Modeling Immigrants’ Legal Status in PWBM’s Microsimulation

Published on June 26, 2019

A. Classifying the Foreign-Born Population by Legal Status

In PWBM’s microsimulation model, foreign-born persons fall into one of four legal status categories: naturalized citizens, lawful permanent residents (LPRs), other lawful immigrants (referred to as “nonimmigrants”) and unauthorized immigrants.

Model parameters governing the demographic and economic attributes and behavior of each class of immigrant are derived from an augmented version of the Current Population Survey’s Annual Social and Economic Supplement (CPS ASEC), in which legal status has been assigned to all immigrants in the survey. PWBM uses a variety of methods and data sources to identify which immigrants in the CPS belong to which category. The legal status assignment sequence and the general approach used for each category are as follows:

  1. Naturalized citizens are identified in the CPS based primarily on a survey question that asks respondents whether they are a U.S. citizen. However, we adjust the CPS data to account for known overreporting of citizenship by recent immigrants. In order to naturalize, an immigrant must either have been in the U.S. for at least five years or be married to a U.S. citizen and have been in the U.S. for at least three years. Immigrants in the CPS who report that they are citizens but do not satisfy these criteria are changed to non-citizens.

  2. Nonimmigrants are foreign-born persons who are in the U.S. on a temporary basis for business, tourism, work, school, medical treatment or other lawful reasons. We are able to identify a subset of these individuals in the CPS by matching immigrants’ characteristics (such as occupation, year of arrival and family relationships) with visa requirements. For example, foreign-born persons who are full-time students at a college or university, arrived in the U.S. within the previous five years and do not have a spouse who is either a U.S. citizen or engaged in paid employment are identified as probable holders of F-1 visas. If they are married, their spouses are identified as probable holders of F-2 visas. Other types of identifiable nonimmigrants include scholars, doctors, diplomats, religious workers, athletes and artists.

    Because the CPS is a survey of U.S. residents, nonimmigrants who remain in the country for short periods (such as tourists and business travelers) are generally not counted in the survey. Consequently, these individuals are not included in our estimates of the nonimmigrant population.

  3. Unauthorized immigrants are identified in the CPS using methods and estimates developed principally by Jeffrey Passel of the Pew Research Center.1 In the first stage, immigrants with characteristics that preclude unauthorized status are identified and classified as “definitely lawful.” This identification includes naturalized citizens and identified nonimmigrants as well as immigrants who meet certain other conditions. For example, government employees and recipients of government benefits not available to unauthorized immigrants are definitely lawful. All definitely lawful immigrants are removed from the foreign-born population to form the pool of potentially unauthorized immigrants.

    In the second stage, we determine the likelihood that each potentially unauthorized immigrant is actually unauthorized and then assign their final status probabilistically. To set the probability that a particular immigrant in the survey is unauthorized, we combine estimates from the Pew Research Center of the unauthorized immigrant population by country of origin and state of residence with our own estimates of the corresponding potentially unauthorized population.

  4. Lawful permanent residents, also known as “Green Card” holders, are identified in the CPS using data from the Department of Homeland Security’s (DHS) Yearbook of Immigration Statistics. The Yearbook reports the number of persons who arrived in the U.S. as LPRs or adjusted to LPR status each year, classified by type of admission (e.g. family-sponsored vs. employment-based), country of origin, state of residence, age, gender, marital status and occupation. Combining these values with PWBM’s estimates of the lawful non-citizen population by year of arrival (as well as emigration, mortality and naturalization) we determine the likelihood that each immigrant in the survey is an LPR and then assign their final status probabilistically.

In the final step, all foreign-born persons in the survey who have not already been assigned a legal status are assumed to be nonimmigrants.

Note that the actual procedures used to assign legal status in the CPS are considerably more complex than the overview provided here.2

B. Legal Status Transitions

In PWBM’s microsimulation (as in reality), newly arriving immigrants may be LPRs, nonimmigrants, or unauthorized immigrants. Over time, however, immigrants who remain in the U.S. may change their legal status. The three main ways this transition happens are naturalization, adjustment to LPR status and visa overstays.


LPRs who are at least 18 and have been in the U.S. at least five years—or who are married to a U.S. citizen and have been in the U.S. at least 3 years—are eligible to naturalize and become U.S. citizens. To estimate the rate at which eligible immigrants naturalize, we combine data on the number of naturalizations from the Yearbook of Immigration Statistics with our CPS-based estimates of the eligible population, described above.

The Yearbook reports the number of persons who naturalized each year by country of origin, age, gender, marital status and occupation. However, except in the case of gender, the Yearbook does not provide cross-tabulations for these characteristics. Using our estimates of the eligible population, we develop a set of naturalization rates across all characteristics jointly that maintain all relative propensities to naturalize implied by the original data. To do this calculation, we calculate the implied naturalization rate for each characteristic sequentially and adjust the rates to ensure consistency with the Yearbook totals for the next characteristic in the sequence. By construction, the resulting set of naturalization rates deliver the correct historical number of naturalizations when applied to our estimates of the eligible population.

These rates are used in the microsimulation to determine the probability that a particular eligible immigrant will naturalize in a given year. When an individual naturalizes, we assume that any children under 18 naturalize with them.

Visa Overstays

Nonimmigrants are typically authorized remain in the U.S. for a specified period of time or as long as they meet certain conditions. For example, visitors entering with B visas (for business or tourism) may remain in the U.S. for up to six months (though usually less), while students with F visas may remain as long as they are enrolled in their educational program. Nonimmigrants who do not depart the U.S. when required—referred to as visa overstays—become unauthorized immigrants.

To estimate the rate at which nonimmigrants overstay, we combine data on the number of visa overstays from DHS’ Entry/Exit Overstay Report with our CPS-based estimates of the unauthorized and nonimmigrant populations, described above. DHS reports the number of overstays from each country—that is, the number of nonimmigrants who were expected to depart in a given year but did not. The scope of the report is somewhat limited, however, as it only includes arrivals through air and sea ports of entry. Overstays are reported separately for business and pleasure travelers (B visas and WB/WT status), students and exchange visitors (F, M, and J visas) and most other nonimmigrants (e.g. temporary workers on H or O visas). As noted above, business or pleasure travelers are not counted in our population estimates because they are not U.S. residents. We therefore treat these “traveler overstays” as equivalent to immigrants who enter the country without authorization, rather than lawful immigrants already present in the U.S. who become unauthorized. For the other two overstay categories, which we refer to as “resident overstays,” we assume that all individuals resided in the U.S. lawfully for at least one year before overstaying and becoming unauthorized. Traveler overstay rates and resident overstay rates require different estimation and modeling approaches.3

Traveler Overstay Rates

To estimate traveler overstay rates, we draw on an approach developed by Robert Warren (e.g., Warren and Kerwin, 2018).4 Warren’s method uses a single year of overstay and survey data to estimate overstay rates for all cohorts of past immigrants. Because we have several years of traveler overstay data (covering 2014 to 2018), we implement the method for each year and then average the results for earlier cohorts.

Following Warren, we first estimate traveler overstay rates for visitors from Mexico and some Central American countries.5 These countries are treated separately because significant numbers of Mexicans and Central Americans enter the unauthorized population directly by crossing the border without authorization. Unauthorized immigrants from all other countries, by contrast, we assume entered the country lawfully and only later became unauthorized by overstaying.

We define the traveler overstay rate as the probability that a recently arrived unauthorized immigrant (one who has resided in the U.S. for a single year) entered the country lawfully and became unauthorized by overstaying a B visa or WB/WT status. We obtain the number of traveler overstays from Mexico and Central America for 2014 to 2018 from the Entry/Exit Overstay Report. To estimate recent arrivals by country, we use the average over the previous three years of annual unauthorized immigrant arrivals, adjusted to account for emigration and mortality. The traveler overstay rate is the ratio of the number of traveler overstays to our estimate of recent unauthorized arrivals.

We calculate these rates for each year from 2014 to 2018. For earlier years, we start from estimates of analogous figures for 1996 derived by Warren using non-public data and follow Warren’s assumption that the overstay rate has roughly doubled since 2005. We then interpolate values for the intervening years.

For all other countries, we assume that 95 percent of recently arrived unauthorized immigrants not from Mexico or Central America overstayed a travel visa.

Resident Overstay Rates

The Entry/Exit Overstay Report provides data on the number of foreign students, workers and other types of resident nonimmigrants who overstayed in 2016, 2017 and 2018. For each year, we identify nonimmigrants in the CPS who might potentially overstay based on their visa type and other characteristics. For example, we assume that nonimmigrants with a U.S. citizen spouse or other close family member do not overstay. Once we have identified the relevant nonimmigrant population, we estimate country-specific resident overstay rates by year as the ratio of the actual number of resident overstays to the population of potential overstays.

For earlier years, we again follow Warren’s assumption that overstay rates have doubled since 2005 and were stable before then.

  1. For the latest release of these estimates and a description of the methodology, see  ↩

  2. For instance, a series of family relationship rules is applied at each stage to ensure consistency of legal status within families. In addition, data must often be adjusted to account for differences across data sources and years, to correct for undercounts and definitional changes in the underlying survey data, and to address other issues.  ↩

  3. The Entry/Exit Overstay Report includes a calculation of an “overstay rate,” but DHS’s definition of this concept differs from ours (described below). DHS defines the overstay rate as the share of all nonimmigrants required to depart in a given year who fail to do so.  ↩

  4. For a recent implementation of Warren’s method, see Warren, R., & Kerwin, D. (2017). The 2,000 Mile Wall in Search of a Purpose: Since 2007 Visa Overstays have Outnumbered Undocumented Border Crossers by a Half Million. Journal on Migration and Human Security, 5(1), 124–136.  ↩

  5. These countries are El Salvador, Guatemala, Honduras and Nicaragua. We also include the Dominican Republic. Estimates are calculated for each country separately.  ↩