were part of the former Soviet Union, even though some of the countries are geographically in Asia. This grouping is designed to maintain maximum consistency over time. “Canada” also includes parts of North America not classified, such as Bermuda and St. Pierre and Miquelon. “Middle East” as defined here includes countries of southwest Asia from Turkey and Cyprus in the north and west to Iran in the east to the Arabian Peninsula in the south; it also includes countries of North Africa (Egypt, Sudan, Libya, Tunisia, Algeria, Morocco and Western Sahara). Note that the Middle East does not include Afghanistan or Pakistan. “South and East Asia” includes the rest of Asia from Afghanistan and Pakistan eastward. “Africa” consists of sub-Saharan Africa.

Cite this publication: Jeffrey S. Passel and D’Vera Cohn. “U.S. Foreign-Born Population: How Much Change from 2009 to 2010?.” Pew Research Center, Washington, D.C. (January 9, 2012) http://www.pewhispanic.org/2012/01/09/u-s-foreign-born-population-how-much-change-from-2009-to-2010/, accessed on July 23, 2014.

  1. The race totals include non Hispanic persons only. For weighting purposes, persons reporting multiple races and persons reporting “some other race” are assigned to one of the five specified groups. The ACS documentation does not describe the race assignment process.
  2. Estimates from IPUMS differ slightly from the Census Bureau’s published estimates that are based on the full ACS sample. For example, the published ACS foreign-born population in 2010 is 39.956 million and the IPUMS figure is 39.929 million. The comparable figures for 2009 are 38.517 million and 38.462 million.
  3. The assignments use the IPUMS variables RACESINGD (a version of bridged race) and PROBWHT, PROBBLK, PROBAI, PROBAPI and PROBOTH which provide bridged race probabilities that a person of some other race or multiple races would provide a single race response of, respectively, white, black, American Indian and Alaska Native, Asian and Pacific Islander, and Some Other Race.
  4. The population estimates used in this assignment process are not the intercensal bridged race estimates but those of the “proper” vintage (e.g., vintage 2009 for the 2009 ACS).
  5. An exception is made for the American Indian and Alaska Native (AIAN) group. Because of the difficulty of assigning mixed AIAN-white responses, the AIAN group is first collapsed, if necessary, with the white population in most instances.