The Use of Theory and Model Averaging for Population Prediction: 

An Application to the U.S. Overseas Population 

Sidney Carl Turner, Joseph Luchman

Fors Marsh Group LLC 

Andrew Therriault

Greenberg Quinlan Rosner 

Brian Griepentrog, Kinsey Gimbel 

Fors Marsh Group LLC 

Fritz Scheuren 

NORC at the University of Chicago 

Ali Mushtaq 

Independent Consultant 

Paul Drugan 

Federal Voting Assistance Program 

Proceedings of the 2013 Federal Committee on Statistical Methodology (FCSM) Research Conference 

The views, opinions, and findings contained in this article are solely those of the authors and should not be 

construed as an official U.S. Department of Defense position, policy, or decision, unless so designated by other 

documentation. 

3

Table Of Contents 

Introduction .......................................................................................................................................................... 4

Past Efforts To Estimate The Overseas U.S. Citizen Population ......................................................................... 6

Methodology ......................................................................................................................................................... 9

A Regression-Based Approach To Estimating The Overseas Population ......................................................... 9

Ensemble Model Averaging (Ema) ............................................................................................................... 10

Mitigating Selection Bias ............................................................................................................................. 12

Identifying And Collecting Foreign Government Estimates (Fges) ................................................................ 15

Predictor Variables ..................................................................................................................................... 18

Administrative Records Variables ................................................................................................................ 20

Theoretical Variables .................................................................................................................................. 23

Measurement Variables ............................................................................................................................... 26

Results ................................................................................................................................................................ 30

THE CONSISTENCY OF THE RESULTS OF THE MODEL WITH THEORY ................................................................. 36

DIFFERENCES BETWEEN THE ESTIMATES FROM THIS METHODOLOGY AND PRIOR ESTIMATES............................ 39

Discussion ........................................................................................................................................................... 43

References ........................................................................................................................................................... 48

Appendix A: Estimates Of The Population Of U.S. Citizens Abroad, By Country, 2000 And 2010 ................ 52

Appendix B: Alternative Modeling Strategies ................................................................................................... 58
4

Introduction 

Analyzing the population of U.S. citizens abroad is complicated by the issues that arise from the lack of available 

data for many (particularly developing) countries, the diverse motivations for U.S. citizens traveling and living 

overseas, and the economic and institutional environments of many of the countries in which U.S. citizens reside. 

Consequently, any attempt to estimate this population will face necessary trade-offs between breadth (i.e., the 

number of countries that can be estimated) and depth (i.e., the accuracy and detail of the estimates that can be 

made). Currently there are several estimates (varying from 1 million to 7 million) that academics, government 

organizations, nongovernmental organizations, and private industry use to plan and implement programs targeted to 

the overseas U.S. citizen population. Unfortunately, some of these estimates have often been accompanied by little 

documentation, have used varying definitions of the population of U.S. citizens abroad, and seem to have suffered 

from problematic or unclear methods. 

This report describes a research effort that expands upon previous overseas citizen demographic research conducted 

by the Federal Voting Assistance Program1

 (FVAP). The result of this effort is a model-based method for estimating 

the population of U.S. citizens abroad that addresses many of the shortcomings of prior research. Specifically, we

model existing estimates of populations of U.S. citizens abroad, by country, for the period 2000 to 2010 as a 

function of theoretically justified, country-level variables that are contemporary to the estimates. This helps to 

mitigate issues with the non-parametric and simple imputation methodologies used by the World Bank and United 

Nations whereby the resulting estimates were generated using extrapolation from decades old data, and thus did not 

incorporate changing political and economic conditions that could have led to rapid change in particular country’s 

population of U.S. citizens abroad, or else used regional averages to impute the U.S. share of a country’s migrant 

population, thus failing to incorporate country-specific factors that influence the size of the U.S. citizen population. 

In addition, the methodology described in this paper specifically models the effect of the instrument (census or 

registry) used by foreign governments to estimate their U.S. population as well differences resulting from the 

 

1

The Uniformed and Overseas Citizens Absentee Voting Act (UOCAVA) requires that States allow certain eligible 

citizens—including members of the uniformed services who are absent from their voting jurisdiction due to their 

service, their family members and dependents, and other U.S. citizens residing outside the United States—to apply

to register to vote and vote by absentee ballot in Federal elections. The Federal Voting Assistance Program (FVAP), 

under the authority of the Secretary of Defense, is the agency charged with administering UOCAVA. 

FVAP sponsored research, the results of which are presented in this report, whose goal was to estimate the size and 

distribution of the UOCAVA population. This project was motivated by the lack of administrative records of the 

UOCAVA population. Although the U.S. Department of Defense has up-to-date information on the number and 

location of military members and their dependents, estimating the number of all U.S. citizens living outside the 

United States is much more difficult; no official census of this population exists. 
5

population (U.S. citizen versus U.S. born) estimated, allowing predictions to be adjusted so as to limit the impact of 

the non-comparability of the foreign government estimates on the accuracy of the model’s predictions. Finally, the 

analysis described in this paper utilizes a weighted model averaging methodology which accounts for issues of 

overfitting that typically plague high dimensional models fitted to small samples. 

This paper is organized as follows. The first part reviews existing estimates and discuss their shortcomings. The 

second part describes the paper’s methodology. Finally, the third part presents the estimates developed from this 

methodology, discusses the geographic distribution and growth trends in the population of U.S. citizens abroad 

implied by the estimates, and compares the results to the World Bank and United Nations estimates. 
6

Past Efforts to Estimate the Overseas U.S. Citizen Population 

In the past, a variety of organizations have attempted to develop estimates of either the population of U.S. citizens 

abroad, specifically, or of migrants worldwide. Different organizations have used different methods to develop their 

estimates, but these efforts have been hampered by methodological issues that limit their ability to accurately 

characterize the number and location of U.S. citizens abroad. 

There have been five significant attempts of which we are aware to develop similar estimates of the overseas U.S. 

citizen population. These efforts provided a substantial starting point for the current work because each effort relied 

on different data sources and estimation procedures. These efforts are described below and include data sources, a 

brief description of the methodology, and the limitations of the methodology and resulting methods for the purpose 

of characterizing the size, growth, and geographic distribution of the population of U.S. citizens abroad. 

U.S. Census Bureau Estimate 

The Census Bureau considered attempting a full enumeration of the population of U.S. citizens abroad for the 2010 

Census. In 2004, the Census Bureau conducted a test to determine the feasibility of conducting an overseas census. 

Several test countries (France, Kuwait, and Mexico) were selected, and questionnaires were distributed through 

overseas organizations that were thought to have substantial contact with overseas U.S. citizens in those countries. 

In addition, a marketing firm was employed to promote the questionnaire to overseas U.S. citizens. Despite these 

efforts, the U.S. Government Accountability Office (GAO; 2004) reported that response rates were low due to the 

voluntary nature of the survey and difficulty in monitoring overseas partners. The GAO also concluded that the 

survey would be difficult to scale up across all countries due to country-specific factors such as privacy laws, the 

lack of address lists for overseas U.S. citizens, the inability to do follow-up interviews, and the lack of Census

Bureau overseas offices, which could deal with localized problems in implementation. As a result of this pilot effort, 

the Census Bureau did not attempt to count overseas U.S. citizens in 2010. 

U.S. State Department Estimate 

The U.S. State Department produces annual estimates of the number of Americans located overseas. Based on 

information that has been released publically about these estimates (GAO, 2007), country-level estimates are based 

on a combination of consulate registrations and an estimate for the U.S. population living in the country who are 

nonregistrants using country-specific information. Country-level estimates are developed primarily to facilitate 

preparation for evacuations of U.S. citizens. A more detailed methodology for developing these estimates has not 

been released publically. According to the GAO (2007), consulates vary in their procedures for estimating the 

number of U.S. citizens. Given that consulate registrations are likely to represent only a fraction of the U.S. 

population residing in a country and that the proportion of the U.S. population that registers at the consulate is likely 

to vary by country, as discussed in the GAO report, the methodology used to estimate the nonregistered part of the 

population is likely to have a significant effect on the final estimates. 
7

Several factors limit the usefulness of the State Department’s estimates as a guide to the size and geographic 

distribution of the overseas U.S. citizen population . Only regional-level data is released publically, so country-level 

estimates are not generally available. In addition, the use of the estimates by the State Department to plan for 

evacuations can result in their estimates including subpopulations that may not be considered long-term residents, or 

individuals who may not be eligible U.S. voters. 

World Bank Estimate 

The World Bank has developed estimates of bilateral migration stocks for all origin-host country pairs for the years 

1960, 1970, 1980, 1990, 2000 (Ozden, Parsons, Schiff, & Walmsley, 2011). Data is primarily based on 

approximately 1,000 decennial censuses and registries, referred to throughout this report as foreign government 

estimates (FGEs), developed by host country governments. The researchers discuss many of the complications 

involved in harmonizing reports from different governments with respect to definitions of migrants and origin 

regions. For the large number of missing values, data is either imputed using a linear trend or is extrapolated using a 

prior or future decade’s migrant composition, in the case that the country missing an observation has data available 

for other years. When a country has two or fewer observed decades, aggregate migration stocks are taken from the 

United Nation’s Trends in Migration Stocks (total migration stocks by country every five years), and the average of

bilateral migration shares from the decades that are available are used to assign portions of the migrant stocks to 

different origin countries. For countries lacking bilateral data, the total migrant stock is divided among countries 

using bilateral data from other countries in the region. 

More specifically, when a country’s number of U.S. residents was missing, that number was imputed based on the 

share of the total number of immigrants in the country composed of individuals born in the United States in earlier 

decades. As a result, the World Bank estimates may underestimate the U.S. population in a country if the propensity 

of U.S. citizens to migrate to that country increased relative to other countries since the last estimate. Further, the 

World Bank uses estimates based on both registries and censuses and makes no adjustment for the fact that different 

FGEs can represent either counts of individuals born in the United States or U.S. citizens, and citizen counts do not 

necessarily include dual citizens. Consequently, estimates may not be comparable across countries. 

United Nations Estimate 

The United Nations (UN) produces estimates using a methodology similar to that used by the World Bank (UN, 

2011), relying on FGEs for countries when available and imputing missing values for missing years. Like the World 

Bank approach, this methodology could result in estimates lower than the “true” number of U.S. born and U.S. 

citizens if the propensity for U.S. citizens to migrate to different countries changes over time. The imputation 

methodology used by the United Nations and World Bank could also result in overestimates of a country’s U.S. 

population if the size of the U.S. population relative to other immigrant communities has declined over time. 

As a result of this methodology, the UN data is likely provide an inaccurate picture given of the distribution of the 

population of U.S. citizens abroad across countries and regions. Also, like the World Bank estimates, the UN 
8

estimates are primarily of U.S.-born individuals, rather than U.S. citizens, and therefore these counts may not 

capture dual citizens very well. 

FVAP 2011 OCC 

In 2010, FVAP commissioned a research team to conduct exploratory research into developing a method for 

estimating the population of U.S. citizens abroad. 

The basic methodology of the 2011 OCC Report was to use FGEs as a proxy for the overseas U.S. citizen 

population, and to then use country-level variables to construct a model of the FGEs. This model was then used to 

produce an estimate of the U.S. citizen population of countries without an FGE. These estimates were then 

compared with counts of U.S. citizens based on administrative records, which were taken as the minimum estimate.

The highest of the FGEs, the imputations, and the administrative-based minimum count was taken as the final 

estimate. 

A major limitation with the model-based methodology used in the 2011 report was that the model was calibrated on 

a relatively small (N=47) sample. Consequently, parameter estimates were susceptible to overfitting, where a given 

predictor might be given a large weight in the model due to its ability to “explain” random measurement error in one 

or a few countries. Because this noise is specific to countries in the sample, out of sample predictions of the model 

are likely to be highly inaccurate. This problem is exacerbated by the choice of predictors, many of whose 

relationship to the population of U.S. citizens abroad has little theoretical or empirical support in the international 

migration literature, increasing the probability that any relationship found between the predictor and the FGEs was 

driven by random noise rather than ‘real’ factors that would extend to countries which were out of sample. In 

addition, the small sample, heavily weighted towards developing countries, means that even parameter estimates not 

driven by noise might not extend to largely developing out of sample countries. 
9

Methodology 

A Regression-based approach to estimating the overseas population 

The method described in this paper builds off of the model-based analysis of the 2011 report. Specifically, it relies 

on estimating the overseas U.S. citizen population using a regression-based methodology where the estimate of a 

country’s U.S. citizen population is based on FGEs of the population and how they interact with multiple predictor 

variables. A cross-country-based modeling approach was selected because it utilizes information on the size of 

overseas U.S. citizen populations already generated by foreign governments, and thus is likely to provide more 

reliable and accurate way of estimating the overseas U.S. citizen population than alternative approaches. This 

methodology involved developing estimates for the overseas U.S. citizen population by using FGEs as the best 

estimate of the “true” U.S. citizen population within a given country. A regression-based modeling approach was 

developed using countries that publish estimates of the U.S. citizen population. Models are used to predict the 

number of U.S. citizens for every country that lacks an FGE as well as adjust the estimates for countries that use 

alternative definitions of in their estimates of overseas U.S. citizens. 

The benefits of using foreign government–produced counts include: 

 FGEs are largely representative of the population of interest (U.S. citizens) by the desired unit of analysis 

(country). 

 FGEs are easily acquired from foreign government statistical agencies and are updated on a routine basis. 

 Prior studies (World Bank and OECD) have relied on FGEs, establishing precedent, albeit limited, in the 

research literature. 

However, there are also drawbacks to using FGEs. These include: 

 FGEs use different instruments by country (census versus registry) that may differ in accuracy. 

 Not all censuses and registries are created equal; the quality of the data is directly dependent on the 

methodology and implementation of the data collection by the individual country. Different countries are 

likely to have different capacities with respect to data collection (the number and quality of census field 

workers) as well as the ability of the central statistical office to compile and analyze the collected data. 

 The definition of a long-term or permanent resident is likely to vary by country based on individual 

immigration statutes. 

 FGEs will have definitional differences (U.S.-born individuals versus U.S. citizens) and so are not strictly 

comparable. 

 Foreign governments may not include dual citizens in their counts of U.S. citizens, leading to 

underestimates of the count of U.S. citizens (Ozden et al., 2011; United Nations, 2011). 

 Because not all countries develop FGEs, using FGEs to create an estimate model could result in the 

possibility of having a potentially unrepresentative sample of countries, even after weighting procedures. 
10

 Unlike the 2011 report, predictor variables include only those that the research on migration has identified as 

predictors of bilateral migration stocks (i.e., population size) and flows (i.e., change in population size) as well as 

counts of particular subpopulations within the country derived from administrative records of U.S. agencies and 

organizations. However, because it is still uncertain how well each variable used in a model predicts the size and 

geographic distribution of the overseas U.S. citizen population, and because extraneous variables increase the danger 

of overfitting to the data, a weighted average of multiple models can be taken. Averaging the estimates from 

different models mitigates the potential for any individual “wrong” model introducing error in the final estimates, 

and this approach has been effectively applied to political forecasting, specifically the prediction of violent conflict 

and election outcomes (Montgomery, Hollenbach, & Ward, 2012). 

Our basic methodology consists of three steps: 

1) Estimate the relationship between counts of U.S. citizens and country characteristics for all countries and years 

for which FGEs are available. 

2) Generate many different models (combinations of predictors) to estimate FGE with the final estimate being an 

average of these models, weighted by their fit (better-fitting models given a greater weight). 

– Although every predictor is considered in the final estimate, the impact of less-effective predictors 

(i.e., worse fit) is mitigated by giving those models a smaller weight. 

Our strategy builds upon previous work in several significant ways. First, it uses variation in the size of the U.S. 

population between countries and differences between countries on relevant characteristics to produce estimates for 

all countries. Second, it accounts for differences in the FGEs based on how U.S. residents were counted and who 

was considered a U.S. resident. And finally, it provides confidence intervals, which reflect at least some of the 

uncertainty in the estimates. The next two sections describe, respectively, the model averaging methodology used to 

define the model space and calibrate the resulting models and the sources for data for the FGEs and predictor 

variables. 

Ensemble Model Averaging (EMA) 

Estimating the overseas U.S. citizen population is complicated by uncertainty about which predictors should be used 

to model this population. To address this uncertainty, a variant of a method called ensemble Bayesian model 

averaging (EBMA) was used, which has been found to yield more accurate out-of-sample predictions than using a 

single model in applications such as armed conflict prediction and forecasting the outcome of presidential 

campaigns (Montgomery et al., 2012). The general approach of EBMA is to take predictions from multiple models 

(i.e., ensembles) and create an average of all the estimates weighted by the model’s fit to the data in combination 

with each model’s correlation or redundancy with predictions derived from other models. The resulting estimate is 

designed to be more accurate than the estimates derived from any single model by minimizing the effects of 

overfitting the data resulting from individual model specifications. At the same time, this method allows the final
11

estimate to incorporate as much information as possible from the predictor variables. The model space from which 

this average prediction is derived takes the form of all possible combinations of predictor variables. For k predictors, 

the number of models, N, equals 2^ (k) (including the model with no theoretical predictors, as described above). As 

applied to the estimation of overseas U.S. citizens, the approach is not likelihood-based (instead, it is based on root 

mean square error; see below) and, therefore, is not Bayesian (See Appendix B for an analysis of merits and 

drawbacks of using likelihood-based weights). Consequently, the modeling approach is simply ensemble model 

averaging (EMA). 

The N models take the form: 

 

  ( )  

Where FGE is the foreign government estimate of the size of the U.S. citizen population in country i in year t; C is a 

vector of variables common to every model that are believed to determine the size of the U.S. citizen population; X

is a vector of predictor variables that are likely to explain variations in the U.S. citizen population of country i

included in model m (and thus will vary from model to model); REGISTRY is a dummy variable that takes a value of 

1 if the country’s FGE is based on a registry count; CITIZEN is a dummy variable that takes a value of 1 if the FGE

pertains to the number of U.S. citizens in the country, and 0 otherwise; DUAL is a dummy variable that takes a value 

of 1 if the country allows dual citizenship with the United States; DUAL * CITIZEN is an interaction variable that 

takes a value of 1 if the country both allows dual citizenship and has an FGE that counts U.S citizens, and 0 

otherwise; and e is an error term. Because the FGE is bounded at 0, each model was estimated using the Poisson 

Pseudo-Maximum Likelihood Estimator, following Santos Silva and Tenreyro (2006). 

The measurement variables (i.e., those not included in vectors C or X) are included to control for differences in how 

FGEs estimated their U.S. population and whom they decided to count. For the purposes of generating predictions, 

REGISTRY is assumed to equal 0, CITIZEN is assumed to be equal to 1, and (DUAL * CITIZEN) is assumed to be 

equal to 0 for all countries. The constraints applied to REGISTRY, CITIZEN, and the DUAL*CITIZEN product were 

applied to make the final predictions more comparable with respect to the population they represent. To be specific,

a count of U.S. citizens (i.e., CITIZEN = 1) is enumerated using a census (REGISTRY = 0). However, this count 

should also seek to include individuals whom foreign governments of countries that allow dual citizenship might 

count as their own citizens. Consequently, the goal is to estimate the difference in the count of overseas U.S. citizens 

between countries that both allow dual citizenship and count the number of U.S. citizens and countries that do not 

meet one or both of these conditions. Specifically, predictions are generated under the assumption that no country 

meets both of these conditions (i.e., DUAL*CITIZEN = 0) as it is under such circumstances one is most likely to 

encounter citizenship misclassification and thus inaccurate citizen counts. In other words, citizenship-based FGEs 

for countries that allow dual citizenship are adjusted such that the prediction incorporates dual citizens. 

Although this adjustment incorporates dual citizens in citizenship-based counts, and predictions between countries 

that allow dual citizenship with the United States and those that do not may still differ, the size of the difference 
12

does not depend on whether the FGE counts citizens or U.S. born. Allowing predictions to vary with DUAL is 

important in the present circumstance because whether a country allows dual citizenship with the United States may 

have an effect on the size of the U.S. citizen population given that the prospect of gaining citizenship in the host 

country while retaining U.S. citizenship may encourage immigration to that country. In addition, DUAL may proxy 

for unobserved policies that encourage U.S. citizen migration as well as historical connections with the United 

States. Many countries encourage dual citizenship as a way to promote continued engagement with their expatriate 

populations (Lafleur, 2012). These policies may therefore promote return migration, reflected in a larger FGE. 

Mitigating Selection Bias 

To account for the selection bias that may result from countries with FGEs being different in ways that may also 

affect the size of their overseas U.S. population, each country is given a weight for the purpose of model estimation: 

 

 

 ( ) 

Where Pr(FGE) is the predicted probability that a country has an FGE during the years 2000 through 2010 based on 

its observable characteristics and n is the number of years for which country i has an FGE. The predicted probability 

of having an FGE is generated using a logit regression where the sample is all countries for which predictions are 

made. Predictor variables include all variables in vectors C and X in the estimation equation along with U.S. State 

Department region dummy variables. Data for the predictor variables for this selection equation were obtained for 

the year 2000. The results of the logit regression are displayed in Table 6. The result of the weighting is that 

countries with FGEs that have a low probability of having an estimate (based on the selection bias equation) will 

have more weight when generating model parameters and predictions, resulting in more accurate EMA predictions 

for countries without estimates and more accurate parameter estimates than those that would be generated in an 

unweighted model. This mitigates selection bias when there is not an unobserved factor (i.e., one not included in the 

model) that affects both the size of the FGE and whether a country has an FGE (Wooldridge, 2002). Including the n 

in the denominator of the weight accounts for the overrepresentation of some countries in the sample because of 

their having FGEs for multiple years. 
13

Table 6. Determinants of a Country having at least one FGE for the period 2000-2010. 

Pr (1 = Country has estimate, 0 = Country does 

not have estimates) 

DUALCITIZENSHIP .16** (.15) 

Ln(# of Social Security Beneficiaries) 1.79 (.66) 

Ln(# of IRS Returns) 3.33** (1.86) 

Ln(STUDENTS) .91 (.22) 

Ln(US Government Employment) .95 (.32) 

Ln(Difference in GDP per capita) .15*** (.10) 

Ln(Population) .79 (.28) 

Ln(Distance) 1.67 (.77) 

Mean(World Governance Indicators) 18.89*** (17.14) 

Ln(Trade) .64 (.21) 

Ln(Immigrants in US) 1.40 (.41) 

Ln(Military Aid) .91 (.06) 

ENGLISH 1.75 (1.37) 

SPANISH 11.30** (12.46) 

Western Hemisphere 20.96** (28.01) 

South/Central Asia .61 (.69) 

Near East 1.24 (2.04) 

Europe 16.26** (18.31) 

East Asia/Pacific .74 (.83) 

N 182 

Adj. R^2 .63 

*p < .10. **p < .05. ***p < .01. Model estimated using a logit regression. Odds ratios reported. Robust standard 

errors reported in parentheses. All predictors are from the year 2000. The reference region is Africa. 

The final estimate of the overseas U.S. citizen population for country i in year t is: 

 ( ) (∑ 

 

 

 

)

Or the average of all predictions for the country across N models, weighted by model validation metric w. The 

sampling variance of (i.e., the square of the standard error of the population estimate) is estimated by: 

 ( ) ∑( )

 ( 

 ) 

 

 

 ∑ ∑ ( 

 

 

)

 

 

 

 
14

Thus, to obtain 95% confidence intervals2 for country i in year t, take: 

 ( ( √ ( )))

The model validation metric w can be expressed in reduced form as: 

 

 

 

∑ 

 

Where 

 is the component of the metric that indicates how well model m fit the data.  can be written as: 

 

 

(

 

 )

∑ (

 

 )

 

 

Where the MSE is the mean squared error. The MSE is determined through K-fold cross-validation (Stone, 1977), 

where each observation in the sample is randomly assigned to one of K subsamples, the model is estimated using the 

K – 1 subsamples, predictions are estimated for the excluded validation sample, and the MSE (weighted by the 

selection bias weight 

, from above) is generated for that subsample. The cross-validation procedure is repeated K

times, with each subsample acting as the validation sample in turn. The cross-validation step is then repeated S

times, with the average of the S * K MSEs used as the model MSE. In this application, it set K = 5 and S = 10. Each 

model’s contribution to the final estimate is therefore determined by its out-of-sample predictive ability, minimizing 

overfitting that could result from determining model performance based on in-sample fit only. Testing the model 

using countries that were not used to build the model allows for a more robust test of the model as its predictive 

power is more likely due to variation in the U.S. citizen populations in these countries and not random measurement 

error (Hawkins, 2004; Ward, Greenhill, & Bakke, 2010). 

The other component of the model validation metric, 

 , captures the degree to which the predictions generated by a 

model are correlated with predictions generated by other models. Specifically: 

 

 

 ∑ ( 

 )

 

 

∑ ( ∑ ( )) 

 

 

 

Corr is the correlation coefficient between models m and j. In other words, 

 is larger when a model is relatively 

uncorrelated with other models. The model validation metric is larger when models simultaneously (1) make 

relatively accurate out-of-sample predictions, and (2) are uncorrelated or not redundant with predictions made from 

other models. The validation metric therefore focuses on the models that are best at prediction, while also being sure 

 

2It should be noted that these confidence intervals only incorporate uncertainty related to sampling variability, 

and not uncertainty related to issues of data quality, particularly for imputed variables, as well as assumptions 

related to the “ideal” set of measurement variables values, specifically the relative accuracy and registry 

versus census. Consequently, the “true” confidence intervals are likely to be wider. One objective of future 

research would be to obtain some sense of the reliability of different FGEs. 
15

to include a diverse set of model specifications rather than just minor variations of the same model. The proposed 

validation metric thus rewards accuracy and penalizes redundancy. 

Data 

Identifying and Collecting Foreign Government Estimates (FGEs) 

FGEs were identified using several different sources of data. The initial estimates were obtained from the OECD 

International Migration Database, which provided data on the number of U.S. citizens during the years 2000 to 2010 

for most OECD countries. Second, estimates were obtained from each of the individual countries or directly from 

their national statistical agencies. Links for foreign government statistical agencies websites were identified using 

the U.S. Census Bureau webpage titled “International Collection of the U.S. Census Bureau Library.”3

 Estimates 

obtained from countries’ websites were usually from their most recent census. In other cases, estimates were 

obtained from specific reports on migration commissioned by the national government. These estimates were 

obtained from foreign government censuses and immigrant registries Third, data were supplemented with an 

additional set of FGEs available in a U.S. Census Bureau internal document titled “Estimating native emigration 

from the United States,” (Schachter, 2008), which was compiled as part of a project to estimate U.S. net emigration. 

Although this document included estimates for a period that roughly covered the years 1990 to 2008, only estimates 

from post-1999 were included (to avoid complexity introduced by the large number of border changes that occurred 

in the 1990s). In cases where a country has an estimate available for more than one year in the 2000–2010 period of 

study, each estimate is included in the sample, but the country is weighted based on the inverse of the number of

years of data. For example, for countries that have estimates available for two years, each estimate is given half the 

weight. This should result in a more representative sample and lead to more accurate estimates. Finally, unmodified 

FGEs for several countries were found in the 2011 OCC Report (FVAP, 2011). For countries without 2010 

estimates, but with estimates in 2011, the 2011 estimate was used in place of the 2010 estimate. The following table 

lists the countries with an FGE by source. Table 1 lists countries for which an FGE was located, and Table 2 lists 

countries for which an FGE was unable to be identified/collected. 

 

3Links to foreign government statistical office websites were retrieved from 

http://www.census.gov/population/international/links/stat_int.html 
16

Table 1. Countries with FGEs by Source 

2011 OCC Report Schachter (2008) OECD Foreign Government 

Statistics Offices 

Colombia, 2005 Argentina, 2001 Australia, 2000-2010 Albania, 2010 

Dominican Republic, 2002 Bahamas, 2000 Austria, 2001-2010 Antigua & Barbuda, 2001 

Panama, 2010 Barbados, 2000 Belgium, 2000-2009 Armenia, 2001 

Russia, 2002 Belize, 2000 Canada, 2001, 2006 Belarus, 2009 

United Kingdom, 2010 Bolivia, 2001 Czech Republic, 2000-

2010 Bermuda, 2000 

Brazil, 2000 Denmark, 2000-2006, 

2008-2010 Cyprus, 2001 

Chile, 2002 Finland, 2000-2010 Latvia, 2000 and 2010 

Costa Rica, 2000 France, 2006-2008 Lithuania, 2004-2010 

Croatia, 2001 Germany, 2000 – 2010 Mauritius, 2000 and 2010 

Ecuador, 2000 Greece, 2001 and 2010 Micronesia, 2000 

Guatemala, 2002 Hungary, 2000-2010 Peru, 2007 

Guyana, 2002 Italy, 2000-2010 Romania, 2002 

Honduras, 2001 Japan, 2000-2010 Sierra Leone, 2004 

Hong Kong, 2006 Korea, 2000-2010 St. Vincent and the 

Grenadines, 2001 

Iceland, 2008 Luxembourg, 2001 Tanzania, 2002 

India, 2001 Mexico, 2000 and 2010 Thailand, 2010 

Israel, 2006 Netherlands, 2000-2010 Uruguay, 2010 

Jamaica, 2001 New Zealand, 2001 and 

2006 

Jordan, 2004 Norway, 2000-2010 

Kiribati, 2005 Poland, 2002 and 2006-

2009 

Malta, 2005 Portugal, 2000-2010 

Nicaragua, 2005 Slovak Republic, 2001 

and 2004-2010 

Panama, 2000 Spain, 2000-2010 

Palau, 2000 Sweden, 2000-2010 

Paraguay, 2002 Switzerland, 2000-2008 

Philippines, 2000 Turkey, 2000 

Samoa, 2001 

Slovenia, 2002 

South Africa, 2001 

St. Kitts and Nevis, 2001 

St. Lucia, 2001 

Trinidad and Tobago, 

2000 
17

United Kingdom, 2006 

Venezuela, 2001 

Zambia, 2000 

Table 2. Countries without an FGE 

Afghanistan Ghana Papua New Guinea 

Algeria Grenada Qatar 

Angola Guinea Rwanda 

Azerbaijan Guinea-Bissau Sao Tome and Principe 

Bahrain Haiti Saudi Arabia 

Bangladesh Indonesia Senegal 

Benin Iran Serbia 

Bhutan Iraq Seychelles 

Bosnia and Herzegovina Kazakhstan Singapore 

Botswana Kenya Solomon Islands 

Brunei Kuwait Somalia 

Bulgaria Kyrgyzstan Sri Lanka 

Burkina Faso Laos Sudan 

Burundi Lebanon Suriname 

Cambodia Lesotho Swaziland 

Cameroon Liberia Syria 

Cape Verde Libya Taiwan 

Central African Republic Macao Tajikistan 

Chad Macedonia Timor-Leste 

China Madagascar Togo 

Comoros Malawi Tonga 

Congo, Dem. Rep. Malaysia Tunisia 

Congo, Republic of Maldives Turkmenistan 

Cote d`Ivoire Mali Uganda 

Cuba Marshall Islands Ukraine 

Djibouti Mauritania United Arab Emirates 

Dominica Moldova Uzbekistan 

Egypt Mongolia Vanuatu 

El Salvador Montenegro Vietnam 

Equatorial Guinea Morocco Yemen 

Eritrea Mozambique Zimbabwe 

Estonia Namibia 

Ethiopia Nepal 

Fiji Niger 

Gabon Nigeria 
18

Predictor Variables 

One of the primary ways that this method builds upon prior work is by having an explicit justification for the 

selection of explanatory variables. When variables are selected without this justification, but rather selected purely 

based on empirical results from a single sample source, it can result in overfitting, especially when working with a 

small sample size. The model introduced in this report includes a number of theoretically established interaction 

variables, including distance (Lewer & Van den Berg, 2008), the difference in income per capita (Grogger & 

Hanson, 2011), and immigrant stocks from the foreign country residing in the United States (Artuc, Docquier, 

Ozden, & Parsons, 2013). Much of these data are publicly available from sources such as the World Bank (The 

World Bank Group, 2012) and the Penn World Table Version 7.1 (Heston, Summers, & Aten, 2012). 

There are a number of theoretical frameworks for modeling and predicting estimates of the aggregate overseas U.S. 

citizen population by country that were examined separately as well as in combination. Two specific models of the 

interaction between the United States and countries that host U.S. citizen populations are (1) a “gravity model” and 

(2) an immigration–emigration model. 

Gravity Model: Assumes that the flow of U.S. migrants to other countries and the resulting stocks of U.S. 

citizens in those countries is a function of (a) the size of the country, usually measured in GDP, with 

countries with larger economies attracting more U.S. migrants; and (b) the distance of the country from the 

United States, with countries closer in distance attracting more U.S. migrants. This modeling approach has 

recently been used to impute migration stocks for all country pairs (Artuc, Docquier, Ozden, & Parsons, 

2013). 

Immigration–Emigration Model (Warren & Peck, 1980): Assumes that the number of U.S. citizens 

residing in another country is a function of the number of immigrants residing in the United States from 

that country, whereby countries that send more immigrants to the United States receive more emigrants 

from the United States in turn. 

These models are not mutually exclusive and can be combined in both a single theoretical and statistical framework. 

Each of the variables used to predict the FGE can be placed into one of three categories: 

(1) Administrative: Administrative records–based counts of the number of particular subpopulations of 

U.S. citizens living in a given country (“count” variables). Variables derived from administrative records 

directly reflect the size of a subset of the overseas U.S. citizen population of a country. Consequently, an 

increase in an administrative records–based variable would be expected, on average, to be reflected in an 

increase in the aggregate FGE. 

(2) Theoretical: Noncount-based variables that have a theoretical relationship with bilateral migration. 

Theoretical variables have been theoretically and empirically identified as correlates of bilateral migration 
19

stocks and flows for samples including all origin countries for which data is available; however, it is 

unclear to what degree they are associated with migration by U.S. citizens. 

(3) Measurement: Capture differences in how foreign governments estimated or counted their U.S. citizen 

population. Measurement variables are used to adjust the predictions of the model such that they reflect the 

size of the population of interest, specifically U.S. citizens. These adjustments require that they be included 

in every model. 

In deriving the estimates, multiple models were tested using a variety of combinations of the three types of 

variables. Descriptive statistics for the FGEs and predictor variables for observations used to generate the estimates 

are listed in Table 3. 
20

Table 3. Descriptive Statistics, In-Sample Country-Years 

Variable N Mean Standard 

Deviation Minimum Maximum 

FGE 272 25151.02 59013.2 41 738103 

Measurement Variables 

Citizenship 272 .75 .43 0 1 

Dualcitizenship 272 .35 .48 0 1 

Dualcitizenship 

* Citizenship 272 .19 .40 0 1 

Registry 272 .69 .46 0 1 

Administrative Records Variables 

Social Security 

Beneficiaries 272 7898.19 13278.69 14.72 102123 

IRS Form 2555s 272 4488.27 6305.65 16.64 34213.93 

Students 272 4000.73 7031.67 0 34024 

Federal 

Government 

Employees 

272 1290.12 3436.97 0 18232 

Theoretical Variables 

Ln(Difference in 

GDP per capita) 272 -.66 .74 -4.11 .51 

Population 272 29630.8 68996.54 46.19 1023295 

Distance 272 3696.60 1153.73 3.45 9093.53 

Mean (World 

Governance 

Indicators) 

272 1.05 .68 -1 1.88 

Trade 272 3.29E+04 6.25E+04 3.52 5.33E+05 

Immigrants in 

U.S. 272 2.10E+05 5.75E+05 1240 6.40E+06 

Military Aid 272 6.26E+09 1.20E+10 0 1.29E+11 

English 272 .54 .50 0 1 

Spanish 272 .41 .49 0 1 

Year of Estimate 272 2004.66 3.29 2000 2010 

Administrative Records Variables 

Administrative records variables serve as potential indicators of the number of U.S. citizens in a particular 

subpopulation within a country. Because they can estimate a subset of the population of interest, there is reason to 

believe that they will help predict the size of the FGE because individuals included in these administrative records 

should also be counted in the FGE. Consequently, they are included in every model. 

 Number of Social Security Beneficiaries, 2000–2010: The number of overseas Social Security beneficiaries

published by the SSA. Counts were available for each year between 2000 and 2010, aggregated for all 
21

regions, but provided individually only for some countries. To create estimates for countries missing 

individual counts, a Poisson regression imputation model of the number of beneficiaries was developed 

using the (logged) number of foreign exchange students, the (logged) number of U.S. Federal Government 

civilian employees, and the additional theoretical variables (see the first column of Table 4) to generate 

predicted Social Security beneficiaries. As opposed to using the predicted values themselves as an estimate 

of Social Security beneficiaries for countries without counts, unassigned beneficiaries in a region (those in 

countries with fewer than 500 beneficiaries) as reported by the SSA were assigned to a country in the 

region missing a count proportional to the predicted number of beneficiaries.4

 Number of Foreign Earned Income Returns, 2000–2010: The estimated number of IRS Form 2555 returns, 

used to declare foreign income, filed by U.S. citizens living in the country in a given year (Hollenbeck & 

Kahr, 2009). Each form represents at least one U.S. citizen residing in the country. Data was not available 

for some countries, and for the subset of countries with estimates, they were only available for 1996, 2001, 

and 2006. To obtain estimates for missing countries and years, the number of returns was first estimated 

using a Poisson regression imputation model with the theoretical variables discussed below as predictors of 

the (logged) number of returns. The total number of Form 2555s filed for countries without an estimated 

number of returns was available by region. Unassigned Form 2555s in each region were assigned to 

countries without an estimate proportional to their predicted number of returns based on the imputation 

model. These were used to create estimates for 1996, 2001, and 2006 for all countries. Using these imputed 

estimates of the number of tax returns, estimates for 2000 and 2002 through -2005 were imputed using 

linear interpolation. To create estimates for the years 2007 through 2010, an imputation model of (logged) 

growth in tax returns between 2001 and 2006 was estimated using tax return growth between 1996 and 

2001, (logged) number of tax returns in 2001, imputed values for Social Security beneficiaries, students, 

government employees, and the theoretical variables for 2001. Using this model, data for 2006 (i.e., growth 

between 2001 and 2006, initial number of returns in 2006, etc.) was used to predict growth between 2006 

and 2011. Using this predicted five-year growth, an estimate of the number of returns in 2011 was created 

for each country. Linear interpolation was then used between the 2006 estimate and the 2011 estimate to 

create estimates for 2007 through 2010. See Table 4 for model results. 

 Number of U.S. Exchange Students, 2000–2010: The total number of U.S. exchange students attending 

foreign universities for each year in the period 2000–2010 (Institute of International Education, 2012). 

 

4The number of Social Security beneficiaries is subject to a natural log transformation for the purpose of 

regression. Other variables that are logged include the number of foreign earned income returns, the number 

of U.S. exchange students, the number of civilian government employees, the ratio of GDP per capita of the 

foreign country to the GDP per capita of the United States (logged difference), foreign country population, 

distance, trade, the number of immigrants originating in the foreign country in the United States, and military 

aid. This transformation reduces the leverage of countries with extreme values on these predictors. Generally, 

when a country has a 0 value on a given predictor, the variable is increased by 1 for each country. This ensures 

that these predictors remain defined for all countries after the log transformation, and can thus be included in 

the regression. 
22

Countries without an estimate for any year were assigned a value of 0. Estimates for countries with at least 

two estimates but with missing years were generated using linear interpolation and/or extrapolation. 

 Number of Civilian U.S. Federal Government Employees, 2000–2010: The number of civilian U.S. Federal 

Government employees residing in a country in a given year, as reported in data provided to FVAP by the 

Office of Personnel Management on April 3, 2013. 

While additional administrative records such as State Department consulate registrations and Department of Defense 

counts of the number of military personnel and their dependents could have been included, these data were not 

publically available due to security considerations. As a result, including this data in the analysis would have 

precluded outside researchers from reproducing the results and thus undermined the transparency of the analysis. 

Therefore, these variables were not included in the analysis. 
23

Table 4. IRS and Social Security Imputations 

# SS Beneficiaries # IRS 2555 Returns (Est.) Growth in 2555s (2001–

2006) 

Ln(IRS Returns, 2001) -.80*** (.30) 

Ln(Growth in IRS 

Returns, 1996-2001) -.77** (.33) 

DUALCITIZENSHIP .47* (.27) .54*** (.20) -.43 (.46) 

Ln(# of SS 

Beneficiaries) -.30 (.20) 

Ln(STUDENTS) -.14 (.09) .19 (.12) 

Ln(US Government 

Employment) .07 (.08) -.88*** (.15) 

Ln(Difference in GDP 

per capita) .73 (.52) .53*** (.20) .66*** (.23) 

Ln(Population) .32* (.16) .16 (.14) .42** (.18) 

Ln(Distance) -.10 (.11) .22*** (.07) -.19 (.22) 

Mean(World 

Governance 

Indicators) 

.44 (.38) -.21 (.20) -.19 (.39) 

Ln(Trade) -.08 (.18) .58*** (.10) .31 (.21) 

Ln(Immigrants in US) .43** (.17) .04 (.09) .32* (.19) 

Ln(Military Aid) .05** (.02) .00 (.01) .23* (.13) 

ENGLISH .78*** (.30) .49*** (.16) -.05 (.33) 

SPANISH .31 (.21) .07 (.18) .21 (.45) 

Year Effects YES YES N/A 

Countries 60 60 182 

N 584 164 182 

Pseudo R^2 .82 .74 .91 

*p < .10. **p < .05. ***p < .01. Model coefficients are estimated using Poisson regression. Robust standard errors 

clustered by country in parentheses. 

Theoretical Variables 

What are referred to as “theoretical variables” are those that have been found in the research literature to be 

associated with higher levels of migration between countries. These studies have typically used comparisons 

between pairs of many different origin and destination countries to empirically test the effects of these variables on 

bilateral migration. There may be differences between what drives emigration from the United States and what 

drives emigration from other countries (as has been found in the empirical literature on international migration) due 

to the failure of many of these empirical studies to account for the changing propensity of residents of particular

origin countries to migrate, or multilateral resistance (Bertoli & Fernandez-Huertas Moraga, 2013). Consequently, 

these variables may be poor predictors of the number of U.S. citizens in foreign countries and lead to inaccurate 

final estimates if included in the regression. For this reason, these variables were only included in some regressions, 

to ascertain whether the inclusion of these variables enhanced or detracted from the ability of the model to predict 
24

the FGEs. The weight given to the individual models was adjusted such that models that produced more accurate 

predictions were given larger weights. Consequently, the influence of these variables on the final estimate was based 

partly on the degree to which they were actually able to predict the FGEs. 

 The Difference Between Foreign Country GDP Per Capita and U.S. GDP Per Capita: The difference 

between the purchasing power parity (PPP)–converted5

 GDP per capita of the foreign country in a given 

year in constant 2005 prices and the GDP per capita of the United States in the same year, as reported by 

Penn World Table Version 7.1 (Heston, Summers, & Aten, 2012). The empirical literature on international 

migration identifies differences in wages between origin and host countries as a primary determinant of 

bilateral migration flows (i.e., travel and resettling between two countries; Grogger & Hanson, 2011; 

Mayda, 2010). Consequently, countries that are highly developed relative to the United States, as 

determined by the difference in GDP per capita, would be expected to be more attractive to U.S. citizens 

and thus have larger U.S. citizen populations. 

 Population: The population (in thousands) of the foreign country, as reported in the Penn World Table 

Version 7.1 (Heston et al., 2012). The empirical literature on international migration has typically found 

that countries with larger populations/economies tend to attract more migrants (Lewer & Van den Berg, 

2008). Consequently, countries with larger populations would be expected to have larger numbers of U.S. 

citizens. 

 Distance from the United States: The distance between the closest foreign country–U.S. pair of cities with 

populations over 750,000. For countries that do not have a city with a population over 750,000, the distance 

between the capital city of the foreign country and the closest U.S. city with a population of at least 

750,000 was used. The latitude and longitude coordinates used to generate the distance measures were 

obtained from the United Nations’ World Urbanization Prospects, the 2011 Revision. Distance has 

typically been found to be associated with lower levels of migration between two countries (Lewer & Van 

den Berg, 2008), likely because of the fact that more distance is related to higher costs of migration (e.g., 

owing to travel and moving expenses). Consequently, countries farther away from the United States would 

be expected to have smaller numbers of U.S. citizens. 

 Trade with the United States: The mean end-of-year product trade (imports + exports) between the United

States and the foreign country for the years in which data are available during the years 2000–2013 as 

reported by the Census Bureau.6

 Trade has been both theoretically and empirically linked to migration 

between trading countries (Felbermayr & Toubal, 2012; Sangita, 2013). Consequently, countries with 

higher levels of trade with the United States would be expected to have larger numbers of U.S. citizens. 

 

5The U.S. dollar value of GDP per capita without a PPP adjustment is a problematic proxy for a country’s level of 

development because it does not reflect differences in prices across countries. By contrast, PPP-converted 

GDP attempts to represent the actual amount of goods and services that the country’s residents can obtain 

given their income. 

6Census Bureau trade data was retrieved from http://www.census.gov/foreign-trade/balance/ 
25

 Institutional Quality: The average of the six World Bank’s World Governance Indicators (Voice and 

Accountability, Political Stability and Absence of Violence, Government Effectiveness, Regulatory 

Quality, Rule of Law, and Control of Corruption) averaged across the years 1996–2011. Institutional 

quality, and particularly the degree of political stability, has been found to be a determinant of net 

migration to countries (Ziesemer, 2010). Consequently, countries with good institutional quality would be 

expected to have higher numbers of U.S. citizens. 

 Number of Immigrants in the United States: The number of immigrants from the foreign country ages 25 

and up in the United States in the year 2000 as reported by Artuc et al. (2013). One type of potential outmigrant from the United States is an immigrant from a foreign country (or his or her offspring) who then 

decides to return to his or her country of origin (Scheuren, 2012). A more general justification for the 

inclusion of this variable is that it may proxy for factors that promote or inhibit migration both to and from 

the United States, such as transportation costs. Consequently, countries with larger numbers of immigrants 

in the United States would be expected to have larger numbers of U.S. citizens. On the other hand, the 

number of immigrants in the United States from the country may also be negatively associated with the 

number of U.S. citizens in that country, if factors that affect migration flows asymmetrically (such as 

political instability) are salient. It is worth noting that the uncertainty regarding relationship direction is not 

a limitation for this predictor because the estimation strategy does not require an assumption of a positive 

or negative relationship. 

 U.S. Military Aid: The total amount of military assistance in constant dollars made by the United States to 

the foreign country between 1946 and 2011 as reported by USAID. Aid to foreign countries by the U.S. 

Government, and the associated interaction between those governments, may promote migration from the 

United States to the foreign beneficiary countries by facilitating the transfer of information about the 

foreign country to potential U.S. migrants (Berthelemy, Beuran, & Maurel, 2009). In addition, aid may be a 

proxy for general diplomatic ties (Alesina & Dollar, 2000) that may be associated with foreign government 

policies that are advantageous to U.S. migrants, leading to increased U.S. migration to the country. Since 

development aid is likely to be inversely correlated to the level of development, the effect of such aid on 

the number of U.S. migrants is ambiguous and may not be predictive of migration and the U.S. population 

overseas (Fleck & Kilby, 2010). Consequently, military aid, which should be a stronger proxy for strategic 

interests and diplomatic ties, is used here (Fleck & Kilby, 2010). 

 English or Spanish: These variables indicate whether English or Spanish is spoken in the foreign country, 

respectively. The information is taken from Ethnologue: Languages of the World (Lewis, Grimes, Simons, 

& Huttar, 2009). These variables may proxy for cultural distance between the United States and the foreign 

country as well as the ability to succeed in the host country’s labor market (Adsera & Pytlikova, 2012). 

Given that English and Spanish are the two most widely spoken languages in the United States, countries 

where these languages are commonly spoken would be expected to attract more U.S. citizens. 

 The Year to Which the FGE Applies: This variable is included to control for unobserved trends in the size 

of the overseas U.S. citizen population common to all countries. These factors may include population 
26

growth through births of U.S. citizens, whether overseas or within the United States, which would be 

expected to affect the total number of overseas U.S. citizens. In addition, this variable may also capture 

changes in transportation costs over the 2000–2010 period of study, which would also be expected to affect 

the tendency of U.S. citizens to migrate. 

Measurement Variables 

One issue with using the FGEs as a proxy for the true overseas U.S. citizen population is that the specific population

of overseas U.S. citizens being counted by each country is likely to vary (Artuc et al., 2013; Ozden et al., 2011). 

These differences may be due to an intentional decision on the part of the foreign government to only count a 

specific part of the U.S. population, such as U.S. citizens versus those who are U.S. born, or single citizenship 

versus dual citizenship. Alternatively, the differences could represent unintentional error resulting from the method 

used to count the U.S. citizen population, such as a registry versus census estimates (Ozden et al., 2011). 

Consequently, it is difficult to interpret what an estimate for a specific country represents, other than whom the 

government is willing or able to count. If the policy/methods applied by a significant number of foreign 

governments result in systematic differences in estimates, overall overseas U.S. citizen population estimates could 

be consistently biased. 

Any approach that uses FGEs as part of its model will need to address the error that is inevitably present in these 

estimates. The potential for measurement error can be addressed in two ways. The first way involves splitting the 

sample of countries with FGEs based on whether the estimate counts U.S. citizens versus non-U.S. citizens and uses 

a registry versus a census. If, for instance, estimates derived from a registry that counts the number of U.S. citizens 

(including dual citizens) most accurately represents the population of interest, the sample used can be restricted to 

build the model to those countries that meet these criteria. Such an approach suffers, however, from the problem of 

small sample size. Only four countries (i.e., Austria, Germany, the Netherlands, and Norway) meet the above 

criteria—too few to construct the models and likely even less representative of the global sample of countries. 

A second way of addressing this issue would be to explicitly model the differences in the country measurement 

instruments. This approach is common to meta-analysis (e.g., Card & Krueger, 1995) and can be incorporated in the 

regression-based gravity and immigration models. 

For instance, in the following model: 

 ( ) 

Where USPOP is the foreign government estimate of the U.S. citizen population, X is a vector of structural variables 

that explain variations in the “true” U.S. citizen population of the country (gravity, immigration to the United States, 

etc.) and M is a series of variables that capture differences in the definition of the U.S. citizen population and the 

methods used to estimate it. Three variables could be used to estimate the conditional difference in USPOP: (1) 

whether a country uses a census or a registry, (2) whether a country counts citizens versus U.S. born, and (3) 

whether a country allows or does not allow dual citizenship with the United States. These variables are not thought 
27

to have an effect on the “true” number of U.S. citizens in the country, but only affect the FGE. Including these 

variables in the regressions provides an estimate of the differences between the population as estimated by the FGE 

and the population of interest. Explicitly including these confounding variables in the prediction models of FGEs 

will ultimately allow for generation of estimates that mitigate these biasing effects and are thus more accurate 

representations of the “true” count of U.S. citizens living in foreign countries. 

 FGE Based on a Registry: A variable indicating if the FGE was generated using the government’s 

administrative-based records. The primary difference between census and registry is that census data is 

drawn from a single source whereas registry data is drawn from a number of sources (e.g., tax forms, visas, 

school records, etc.; Ewing, 1998; Punch, 2001). Utilizing data from multiple sources is beneficial in that it 

may allow for more complete coverage of overseas U.S. citizens (because a citizen is unlikely to be 

“missed” by several different sources). However, one major disadvantage of registries is that data quality is 

completely dependent upon the quality of the administrative records on which the data are based (United 

Nations, 1969), and when attempting to enumerate overseas citizens, registries can be particularly 

problematic. One of the major problems is that migrants who have registered with a host country often do 

not de-register upon leaving—thus resulting in an overcount of overseas citizens (Dumont & Lemaître, 

2005). A census conducted in a country may have a longer tradition, broader usage, and may be able to 

capture more data elements by asking multiple questions about citizenship, birth country, dual citizenship, 

and employment. 

Relatively few nations currently use a population registry. Although a number of countries are transitioning 

to a population registry (Singapore Department of Statistics, 1999; Statistics Netherlands, 2012) or are 

considering transitioning to a register-based system, most countries, including those in the sample, still use 

the traditional census. See Table 5 for information on which countries use a census. 
28

Table 5. Countries with FGEs Based on Census 

Albania Croatia Kiribati Sierra Leone 

Antigua and Barbuda Cyprus Lithuania Slovak Republic 

Argentina Czech Republic Luxembourg Slovenia 

Armenia Ecuador Malta South Africa 

Australia Finland Mauritius South Korea 

Bahamas France Mexico St. Kitts & Nevis 

Barbados Greece Micronesia St. Lucia 

Belarus Guatemala New Zealand St. Vincent & 

Grenadines 

Belgium Guyana Nicaragua Taiwan 

Belize Honduras Panama Tanzania 

Bermuda Hong Kong Paraguay Thailand 

Bolivia Hungary Peru Trinidad and 

Tobago 

Brazil India Philippines Turkey 

Canada Ireland Poland Uganda 

Chile Italy Portugal United Kingdom 

China Jamaica Romania Uruguay 

Colombia Japan Russia Venezuela 

Costa Rica Jordan Samoa Zambia 

Countries with registries (i.e., Austria, Germany, the Netherlands, and Norway) and those without appear to 

differ with respect to factors that influence the size of their U.S. citizen populations. For example, nations 

with registries tend to be well-developed and European, both of which are characteristics that attract U.S. 

citizens (Wennersten, 2008). Consequently, any simple calculation of the mean difference in the FGE 

between registry and nonregistry countries cannot be interpreted as systematic “measurement” difference 

between a census and a registry, but may be due to real differences in the size of the U.S. citizen 

population. This indicator variable is therefore included to account for this possibility and to adjust the 

predictions so they represent what the model would generate if the FGE had been constructed using a 

government census, while controlling for the other country characteristics. Data on whether a government 

used a registry or census was obtained from the 2011 OCC Report, the U.S. Census Bureau internal 

document titled “Estimating native emigration from the United States,” (Schachter, 2008), and websites of 

individual foreign government statistical agencies or through phone calls to those agencies. 

 FGE Counts of U.S. Citizens: A variable indicating if the FGE was a count of U.S. citizens as opposed to 

U.S.-born individuals was included to focus on the number of overseas U.S. citizens who can potentially 

vote. Therefore, the estimate should exclude U.S.-born individuals who migrated overseas and who, for 

whatever reason, are no longer U.S. citizens with the right to vote in U.S. elections. Including this variable
29

also accounts for the potential underestimation that could result from children born to overseas U.S. 

citizens being excluded from an FGE that only includes U.S.-born individuals. Data on whether a 

government counted only U.S. citizens (rather than U.S.-born individuals) was obtained from the 2011 

OCC Report, the Census Bureau data set (Schachter, 2008), and websites of individual foreign government 

statistical agencies. 

 Country Allows Dual Citizenship with the United States: a variable indicating whether a foreign country 

generally allows its citizens to also have U.S. citizenship after they have migrated to the United States.7

This variable acts as a proxy for a foreign government’s attitude toward dual citizens. FGEs taken from 

countries that allow dual citizenship may undercount the number of resident U.S. citizens because dual 

citizens may be treated as citizens of their host country rather than as U.S. citizens. Including an indicator 

of whether a country allows dual citizenship with the United States allows for the potential mitigation of 

this source of error (see Appendix C for more information). 

The definition of the U.S. citizen population also remains an issue in this study. For the purposes of this project, 

individual host country governments define what constitutes a resident U.S. population, using the number of longterm residents rather than the total number of U.S. born/citizens when such a subpopulation is enumerated. It should 

be noted that even what constitutes a resident typically varies by country. These definitional issues should be kept in 

mind in interpreting the final results of the analysis. 

 

7Information on whether a country allows dual citizenship with the United States was obtained from immihelp, 

a website that provides information to recent immigrants to the United States concerning green cards, visas, 

and other necessary documents. Retrieved from http://www.immihelp.com/citizenship/dual-citizenshiprecognize-countries.html 
30

Results 

Table 7. displays aggregates of the estimates resulting from the EMA methodology by State Department regions8

; 

individual country estimates for 2010 are provided in Appendix A. 

The estimates show that the number of U.S. citizens living overseas has grown steadily from 2000 to 2013, 

increasing 60% overall during that period. These estimates also show that the majority of the population of U.S. 

citizens abroad is located in the Western Hemisphere and Europe, and this remained the case throughout the 2000–

2010 period. 

Table 7. Estimate of the Population of U.S. Citizens Abroad by Global Region, 2000–2010 

Year Africa East Asia 

& Pacific 

Europe & 

Eurasia 

Near 

East 

South & 

Central 

Asia 

Western 

Hemisphere 

Global 

Total 

2000 52,763 370,009 923,066 119,414 33,259 1,203,359 2,701,869 

2001 54,852 380,651 948,868 119,358 33,112 1,223,450 2,760,291 

2002 54,298 392,833 969,335 112,028 39,512 1,261,526 2,829,533 

2003 58,033 416,567 1,002,806 127,111 45,102 1,317,421 2,967,039 

2004 62,538 438,368 1,048,491 149,712 53,070 1,383,127 3,135,305 

2005 69,460 462,839 1,089,428 162,078 61,763 1,455,999 3,301,566 

2006 67,516 518,835 1,123,249 169,325 65,897 1,507,595 3,452,418 

2007 77,297 578,090 1,176,333 189,119 78,893 1,781,450 3,881,182 

2008 89,888 603,188 1,179,756 203,939 85,259 1,953,433 4,115,463 

2009 91,470 601,856 1,109,921 211,874 95,017 2,018,579 4,128,716 

2010 100,052 626,189 1,071,890 234,552 107,732 2,189,973 4,330,387 

% Change, 

2000-2010 90% 69% 16% 96% 224% 82% 60% 

Average 

Annual 

Growth Rate 

6.61% 5.40% 1.51% 6.98% 12.47% 6.17% 4.83% 

Note: Totals are rounded to the nearest person. The sum of the region totals will consequently not equal the global 

totals. 

However, the data also show that Europe displayed by far the slowest rate of growth, while the U.S. populations in

Africa, the Near East, and South and Central Asia grew at much higher rates. Among the other regions, East Asia 

and the Pacific dominate, with a U.S. population that exceeds that of Africa, the Near East, and South and Central 

Asia combined. In the Western Hemisphere, the majority of the estimated population is accounted for by Mexico. 

Within Europe, the largest U.S. populations are in the United Kingdom, France, and Germany. Countries with the 

largest estimates tend to be those with the largest number of reported Social Security beneficiaries, 

individuals/households filing tax returns, and exchange students. In addition, countries with the greatest degree of 

 

8State Department Region definitions were retrieved from http://www.state.gov/countries/ 
31

economic (trade), demographic (immigration to the United States), and diplomatic (military aid) interaction with the 

United States also tend have the largest estimated populations of U.S. citizens. 

Country-level estimates for 2000 through 2010 are provided in a separate Excel document, but Table 8 displays the 

countries with the 10 highest and 10 lowest U.S. citizen population estimates for 2010. 

Table 8. Largest and Smallest Estimated Populations of U.S. Citizens Abroad, 2010 

10 Largest Estimates 10 Smallest Estimates 

Country Estimate Country Estimate 

Mexico 1,109,974 East Timor 18 

Canada 365,514 Bhutan 25 

United 

Kingdom 221,118 Solomon Islands 41 

France 175,994 Guinea-Bissau 54 

Israel 134,647 Sao Tome and 

Principe 54 

Germany 102,894 Comoros 73 

Australia 102,176 Vanuatu 81 

Japan 94,709 Maldives 96 

Taiwan 82,598 Kiribati 111 

India 79,562 Djibouti 135 

Table 9 shows the countries with the fastest growth and slowest average annual growth rates in U.S. citizen 

populations over the 2000 to 2010 period. Countries with the fastest growth rates in their estimated number of U.S. 

citizen residents tended to have an initially small estimated population of U.S. citizens in 2000 and to have 

traditionally experienced internal and external conflict. Many countries with the highest growth rates in estimated 

U.S. citizen populations have had historic conflict with the United States. By contrast, countries with the slowest 

growth rates in estimated U.S. citizen populations are countries with relatively large U.S. populations at the 

beginning of the period of interest, and small island states. 
32

Table 9. Largest and Smallest Annual Average Percent Change in Estimated Populations of U.S. 

Citizens Abroad, 2000–2010 

10 Fastest-Growing 

Countries 10 Slowest-Growing Countries 

Country Growth 

Rate Country Growth Rate 

Afghanistan 41% Samoa -3.83% 

Jordan 24% Zimbabwe -3.75% 

Vietnam 24% United 

Kingdom -3.61% 

Chad 22% Hong Kong -3.32% 

Libya 22% Kiribati -2.95% 

Algeria 21% Solomon 

Islands -2.73% 

Iran 22% Germany -2.71% 

Laos 21% Macao -2.62% 

Lithuania 21% Micronesia -2.54% 

Lebanon 21% Marshall 

Islands -2.53% 

The tendency for countries with initially small estimated U.S. citizen populations to see greater growth is consistent 

with trends at the regional level. While the estimated population of U.S. citizens in Europe is relatively high, that 

region also saw the lowest rates of growth over the 2000–2010 period. By contrast, Africa, the Middle East, and 

Southern Asia, while having the lowest totals throughout the period, saw the fastest growth. This is consistent with a 

change in the geographic distribution of the population of U.S. citizens abroad, with U.S. citizens becoming less

concentrated over time, and the population of lagging regions beginning to converge with the higher population 

regions. This is also consistent with trends in the World Bank’s estimates of the size of overseas U.S. born/citizen 

populations by country for the period 1990–2000, where countries with relatively small U.S. populations in 1990 

saw faster growth over the subsequent decade than countries with relatively large populations (Ozden, et al., 2011). 

Figures 2, 3, and 49

 identify the location of the countries with large, but slow-growing overseas U.S citizen 

populations and those with small, but fast growing populations. 

 

9In all maps, China, Hong Kong, and Macao are treated as a single observation. 
33

Figure 2. Total Number of Estimated Overseas U.S. Citizens by Country, 2000 

Figure 3. Total Number of Estimated Overseas U.S. Citizens by Country, 2010 
34

While Western European countries and former British dominions outside Southeast Asia (e.g., Canada, Australia) 

are in the top quartile of countries with respect to the size of their population in both 2000 and 2010, they are in the

lower two quartiles with respect to the growth of their estimated overseas U.S. citizen populations. By contrast, 

many countries in Africa are in the lower two quartiles in the size of their estimated U.S citizen population in 2000 

and 2010, but are in the upper quartile of countries in terms of the growth in that population. It should be noted, 

however, that several countries in Latin America such as Brazil, Argentina, and Chile are in the top quartiles both in 

terms of the size of their overseas U.S citizen population at the beginning and end of the 2000–2010 period and are 

among the top countries with respect to growth. This is consistent with the Western Hemisphere already having the 

highest estimated number of overseas U.S. citizens in 2000 while still seeing significant estimated growth for the 

2000–2010 period. 

Figure 4. Growth in the Number of Estimated Overseas U.S. Citizens by Country, 2000–2010 

This trend can be seen in Figure 5, where the ratio of estimated overseas U.S. citizens in the top 25% versus bottom 

25% of countries is plotted across time. If overseas U.S. citizens were equally distributed across the world, this ratio 

would be expected to take a value of 1, with higher values representing greater departure from equal distribution. 
35

Figure 5. Trends in the Deconcentration of Estimated U.S. Citizens Abroad 

Note: The vertical access is the ratio of the total number of estimated U.S. citizens abroad in countries in the top 

quartile to the total number of estimated U.S. citizens abroad in the bottom quartile. 

In Figure 5, there is an apparent downward trend in the concentration of U.S. citizens abroad. Specifically, in 2000 

there were approximately 249 estimated overseas U.S. citizens in the top 25% of countries for every one U.S. citizen 

in the bottom 25% of countries, but by 2010 there were only 207 estimated U.S. citizens in the top 25% of countries 

for every U.S. citizen in the bottom 25% of countries. When Mexico is excluded, this trend becomes even more 

prominent, with 203 estimated U.S. citizens in the top quartile for every U.S. citizen in the bottom quartile in 2000 

declining to approximately 149 estimated U.S. citizens in the top quartile of countries for every U.S. citizen in the 

bottom quartile in 2010.

Any estimate of the population of U.S. citizens living abroad will have some level of uncertainty because of data and 

sample issues; this uncertainty is reflected in the confidence interval. A confidence interval reflects the range of 

estimates that has a high probability (95%) of containing the true population count. Table 10 shows the countries 

whose 2010 estimates displayed the largest and smallest confidence intervals, relative to their mean estimate. 
36

Table 10. Largest and Smallest Confidence Intervals of Estimated Populations 

of U.S. Citizens Abroad, 2010 

10 Largest Confidence Intervals 10 Smallest Confidence Intervals 

Country Lower 

Bound Mean Upper Bound Country Lower Bound Mean Upper Bound 

Afghanistan 249 3,619 52,488 Belgium 21,611 23,811 26,236 

Libya 409 2,143 11,238 Barbados 4,085 4,607 5,196 

Laos 234 1,152 5,668 Iceland 670 782 913 

Iran 2,030 9,059 40,425 Philippines 57,931 68,449 80,876 

Vietnam 5,358 23,420 102,362 Singapore 6,625 7,840 9,278 

Lithuania 1,368 5,645 23,292 Namibia 976 1,173 1,409 

Algeria 907 3,738 15,402 Netherlands 20,219 24,312 29,234 

Lebanon 2,383 9,325 36,490 Maldives 79 96 116 

Iraq 1,400 5,264 19,792 Canada 297,742 365,514 448,713 

Azerbaijan 382 1,407 5,179 Kenya 5,004 6,194 7,667 

Countries with large confidence intervals tend to be those with a high growth in the estimated size of their U.S.

citizen populations from 2000 to 2010. This growth appears to be driven to a large degree by high values along 

country characteristics such as administrative records variables and/or trade. In these countries with large confidence 

intervals, predictions made by the different models also tend to be similar; this increases the uncertainty for these 

countries’ estimates. By contrast, those countries that have characteristics that result in different models producing 

less-similar estimates of the number of U.S. citizens tend to have smaller confidence intervals. These less-similar 

estimates produced by the different models likely result in a “cancelling out” of the error introduced in the different

models by limited sample size, resulting in a smaller range that likely contains the true value. 

The Consistency of the Results of the Model with Theory 

The validity of the analysis in the prior section is dependent upon the validity of the models used to generate 

estimates of the overseas U.S. citizen populations. This in turn is dependent upon the validity of the predictors. One 

way to test this validity is to examine the relationship between the final estimates and the country-level predictors 

and test if the direction of that relationship is consistent with expectations set by the theory used to choose the 

predictors in the first place. If the predictors are unrelated to the final estimates or the relationship is in the “wrong” 

direction, this potentially calls into question the model(s) and resulting final estimates because it would indicate a 

failure to capture the factors that explain the relative sizes of overseas U.S. citizen populations. Descriptive statistics 

for the FGEs and predictor variables for all country-years for which an estimate was made are listed in Table 11. 
37

Table 11. Descriptive Statistics, All Estimated Country-Years 

Variable N Mean Standard 

Deviation Minimum Maximum 

FVAP Estimate 2012 18689.75 67605.28 6.34 1109974 

World Bank Estimate 182 10097.4 36821.78 0 350626 

United Nations Estimates 274 15224.82 51797.21 3 563315 

Dualcitizenship 2012 .31 .46 0 1 

Administrative Records Variables 

Social Security Beneficiaries 2012 2503.59 9591.34 .04 108194 

IRS Form 2555s 2012 1872.06 4490.44 1.20 48644.31 

Students 2012 1125.22 3816.23 0 34024 

Federal Government 

Employees 2012 234.38 1340.96 0 18232 

Theoretical Variables 

Ln(Difference in GDP per 

capita) 2012 -2.02 1.34 -5.40 1.19 

Population 2012 33283.31 127604.6 45.66 1330141 

Distance 2012 4593.24 2014.07 3.45 9093.53 

Mean (World Governance 

Indicators) 2012 -.07 .89 -2.24 1.88 

Trade 2012 13745.44 50332.71 .2 600641.2 

Immigrants in U.S. 2012 132461.5 503087.5 0 6400000 

Military Aid 2012 3.77E+09 1.34E+10 0 1.29E+11 

English 2012 .50 .50 0 1 

Spanish 2012 .19 .39 0 1 

Year of Estimate 2012 2005.00 3.16 2000 2010 

In order to examine the relationships between the predictors and estimates, in the first three columns of Table 12 the 

final estimate is regressed on the administrative records and theoretical variables. In the first column, both the 

administrative records variables and theoretical variables are included to examine the association between each 

variable and the final estimate, conditional on the other variables. In the second column, the administrative records 

variables are dropped because it is expected that the effect of the theoretical variables on the final estimates would 

be mediated by the size of the different subgroups reflected in the administrative records variables, and thus 

controlling for them would attenuate the expected relationship of the theoretical variables with the final estimate. 

Finally, in the third column, the theoretical variables that directly measure the interaction between the United States 

and the host country (trade, immigration to the United States, and military aid) are dropped so that the effects of the 

structural variables (level of economic and institutional development, population, distance, and language) can be 

identified. 
38

Table 12. Determinants of Final Estimates 

Variable (1) (2) (3)

Ln(# of Social Security 

Beneficiaries) 

.28*** (.03) 

Ln(# of IRS Returns) .45*** (.03) 

Ln(STUDENTS) .18*** (.02) 

Ln(U.S. Government 

Employment) 

-.04 (.02) 

Ln(Difference in GDP per 

capita) 

-.40*** (.08) .15 (.10) .58*** (.11) 

Ln(Population) -.18*** (.04) .07 (.08) .61*** (.05) 

Ln(Distance) -.09*** (.02) -.09** (.04) -.30*** (.04) 

Mean(World Governance 

Indicators) 

.03 (.07) .33** (.15) .30* (.16) 

Ln(Trade) .17*** (.03) .29*** (.07) 

Ln(Immigrants in U.S.) .10*** (.03) .35*** (.08) 

Ln(Military Aid) .01** (.01) .04** (.02) 

ENGLISH .11 (.07) .36** (.14) .60*** (.18) 

SPANISH .07 (.10) .43* (.23) .59* (.31) 

Year -.00 (.00) .03** (.01) .04*** (.01) 

Countries 183 183 183 

N 2012 2012 2012 

Pseudo R^2 .99 .94 .89 

*p < .10. **p < .05. ***p < .01. Model estimated using a Poisson regression. Robust standard errors clustered by 

country in parentheses. 

As indicated in Column 1, the number of Social Security beneficiaries, tax returns filed by U.S. citizens, and 

students abroad are all positively and significantly associated with the final estimate, consistent with expectation. By 

contrast, the coefficient on the number of U.S. civilian government employees is statistically insignificant and has a 

negative sign. This may be due to the fact that government employees may be more likely to be posted to countries 

subject to external and internal security threats and political instability, which may discourage migration (Ziesemer,

2010). Consequently, this variable could be capturing unobserved conditions in a country that makes it less 

attractive as a destination to many U.S. migrants. 

Among the theoretical variables that capture interactions between the United States and the host country, trade, 

migration, and military aid are each, as expected, positively and statistically significantly associated with the final 

estimate, both when controlling for the administrative records variables and after dropping them. When the 

administrative records variables are dropped, the coefficient on each theoretical variable becomes larger. This 

indicates that while the administrative records variables might be capturing some of the effect of these interaction 

variables on the final estimates, the interaction variables may be proxying for the existence of populations not 

directly captured in the administrative records variables. Finally, the coefficients for the “structural” variables, with 
39

the exception of distance, are either statistically insignificant (English and Spanish dummies, institutional quality), 

or have the wrong sign (population and difference in GDP per capita) when controlling for both the administrative 

records and interaction variables. Once the administrative records variables are dropped in the second column, none

of the structural variables have the wrong sign, and some (the language dummies, institutions) gain statistical 

significance. Once the interaction variables are dropped in the third column, each structural variable has both the 

expected sign and is statistically significant. This indicates that while the estimates have the theoretically expected 

relationship with the predictor variables, the structural variables added relatively little additional explanatory power 

to the model set. 

Differences between the Estimates from this Methodology and Prior Estimates 

In Table 13, the impacts of the administrative records and theoretical variables on the size of the estimates relative to 

the World Bank and United Nations estimates are analyzed by regressing the logged ratio of the World Bank and 

United Nations estimates to the FVAP estimates. In columns 1 and 2, the dependent variable is the ratio the World 

Bank estimate to the FVAP estimate. In columns 3 and 4, the dependent variable is the United Nations estimate to 

the FVAP estimate. Positive coefficients indicate that countries with high values on a given predictor have FVAP

estimates that are small relative to their World Bank/United Nations estimates, and countries with negative 

coefficients have FVAP estimates that are relatively large. 
40

Table 13. Correlates of Deviations from Prior Estimates 

Variable World Bank/FVAP Estimates, 2000 United Nations/FVAP Estimates, 2000 

and 2010 

DUALCITIZENSHIP -.93*** (.28) -.95*** (.24) -.63** (.25) -.78*** (.22) 

Ln(# of Social 

Security 

Beneficiaries) 

.25* (.14) -.07 (.11) 

Ln(# of IRS Returns) -.03 (.21) -.35*** (.09) 

Ln(STUDENTS) -.01 (.06) .03 (.07) 

Ln(U.S. Government 

Employment) .15** (.07) -.05 (.09) 

Ln(Difference in 

GDP per capita) .41** (.19) .44*** (.14) .10 (.15) -.06 (.15) 

Ln(Population) .38** (.10) .45*** (.11) .48*** (.12) .45*** (.12) 

Ln(Distance) .27 (.31) .14 (.29) -.22* (.13) -.28** (.12) 

Mean(World 

Governance 

Indicators) 

-.24 (.22) -.04 (.20) .44** (.22) .54** (.23) 

Ln(Trade) -.39** (.17) -.35*** (.10) -.14 (.10) -.37*** (.08) 

Ln(Immigrants in 

U.S.) -.22*** (.07) -.12** (.05) -.05 (.08) -.10 (.07) 

Ln(Military Aid) -.10*** (.02) -.08*** (.02) -.07*** (.02) -.10*** (.01) 

ENGLISH .21 (.25) .23 (.20) .87*** (.32) .74*** (.26) 

SPANISH -.66** (.33) -.46 (.29) -.03 (.36) -.05 (.34) 

Western Hemisphere 1.37** (.61) 1.50** (1.03) .23 (.56) .42 (.50) 

South/Central Asia -.46 (.41) -.77** (.35) .70 (.45) .95** (.43) 

Near East 1.51*** (.37) 1.60*** (.29) 1.72*** (.43) 1.87*** (.42) 

Europe .62 (.50) .91 (.71) -.03 (.43) .00 (.38) 

East Asia/Pacific .03 (.34) .05 (.36) -.03 (.38) -.15 (.40) 

2010 -.36* (.20) -.16** (.07) 

Countries 182 182 137 137 

N 182 182 274 274 

Pseudo R^2 .42 .40 .61 .59 

*p <.10. **p < .05. ***p < .01. Model estimated using a Poisson regression. Robust standard errors clustered by 

country in parentheses. The reference region is Africa. 

There are several variables for which the sign is consistent for both the World Bank and United Nations 

regressions.10 The results indicate that countries that allow dual citizenship with the United States have FVAP

estimates which are large relative to the World Bank and United Nations estimates. This can be explained by the 

 

10Although there are some variables that have opposite signs for the World Bank and United Nations 

regressions, the documentation on the generation of the United Nations is relatively light, and does not offer a 

basis for explaining differences between the two alternate sets of estimates. 
41

adjustments made to the FVAP estimates to ensure that countries that provide a count of citizens also count dual 

citizens. Regressions also indicate that countries with large populations tend to have World Bank and UN estimates 

that are large relative to their FVAP estimates. This may be an artifact of how the World Bank (and potentially the 

United Nations) imputed values for missing later decades. Specifically, they would assume that the share of total 

migrants in a country composed of individuals originating in the United States remained fixed relative to some prior 

decade or else took on a regional average. Consequently, if countries with large populations also had large numbers 

of migrants (from any country), then the number of U.S. born/citizens in the country would rise with population. By 

contrast, the FVAP estimates are derived using the empirical association between population and the size of the 

overseas U.S. citizen population. 

The other consistent difference between the FVAP estimates and the World Bank and United Nations estimates is 

that the countries with high values on trade and military aid have FVAP estimates that are large relative to the World 

Bank and United Nations estimates. Given that each of these variables also was positively associated with the 

absolute size of the FVAP estimate, this may simply reflect the fact that these variables do not have an association 

with the data used to generate the World Bank and United Nations estimates. This might reflect the fact that the 

World Bank and UN estimates were imputed based on past estimates and/or regional averages. If there have been 

significant changes in the patterns of trade, perhaps because of the end of the Cold War and other factors that are 

leading to a more integrated global economy, then countries that have significant trade with the United States today 

would not necessarily have had significant trade with the United States in the past. With respect to military aid, if 

military aid is assigned based on need, then countries that are receiving military aid may not be attractive 

destinations for migrants. However, if that aid leads to better relations with the United States, then over the long run 

the number of U.S. migrants in the recipient country of the aid might increase. Thus, military aid might have an 

insignificant or even negative association with past migration, but a positive relationship with contemporary 

migration. 
42

Figure 6. FVAP Estimate Relative to the World Bank Estimate, 2000 

Further evidence for the importance of lagged data in explaining the difference between the FVAP estimates and the 

World Bank estimates is presented in Figure 6, which depicts the ratio of the 2000 FVAP estimate to the World 

Bank estimate in quartiles. Note that countries in the top quartile (i.e., those where the FVAP estimate is particularly 

high relative to the World Bank estimates) are heavily clustered in the former Soviet Union.11 This likely reflects a 

situation that dominated in the Cold War, where there was limited migration between the United States and the 

former Soviet Union, but is less true now. Consequently, the interpretation of the differences between the size of the 

World Bank and United Nations estimates and the FVAP estimates is that the latter are produced using 

contemporary cross-country relationships between predictors and FGEs. By contrast, the World Bank estimates are 

imputed based on lagged data, resulting in the World Bank and United Nations estimates having relatively higher 

estimates in countries to which U.S. citizens have traditionally migrated, while the FVAP estimates are relatively 

high for countries with which the United States currently has strong links with respect to trade and migration. 

 

11The United Nations does not provide estimates for many countries, and specifically many countries in the 

former Soviet Union. Consequently, a comparison based upon quartiles would not provide much information. 
43

Discussion 

Although no estimate should ever be considered “final,” the methodology described in this report produced countrylevel estimates for each year from 2000 to 2010, using a method that can be reproduced and refined by future 

researchers. In contrast to the full enumeration methodology considered by the Census Bureau, this method did not 

require extensive field collection work to produce data, but rather utilizes data already produced by foreign 

governments, which presumably have greater capacity to estimate U.S. citizens in their own territories. By 

developing a model of these estimates, the size of the population of U.S. citizens abroad can be estimated more 

efficiently than by using a full enumeration approach. Unlike the World Bank and United Nations data sets, these 

estimates are made using relatively contemporary (2000–2010) FGEs and related predictors of the size of the 

overseas U.S. population. Consequently, this method of estimating should better reflect the current geographic 

distribution and dating of this population. Because our model-based methodology uses contemporary predictors of 

migration to predict overseas citizen populations, rather than lagged migration data, the set of estimates provided in 

this report are likely to suffer less from the shortcomings described above. In addition, these estimates were 

generated using predictors that are theoretically justified, and the estimation procedure mitigates issues related to 

sample selection by weighting observations and predictions from different models such that the estimates are more 

likely to be valid for countries for which FGEs are unavailable. Finally, this methodology is has been subject to a 

variety of robustness checks discussed in Appendixes B and C. 

The estimates provided in this report help to provide a picture of the size and geographic distribution of the 

population of U.S. citizens abroad as well as its change over time, and the changing geographic distribution of the 

overseas U.S. citizen population revealed could have strong implications for how organizations which provide 

services and information to overseas U.S. citizens allocate resources in the future. Specifically, while the estimates 

indicate the U.S. citizen population is to a large extent concentrated in Europe and the Western Hemisphere and has

remained so throughout the 2000–2010 period, there are substantial differences in the estimated rate of growth 

between countries and regions that suggest an increase in the geographic dispersion of U.S. citizens. Though there is 

a large degree of uncertainty in the numbers of U.S. citizens located in the countries seeing the fastest growth,

organizations that hope to engage with this population may wish to consider how it will adapt to a potential rise in 

the number of U.S. citizens in Africa, Asia, and the Near East. 

While the total number of overseas U.S. citizens within a country gives some indication of the benefit to 

organizations interested in engaging with overseas U.S. citizens in investing resources in the country, another 

relevant factor is the cost of reaching out to these citizens, which is likely to vary by country. Two proxies for these 

costs are used: population and land area. 
44

Figure 7. Ratio of Estimated U.S. Citizens Abroad to Country Population, 2010 

The necessity to identify a country’s residents as either U.S. citizens or non-U.S. citizens might be greater in 

countries with large total populations, holding the number of U.S. citizens constant, as the probability that any given 

resident of the country is a U.S. citizen will be lower. If distinguishing between U.S. citizens and noncitizens is 

costly, then investing resources in a country with a large U.S. citizen population but where U.S. citizens make up a 

small percentage of the total population may be inefficient. Figure 7 displays countries coded by the ratios of the 

estimated number of U.S. citizens in 2010 to the country’s total population. U.S. citizens comprise a relatively large 

(top two quartiles) percentage of the total population in Europe, North America, and Latin America as well as in 

some East Asia and Pacific countries. By contrast, countries with a relatively low fraction of their total population 

composed of U.S. citizens are largely concentrated in Africa, the former Soviet Union, and the Asian mainland. 
45

Figure 8. Ratio of Estimated U.S. Citizens Abroad to Country Land Area, 2010 

It is also expected to be costly to identify and engage with U.S. citizens in geographically large countries because 

the transportation costs involved in reaching these populations may be large in these countries. As seen in Figure 8, 

geographic patterns in the percentage of a country’s total population composed of U.S. citizens largely holds when 

the ratio of U.S. citizens to land area is used instead, though in this case the former Soviet Union is relatively worse 

off with respect to the density of U.S. citizens than the Asian mainland. It should be noted that while population and 

land area may influence the costs of engaging in face-to-face outreach, they may be less relevant in countries where 

social media and other forms of online communication are viable. On the other hand, many countries in which there 

is the greatest density (per capita or per unit land area) of U.S. citizens are also likely to have the most developed 

Internet infrastructure, as indicated by the high density of U.S. citizens in Western Europe, former European 

colonies, and Japan. 

With all of that being said, it is also key to remember that a handful of countries—Mexico, Canada, the United 

Kingdom, France, Israel, Germany, and Australia—continue to represent slightly over half (approximately 52%) of 

the population of U.S. citizens abroad. Any outreach that address those countries will continue to target most 

overseas U.S. citizens. 

Limitations 

Within any study of this nature, there are inherent limitations. Most have been covered within the discussion. It 

makes sense, however, to summarize them as a way to frame expectations and look for improvements in the future. 
46

The first limitation is that the analysis relied heavily on existing, largely official statistical sources. These were 

censuses and registries, drawn from U.S. and other national statistical offices around the world. This meant that the 

results were subject to differences in approach, usually driven by the individual country or administrative source. 

These sources were originally available for a purpose other than the use intended here. Timing and definitional 

differences were major challenges, not always surmountable. Fortunately, because of the European Union (EU) 

there was somewhat greater uniformity of reporting in that part of the world. Still, much of the problem is model- or 

adjustment-driven. 

Efforts were made to align the foreign country-by-country results provided here to make the exercise as consistent as 

possible. However, these adjustments assume that the observed association between having a registry or census and

the estimate of the size of the overseas U.S. population reflects differences in how the foreign government estimated 

the population rather than differences in the “true” U.S. population. If there are systematic, unobserved differences

between countries that produced an estimate with a registry or census, and these differences affect the size of a 

country’s U.S. citizen population, then bias may be introduced in the final estimates. This approach thus relies on 

the assumption that the administrative records–based variables and theoretical variables captured these systematic 

differences. However, with this assumption, the incomparability between census- and registry-based estimates has 

been more or less satisfactorily addressed. 

Another limitation to the statistical methodology relates to how the possibility that the sample of countries was not 

representative was addressed. Inverse-probability weighting corrects for nonresponse bias to the degree that there 

are not unobserved factors that affect both the size of the FGE and probability that a country has an FGE. If the logit 

model did not capture all relevant nonignorable factors, then the results will still suffer from selection bias, and MSE 

and other measures of fit will not reliably indicate the quality of a model with respect to its ability to create an 

accurate prediction for countries without an FGE. This selection bias is potentially exacerbated by the fact that for 

many countries outside the sample, the administrative records variables had to be imputed, and are thus likely of 

lower quality. This adds additional uncertainty to the FVAP estimates for these countries that is not incorporated 

into the confidence intervals. 

Conclusion 

This paper addressed a difficult problem: how to estimate the size and location of the population of U.S. citizens 

abroad. Data on this population is collected by different governments using different methodologies as well as 

different definitions of resident “Americans”. This makes any attempt to use these foreign government estimates to 

estimate the size and geographic distribution of U.S. citizens abroad subject to substantial measurement error. In 

addition, data on the size of contemporary overseas U.S. populations are only available for non-representative subset 

of countries, limiting the size of the sample that can be used for any attempt to model the population for out-ofsample countries. This increases the danger of inaccurate predictions due to overfitting and selection bias. Past 

attempts at estimating this population by organizations such as the World Bank and United Nations have attempted 

to overcome the limitations of a model based approach by incorporating observations of country-level U.S. 

populations over a long span of time and using information about other countries in the region to impute a country’s 
47

U.S. migrant share. Estimates for a country were then generated by extrapolating from past U.S. shares of a 

country’s migrant population or by using contemporary regional averages of the U.S. migrant share. However, these 

estimates do not incorporate contemporary, country-specific factors in generating predictions and are thus likely to

have substantial error, especially for countries in heterogeneous regions whose economic and political relationship

with the United States has changed substantially in recent years. 

This paper employed an alternative model-based approach, Ensemble Model Averaging, which preserves the 

benefits of parametric modeling approaches while mitigating their limitations. Specifically, final estimates represent 

weighted averages of predictions from models defined from subsets of theoretically grounded predictor variables. 

The weights are determined by the predictive accuracy of the model that generates the prediction and its lack of 

redundancy with other models. This allows for the incorporation of relevant information for a large number of 

predictors while mitigating the risk of overfitting. This analysis also incorporated two other methodologies which 

attempted to overcome problems that plagued earlier attempts to estimate U.S. citizens abroad: the use of inverse 

probability weights for country-years, to mitigate the role of selection bias; and the modeling of measurement error 

to deal with the non-comparability of different government’s estimates and ensure that the final predictions represent 

the populations of our population of interest, namely U.S. citizens. These methods can be used to model the size and 

location of other populations when the underlying data generating process is complex and the data is sparse and 

heterogeneous in quality. 
48

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52

Appendix A: Estimates of the Population of U.S. Citizens Abroad, by Country, 2000 and 2010 

2000 2010 

Growth in Overseas 

Citizens Populations, 

2000-2010 

Country 

95% CI 

Lower 

Bound

Mean 

Estimate 

95% CI 

Upper 

Bound 

95% CI 

Lower 

Bound 

Mean 

Estimate 

95% CI 

Upper 

Bound 

% 

Change 

in Mean 

Estimate, 

2000–

2010 

Averag

e 

Annual 

Growth 

Rate 

Global Totals 1,832,636 2,701,86

9 4,210,347 2,622,359 4,330,387 7,790,496 60% 4.83% 

Afghanistan 8 113 1,642 249 3,619 52,488 3097% 41.41% 

Albania 373 643 1,110 886 1,527 2,633 137% 9.03% 

Algeria 130 537 2,213 907 3,738 15,402 596% 21.41% 

Angola 373 627 1,056 816 1,373 2,311 119% 8.15% 

Antigua and 

Barbuda 1,015 1,474 2,142 1,108 1,610 2,339 9% .88% 

Argentina 4,944 13,989 39,581 17,246 48,798 138,078 249% 13.31% 

Armenia 148 346 809 463 1,083 2,533 213% 12.09% 

Australia 54,067 69,101 88,315 79,950 102,176 130,580 48% 3.99% 

Austria 4,980 8,371 14,071 10,045 16,884 28,382 102% 7.27% 

Azerbaijan 72 266 978 382 1,407 5,179 429% 18.13% 

Bahamas 1,723 3,045 5,380 2,557 4,517 7,980 48% 4.02% 

Bahrain 352 616 1,079 505 884 1,548 44% 3.68% 

Bangladesh 1,611 2,998 5,577 3,336 6,206 11,548 107% 7.55% 

Barbados 3,801 4,282 4,824 4,085 4,607 5,196 8% .73% 

Belarus 213 512 1,230 827 1,986 4,769 288% 14.51% 

Belgium 23,016 25,335 27,887 21,611 23,811 26,236 -6% -.62% 

Belize* 

Benin 241 456 864 509 963 1,823 111% 7.76% 

Bermuda* 

Bhutan 8 15 27 13 25 46 71% 5.51% 

Bolivia 871 1,550 2,758 1,901 3,384 6,023 118% 8.12% 

Bosnia and 

Herzegovina 309 628 1,279 726 1,478 3,008 135% 8.93% 

Botswana 294 488 811 478 794 1,319 63% 4.98% 

Brazil 9,525 21,513 48,589 29,937 67,623 152,751 214% 12.13% 

Brunei 154 213 294 147 203 281 -5% -.46% 

Bulgaria 2,348 2,987 3,800 3,186 4,052 5,155 36% 3.10% 

Burkina Faso 171 259 391 241 364 551 41% 3.49% 

Burundi 26 68 176 86 222 572 226% 12.53% 

Cambodia 1,655 4,143 10,375 5,960 14,924 37,367 260% 13.67% 
53

Cameroon 694 1,344 2,603 1,388 2,690 5,211 100% 7.19% 

Canada 338,523 415,642 510,330 297,742 365,514 448,713 -12% -1.28% 

Cape Verde 233 338 490 358 519 752 54% 4.38% 

Central 

African 

Republic 

70 136 264 141 272 528 100% 7.18% 

Chad 40 142 509 301 1,075 3,845 656% 22.42% 

Chile 5,253 12,893 31,649 17,198 42,217 103,634 227% 12.59% 

China 6,277 18,414 54,018 25,376 74,429 218,307 304% 14.99% 

Colombia 9,421 17,523 32,596 22,541 41,922 77,966 139% 9.11% 

Comoros 19 37 72 37 73 144 100% 7.19% 

Congo, Dem. 

Rep. 154 406 1,069 528 1,390 3,661 242% 13.10% 

Congo, 

Republic of 145 398 1,091 543 1,489 4,079 274% 14.09% 

Costa Rica 14,841 23,581 37,467 25,882 41,141 65,394 74% 5.72% 

Cote d`Ivoire 1,099 1,714 2,672 1,801 2,809 4,380 64% 5.06% 

Croatia 2,237 3,891 6,768 5,023 8,737 15,197 125% 8.43% 

Cuba 328 812 2,008 991 2,452 6,063 202% 11.69% 

Cyprus 1,307 2,149 3,533 1,368 2,248 3,697 5% .45% 

Czech 

Republic 1,190 3,770 11,949 5,358 16,984 53,835 351% 16.24% 

Denmark 3,113 7,182 16,572 10,385 23,963 55,292 234% 12.80% 

Djibouti 32 57 100 77 135 239 138% 9.08% 

Dominica 439 877 1,751 1,059 2,114 4,220 141% 9.19% 

Dominican 

Republic 41,859 54,406 70,714 61,201 79,530 103,350 46% 3.87% 

Ecuador 20,431 35,608 62,061 44,289 77,226 134,658 117% 8.05% 

Egypt 3,587 7,495 15,662 9,840 20,563 42,972 174% 10.62% 

El Salvador 7,100 12,654 22,550 17,072 30,422 54,209 140% 9.17% 

Equatorial 

Guinea 221 440 877 563 1,122 2,236 155% 9.81% 

Eritrea 181 378 791 344 720 1,508 91% 6.66% 

Estonia 349 773 1,712 909 2,013 4,460 160% 10.04% 

Ethiopia 556 1,386 3,456 2,035 5,074 12,655 266% 13.86% 

Fiji 1,141 1,479 1,916 1,850 2,397 3,106 62% 4.95% 

Finland 1,710 3,989 9,307 4,337 10,120 23,615 154% 9.76% 

France 67,133 99,365 147,073 118,906 175,994 260,489 77% 5.88% 

Gabon 247 436 771 435 770 1,361 76% 5.84% 

Gambia, The 127 206 335 201 327 531 58% 4.71% 

Georgia 121 282 658 442 1,034 2,415 267% 13.88% 

Germany 101,631 135,483 180,613 77,176 102,894 137,181 -24% -2.71% 

Ghana 5,155 7,206 10,072 8,280 11,570 16,167 61% 4.85% 
54

Greece 23,723 30,712 39,759 30,841 39,904 51,630 30% 2.65% 

Grenada 805 1,434 2,554 1,619 2,883 5,135 101% 7.23% 

Guatemala 10,334 18,445 32,921 23,390 41,746 74,509 126% 8.51% 

Guinea 191 282 415 314 464 684 65% 5.11% 

Guinea-Bissau 10 20 41 27 54 108 164% 10.19% 

Guyana 613 1,075 1,885 1,615 2,832 4,965 163% 10.17% 

Haiti 946 1,918 3,892 2,375 4,819 9,779 151% 9.65% 

Honduras 7,725 12,455 20,081 14,911 24,042 38,763 93% 6.80% 

Hong Kong 24,316 31,598 41,063 17,360 22,550 29,292 -29% -3.32% 

Hungary 6,509 9,771 14,667 12,039 18,067 27,114 85% 6.34% 

Iceland 721 842 984 670 782 913 -7% -.74% 

India 7,318 19,366 51,249 30,066 79,562 210,542 311% 15.18% 

Indonesia 4,014 8,646 18,625 9,072 19,543 42,100 126% 8.50% 

Iran 293 1,306 5,829 2,030 9,059 40,425 593% 21.37% 

Iraq 339 1,274 4,792 1,400 5,264 19,792 313% 15.24% 

Ireland 25,034 31,969 40,825 29,161 37,240 47,556 16% 1.54% 

Israel 61,089 86,797 123,322 94,778 134,647 191,287 55% 4.49% 

Italy 53,364 66,443 82,728 50,121 62,408 77,707 -6% -.62% 

Jamaica 16,645 22,520 30,468 24,557 33,223 44,948 48% 3.97% 

Japan 57,994 82,049 116,082 66,943 94,709 133,991 15% 1.45% 

Jordan 221 809 2,962 1,951 7,144 26,161 783% 24.34% 

Kazakhstan 188 421 944 475 1,065 2,387 153% 9.72% 

Kenya 4,036 4,999 6,191 5,004 6,194 7,667 24% 2.17% 

Kiribati 105 149 212 78 111 157 -26% -2.95% 

Korea, 

Republic of 17,559 23,807 32,278 25,294 34,287 46,477 44% 3.72% 

Kuwait 339 597 1,050 494 868 1,527 45% 3.81% 

Kyrgyzstan 42 82 161 97 191 377 133% 8.84% 

Laos 34 169 832 234 1,152 5,668 581% 21.15% 

Latvia 1,140 2,253 4,450 2,487 4,913 9,708 118% 8.11% 

Lebanon 364 1,424 5,571 2,383 9,325 36,490 555% 20.68% 

Lesotho 356 585 962 347 571 939 -2% -.25% 

Liberia 179 538 1,613 821 2,462 7,389 358% 16.44% 

Libya 57 300 1,572 409 2,143 11,238 615% 21.74% 

Lithuania 202 833 3,437 1,368 5,645 23,292 577% 21.09% 

Luxembourg 314 434 600 303 419 579 -3% -.35% 

Macao 863 1,268 1,863 662 972 1,428 -23% -2.62% 

Macedonia 305 579 1,098 524 994 1,884 72% 5.55% 

Madagascar 550 789 1,131 953 1,366 1,959 73% 5.65% 

Malawi 326 484 719 513 761 1,130 57% 4.63% 
55

Malaysia 2,496 5,617 12,639 6,653 14,971 33,688 167% 10.30% 

Maldives 90 109 132 79 96 116 -12% -1.28% 

Mali 129 206 329 230 368 588 79% 5.97% 

Malta 1,646 2,537 3,909 2,480 3,823 5,891 51% 4.19% 

Marshall 

Islands 384 503 660 297 390 510 -23% -2.53% 

Mauritania 55 111 223 157 318 641 187% 11.11% 

Mauritius 403 615 939 670 1,023 1,562 66% 5.22% 

Mexico 250,509 467,880 873,870 594,335 1,109,974 2,072,977 137% 9.02% 

Micronesia, 

Fed. Sts. 290 446 686 224 345 530 -23% -2.54% 

Moldova 250 368 542 315 464 684 26% 2.35% 

Mongolia 124 207 344 272 452 752 119% 8.14% 

Montenegro* 

Morocco 2,655 6,304 14,965 8,181 19,421 46,105 208% 11.91% 

Mozambique 390 484 601 310 384 476 -21% -2.29% 

Namibia 879 1,057 1,270 976 1,173 1,409 11% 1.05% 

Nepal 590 885 1,329 891 1,337 2,006 51% 4.21% 

Netherlands 15,655 18,825 22,636 20,219 24,312 29,234 29% 2.59% 

New Zealand 11,615 16,034 22,134 19,867 27,422 37,849 71% 5.51% 

Nicaragua 685 2,478 8,961 3,966 14,340 51,853 479% 19.19% 

Niger 83 166 333 167 335 670 101% 7.26% 

Nigeria 7,204 11,519 18,416 13,791 22,045 35,242 91% 6.71% 

Norway 4,097 10,108 24,939 13,388 33,035 81,515 227% 12.57% 

Oman 170 439 1,137 631 1,632 4,221 271% 14.02% 

Pakistan 1,815 3,320 6,073 4,579 8,378 15,325 152% 9.70% 

Palau 

Panama 7,715 11,771 17,960 12,159 18,551 28,306 58% 4.65% 

Papua New 

Guinea 522 701 940 665 893 1,198 27% 2.45% 

Paraguay 509 972 1,854 1,130 2,156 4,113 122% 8.29% 

Peru 6,839 15,916 37,040 22,293 51,878 120,727 226% 12.54% 

Philippines 48,384 57,181 67,577 57,931 68,449 80,876 20% 1.81% 

Poland 6,083 15,944 41,792 21,710 56,909 149,178 257% 13.57% 

Portugal 5,284 8,016 12,160 6,482 9,834 14,920 23% 2.07% 

Qatar 70 150 321 142 302 646 101% 7.25% 

Romania 3,876 6,069 9,501 7,294 11,418 17,875 88% 6.52% 

Russia 2,801 6,823 16,622 8,186 19,943 48,586 192% 11.32% 

Rwanda 115 237 489 292 603 1,246 155% 9.80% 

Samoa 513 737 1,058 347 498 715 -32% -3.84% 

Sao Tome and 

Principe 17 28 45 34 54 87 93% 6.79% 
56

Saudi Arabia 3,970 5,094 6,535 3,452 4,428 5,679 -13% -1.39% 

Senegal 266 575 1,242 786 1,698 3,667 195% 11.43% 

Serbia 568 863 1,311 1,147 1,743 2,650 102% 7.29% 

Seychelles 142 225 356 147 232 367 3% .31% 

Sierra Leone 115 330 947 520 1,491 4,272 351% 16.27% 

Singapore 5,791 6,854 8,114 6,625 7,840 9,278 14% 1.35% 

Slovak 

Republic 321 1,063 3,521 1,588 5,260 17,421 395% 17.34% 

Slovenia 1,335 2,281 3,897 2,161 3,693 6,312 62% 4.94% 

Solomon 

Islands 44 54 68 33 41 51 -24% -2.73% 

Somalia 60 211 740 247 866 3,038 311% 15.17% 

South Africa 5,649 8,491 12,761 10,505 15,787 23,724 86% 6.40% 

Spain 21,485 27,807 35,989 31,650 40,960 53,010 47% 3.95% 

Sri Lanka 4,033 5,410 7,257 4,296 5,761 7,726 6% .63% 

St. Kitts & 

Nevis 707 1,178 1,963 1,291 2,152 3,587 83% 6.21% 

St. Lucia 690 1,395 2,821 1,594 3,222 6,514 131% 8.73% 

St. Vincent & 

Grenadines 205 354 611 440 760 1,313 115% 7.95% 

Sudan 151 387 993 499 1,279 3,281 230% 12.70% 

Suriname 352 529 793 616 924 1,386 75% 5.74% 

Swaziland 256 402 629 405 635 994 58% 4.68% 

Sweden 5,665 7,586 10,158 5,320 7,126 9,545 -6% -.62% 

Switzerland 28,667 38,680 52,191 23,735 32,035 43,238 -17% -1.87% 

Syria 488 1,175 2,830 1,840 4,432 10,674 277% 14.19% 

Taiwan 8,355 21,713 56,427 31,788 82,598 214,623 280% 14.29% 

Tajikistan 27 80 239 131 387 1,149 382% 17.02% 

Tanzania 589 1,002 1,704 1,263 2,149 3,657 115% 7.93% 

Thailand 9,922 15,657 24,707 19,338 30,516 48,155 95% 6.90% 

Timor-Leste 8 18 40 

Togo 214 363 614 388 657 1,113 81% 6.12% 

Tonga 263 411 640 516 805 1,256 96% 6.96% 

Trinidad 

&Tobago 4,238 6,286 9,323 7,315 10,850 16,094 73% 5.61% 

Tunisia 880 2,273 5,870 2,437 6,294 16,260 177% 10.72% 

Turkey 8,780 13,900 22,005 15,741 24,933 39,495 79% 6.02% 

Turkmenistan 90 135 202 130 195 293 44% 3.75% 

Uganda 348 676 1,314 926 1,801 3,502 167% 10.30% 

Ukraine 1,439 3,169 6,980 3,947 8,693 19,149 174% 10.62% 

United Arab 

Emirates 650 1,381 2,932 1,195 2,539 5,392 84% 6.28% 

United 243,778 319,218 418,005 168,937 221,118 289,417 -31% -3.61% 
57

Kingdom 

Uruguay 598 1,783 5,320 2,390 7,130 21,270 300% 14.86% 

Uzbekistan 156 327 681 436 910 1,900 179% 10.80% 

Vanuatu 43 69 112 50 81 130 16% 1.51% 

Venezuela 5,291 15,121 43,218 15,886 45,415 129,831 200% 11.62% 

Vietnam 638 2,788 12,186 5,358 23,420 102,362 740% 23.72% 

Yemen 838 1,444 2,487 1,085 1,869 3,221 30% 2.62% 

Zambia 276 451 737 515 842 1,377 87% 6.45% 

Zimbabwe 769 1,011 1,328 525 689 906 -32% -3.75% 
58

Appendix B: Alternative Modeling Strategies 

In addition to model averaging using cross-validated based weights, three other estimation methodologies were 

considered. One model estimation approach considered was Bayesian model averaging (BMA), a model averaging 

routine very similar to the preferred method, but one that uses an alternative model weighting scheme based on the 

Bayesian information criterion (BIC). The other two model estimation approaches considered were random forests 

and additive regression imputation. Random forests is a machine learning algorithm that uses heuristic rules to 

search the model space in a manner that is potentially more efficient than the model averaging methods. Additive

regression, by contrast, is similar to a generalized linear model, save for it fits some function of each predictor to the 

data in predicting the outcome. This Appendix briefly describes these three alternative methods, and explains the 

procedure used to settle on a final methodology. 

 Bayesian Model Averaging is a method of deriving parameter estimates by creating a weighted average of 

parameters and/or predictions from a set of possible models, where the weight is typically a function of the 

probability of observing the dependent variable given a model, or model likelihood (Montgomery and 

Nyhan, 2010). This measure of model likelihood reflects how well the model fits data. A critical difference 

between this report’s methodology and BMA is that the measure of fitness in BMA is typically based on insample fit, rather than explicitly testing how well the models predict observations that were not used to 

calibrate the model. A traditionally popular choice of metrics used to generate model weights in BMA is 

the BIC, where the BIC can be written as: 

 ( ) ( )

where L is the likelihood, or fitness of model m, k is the number of parameters in model m, and p is the 

number of observations. Higher values of the BIC correspond to a lower model fitness, and BIC-based 

weights are inversely related to the value of the BIC. Note that as the number of parameters increases, the 

BIC increases, and the model weight declines. Given that additional parameters that do not increase model 

fitness may lead to overfitting, the BIC in theory mitigates problems related to overfitting. In addition, 

models that have many parameters may be expected to produce predictions highly correlated with 

predictions from models that use some subset parameters. Consequently, a BIC-based weight may also 

punish model redundancy, similar to the correlation-based component of the model weights in the preferred 

method. 

The implementation of BMA considered here uses weights based on BIC that take the following form: 

 

 

∑ 

 

 

Unlike Burnham and Anderson (2004) and Montgomery and Nyhan (2010), the anti-log of the BIC was not 

taken because, in practice, the resulting numerators and denominators were too small for the software to 

process. In practice, the variant of the BIC weight would be expected to lead to greater equalities in weights 
59

across all models than would be the case if the BIC were subject to an anti-log transformation. To account 

for nonindependence in the observations, the number of countries (79) is used to calculate BIC rather than 

the number of country-years. 

 Random Forests Imputation is a nonparametric, regression-tree based ensemble method that imputes 

missing values for all missing data. The random forest imputation procedure is sequential, imputing values 

for each variable with missing values in turn as the algorithm can have only one dependent variable at a 

time. The random forest imputation procedure then proceeds by imputing plausible values into all missing 

data points (often the mean [continuous variables] or mode [categorical variables]). A random forest 

algorithm (Breiman, 2001) is then run on the observed values of each variable in the data set with missing 

data. Random forests are recursive partitioning algorithms in which the data are divided into subsets based 

on splits defined by predictor variables that optimally predict the outcome. The result of a single recursive 

partitioning estimation run is a “tree” of splits or “decision points” that define the subgroups that optimally 

predict the outcome. The random forest algorithm computes many (i.e., hundreds or thousands) of 

individual trees with very low predictive quality standards (hence, “grows a random forest”). However, 

predicted values are derived as a weighted average (or modal category) of all the trees and, perhaps 

counterintuitively, usually constitutes a better prediction than a predictive algorithm with more stringent 

predictive quality standards. Based on the random forest results, predicted values are imputed for the 

missing values for each variable. The difference between the newly imputed and previously imputed values 

is assessed. If a stopping criterion is met based on the difference between the new and old imputed results, 

the algorithm stops; otherwise, the random forests imputation procedure continues (Stekhoven & 

Buehlmann, 2012). 

 Additive Regression with Observation Matching is a nonparametric methodology imputing values into 

variables based on nonlinear functions of all other observed variables. Specifically, the additive regression 

with observation matching proceeds in two steps. First, for each variable with missing values in turn, the 

observed values on the focal dependent variable are used in an additive regression onto the observed values 

for all other variables in the data set; the process is also bootstrapped—obtaining subsets of observations 

with replacement from the data to fit additive regression functions. Additive regression is a method 

whereby each input variable is allowed to vary in its functional form and is fit using regression splines yet 

still producing functions for each variable that are independent of the other input variables (i.e., no 

interactions “built into” estimates; e.g., Stone, 1985) using a process known as “backfitting” (see Buja, 

Hastie, & Tibshirani, 1989). The ideal functional form obtained through a series of cross-validations and 

bootstrap samples. Second, values for missing data are then “donated” or imputed from the most similar 

observed values’ predicted value based on the additive regression or from a weighted combination of 

several predicted values (e.g., Abrahantes, Sotto, Molenberghs, Vromman, & Bierinckx, 2011). 
60

In determining which of these approaches to take, the primary interest was in how the resulting models, or model 

averages, predicted country-years for which FGEs were unavailable. Consequently, each method was subjected to 

five-fold cross-validation, where each country-year in the full sample of observations used to calibrate the core 

model was randomly assigned to one of five groups. Each method is then executed five times, with the models 

calibrated using all observations from four of the groups and none from one of the five groups. The fitness metric for 

each of these runs is based on the Root Mean Squared Errors (RMSE) and squared correlation coefficient (R^2) for 

the excluded group. A higher RMSE corresponds to a worse fit. A higher R^2 corresponds to a better fit. The 

observations are randomly assigned to five mutually exclusive groups ten times, for a total of fifty different groups 

and runs. The mean of the RMSE across all fifty runs is used to assess model performance. Only a random 10% of 

the model space is used in the EMA and BMA methods in order to conserve computational resources. Trial runs 

revealed that there was little difference in the point estimates when using a random subset of models versus using 

the entire model space. The predictor set for each method includes all the measurement, administrative records, and 

theoretical variables, with the EMA and BMA methods including the measurement and administrative records 

variables in all models. All observations are given the same weight. 

Method Validation 

Method Mean RMSE Mean Pseudo R^2 

EMA 22,976.15 .89 

BMA 23,048.9 .89 

Random Forests 30,156.82 .83 

Additive Regression 37,467.75 .70 

The EMA and BMA estimates both have a substantially better out-of-sample fit, as measured by the mean RMSE 

and R^2 across all folds, than the two nonparametric methodologies. This implies that the random forests and 

additive regression were both overfitting the data. Note, however, that with the exception of the additive regression, 

all methods have respectable out-of-sample performance as indicated by the R^2. This potentially speaks to the 

quality of the predictor variables with respect to their ability to predict the FGEs. Between the model averaging 

methodologies, the EMA performs slightly better on the mean MSE metric than the BMA, but has approximately 

equal performance on the R^2 metric. However, they are both quite similar with respect to both metrics. Despite 

their similar performance, given the difficulties with specifying the “correct” anti-logged BIC weight discussed 

above, and the fact that the cross-validated model weights used by EMA directly test for model overfitting and 

correlation, the EMA approach was preferred. 

Feedback on the preferred Ensemble Model Averaging was provided by several external reviewers. We would like 

to thank Jason Schachter of the United Nations Economic Commission for Europe; Melissa Scopilitti of the United 

States Census Bureau’s Net International Migration Branch; Kirsten West of the United States Census Bureau’s 

Methodology, Research, and Development Branch; and Dr. Jacob Montgomery of the Department of Political 

Science at Washington University in St. Louis.