Estimating Foreign-Born Emigration from the United States Using 

Data from the American Community Survey 

Mark A. Leach 

Eric B. Jensen 

Population Division

U.S. Census Bureau

4600 Silver Hill Road 

Washington, D.C. 20233 

mark.a.leach@census.gov

eric.b.jensen@census.gov

Paper presented at the Federal Committee on Statistical Methodology Research Conference

November 4-6, 2013

Washington, D.C. 

Abstract

In the absence of comprehensive data on foreign-born persons who leave the United States, demographers often use 

a residual method to estimate annual rates of foreign-born emigration. Historically, demographers used data from

two subsequent decennial censuses to enumerate the foreign-born population in an earlier census, survive that 

population forward ten years, and compare the expected survived population to the enumerated population in the 

second Census. The difference, or residual, between the survived and enumerated populations, excluding immigrants

who arrived in the interim, is assumed to be due to emigration. The main critique of this method is that only a small

proportion of emigration that occurs within ten years of first arriving in the United States, common among groups 

such as the Mexican born, is measured. Annual data from the American Community Survey, however, may provide

sufficient sample size of the foreign-born to overcome this weakness of the residual method. The present study

assesses the feasibility of using data from the American Community Survey to estimate foreign-born emigration and

presents comparisons with estimates based on other data sources and methods.

This paper is released to inform interested parties of ongoing research and to encourage discussion of work in

progress. Any views expressed on statistical, methodological, technical, or operational issues are those of the

authors and not necessarily those of the U.S. Census Bureau. 

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Introduction

One of the more difficult tasks that demographers must undertake to estimate change in a national population is to

measure the number of people that leave, or emigrate, to reside in another country. In the United States, immigration 

is a large driver of emigration. In other words, some immigrants who come to the United States stay only 

temporarily, as in the cases of university students or those with temporary work visas. Other immigrants who come

here to work for twenty or thirty years may eventually return home after retirement. However long the duration of

their stay and whatever the reasons for leaving, the number of people that emigrate is one of the most difficult 

components of population change to measure. The U.S. government does not track systematically people who leave 

the country, and the number of places to which they go makes individual data collection impossible. 

The purpose of this research is to assess the feasibility of using data from the American Community Survey (ACS) 

to estimate foreign-born emigration from the United States. In the absence of comprehensive data on foreign-born

persons who leave the United States, demographers have used the residual method to measure indirectly foreignborn emigration. Data from two subsequent decennial censuses are used typically to compare a foreign-born

population enumerated at two points in time after accounting for mortality and new immigrant arrivals. The 

difference, or residual, is assumed to be due to emigration. While theoretical weaknesses of the residual method

have long been known, publication in recent years of emigration estimates based on other data sources and methods 

have shed further light on potential bias in residual-based emigration estimates. 

This research is part of work at the U.S. Census Bureau to improve its method of estimating foreign-born emigration 

for its Population Estimates Program. For its Vintage 2012 population estimates, the Census Bureau used data from

Census 2000 and several years of ACS microdata to estimate emigration levels and rates. Continuing to rely on

Census 2000, however, presents similar problems as decennial-to-decennial estimates. We use annual data from the 

ACS to estimate foreign-born emigration rates. Emigration rates based on annual ACS data overcome weaknesses of

the residual method by measuring emigration over a shorter period of time. This results in more timely emigration

estimates by including immigrants who arrived in the United States relatively recently (Van Hook et al. 2006). A 

shorter observation period also better reflects the typical timing of emigration relative to immigrants’ arrival in the 

United States. Return migration often occurs within the first few years after arrival in the United States, especially 

among Mexican immigrants who are relatively more likely than other immigrants to return home (Massey, Durand

and Malone 2002; Riosmena 2004). By averaging emigration over ten years, however, a decennial-to-decennial 

estimate implicitly assumes that emigration is distributed evenly over a decade, which likely results in an estimate 

that is biased downward. Our research findings suggest that reducing the number of years over which a foreign-born 

population is observed improves residual-based measures of emigration relative to previous residual-based estimates 

and estimates based on other methods and data sources.

Previous Research and Methods

The residual method was first developed by Warren and Peck (1980) to estimate foreign-born emigration from the 

United States between 1960 and 1970. They estimated foreign-born emigration by subtracting the observed foreignborn population in the 1970 census from the expected foreign-born population in 1970 derived from the 1960

census. The difference, or residual, is assumed to be due to emigration. The expected population was calculated by

subtracting an estimated number of deaths experienced in the foreign-born population between 1960 and 1970 and 

adding an estimate of new arrivals during the decade. Warren and Peck also adjusted for what the authors referred to

as “nativity bias” or when foreign-born respondents misreport their nativity status. They also calculated annual rates 

of emigration by dividing a residual by the foreign-born population at risk of emigrating, enumerated in the most

recent census. Using the 1980 and 1990 censuses, Ahmed and Robinson (1994) refined the method by adjusting 

assumptions about emigration of foreign born who arrived during the period between 1980 and 1990. In another

widely-cited study, Mulder (2003) used the 1990 and 2000 censuses to assess trends in emigration during the 1990s.

The U.S. Census Bureau currently uses Census 2000 data in combination with annual data from the ACS to estimate 

emigration rates for several foreign-born subpopulations (Bhaskar, Arenas-Germosen and Dick 2013; Bhaskar, 

Rastogi and Kennedy-Puthoff 2008).

There are several common criticisms of the residual method, some of which focus on its reliance on data from

decennial censuses. First, in general the residual method is sensitive to coverage or measurement error in census or 

survey data. For instance, if the coverage of the foreign-born population is relatively poor in an earlier census, the 

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foreign-born population will be underestimated and an emigration residual will be lower than it otherwise would

have been had there been no undercount. This will result in an underestimate of emigration.

Second, a decennial-to-decennial estimate of emigration lacks timeliness both in terms of annual variation on

international migration flows and in terms of the cohort of immigrants included in a measure emigration.

International migration fluctuates annually due to economic, social and political dynamics in sending and receiving 

countries (Bean and Stevens 2003). For example, the enumerated Mexican-born population was 9.6 million in

Census 2000, grew to an estimated 12.6 million in 2007, and declined to 12.3 million in 2010 (Passel, Cohn and

Gonzalez-Barrera 2012), suggesting more emigration occurred at the end of the decade relative to the first half of the 

decade. A decennial-to-decennial measure of emigration will not reflect this variation (Passel, Cohn and GonzalezBarrera 2012; Rendall, Brownell and Kups 2011). 

In addition, decennial-to-decennial emigration estimates do not include the most recently-arrived immigrants (Van

Hook and Zhang 2011; Van Hook et al. 2006). Estimates produced using 1990 and 2000 census data were based on

the foreign-born population that had arrived in the United States prior to 1990. As such, estimates produced in the 

early 2000s did not include immigrants that arrived since 1990. Previously, researchers either assumed that recent 

arrivals have similar rates of emigration as earlier arrivals or made assumptions about differences in emigration

behavior, neither of which can be validated. In either case, emigration trends among recent arrivals, perhaps the

most important group to measure emigration given their propensity to return to their home country, are not captured 

in the estimate.

Also related to recent arrivals, a criticism of the residual method is that measuring emigration over ten years may not 

accurately reflect actual patterns of international migration. Return migration typically occurs within just a few years

after arriving in the United States, especially in the Mexican-born population which has relatively high rates of

return migration (Massey, Durand and Malone 2002; Massey and Singer 1995). The residual method assumes that 

emigration is evenly distributed across an observation horizon by annualizing total emigration in a period to 

calculate an annual emigration rate. If most emigration occurs in the first few years of an intercensal period and

subsequently declines, average annual emigration will be underestimated by including years for which emigration is 

minimal. For example, an emigration residual based on 1990 and 2000 Censuses measures emigration behavior of

the foreign-born population that arrived prior to 1990. Most emigration for this cohort of immigrants likely occurred

in the beginning of the 1990s when a greater proportion of the cohort had relatively less experience in the United

States. To the extent that emigration declined between 1995 and 2000, a 1990-2000 ten-year residual would be only 

slightly larger than a 1990-1995 five-year residual. When each is annualized, the five-year average will be close to

twice that of the ten-year average, and the ten-year average will underestimate emigration.

In response to these weaknesses, researchers have increasingly sought alternative methods and data to measure

foreign-born emigration, using administrative data, household surveys, and census data from other countries (Jasso

and Rosenzweig 1982; Passel, Cohn and Gonzalez-Barrera 2012; Rendall, Brownell and Kups 2011; Schwabish

2011; Van Hook et al. 2006; Woodrow-Lafield 1996). Jasso and Rosenzweig (1982) used administrative data from

the former Immigration and Naturalization Service, now part of the U.S. Department of Homeland Security (DHS), 

for a cohort (1971) of legal immigrants to the United States. By linking administrative data records in 1979 to 

members of the 1971 cohort, the authors were able to estimate cumulative emigration rates for that cohort based on

attrition from the administrative data as well as estimates of mortality. However, the analysis only included legal 

immigrants and used data that are not readily available. Woodrow-Lafield (1996) used household surveys that asked 

respondents to report on the residence status of household members and other close relatives living abroad to

estimate emigration from the United States. To accurately derive estimates from surveys with this design (network 

sampling), a multiplicity adjustment must be calculated to ensure that multiple survey respondents are not reporting

the same individual living abroad. In this study, the multiplicity adjustment reduced the initial number of emigrants 

reported through the household surveys by nearly 80 percent, making the estimates extremely sensitive to the 

assumptions used to make the adjustment. Massey and Singer (1995) analyzed survey data collected in Mexico from

1987-1992 containing life histories of return migrants. However, it is difficult to compare their method to other 

methods because it measures gross migration rates (number of trips), not net migration rates (number of people).

More recently, Van Hook et al. (2006) used matched files from the Current Population Survey (CPS) to estimate

emigration of the foreign born. The CPS has a quasi-longitudinal design in which the same household is included in

the survey for four consecutive months and then rotates out of the survey for eight months; they are then brought 

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back into the sample for the same four months the following year. The sampling frame for the CPS is made up of 

addresses, not individuals, so respondents who move to a new address drop out of the CPS sample. Van Hook et al. 

estimate the probability that a foreign-born household was not followed-up in the subsequent CPS sample because 

of emigration. Because the CPS contains detailed social and economic data, the method can produce emigration 

rates by demographic and social characteristics. In addition, the method incorporates the most recent arrivals which 

is evident in much higher estimated emigration rates relative to rates produced using the residual method. 

Schwabish (2011) estimated the probability of emigrating using longitudinal administrative earnings data from the 

U.S. Social Security Administration (SSA). The method tracks the sequence of earnings over time and identifies 

periods of positive earnings followed by a period of no earnings as an emigration event. A limitation of the method

is that the sample is limited to workers that are part of the Social Security System, which systematically excludes

immigrants that are not in the labor force or undocumented immigrants who do not participate in the formal 

economy. 

Researchers also have used survey and census data from other countries, particularly Mexico, to estimate foreignborn emigration from the United States. Rendall, Brownell and Kups (2011) analyzed micro data from the National 

Survey of Occupation and Employment (ENOE) in Mexico to measure return migration to Mexico during the 2008-

2009 economic recession. The ENOE is a quarterly household employment survey where a household remains in the

sample for five consecutive quarterly interviews. By analyzing changes to household rosters between quarters,

Rendall, Brownell and Kups (2011) were able to measure return migration to Mexico from the United States. 

Similarly, Passel, Cohn and Gonzalez-Barrera (2012) used data from Mexico’s 2010 census which reported a

respondent’s residence five years ago to show that return migration to Mexico had increased substantially in the late 

2000s. We replicate a summary of previous estimates provided by Van Hook et al. (2006) and add more recent 

estimates in Table 1. 

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Table 1. Previously Published Rates of Foreign-Born Emigration, 1960 – 2010.
 

 

Et1-t2 = (Pt1 – Dt1-t2) – Pt2, 

 

R t1-t2 = Et1-t2 / (PYt1-t2 – 0.5* Et1-t2)* 100

 

 

 

 

 

Residual Method of Estimating Emigration

We estimate foreign-born emigration using a residual method similar to that developed by Warren and Peck (1980) 

and refined by Ahmed and Robinson (1994) and Mulder (2003). The basic equation to estimate emigration between 

two points in time is 

(1)

where Et1-t2 is an emigration residual, or estimated number of foreign-born who emigrated between time 1 

and time 2 (we refer to this period as the residual survival period),

Pt1 is the estimated foreign-born population at time 1,

Dt1-t2 is the estimated number of deaths experienced between time 1 and time 2 in the foreign-born

population estimated at time 1, such that 

Pt1 - Dt1-t2 is the expected survived foreign-born population at time 2 assuming no emigration, and 

Pt2 is the estimated foreign-born population at time 2 that arrived prior to time 1.

Annual rates of emigration are useful to compare estimates based on different methods, data sources, and time 

periods. Ahmed and Robinson (1994) estimated annual emigration rates for the 1980s by dividing E1980-1990 by 10 to

annualize the residual and dividing again by P1980, the estimated at-risk population. In the 2012 Vintage of

Population Estimates, the Census Bureau divided an annualized emigration residual by an estimate of the foreignborn population at the mid-point of a residual period. This divisor takes into account deaths and emigration during

the residual period, each reducing the population at risk of emigrating. We calculate an annual emigration rate with

the following equation:

(2)

where Rt1-t2 is an annual rate of emigration between time 1 and time 2, expressed as a percent or number of 

emigrants per 100 population,

Et1-t2 is an emigration residual calculated using Equation (1), and 

PYt1-t2 is total person-years survived in Pt1 between time 1 and time 2, which accounts for mortality in the 

at-risk population. Subtracting one half of the residual from person-years survived accounts for

emigration during a residual period, which also reduces the population at risk of emigrating at a given 

point in time. 

Estimating Emigration Using Data from the American Community Survey

We use individual-level micro data from the ACS to estimate both Pt1 and Pt2 in Equation 1 above. In general, the 

relatively large sample of the foreign-born population in the ACS offers an advantage over other survey data 

because foreign-born emigration is a relatively rare event. The residual method in particular requires a large sample 

because one must estimate population cells by single year of age and by sex to account for mortality between time 1 

and time 2. Census data offered a similar advantage.

The primary purpose of this research, however, is to assess whether estimating Pt1 and Pt2 using the ACS improves a 

residual estimate of emigration relative to a decennial-to-decennial estimate. Annual ACS data allow us to calculate 

emigration rates based on observation periods much shorter than ten years. In fact, one may estimate Pt1 and Pt2

using any combination of available ACS micro data, 2005 through 2012. For example, one may estimate Pt1 using

the 2006 ACS and estimate Pt2 with the 2008 ACS to calculate a 2-year residual. Or one may use the 2008 and 2012

ACS to create a 4-year residual. 

To reduce the number of possible combinations, we focus on the 2006 to 2010 ACS samples. The 2006-2010 

timeframe serves two primary purposes. First, we believe a five-year observation horizon more closely aligns with

previous research that shows emigration is most likely within a few years after arrival in the United States. We 

expect that annual emigration rates based on one- to four-year observation horizons will lead to better estimates that 

are more aligned with estimates based on other data and methods. Second, the 2006 to 2010 period in particular

allows us to assess the effect of the length of an observation horizon by making comparisons with estimates based 

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on Census 2000 and the 2010 ACS, which have a ten year observation horizon similar to previous decennial-todecennial estimates. 

We extract household records (which excludes the relatively small population of foreign born that resides in group 

quarters) from the 2006-2010 five-year ACS micro data file for consistency in population controls and weighting

methods and disaggregate the data by survey year.1 With the five years of sample data, we calculate a series of 

emigration residuals and annual emigration rates based on two-, three-, and four-year observation horizons.2 There is 

only one way to calculate a 4-year residual, using the 2006 and 2010 samples, but there are multiple ways to

calculate two- and three-year residuals. For example, one may calculate three two-year residuals based on estimates 

of Pt1 in 2006, 2007, and 2008 paired with Pt2 estimates in 2008, 2009, and 2010, respectively. 

Table 2 shows sample sizes, population estimates, and margins of error for estimates of Pt1 and Pt2 that we use to

calculate emigration residuals using the Census Bureau’s internal 2006-2010 ACS micro data file. The table 

includes samples and estimates by four foreign-born subpopulations for which the Census Bureau estimated foreignborn emigration separately in the Vintage 2012 population estimates: recently-arrived Mexican-born, earlier-arrived

Mexican-born, recently-arrived non-Mexican-born, and not recently-arrived non-Mexican-born. To compare our 

estimates to previously-published estimates, we also calculate rates for the total foreign-born population, for 

immigrants in the United States for less than 10 years, and for the Mexican-born population. Recent arrival is 

defined as having a year of entry less than or equal to ten years prior to Pt1. Mexican origin is identified by the place 

of birth question in the ACS.

We expect two-, three-, and four-year emigration residuals and rates to vary for several reasons. First, residual 

periods with different numbers of years will be based on different populations estimated at either time 1 or time 2, or

both. The compositions of two base populations may differ enough to make one population more or less prone to

emigration than another, or historical events may affect one base population more than another. Second, the length

of a residual period carries implications for the amount of emigration represented in a residual and the number of

years over which the migration is averaged. One or both of these factors may affect differences in emigration rates. 

Sampling and non-sampling error may affect variability in the rates we calculate. We show margins of error for Pt1

and Pt2 population estimates in Table 2. Calculating a true margin of error for a residual-based emigration rate is 

more difficult, however, given that we use population estimates from multiple samples. To simplify, we construct a 

pseudo-margin of error for an emigration residual based on the 90-percent confidence intervals of Pt1 and Pt2. First, 

we calculate an average survival rate for a foreign-born subpopulation and apply that rate to the limits of the 

confidence interval for Pt1. Second, the lowest possible residual estimate between Pt1 and Pt2 is the difference 

between the lower limit of the Pt1 confidence interval (after applying the survival rate) and the upper limit of the Pt2

interval. The largest possible residual estimate is the upper limit of Pt1 and the lower limit of Pt2. Third, we divide 

each residual difference by the denominator in Equation 2 to calculate upper and lower limits for an emigration rate. 

The pseudo-margin of error of a rate is the absolute difference between the upper (or lower) limit of a rate and Rt1-t2. 

For example, the estimated size of the recent Mexican-born population in 2007 is 4,771,300 (Pt1) with a margin of 

error of 65,900 (Table 2). After surviving this population forward two years to 2009 by age and sex, we may find

that the population as a whole has an average survival rate of 0.98. We then multiply the upper and lower confidence 

limits of the Pt1 population estimate, 4,837,200 and 4,705,400 respectively, by the average survival rate of 0.98. For

the lower limit of a 2007-2009 two-year residual, we then subtract the upper limit of Pt2 (4,426,900+62,600, Table 

2) from 4,611,292, the product of 4,705,400 and 0.98. The upper limit of the residual is the survived upper limit of

Pt1, 4,837,200*0.98, minus the lower limit of Pt2, 4,426,900-62,600. We then divide each limit for the residual by the

1

Person weights in a single-year ACS file are controlled to the vintage of population estimates of the same year. 

Population estimates, and thus weighting controls, for a particular year may change from vintage to vintage due to 

updated data and change in methods. The Census Bureau does not recalculate person weights for prior single-year 

ACS files. It does, however, use consistent population controls when it creates each five-year ACS file. For annual 

population estimates from a five-year ACS file, we multiply each person weight by five. 

2 After a preliminary analysis we decided to forego presenting estimates based on a observation horizon of just one

year. We found most of the one-year residuals that we calculated to be negative, which implies that there were more 

immigrants estimated at time 2 after subtracting deaths from the time 1 population estimate, which is not

demographically possible.

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denominator in Equation 2 (not shown in a table) to calculate the upper and lower limits for the emigration rate. 

In the results section that follows, we first assess differences between 2-year, 3-year, and 4-year emigration rates we

estimate using the 2006-2010 ACS. We then compare our ACS-to-ACS estimates to previously-published

emigration rates based on other data sources and estimation methods. Finally, we assess the implications of the

length of a residual period specifically by comparing our estimates to rates based on Census-to-ACS residuals

estimated by the Census Bureau for its Vintage 2012 Population Estimates. 

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Table 2. Sample Size and Population Estimates for Pt1 and Pt2 Used to Estimate Foreign-Born Emigration Rates, United States, 2006 – 2010. 
 

 

 

 

 

 

 

 

 

Results

Table 3 shows our estimated rates of emigration, expressed as emigrants per 100 foreign-born population, for the 

total foreign-born population, the foreign-born population by time in the United States, and the foreign-born

population by place of birth (Mexican, non-Mexican). 

 

       

       

       

     

Table 3. Estimated Rates of Foreign-Born Emigration Using the 2006 – 2010 American Community Survey.
 

 

 

 

 

 

 

 

 

 

A temporary change in data collection operations led to a relatively high number of missing values, and thus high

imputation rates, in the 2008 ACS sample.4 Given our results, we suspect the change may have increased nonsampling error in 2008 data and leads to downwardly biased estimates of the foreign-born population. Low 

population estimates, in turn, may be causing biased emigration rates. As we find in our results, if Pt1 is 

underestimated, the residual calculation will result in a lower than expected, if not negative, emigration rate. An

underestimate of Pt2, however, will result in higher than expected residual and emigration rate. Given the uncertainty 

in estimates based on 2008 data, we proceed by excluding such rates from the analyses and discussion that follows.

When we exclude emigration rates based on 2008 data, there is not a lot of variation in rates estimated for each

subpopulation. Rates for the total foreign-born population range between 0.25 and 0.95, with only 0.25 (the 2007-

2010 three-year rate) and 0.95 (the 2006-2009 three-year rate) differing by more than the pseudo-margins of error 

for the two rates. 

In terms of differences across foreign-born subpopulations, our estimated emigration rates vary in expected

directions. Recently-arrived immigrants emigrate at relatively higher rates (0.8 to 1.8) than earlier arrivals (0.0 to 

0.4, assuming a negative rate implies zero). And Mexican-born immigrants leave the country at higher rates (1.24 to

2.16) than immigrants who are not from Mexico (0.0 to 0.6).

The 2006-2010 residual-based emigration rates for the total foreign-born population are relatively lower than 

estimates based on other time periods, data sources, and estimation methods (Figure 1). In particular, our rates are 

lower than previous decennial-to-decennial residual estimates, which is somewhat surprising given our expectation 

that a shorter observation horizon will lead to rates that are comparable to non-residual-based estimates. We suspect 

the low rates are due to a more diverse foreign-born population in 2006 relative to 1960, 1980, or 1990. The foreignborn population in the 2000s was comprised of more immigrants who tend to settle permanently upon arrival and

not return home such as Asians and Africans (Gibson and Jung 2006; Grieco et al. 2012). This may not have been 

the case in the 1970s when Caribbean, Mexican, and Central American immigration grew rapidly, and the foreignborn population was more prone to return migration. This highlights a need to estimate emigration separately for 

foreign-born subpopulations that are known to have different migration and settlement patterns. Rates based on the 

residual method in general appear to be comparable to Schwabish’s (2011) rates using administrative data but much

lower than Van Hook et al.’s (2006). 

4

See note “2008 ACS Failed Edit Follow-up Operation” at 

http://www.census.gov/acs/www/data_documentation/user_notes/

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Figure 1. Selected Rates of Foreign-Born Emigration, Total Foreign-Born Population in the United States, 

1960 – 2010 

Figure 2 compares emigration rates for recently-arrived immigrants. The 2006-2010 estimated rates for recent

arrivals are relatively lower than residual-based rates of both Warren and Peck (1980) and Borjas and Bratsberg 

(1996) but not those estimated by Mulder (2003). Again, it is difficult to ascertain whether differences are due more 

to methodological differences or change in the composition of the recently-arrived foreign-born population over

time. Immigration in the 1950s and 1960s began to grow relative to historically small flows in the 1930s and 1940s 

(Gibson and Jung 2006). The growth was driven by immigration from Mexico and included many circular migrants

(Bean and Stevens 2003; Massey, Durand and Malone 2002). More recently, immigration flows come from across 

the globe with some national origin groups settling permanently upon arrival while others emigrate with much

greater propensity (Bean and Stevens 2003; Gibson and Jung 2006). Schwabish (2011), who calculates annual rates 

over 20 years, shows declining rates through the 1980s and 1990s. 

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Figure 2. Selected Rates of Foreign-Born Emigration, Foreign-Born in the United States for 10 Years or Less, 

1960 – 2010 

Unlike for the total foreign-born population, our 2006-2010 emigration rates for Mexican-born immigrants are

relatively higher than previous residual estimates (Figure 3). It also is notable that our Mexican-born rates are more 

closely aligned with estimates based on other data and methods. While there is much variation in non-residualbased estimates, our Mexican-born emigration rates fall between rates based on Mexico Census data (Passel, Cohn

and Gonzalez-Barrera 2012) and administrative data from the Social Security system (Schwabish 2011). These 

results support our expectation that residual-based emigration rates calculated using relatively shorter observation

horizons produce better estimates, at least in terms of being more aligned with estimates based on other data and

methods. This appears to be particularly true for a foreign-born subpopulation that has a relatively high propensity

of return migration. 

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Figure 3. Selected Rates of Foreign-Born Emigration, Mexican-Born Population, 1960 – 2010

In spite of the promising results for Mexican-born emigration rates, comparisons between 2006-2010 residual

estimates and previous decennial-to-decennial estimates may be confounded by historical context and population 

composition in addition to length of an observation horizon. The composition of the foreign-born population in the 

United States continues to change with respect to national origins that have different propensities to emigrate 

(Grieco et al. 2012; Jensen and Arenas-Germosen 2012). And historical events such as the terrorist attacks in 2001

and the 2008-2009 economic recession may also affect differences in propensity to emigrate across time periods. To 

investigate further the effect of length of observation horizon, we compare the 2006-2010 emigration rates to 2000-

to-2010 emigration rates calculated using Census 2000 data and 2009 and 2010 ACS data. As noted above, the 

Census Bureau’s current method of estimating foreign-born emigration relies on Census 2000 and ACS data. Also, 

we make comparisons both by recency of arrival (<=10 years, >10 years) and by place of birth (Mexico, nonMexico) to simulate the Census Bureau’s method of calculating emigration rates separately for the four foreign-born

subpopulations. 

Table 4 shows ACS-to-ACS and Census-to-ACS based emigration rates. In general, both methods generate

emigration rates that differ between foreign-born subpopulations in expected ways. Earlier arrivals, whether

Mexican or non-Mexican, tend to emigrate at lower rates relative to recent arrivals of similar national origin. It is 

also evident that the Mexican-born population emigrates at relatively higher rates than other foreign-born groups, 

just as we expected. 

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Table 4. Estimated Annual Rates of Foreign-Born Emigration Based on 2006 – 2010 ACS Five-Year Data and 

Census 2000 and 2009-2010 ACS Single-Year Data. 

           

                               
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

irregular data collection methods in that year. The direction of the bias depends on whether 2008 data are used to

estimate the foreign-born population at the beginning or end of a residual period. This finding suggests the 

importance of calculating multiple rates based on different samples and varying residual periods when using the 

ACS to estimate emigration. Given the uncertainty surrounding the 2008-based rates, we proceeded with the

analysis by excluding rates based on 2008 data. 

Comparisons between ACS-to-ACS emigration estimates to previously published emigration rates reveal that ACSto-ACS rates tend to be lower than previously-published estimates for the total foreign-born population (Figure 1) 

and foreign-born recent arrivals (Figure 2). ACS-based emigration rates for the total Mexican-born population,

however, are relatively higher than previous residual-based estimates and fall within the range of estimates based on

other data and methods (Figure 3). Given Mexican immigrants’ known propensity to return home, a shorter residual

period appears to address the main critique of the residual method and enhances the validity of a residual-based 

measure. When comparing rates based on different data, methods and time periods, however, differences also could 

be due to economic, social, and historical contexts and population composition. 

To minimize the effects of context and composition, we compare ACS-to-ACS emigration rates to emigration rates 

based on Census 2000 and ACS data from 2009 and 2010. This provides a comparison for rates based on similar 

time periods but with different residual lengths. Emigration rates for the recently-arrived Mexican-born population 

were the only rates that differ significantly. This finding provides additional support for the notion that shortening a 

residual period enhances measurement of emigration, especially for a group with a relatively high propensity to

emigrate. 

To conclude, the present analysis shows that reducing the length of time use to calculate an emigration residual

likely enhances estimates of foreign-born emigration.

References

Ahmed, B.and J.G. Robinson. 1994. "Estimates of Emigration of the Foreign-born Population: 1980-1990." 

Population Division Working Paper No. 9. Washington DC: U.S. Census Bureau.

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