Employer Verification Mandates and Infant Health

Abstract

In recent decades, several states have enacted their own immigration enforcement policies. This reflects substantial variation in the social environments faced by immigrants and native-born citizens, and has raised concerns about unintended consequences. E-Verify mandates, which require employers to use an electronic system to ascertain legal status as a pre-requisite for employment, are a common example of this trend. Drawing on birth certificate data from 2007-2014, during which 21 states enacted E-Verify mandates, we find that these mandates are associated with a decline in birthweight and gestational age for infants born to immigrant mothers with demographic profiles matching the undocumented population in their state as well as for infants of native-born mothers. In observing negative trends for both immigrants and natives, our findings do not support the hypothesis that E-Verify has a distinct impact on immigrant health; however, the broader economic, political, and demographic contexts that coincide with these policies, which likely impact the broader community of both immigrants and natives, may pose risks to infant health.

Employer Verification Mandates and Infant Health among Foreign-born Women

A constellation of economic, political, and demographic factors have created an unprecedented amount of geographic variation in how immigrants and their receiving communities interact with one another in the U.S. Driven in large part by shifting labor demands, immigrants over recent decades have increasingly settled in “new destinations” throughout the mid-West and South, rather than the traditional “gateways” (e.g., California, Texas, New York, and Illinois) that had previously been home to most immigrants. This trend has resulted in sometimes striking demographic and social change as communities that were predominantly white and native-born have become increasingly diverse in terms of race, ethnicity, and nativity (Lichter 2012; Massey and Capoferro 2008). While federal legislators have remained at an impasse on immigration reform, states and localities have responded to their changing communities with a flurry of legislative action. At one extreme are state and local lawmakers, often from “new destination” locations, who argue that the federal government has not done enough to regulate immigration, and have taken it on themselves to pass restrictive immigration-related bills designed to increase deportations and cut undocumented immigrants off from jobs and public services. At the other extreme, are localities that do not approve of the rising number of deportations by the federal government, and refuse to assist federal authorities with immigration enforcement.

Against this backdrop, this analysis focuses on E-Verify mandates, an example of a restrictive immigration bill, which require employers in a state to use a federal electronic system to ascertain whether job applicants are legally authorized to be in the United States. Using birth certificate data between 2007 and 2014, during which 21 states enacted E-Verify mandates, we assess how their enactment correlates with infant health trends for three groups of mothers: (i) immigrants with demographic attributes that align with the estimated undocumented population in their state of residence—these mothers should be most directly impacted by the policy itself, while also experiencing the economic, political, and demographic factors that drive the enactment of E-Verify mandates; (ii) a broader category of all immigrant women coming from the top 25 sending countries for the undocumented population—relative to the first category, more of the women in this group will be “documented” and therefore will not be impacted directly by the enactment of E-Verify mandates, but will still experience the general receptivity of immigrants in the community and the broader factors leading to the policy’s enactment; and finally (iii) native-born non-Hispanic white women, all of whom should not be directly impacted by E-Verify mandates, but will experience the various factors changing their communities and driving the legislation. To delineate the first group of mothers, we develop a novel strategy that uses state-specific distributions of the demographic attributes of undocumented populations to estimate probabilities that mothers are undocumented. We also explore the extent to which our correlations between E-Verify and infant health are potentially affected by selective patterns of fertility or outmigration from states that enact E-Verify.

Infant health measures, like birth weight and gestational age, are important determinants of health and well-being over the life course: those born with low birth weight and/or preterm are more likely to experience health problems, attain lower levels of education, and fare worse in the labor market than their peers born with regular levels of birth weight (Behrman and Rosenzweig 2004; Bharadwaj, Lundborg and Rooth 2017; Figlio et al. 2016). Restrictive local immigration policies, and the economic, demographic, and political factors driving them, mark an important feature of the current social context in the U.S. and a potentially important determinant of health for the next generation. Since the early 2000s, between seven and nine percent of births each year were to undocumented immigrants (Passel and Cohn 2017). If restrictive immigration laws amplify the challenges facing children born to undocumented immigrants, the U.S. citizen descendants of today’s undocumented immigrants may be destined for worse health, and thus less able to successfully contribute to their families, communities, and the U.S. at large. Native-born residents of communities enacting restrictive immigration policies may also face important health vulnerabilities because the conditions that tend to precede such policies (e.g., declining quality of local jobs, perceived threats to community) and the unintended consequences of the policies (e.g., housing vacancies and crime) may threaten maternal and infant health (Bohn, Lofstrom and Rafael 2014; Nowrasteh 2018; Commins and Wills 2017; Ybarra, Sanchez and Sanchez 2016).

Concerns about the consequences of local immigration enforcement on children and families have been increasing (Beniflah et al. 2013; Fountain and Bearman 2011; Hacker et al. 2012; Philbin et al. 2017), and a handful of researchers focusing on particular cases of enforcement or policy in single states or communities have found worsening infant and child health for immigrant groups following new legislation or major enforcement actions (Beniflah et al. 2013; Novak 2017; Torche 2018). This study of infant health builds on and complements this work, but also stands apart in two key ways. First, rather than focusing on a single case of legislation in a given state (e.g., the highly restrictive and sweeping bills passed in Arizona or Georgia), we analyze a general category of restrictive immigration laws—E-Verify mandates—that have been passed in several U.S. states. This allows us to illuminate trends that may be more generalizable to a broader swath of localities enacting both more and less restrictive immigration policies. Second, we employ a novel proxy strategy that uses state-specific distributions of demographic variables for identifying categories of women most likely to be impacted by the policy.

E-Verify Mandates and the Factors that Drive Their Enactment

The federal government’s Internet-based system for verifying work eligibility, known as E-Verify, started as a pilot program through the Illegal Immigration Reform and Immigration Responsibility Act of 1996. Employers enter a job applicant’s biographical information (e.g., social security number, date of birth, name, etc.) into E-Verify and receive either a confirmation of the applicants work authorization or a “tentative non-confirmation.” Employees have eight business days to resolve tentative non-confirmations before the employee/applicant is terminated (Rosenblum and Hoyt 2011).

Use of E-Verify is mandatory for federal employees and their sub/contractors, but its use was intended to be voluntary for other employers. However, since 2000 a number of states have enacted laws that mandate employers in the state to use E-Verify. In 11 cases, states enacted circumscribed versions of E-Verify mandates that require only state agencies and their sub/contractors to use E-Verify while the program remains voluntary for other employers in the state, hereafter referred to as “public E-Verify.” In 10 other cases, states enacted much more sweeping mandates that require all employers in the state to use E-Verify, hereafter referred to as “universal E-Verify.” As shown in Figure 1, public E-Verify has been enacted in a number of states across the country, whereas universal E-Verify has been mostly concentrated in new immigrant destinations predominantly in the South East, with Arizona and Utah as notable exceptions in the West. It is also important to note that universal mandates emerged in varying ways. For some states (i.e., Louisiana, Mississippi, North Carolina, and Tennessee), universal E-Verify mandates are the predominant feature of the relevant bill and reflect one of the more stringent pieces of immigration legislation enacted in the state. However, in other states (i.e., Alabama, Arizona, Georgia, Indiana, South Carolina, and Utah), E-Verify mandates preceded or were part of much more sweeping omnibus bills that attempted to make many aspects of immigrants’ lives more difficult, for instance, by empowering local police to check immigration status of those apprehended, making it a crime to transport undocumented immigrants, and limiting access to health care and public education. Many of the harsher parts of these omnibus bills were legally challenged and never passed; however, in all cases E-Verify mandates were enacted and in all but one case laws augmenting police authority to check immigration status were enacted.

Figure 1.

Geographical Distribution of States Mandating Universal and Public Use of E-Verify, 2006-2014¹

¹ Alabama, Georgia, Indiana, Louisiana, North Carolina, South Carolina and Utah first enacted public E-Verify mandates and later enacted universal E-Verify mandates. Here we show only universal E-Verify for those states since that reflects the more sweeping version of the legislation.

Among the array of factors that may contribute to local immigration policies, prior literature suggests that two factors are particularly salient for the passage of restrictive immigration laws like E-Verify mandates: first, is a large relative increase in the size of the foreign-born population in the area, and, second, is a Republican-dominated local or state government.¹ Large relative increases in the size of the foreign-born population reflect the broader trend of immigrants increasingly settling in “new destination” locations. These locations experiencing upticks in the immigrant population also tend to be experiencing the downsides of industrial restructuring—namely, a loss of unionized, high-wage jobs; an increase in low-skilled, non-unionized, low-wage jobs; and an associated outmigration of younger native-born workers who can compete for better jobs in other places (Austin 2017; Paral 2017). Indeed, one of the main factors attracting immigrants to new destination locations is the availability of undesirable, low-wage jobs that are typically avoided by natives.

Group threat theory predicts that growing immigrant populations, particularly when the size of the immigrant population had been smaller in the past and economic resources are scarce, will engender negative attitudes toward immigrants among local native-born residents (Blumer 1958; Quillian 1995). Both observational and experimental studies support this prediction (Anastasopoulous 2014; Newman et al. 2012; Steil and Vasi 2014; Walker and Leitner 2011). As immigrants move in and neighborhoods begin to look different, and pay and work conditions decline with industrial restructuring, native-born residents may begin to feel their jobs and ways of life are threatened. This can galvanize support for the enactment of measures like E-Verify which explicitly seek to protect job opportunities for natives (Commins and Wills 2017; Ybarra, Sanchez and Sanchez 2016).²

In addition to the size of the immigrant population, the governing party of the state is another important condition for E-Verify mandates: Restrictive immigration laws are typically endorsed and signed by Republican lawmakers (Zingher 2014). This often means that the enactment of E-Verify laws tends to occur alongside the passage of other conservative policies, such as reductions in discretionary social service programs which tend to benefit under-resourced communities often inhabited by immigrant families. Of particular relevance is research which finds that when states experience an increase in immigration, they lessen the generosity of social safety net programs like Temporary Assistance for Needy Families (Hawes and McCrea 2018). Such reductions in welfare support can be particularly harmful to low-income native residents given the volatile economic contexts in which punitive immigration policies are enacted.

E-Verify and Birth Outcomes of Immigrant Mothers

The most direct way that E-Verify could harm birth outcomes for immigrant mothers would be by reducing access to jobs in the mainstream labor market for undocumented pregnant women and/or their spouses, partners, and other family members. Since many immigrant families have mixed statuses (e.g., one spouse has work authorization and the other does not), pregnant immigrant women who are legally present may still face the loss of a partner’s income with the passage of E-Verify if s/he is undocumented. Using data from the Current Population Survey, Ameudo-Dorantes and Bansak (2012, 2014) found that the likelihood of employment among Hispanic, non-citizens, under 45 with a high school degree or less is reduced by 4.6 percentage points following the enactment of universal E-Verify and by 2 percentage points following the enactment of public E-Verify. Using data from the state of Arizona, Bohn and Lofstrom (2012) also found that, for Hispanic non-citizens, passage of universal E-Verify was associated with an increase in reports of self-employment, suggesting that undocumented workers turn to informal jobs once formal options require E-Verify confirmation. Informal employment tends to be associated with lower wages and greater occupational health risks (Bruce and Schuetze 2004; O’Campo et al. 2004). There is also evidence that access to health care for immigrants is diminished following the passage of restrictive immigration laws (Beniflah et al. 2013; Toomey et al. 2014; Vargas 2015; Watson 2014; White et al. 2014).

E-Verify mandates could also harm maternal and infant health via psychosocial pathways. Even if E-Verify does not directly lead to unemployment for oneself or one’s spouse/partner, it may still heighten worry over losing a job or anxiety about finding a new job should one be laid off. Studies show that feelings of job insecurity are associated with worse mental and physical health, even without the occurrence of an actual job loss (Burgard et al. 2009). It also noteworthy that living in a state with E-Verify mandates was associated with more fear of deportation in a survey of immigrants returning to Mexico from the U.S. (Amuedo-Dorantes, Puttitanun and Martinez-Donate 2013). E-Verify mandates, which target employment opportunities, do not directly increase the risk of deportation. But, in some cases, they do coincide with omnibus bills, which as noted above seek to increase deportations. Forced family separations because of deportations, as well as the real or perceived threat of such separations, can be very damaging for psychosocial wellbeing and health behaviors (Dreby 2015).

E-Verify mandates could also influence the health of babies born to immigrant mothers by increasing experiences of discrimination or more generally signaling a less welcoming environment. Using data from the National Latino Health Care Survey, Almeida et al (2016), found that almost 70% of respondents experienced discrimination, and living in an area with more anti-immigrant policies was associated with higher levels of discrimination. Such evidence suggests that E-Verify might compromise infant health since pregnant women’s experiences with discrimination correlate with poorer infant health outcomes (David and Collins 1997; Collins et al. 2004; Lauderdale 2006)

While this is the first study to explore the infant health consequences of broadly implemented E-Verify mandates, prior work focusing on legislation or enforcement in particular states or communities documents worsening health for the children of immigrants. Beniflah et al. (2013), analyzing medical records, found that children visiting emergency departments in Georgia presented with more severe conditions following the passage of its omnibus bill. Highly relevant to our present study, Torche and Sirois (2018) applied synthetic control methods to natality data and found lower birth weights for Latin American immigrant women following the passage of Arizona’s omnibus bill, relative to the control group of other states. Additionally, Novak et al. (2017) analyzed Iowa birth certificate data and found higher risk of low birth weight for both native and foreign-born Hispanic mothers following one of the largest immigration raids at the time occurring in Postville, IA. In the present study, we will explore whether like relationships hold when assessing trends in infant health following E-Verify mandates implemented across several states in the U.S.

E-Verify and Birth Outcomes of U.S.-Born Mothers

Given that E-Verify mandates are designed to reduce job competition from undocumented workers, it is plausible that they could be associated with improvements in infant health for U.S.-born mothers. Of note, Amuedo-Dorantes and Bansak (2014) find that E-Verify mandates increase employment likelihoods for non-Hispanic native men and women by two percentage points and have a borderline significant positive association with wages for non-Hispanic native men. Such increases in economic resources could translate into health advantages among natives who now have less competition for jobs.

On the other hand, E-Verify mandates could be correlated with worsening infant health outcomes for native-born mothers given that they are typically passed in response to the dual forces of rising immigration and economic decline, and are often accompanied by cuts to social welfare programs like TANF. Additionally, there is evidence that E-Verify mandates may have unintended negative spill-over effects on the native-born in the community. Research to date shows that when states enact restrictive immigration policies they experience a decline in the size of their undocumented populations, potentially by as much as 40% following E-Verify as undocumented individuals relocate to incorporating states, leave the U.S. entirely, or seek to change their status (Leerkes, Bachmeier and Leach 2013; Leerkes, Leach and Bachmeier 2012; Orrenius and Zavodny 2016). With this outmigration, there are increasing rates of residential vacancies (Bohn, Lofstrom and Raphael 2014), which may contribute to diminished property values. Further, as is often the case when employment opportunities are constrained, states that enacted E-Verify experienced a rise in crime among non-citizens (Nowrasteh 2018), which could impact perceptions of community safety. Though intended to improve the lives of natives, there is evidence suggesting that the overall socioeconomic climate might suffer as E-Verify is enacted – potentially exacerbating the effects of economic decline that initially spurred the passage of these policies.

E-Verify and Changes in the Composition of Live Births

E-Verify mandates are likely to be correlated with changes in the composition of live births among both immigrant and native-born populations. Restrictive immigration policies seek to make the state less appealing to undocumented immigrants, and in response, many of them migrate out of the state. The economic declines and industrial restructuring that characterize “new destination” locations also imply that E-Verify may correlate with out-migration of native-born workers as well. In addition to out-migration, fertility behavior is also likely to change in these contexts as women facing poorer local economic prospects and, in the case of immigrants, more enforcement activities as well, may choose to delay or forego childbearing (Amuedo-Dorantes and Arenas-Arroy 2017; Dehejia and Lleras-Muney 2004).

Beyond declining fertility, shifts in the composition of women giving birth are most concerning for infant health. If, within the population of undocumented women, those with the most human capital and resources are more likely to leave the state or not have children following E-Verify, this composition change could lead to worsening health trends for undocumented women over and above any potential negative health consequences of the policy itself. On the other hand, if undocumented women with the least capital and resources are more likely to leave or not have children following E-Verify, this alternative composition shift could lead to improving health trends for undocumented women, which might obscure any negative consequences of the policy itself. The latter trend may be the more likely given prior work showing that declines in births associated with enforcement activities or a restrictive omnibus bill are more notable for disadvantaged immigrant mothers (Amuedo-Dorantes and Arenas-Arroy 2017, Torche and Sirois 2018). For the white native-born mothers in our analysis, composition change is more likely to reflect an over-representation of disadvantage since more skilled workers with better prospects elsewhere are more likely to leave in the contexts associated with E-Verify, and weaker labor markets are associated with a larger share of white births to less educated mothers (Dehejia and Lleras-Muney 2004). Unfortunately, the data we use in our analysis does not allow us to parse effects owing to out-migration apart from effects owing to changes in fertility behaviors, but they do allow us to assess trends in the demographics of mothers giving birth in states before and after E-Verify mandates are put in place.

Methodological Challenges in Studying Policy Effects on Undocumented Immigrants

A key challenge in studying the health of undocumented immigrants using national-level surveys is estimating which groups of sample members include the most undocumented respondents. Direct queries about documentation status are controversial and rare because they raise concerns about political agendas (or at least the perception of them) and immigrants’ distrust and non-participation. Even without direct queries of citizenship or documentation status, there are on-going concerns that undocumented individuals may be under-represented in national surveys because they are frightened to participate in a government-sponsored survey or, if they participate, may misreport their citizenship status due to fear of arrest and deportation (Brown et al. 2019).

Given these issues, most researchers have relied on national surveys with sizeable immigrant subsamples and used proxy strategies to identify a subsample containing higher numbers of undocumented immigrants. The most common proxy method is to select sample members who report that they (i) lack citizenship, legal permanent residency, or temporary protected status; (ii) come from Mexico and other Latin American countries; and (iii) have education below a certain threshold (most often a high school degree). Referred to as a form of “logical imputation” (Van Hook et al. 2015), variations of this approach have been used to examine the effect of E-Verify on labor market outcomes (Amuedo-Dorantes and Bansak 2014) and on migration patterns (Orrenius and Zavodny 2016). Since, at the national level, a substantial share of undocumented immigrants are from Latin America and have low levels of education, this is a defensible proxy strategy. However, this approach overlooks considerable state-level variation in the country of origin and educational attainment levels of undocumented immigrants. For example, in Texas and New Mexico, the vast majority of likely undocumented immigrants are from Mexico and Central America (88%), whereas in states like Michigan and Virginia, a little less than half of likely undocumented immigrants are from Mexico and Central America. With respect to educational attainment, less than 10% of likely undocumented immigrants in Alabama and Nevada have a bachelor’s degree, while more than 20% of likely undocumented immigrants in New Jersey and Pennsylvania have a bachelor’s degree. Therefore, relying on country of origin and education level to blanketly identify those likely to be undocumented plausibly introduces substantial measurement error. Moreover, this approach may limit the generalizability of findings to the broader undocumented population which includes immigrants from different regions of the world as well as some with higher levels of education.

As Massey (2013) states, “When it comes to studying unauthorized migration, there is no prefect dataset…the best one can hope for is a triangulation that gets at the truth from multiple angles using diverse data sources that have complementary strengths and weaknesses. (p. 1093)” We contribute to this collective scientific effort to empirically study undocumented immigration in the U.S. by extending the logical imputation approach to incorporate probabilities of being undocumented based on state-specific information. Using data on the demographic attributes for foreign-born women of child-bearing age coming from the top 25 countries that send undocumented immigrants to the U.S., we assign all mothers from these countries a probability of being undocumented based on state-specific distributions for countries of origin, ages, martial statuses, and education levels. The incorporation of state-specific information should reduce measurement error in our proxy. Additionally, generating a continuum of probabilities for being undocumented, rather than just a single dichotomous indicator, allows us to present estimates that should have lower risks of misclassification, but more limited generalizability (i.e., women with closer matches to the relevant demographic attributes, but who will have limited demographic variation), as well as estimates at greater risk for misclassification, but that maximize generalizability (i.e., estimates across the range of the proxy measure with more demographic heterogeneity). Another important strength of our approach is our reliance on administrative data from birth certificates rather than survey data. While it is highly plausible that many undocumented individuals avoid participation in government-sponsored surveys, with few rare exceptions all live births in the U.S. overseen by licensed medical professionals are registered via a birth certificate.

Data and Methods

Data

The primary data source for this analysis is the Center for Disease Control’s (CDC) Natality-Limited Geography files from the years 2007-2014. These data are based on birth certificate records for all live births occurring in the U.S. and they contain information on key measures of infant health as well as maternal demographics, state of residence, and country of origin. We start with 2007 because it is the first year that detailed information about the countries of origin for foreign-born mothers became available. We merged the individual-level data in these natality files with time-varying state-level measures of whether universal or public E-Verify was in place in a given state and year along with several state-level control variables measuring economic, demographic, and policy conditions in the state. We also added to the natality files state-level information about the demographic composition of a proxy-identified population of likely undocumented women of childbearing age. We use these demographic distributions, which were compiled by the Center for Migration Studies (CMS) using data from the American Community Survey (ACS), to construct our probability measure of likely undocumented status among foreign-born mothers.

To reduce noise from small cell counts when testing for composition changes, we exclude from the analysis states that have small foreign-born populations in which the count for live births is smaller than 100 for either of immigrants groups we analyze in one more years in the time series.³ Additionally, we limit the natality records to women residing in states that had adopted the 2003 revision to U.S. birth certificates in a given year. In 2003, the federal government revised the format of birth certificates, but not all states adopted this revised format at the same time. For this analysis, we must rely on data from states that have implemented these revisions because data based on the earlier unrevised certificates do not contain critical variables that we need to undertake our analysis, namely mother’s country of origin and education level.⁴ This creates essentially an “unbalanced panel” where certain state-year cells are missing. This is depicted in Table 1, where the rows reflect all the states with sufficiently large immigrant populations to be included in our analysis and all necessary control variables, the columns reflect each year in our time series, and E-Verify mandates passed in a given year are noted in the appropriate cells. The unshaded state-year cells in Table 1 are excluded from the analysis because the 2003 version of the birth certificate was not yet adopted; the shaded cells are included in the analysis. An unfortunate byproduct of the missing cells is that policy changes occurring in some states (e.g., the enactment of universal E-Verify in Arizona or Alabama) are not observed in our data, and our findings may not extend to these states. However, even with these limitations, we are able to assess the relationship between the passage of E-Verify mandates and infant health drawing on data from 43 states covering all major regions of the country.

Table 1:

States Mandating Universal (U) and Public (P) Use of E-Verify, in Combination with the Timing of States Adopting the 2003 Birth Certificate Revision (shaded cells)¹

	2007	2008	2009	2010	2011	2012	2013	2014
Alabama						U	U	U
Arizona		U	U	U	U	U	U	U
Arkansas
California
Colorado2	P	P	P	P	P	P	P	P
Connecticut
Delaware
Florida					P	P	P	P
Georgia	P	P	P	P	P	P	U	U
Hawaii
Idaho			P	P	P	P	P	P
Illinois
Indiana					U	U	U	U
Iowa
Kansas
Kentucky
Louisiana						U	U	U
Maryland
Massachusetts
Michigan						P	P	P
Minnesota		P	P	P	P	P	P	P
Mississippi					U	U	U	U
Missouri			P	P	P	P	P	P
Nevada
New Jersey3
New Mexico
New York
North Carolina	P	P	P	P	P	P	U	U
Ohio
Oklahoma	P	P	P	P	P	P	P	P
Oregon
Pennsylvania							P	P
Rhode Island		P	P	P	P	P	P	P
South Carolina			P	P	U	U	U	U
Tennessee							U	U
Texas								P
Utah				U	U	U	U	U
Vermont
Virginia						P	P	P
Washington
Wisconsin
Wyoming

Notes:

¹Shaded cells indicate that a state adopted the 2003 birth certificate revision and therefore all relevant variables are available for our analysis.

The following states are excluded from our analysis because of a small number of births to foreign-born women: Maine, Montana, New Hampshire, North Dakota, South Dakota, Vermont, West Virginia, and Alaska.

²Colorado adopted public E-Verify in 2006 before the start of our time series.

³Detailed data on maternal race is unavailable from New Jersey and therefore New Jersey is not included in our analysis. The District of Columbia and Nebraska are also excluded because the control variable for the percent Republican in state government is not available for these areas. D.C. is not a state and Nebraska has non-partisan unicameral state legislature, which makes this measure irrelevant for these locations.

Undocumented probability measure

We extend the logical imputation strategy employed by most researchers to date by assigning foreign-born mothers a value that indicates the probability that they are undocumented based on state-level variation in characteristics of the immigrant population. To do so, we use data compiled by CMS which includes the sociodemographic composition of a population estimated to be undocumented based on data from the 2010-2013 American Community Survey.⁵ For each state, CMS provided distributions of four sociodemographic variables that also appear on birth certificates: country of origin, age, level of education, and marital status. To avoid noise from small counts and produce reliable estimates, particularly for country of origin, CMS only produces estimates of undocumented immigrants coming from the top 25 sending countries to the U.S. ⁶ Given our focus on maternal and infant health we further refine the CMS estimates to reflect women of child-bearing age (i.e., 18-44)⁷. In order to align the birth records for foreign-born mothers with the CMS estimates, we limit the birth certificate data for immigrant women to ages 18-44 coming from the top 25 sending countries of undocumented immigrants to the U.S.

In non-technical terms, we assigned each foreign-born mother a probability that they were undocumented based on how similar their sociodemographic attributes were to that of the CMS-estimated population of undocumented immigrants living in their state. For example, CMS estimated that those most likely to be undocumented in the state of Georgia were those born in Guatemala (78% of female Guatemalan immigrants are estimated to be undocumented), those with a high school diploma or less (71% of female immigrants with a high school or less are estimated to be undocumented), those who were single (44% of female immigrants who were single were estimated to be undocumented), and those who were between the ages of 21-24 (45% of female immigrants between the ages of 21-24 were estimated to be undocumented). In the case of Georgia then, a 35-year old married mother from Canada with a college degree will have a lower probability of being undocumented than a 22-year old single mother from Guatemala with only a high school diploma.

In technical terms, we have state-level estimates from CMS of the form Pr(Undoc|X_j), where X_j is a single individual-level characteristic; there are four such characteristics (country of origin, age, marital status, and level of education), so j = 1, …,4 and k = 1, …,4 with j ≠ k. Under the assumption that the probabilities are mutually conditionally independent (i.e., that Pr(X_j, X_k|Undoc) = Pr(X_j|Undoc)Pr(X_k|Undoc) for all j and k), we can combine the estimates of Pr(Undoc|X_j) to the desired Pr(Undoc|X₁, X₂, X₃, X₄).⁸ This calculation also depends on the marginal probability Pr(Undoc) since, e.g., Pr(Undoc|X₁) only impacts our estimate of Pr(Undoc|X₁, X₂, X₃, X₄) to the extent that Pr(Undoc|X₁) differs from Pr(Doc|X₁). Finally, all calculations are performed at the state level and so state is implicitly conditioned upon. See the Appendix for technical detail on the derivation of these probabilities.

After assigning probabilities of undocumented status to all women from the top 25 sending countries, we define a preferred, but still arbitrary, demarcation of the top quartile of the distribution of the probabilities that we calculated.⁹ These women have probabilities of being undocumented based on the four demographic variables greater than or equal to .86. While classification error cannot be eliminated, it should be substantially reduced by selecting this high threshold. However, this reduction in classification error substantially reduces demographic heterogeneity as well. Of immigrant mothers in the top quartile, nearly all come from Latin American countries, with 81% from Mexico specifically. Additionally, as shown in Table 2, 85% of these women have less than a high school education and only 32% are married. While this group aggregated across many states roughly aligns with previous logical imputation proxy measures that condition on Latin American origin and education level, our incorporation of state-specific information should still improve estimates given state differences in the share of the undocumented population coming from Latin America.

Table 2:

Summary Statistics for Infant Health Outcomes, Individual- and State-Level Characteristics

	Top quartile of undocumented probability distribution for foreign- born women from top 25 sending countries	All foreign-born women from top 25 sending countries	U.S.-born white women
Variable	Mean (SD)	Mean (SD)	Mean (SD)
Dependent Variables
Low birth weight	0.05	0.05	0.05
Pre-term birth	0.11	0.10	0.08
Small for gestational age (SGA)	0.10	0.10	0.09
Independent Variables
Public E-Verify	0.16	0.09	0.16
Universal E-Verify	0.05	0.03	0.07
Individual-Level Characteristics
Maternal age
18-21	0.16	0.07	0.09
21-24	0.29	0.16	0.19
25-34	0.47	0.57	0.58
35-44	0.08	0.20	0.14
Educational attainment
Less than high school	0.85	0.40	0.09
High school	0.15	0.24	0.23
Some college	0.00	0.15	0.32
College or more	0.00	0.21	0.36
Race
Hispanic	0.99	0.71	0.00
Non-Hispanic white	0.01	0.03	1.00
Non-Hispanic black	0.00	0.05	0.00
Non-Hispanic other	0.00	0.20	0.00
Married	0.32	0.62	0.70
Birth order
1st	0.26	0.32	0.42
2nd	0.31	0.33	0.33
3rd	0.24	0.21	0.16
4th or higher	0.20	0.15	0.10
State-Level Characteristics
State total population (1,000,000s)	15.53 (10.38)	22.47 (12.33)	13.07 (10.07)
Proportion foreign-born	0.14 (0.07)	0.18 (0.07)	0.11 (0.08)
Medicaid expenditure ($1,000,000,000)	7.56 (6.96)	12.28 (8.73)	6.82 (7.05)
Unemployment rate	7.52 (2.10)	7.91 (2.27)	7.59 (2.09)
TANF benefits ($100)	4.04 (1.77)	5.02 (2.08)	4.21 (1.66)
Poverty rate	14.93 (2.54)	15.22 (2.17)	14.49 (2.61)
% uninsured	16.52 (2.56)	16.744 (4.570)	14.42 (4.42)
% of state legislature democrat	0.47 (0.12)	0.522 (0.134)	0.45 (0.13)
State governor democrat	0.41 (0.49)	0.421 (0.494)	0.47 (0.13)
Minimum wage ($1)	7.25 (0.87)	7.50 (0.77)	7.30 (0.80)
TANF for non-qualified children	.22	.45	.21
Medicaid for undocumented pregnant women	.54	.71	.45
N	1,001,776	4,104,491	10,828,653

Note: Standard deviations (SD) shown for continuous variables only. Estimates based on the state-year cells shaded grey in Table 1 reflecting the adoption of the 2003 birth certificate revision.

To incorporate more demographic heterogeneity into our results, we also run models for all women from the top 25 sending countries for undocumented immigrants. The mean probability of being undocumented in this group is .61, so while a reasonable share of women in this group should still be undocumented, the risk of misclassification error is necessarily higher. On the other hand, this is also a more diverse group with a lower concentration of disadvantage. As shown in Table 2, 35% of these women have at least some college education and 62% are married. They also come from a broader range of countries; for instance, only 53% come from Mexico and about 20% come from Asian nations. The final column in Table 2 lists the attributes for the white U.S.-born mothers.

Methods

We present logistic regression models at the individual-level to test whether infant health outcomes change following the enactment of E-Verify policies.¹⁰ These models are of the following form:

$$\begin{gathered} \text{Pr}(Y_{\mathit{ist}}\mid X)=\alpha +{\beta }_1\ast E-{\mathrm{verify}}_{ist}+{\beta }_2\ast {\mathrm{individual}\mathrm{controls}}_{\mathit{ist}}+{\beta }_3\ast \\ \mathrm{state}{\mathrm{controls}}_{st}+{\beta }_4\ast {\mathrm{state}}_t+{\beta }_5\ast {\mathrm{year}}_s+{\epsilon }_{\mathit{ist}} \end{gathered}$$ (equation 1)

where i refers to individuals, s refers to states, and t refers to the calendar year of birth. Y_ist is an individual-level dichotomous measure of either low birth weight, preterm birth, or small for gestational age. E-Verify_ist reflects two dichotomous variables indicating whether a woman was exposed to public E-Verify or universal E-Verify in her state of residence for the duration of her pregnancy. Individual controls_ist refers to a set of individual-level control variables that adjust for maternal and baby characteristics. State controls_st refers to a set of state-level control variables that vary across calendar years and adjust for economic, demographic, and policy conditions in the state. State_t refers to state fixed effects (i.e., dummy variables for state of residence) and year_s refers to year fixed effects (i.e., dummy variables for the calendar year of birth). The state fixed effects hold constant unmeasured time-invariant differences across states (e.g., stable differences in political attitudes, receptivity toward immigrants, etc.), while the year fixed effects hold constant national-level time trends (e.g., national economic trends, etc.). We present results from equation 1 separately for the immigrant women in the top quartile of the probability measure, for all immigrant mothers coming from the top 25 sending countries, and for native-born white mothers. We then assess whether the trends for the two immigrant groups are statistically significantly different from the native trends by running additional models that pool data from each immigrant group with the native born group and include interaction terms between E-Verify policy and nativity. These models are of the following form:

$$\begin{gathered} \text{Pr}(Y_{\mathit{ist}}\mid X)=\alpha +{\beta }_1\ast E-{\mathit{verify}}_{\mathit{ist}}+{\beta }_1\ast {\mathit{immigrant}}_{\mathit{ist}}+{\beta }_1\ast E-\mathit{verify}\ast \\ {\mathrm{immigrant}}_{ist}+{\beta }_2\ast \mathrm{individual}{\mathrm{controls}}_{ist}+{\beta }_3\ast \mathrm{state}{\mathrm{controls}}_{st}+{\beta }_4\ast \\ {\mathrm{state}}_t+{\beta }_5\ast {\mathrm{year}}_s+{\epsilon }_{\mathit{ist}} \end{gathered}$$ (equation 2)

where immigrant_ist is a dichotomous indicator for being in one of the immigrant groups and native whites serve as the reference group. E – verify * immigrant_ist is an interaction term between the immigrant indicator and the indicator for exposure to E-Verify and all other aspects of the model are equivalent to equation 1 above.¹¹

Since there are several reasons to expect that the composition of live births could vary with E-Verify, we estimate aggregated state-level models to evaluate whether the demographic composition of women having live births in the state changes following the enactment of E-Verify policies. We run such state-level models of the following form:

$$\begin{gathered} Y_{\mathit{st}}=\alpha +{\beta }_1\ast E-{\mathit{Verify}}_{st-1}+{\beta }_2\ast {\mathrm{state}\mathrm{controls}}_{st-1}+{\beta }_3\ast {\mathrm{state}}_t+{\beta }_4\ast \\ {\mathrm{year}}_s+{\epsilon }_{\mathit{st}} \end{gathered}$$ (equation 3)

where s refers to states and t refers to the calendar year of birth. Y_st is a continuous measure of the percentage of births in a given state and a given year to mothers with a particular demographic attribute (namely, having a high school degree or higher or being married). E-Verify_st-1 reflects two dichotomous variables indicating whether public E-Verify or universal E-Verify was in effect for all or part of the calendar year before the birth. State controls_st-1 are the same as those in equation 1, but in this case for the calendar year before the birth. The state control variables and E-Verify indicators are lagged by one year in this model to better capture circumstances around the time of conception when effects of social conditions on fertility intentions should be most pronounced (about 2/3rds of births in a given calendar year are conceived in the prior calendar year). As in equation 1, State_t refers to state fixed effects and year_s refers to year fixed effects. We produced all estimates using Stata 15.

Variables

The three dependent variables in this analysis are dichotomous indicators for low birth weight (weight less than 2,500 gm), preterm delivery (gestational age less than 37 weeks), and small for gestational age (SGA; weight less than 10^th percentile for gestational age measured in weeks; Oken et al. 2003). Birth weight reflects the combination of time spent in the womb as well as an infant’s rate of growth. Presenting results for preterm delivery and SGA will allow us to assess whether E-Verify has different associations with these two components of birth weight. We present results for dichotomized indicators, but the general pattern of results was similar for continuous measures of birth weight (in grams), gestational age (in weeks), and fetal growth (birth weight divided by gestational age).

We also include several individual-level control variables that may jointly influence infant health and the likelihood of giving birth in a state with E-Verify: maternal age (dichotomous indicators for 18-21, 21-24, 25-34, and 35-44, with 18-24 serving as the reference group); maternal education (dichotomous indicators for less than high school, high school, some college, and college or more, with less than high school as the reference group); maternal race-ethnicity (dichotomous indicators for Hispanic, non-Hispanic white, non-Hispanic black, and non-Hispanic other, with Hispanic serving as the reference category); maternal marital status (a dichotomous indicator for being married); child gender (a dichotomous indicator for whether the child is male); and birth order (dichotomous indicators for whether the mother has had 0, 1, 2, 3, or 4+ previous live births, with 1 serving as the reference category).

The primary exposure of interest in the analysis are dichotomous indicators for public E-Verify and universal E-Verify. These variables are coded one if a woman was exposed to the relevant E-Verify policy in her state of residence for the duration of her pregnancy and women exposed to no E-Verify during their pregnancy serve as the reference group. These measures vary over time within state, so for instance, women in Georgia whose estimated conception dates are prior to the enactment of public E-Verify in July 2007 fall in reference group, those whose conceptions fall after July 2007 but before the enactment of universal E-Verify in January 2012 are coded one for public E-Verify and zero for universal E-Verify, and those conceiving after universal E-Verify began in January 2012 are coded one universal E-Verify and zero for public. We treat any case as exposed when the date of conception (calculated by subtracting the estimated gestational age from the date of birth) is equal to or greater than the date of the relevant E-Verify enactment.¹² Our coding of E-Verify policies and enactment dates is based on the immigration policy database compiled by the National Conference of State Legislatures (NCSL Immigration Policy Project 2015).

We also include in our models several state-level control variables that vary across calendar years and may be jointly correlated with infant health and the enactment of E-Verify: total population (source: ACS); proportion of the population that is foreign-born (source: ACS); percent uninsured (source: ACS); Medicaid expenditures (measured in hundreds of billions of dollars; source: U.S. Department of Health and Human Services); whether or not the state makes TANF available for non-qualified children (source: Urban Institute State Immigration Policy Resource [UISIPR]); whether or not the state makes Medicaid available to undocumented pregnant women (source: UISIPR); unemployment rate source: University of Kentucky Center for Poverty Research [UKCPR]); poverty rate (source: UKCPR); TANF benefits (based on a family of three and measured in single dollars; source: UKCPR); average percent of senate and house that are democrats (source: UKCPR); whether governor is democrat (source: UKCPR); and, minimum wage (measured in single dollars; source: UKCPR). In the individual-level models (equation 1) these variables reflect conditions in the year of birth; whereas in the state-level models evaluating composition change (equation 2), they reflect conditions in the year before birth when most conceptions occur.

When running state-level models to test for changes in the demographic composition of mothers giving birth, we aggregate up the individual-level records into state-year cells and construct two dependent variables – % of births to married mothers and % of births to mothers with high school degrees or more – for each of the three nativity groups. Mothers being married and having more education are typically associated with better birth outcomes. In these variables the numerator is the count of births to women with the relevant attribute (e.g., being married) in the relevant group (e.g., the top quartile of the undocumented probability distribution) in a given state and year, and the denominator is the count of births to the relevant group in a given state and year. In the state-level models, the covariates of primary interest are dichotomous variables for whether a universal or public E-Verify mandate was in effect in the state for some or all of the previous calendar year.

Results

Sample means and standard deviations are presented in Table 2 for the three key groups in our analytic sample. Rates of low birth weight and small for gestational age are similar across all three groups, and rates of preterm birth are only slightly higher in the immigrant groups, relative to the native group. Given that the native group has much higher education levels than both immigrant groups, the similarity of these rates coincide with the well-known pattern in which foreign-born women have healthy birth outcomes, despite socioeconomic disadvantages (Acevedo-Garcia, Soobader and Berkman 2005; Fuentes-Afflick and Lurie 1997). It is also worth noting that more births in the file were exposed to public E-Verify (between 9-16% of births) than universal E-Verify (between 3-7% of births).

Table 3 summarizes the key findings from our individual-level analyses (equation 1). In this table, each column and panel represents the odds ratio for our E-Verify indicators from a different logistic regression model. All models contain all the individual- and state-level control variables described above along with state and year fixed effects, but we suppress their associated parameter estimates for clarity of presentation. Complete tables listing results for all control variables are included in Appendix 1. Beginning with the first column showing odds ratios for low birth weight, we find that, for the top quartile of the undocumented probability distribution (panel 1), universal E-Verify is associated with an 18% increase in the odds of low birth weight, but there is no significant association between public E-Verify and low birth weight for this group. For the more encompassing immigrant category of all women from the top 25 sending countries (panel 2), universal E-Verify mandates are associated with a 15% increase in the odds of low birth weight, and public E-Verify is associated with a more modest, but still statistically significant, 7% increase in the odds of low birth weight. For native-born white mothers (panel 3), universal E-Verify is associated with an 12% increase in the odds of low birth weight and public E-Verify is associated with relatively similar 10% increase in the odds of low birth weight.¹³

Table 3:

Odds Ratios from Individual-Level Logistic Regression Models Predicting Low Birth Weight, Pre-term Delivery, and Small for Gestational Age after E-Verify Mandates

	Low Birth Weight	Pre-term Delivery	Small for Gestational Age
Panel 1: Top quartile of undocumented probability distribution for foreign-born women from top 25 immigrant sending countries
Universal E-Verify	1.181*** (0.055)	1.204** (0.078)	1.015 (0.027)
Public E-Verify	1.054 (0.040)	1.104** (0.037)	0.976 (0.022)
N	1,001,776	1,001,776	1,001,776
Panel 2: All foreign-born women from top 25 immigrant sending countries
Universal E-Verify	1.154*** (0.042)	1.197** (0.076)	1.030 (0.017)
Public E-Verify	1.076** (0.025)	1.149*** (0.029)	1.001 (0.010)
N	4,104,491	4,104,491	4,104,491
Panel 3: White Native-born Mothers
Universal E-Verify	1.120*** (0.030)	1.148*** (0.035)	0.990 (0.013)
Public E-Verify	1.102*** (0.021)	1.128*** (0.024)	1.005 (0.009)
N	10,828,653	10,828,653	10,828,653

Notes:

⁽¹⁾Standard errors in parentheses

^*p < 0.05

^**p < 0.01

^***p < 0.001.

⁽²⁾Each column and panel is from a different logistic regression. Estimates based on the state-year cells shaded grey in Table 1 reflecting the adoption of the 2003 birth certificate revision.

⁽³⁾Control variables include maternal characteristics (age, education, marital status, and race/ethnicity), infant demographic characteristics (sex and birth order), and state characteristics (state population, proportion foreign-born, Medicaid expenditure, unemployment rate, TANF benefits for a family of three, poverty rate, % uninsured, % democrat in state legislature, whether state governor is democrat, minimum wage, whether the state provides TANF to non-qualified children, and whether Medicaid covers undocumented pregnant women in the state). All models contain state and year fixed effects.

⁽⁴⁾Complete tables listing all coefficients are shown in the Appendix 1, Tables 1A and 2A.

⁽⁵⁾In panels 1 and 2 for the immigrant groups, odds ratios for universal and public E-Verify are statistically significantly different at the .05 level when predicting low birth weight, but cannot be statistically distinguished when predicting pre-term birth or small for gestational age. In panel 3 for the native-born group, odds ratios for universal and public E-Verify are statistically equivalent for all three outcomes.

The second and third columns in Table 3 list results for the pre-term delivery and small for gestational age outcomes. Both universal and public E-Verify are significantly associated with higher odds of pre-term delivery for all three groups; whereas all the odds ratios predicting small for gestational age are statistically non-significant. This suggests that associations between E-Verify and low birth weight most likely reflect shorter gestational ages rather than fetal growth restriction. For the immigrant groups presented in panels 1 and 2, universal E-Verify is associated with a 20% increase and public E-Verify is associated with a 10%-15% increase in the odds of pre-term delivery. For the native white mothers presented in panel 3, universal E-Verify is associated with a 15% increase and public E-Verify is associated with a 13% increase in the odds of pre-term delivery.¹⁴

Table 4 presents results from equation 2 that incorporates interaction terms between nativity and E-Verify exposure. Panel 1 presents main effects and interaction terms for an indicator comparing the top quartile category with the white native-born reference group, and panel 2 presents equivalent results for an indicator comparing the immigrant group including all women from the top 25 countries and the white native reference group. The key feature of these results is that none of the interaction terms between the nativity indicators and E-Verify exposure are statistically significant, suggesting that E-Verify and the surrounding conditions correspond with similar downward health trends for both native and immigrant groups.

Table 4:

Interactions between E-Verify Policy and Nativity Group from Individual-Level Logistic Regression Models Predicting Low Birth Weight, Pre-term Delivery, and Small for Gestational Age after E-Verify Mandates

	Low Birth Weight	Pre-term Delivery	Small for Gestational Age
Panel 1: Top quartile of undocumented probability distribution for foreign-born women from top 25 immigrant sending countries
Top quartile (Ref=White Native)	0.657*** (0.029)	0.943 (0.043)	0.676*** (0.026)
Universal E-Verify	1.122*** (0.029)	1.151*** (0.037)	0.993 (0.011)
Top quartile*Universal E-Verify	1.022 (0.053)	1.020 (0.0353)	0.988 (0.0353)
Public E-Verify	1.100*** (0.021)	1.125*** (0.023)	1.006 (0.009)
Top quartile*Public E-Verify	0.978 (0.022)	0.991 (0.027)	0.963 (0.026)
N	11,830,429	11,830,429	11,830,429
Panel 2: All foreign-born women from top 25 immigrant sending countries
Immigrant from top 25 countries(Ref=White Native)	0.894*** (0.019)	0.936*** (0.016)	0.981 (0.019)
Universal E-Verify	1.131*** (0.0326)	1.154*** (0.0414)	1.003 (0.013)
Immigrant*Universal E-Verify	0.934 (0.043)	0.984 (0.026)	0.961 (0.034)
Public E-Verify	1.109*** (0.021)	1.130*** (0.022)	1.011 (0.010)
Immigrant*Public E-Verify	0.936 (0.038)	1.005 (0.040)	0.970 (0.030)
N	14,933,144	14,933,144	14,933,144

Notes:

⁽¹⁾Standard errors in parentheses

^*p < 0.05

^**p < 0.01

^***p < 0.001.

⁽²⁾Each column and panel is from a different logistic regression. Estimates based on the state-year cells shaded grey in Table 1 reflecting the adoption of the 2003 birth certificate revision.

⁽³⁾Control variables include maternal characteristics (age, education, marital status, and race/ethnicity), infant demographic characteristics (sex and birth order), and state characteristics (state population, proportion foreign-born, Medicaid expenditure, unemployment rate, TANF benefits for a family of three, poverty rate, % uninsured, % democrat in state legislature, whether state governor is democrat, minimum wage, whether the state provides TANF to non-qualified children, and whether Medicaid covers undocumented pregnant women in the state). All models contain state and year fixed effects.

⁽⁴⁾Complete tables listing all coefficients are shown in the Appendix 1, Tables 3A.

In analyses not shown, these downward trends in infant health for both immigrant and native-born mothers were robust to lagging the state-level control variables by one or two years. It is also noteworthy that the worsening infant health for native-born mothers was found across all education levels as well as for non-Hispanic black and Hispanic natives. Additionally, we replicated our results using the more typical logical imputation approach in which only Latin American women with a high school degree or less are treated as potentially undocumented. With this strategy we found consistent patterns of rising rates of low birth weight and preterm birth, implying these findings are unlikely to be an artifact of the particular assumptions of our proxy strategy (e.g., conditional independence).

As noted above, an important factor that could contribute to health trends following the passage of E-Verify is a change in the composition of women giving birth in the state. To explore this possibility, Table 5 summarizes the E-Verify coefficients from our aggregated state-level regression models (equation 3) predicting the percentage of births in each of our three focal sociodemographic subgroups who are born to married mothers and the percentage born to mothers with a high school diploma or more. Each model includes all the state-level control variables and state and year fixed effects, but these are not shown for efficiency of space (see Appendix 1 for listing of all coefficients from these models).

Table 5:

Coefficients and Standard Errors from Aggregated State-Level OLS Regressions Predicting the Percentage of Births to Married Mother and More Educated Mothers

	Top Quartile of Undocumented Probability Distribution		All foreign-born women from Top 25 Immigrant Sending Countries		Native-born White Mothers
	% Births to Married Mothers	% Births to Mother with High School or More	% Births to Married Mothers	% Births to Mother with High School or More	% Births to Married Mothers	% Births to Mothers with High School or More
	Model (1)	Model (2)	Model (3)	Model (4)	Model (5)	Model (6)
Universal E-Verify	−0.051 (1.349)	1.364 (0.856)	−0.255 (0.558)	0.571 (0.626)	−0.859** (0.315)	0.774** (0.279)
Public E-Verify	0.142 (0.983)	−1.073 (0.623)	−0.178 (0.407)	−0.908* (0.456)	−0.977*** (0.230)	−0.163 (0.203)
N	217	217	220	220	220	220

Notes:

⁽¹⁾Standard errors in parentheses

^*p < 0.05

^**p < 0.01

^***p < 0.001.

⁽²⁾Each column and panel is from a different OLS regression. Estimates based on the state-year cells shaded grey in Table 1 reflecting the adoption of the 2003 birth certificate revision

⁽³⁾Control variables include state characteristics (state population, proportion foreign-born, Medicaid expenditure, unemployment rate, TANF benefits for a family of three, poverty rate, % uninsured, % democrat in state legislature, whether state governor is democrat, minimum wage, whether the state provides TANF to non-qualified children, and whether Medicaid covers undocumented pregnant women in the state). All models contain state and year fixed effects.

⁽⁴⁾Complete tables listing all coefficients are shown in the Appendix 1, Table 4A

For mothers in the top quartile of the undocumented proxy measure, there are no significant associations between E-Verify and the share of births to married mothers or more educated mothers. For the more encompassing category of all women from top-25 sending countries, Model 4 reveals a statistically significant negative association of .9 percentage points between public E-Verify and the share of births to mothers with high school or more. But, a similar trend does not emerge for universal E-Verify in Model 4, nor for the share of births to married immigrant mothers in Model 3. For the group of white U.S.-born mothers, several coefficients are significant, but the trends are mixed: in Model 5, both universal and public E-Verify are associated with a .86 to .98 point reduction in the percentage of births to married mothers; whereas in Model 6, universal E-Verify is associated with a .77 point increase in the percentage of births by mothers with high school or higher.

Discussion

Using natality data spanning the years from 2007 to 2014, when 21 states enacted E-Verify laws, we found that the passage of E-Verify, both its more limited version (public E-Verify) and its more encompassing version (universal E-Verify), was associated with an increase in the odds of low birth weight and pre-term delivery to foreign-born mothers from the top 25 sending countries for undocumented immigrants as well as U.S.-born mothers. For low birth weight, the relative increase in risk associated with the passage of E-Verify ranged from 8% to 20%; and, for preterm delivery, the relative increase in risk ranged from 10% to 20%. These trends for immigrant and native groups could not be distinguished statistically according to the interaction terms between nativity group and policy exposure in Table 4. Notably, there was no increase in the rate of small-for-gestational-age births for the immigrant or native groups, suggesting that lower birth weights were driven primarily by shorter gestational ages rather than growth retardation.

Three different scenarios may drive these similar trends for immigrant and native mothers in E-Verify states. First, E-Verify may have negative effects on infant health for both groups of mothers. Immigrant mothers will bear the direct and intentional effects of E-Verify, namely lower employment prospects for undocumented immigrants (Amuedo-Dorantes and Bansak 2012, 2014). On the other hand, native and immigrant mothers alike will experience the indirect effects of E-Verify on communities, such as population loss as immigrants move away and potentially lower property values as communities experience these difficulties (Bohn, Lofstrom and Raphael 2014; Orrenius and Zavodny 2016). In this case, the health effects of E-Verify may spill-out, well beyond the intended targets of undocumented immigrants. Such an explanation for our results highlights the ways that immigrant and native wellbeing are intertwined, in contrast to the “us” versus “them” portrayal that often pervades contemporary discussions of immigration and immigration policy.

Second, and alternatively, the environments that inspire E-Verify, but not the policy itself, may negatively impact maternal and infant health for both groups. Our models controlled for a number of time-varying potential confounders in the state, including social spending levels and unemployment rates. However, some potential confounders, such as industrial restructuring and worsening of the local labor markets, may play out on a more local level than the state and should negatively impact natives as well as immigrants. Since non-metro areas are more likely to experience the industrial restructuring that can spur new settlement patterns (Kandel and Parrado 2005), we conducted a sensitivity analysis by replicating the models for native-born mothers stratified by metro and non-metro counties. We found similar associations for E-Verify across both categories of counties. This was only a crude test, but it does not support the possibility that confounders that differ across metro and non-metro area are driving the native results. Third, the similar trends among immigrants and natives may be driven by a combination of the first and second scenarios in which immigrant health is negatively affected by the policy itself, whereas native health is negatively affected by environmental risk factors that correlate with E-Verify.

Unfortunately, parsing these different explanations is beyond the scope of our data, but one clear messages that emerges from these results is that giving birth in a state that passes E-Verify is associated with a higher risk of poor infant health in the general community, for immigrants and natives alike. While a naïve accounting of policy effects would typically predict null findings for a “comparison group,” like native whites, not directed affected by the policy, this study brings to the forefront the complexity of the environments generating restrictive immigration policies and potential effects for the broader population. Worsening infant health among immigrants following E-Verify aligns with prior work examining more local-level enforcement actions (Novak et al. 2017; Torche and Sirois 2018). However, this prior work did not find worsening infant health among natives whites as we did here, perhaps because our analysis includes a more diverse set of state contexts spanning a longer time series than these prior studies.

Using state-level aggregate data, we also tested whether E-Verify was correlated with changes in the composition of live births in a state. While there was no significant composition change for the group with the highest share of likely undocumented (i.e., the first quartile of our proxy measure), for the broader group of all immigrant mothers from top 25-sending countries, public E-Verify was associated with a decline in the percentage of births to mothers with at least high school degrees—a trend that could contribute to lower birth weights following E-Verify. For native mothers, composition change was detected, but appeared to operate in countervailing ways. E-Verify (both universal and public versions) was associated with a decline in births to U.S.-born married mothers—a trend that could contribute to lower birth weights—but, universal E-Verify was also associated with an increase in births to more educated U.S.-born mothers—a trend that could contribute to higher birth weights. Ultimately, it is ambiguous whether and how these composition trends contribute to associations between E-Verify and infant health. The countervailing trends for natives may offset each other, and the fact that the immigrant trends were not apparent in the most-likely undocumented group counters a claim that composition change primarily drives the worsening health for immigrant births.

Our study employed a new continuous proxy measure that used state-specific demographic distributions to probabilistically identify potentially undocumented immigrants in administrative data. Beyond the additional information supplied by state-specific data, a key strength of our measure is that the continuous distribution allows for more flexibility than the more standard “logical imputation” approach. We used the top quartile of the proxy measure as a key demarcation for those women most likely to be undocumented, but demarcations could be made at any points in the distribution, or the probability measure could be entered as a covariate and interacted with an exposure of interest.¹⁵ Though the construction of this measure was intended to serve as an analytic step in support of testing our substantive hypotheses, it suggests the potential for using administrative data sources in creative ways to study populations that are hard to reach in traditional sample surveys.

While our study offered multiple strengths, including a novel proxy strategy and population data on live births occurring across a large number of states in the U.S., important limitations must be kept in mind. As discussed previously, data limitations related to the 2003 revision to the U.S. birth certificate means that we are lacking data for a number state-year cells (see summary in Table 1). Birth certificate data also lack information on relevant individual-level variables like employment status and income. The Great Recession in the U.S. also overlaps with the passage of several E-Verify bills and other restrictive immigration policies. Confounding from the Great Recession is a common concern when testing immigration policy effects and this analysis is not immune. Finally, while our proxy strategy offers key strengths, it also requires untestable assumptions (most notably, conditional independence), and, like all proxy measures, will involve some level of misclassification. Understanding the effects of immigration policies is an on-going and collective effort and future researchers may want to further test health trends associated with E-Verify using alternative data with more individual-level measures and/or alternative methods like correlation of aggregate time series (Catalano 1981) or synthetic control methods (Kreif et al. 2015).

Although our analysis raises unanswered questions about the underlying factors driving poorer infant health among native mothers following E-Verify, a key take-away message from our findings is that infants born in E-Verify states, to both immigrant and native mothers, may face health vulnerabilities. Future researchers interested in local immigration enforcement policy as well as geographic variations in health more broadly would do well to recognize the economic, social, and political factors that drive and correspond with new immigration settlement patterns and harsher immigration policies because the above results are highly suggestive that these are important determinants of infant health for a wide range of groups in a state.

Appendix 1

Table 1A:

Odds Ratios from Individual-level Logistic Regression Models Predicting Infant Health for Mothers from Top 25 Sending Countries of Undocumented Immigrants in the US

	Top quartile of undocumented probability distribution for foreign-born women from top 25 sending countries			All foreign-born women from top 25 sending countries
	Model 1 Low birth weight	Model 2 Pre-term delivery	Model 3 Small for gestational age	Model 4 Low birth weight	Model 5 Pre-term delivery	Model 6 Small for gestational age
Universal E-Verify	1.181*** (0.055)	1.204** (0.077)	1.015 (0.027)	1.154*** (0.042)	1.197** (0.076)	1.031 (0.016)
Public E-Verify	1.054 (0.039)	1.104** (0.037)	0.976 (0.022)	1.076** (0.025)	1.149*** (0.029)	1.001 (0.010)
High school	0.976 (0.017)	0.905*** (0.012)	0.948*** (0.012)	0.981** (0.007)	0.950*** (0.009)	0.954*** (0.009)
Some college	0.978 (0.097)	0.922* (0.036)	0.906 (0.059)	0.962* (0.016)	0.921*** (0.012)	0.911*** (0.021)
College or more	0.780 (0.197)	0.709 (0.169)	0.824 (0.138)	0.839*** (0.034)	0.758*** (0.021)	0.921* (0.031)
Maternal age
21-24	0.922*** (0.014)	0.857*** (0.015)	0.940*** (0.006)	0.927*** (0.010)	0.872*** (0.007)	0.935*** (0.008)
25-34	1.048** (0.017)	0.842*** (0.017)	0.879*** (0.007)	1.039** (0.013)	0.892*** (0.014)	0.878*** (0.008)
35-44	1.522*** (0.039)	1.091*** (0.028)	0.900*** (0.018)	1.449*** (0.024)	1.209*** (0.029)	0.888*** (0.011)
Married	0.949*** (0.010)	0.873*** (0.010)	0.951*** (0.009)	0.910*** (0.004)	0.864*** (0.005)	0.947*** (0.004)
Male	0.933*** (0.012)	1.161*** (0.008)	1.067*** (0.008)	0.907*** (0.010)	1.166*** (0.015)	1.056*** (0.006)
Birth Order
2nd	0.648*** (0.008)	0.972 (0.016)	0.658*** (0.009)	0.648*** (0.005)	0.943*** (0.011)	0.643*** (0.005)
3rd	0.626*** (0.010)	1.047 (0.028)	0.587*** (0.010)	0.628*** (0.005)	1.028*** (0.008)	0.578*** (0.008)
4th or higher	0.632*** (0.019)	1.203*** (0.038)	0.543*** (0.012)	0.649*** (0.005)	1.162*** (0.009)	0.546*** (0.006)
Non-Hispanic white	1.087* (0.038)	1.009 (0.037)	0.984 (0.036)	0.837*** (0.035)	0.852*** (0.014)	0.841*** (0.022)
Non-Hispanic black	1.753*** (0.249)	1.405*** (0.087)	1.288*** (0.091)	1.477*** (0.130)	1.229*** (0.040)	1.226** (0.084)
Non-Hispanic other	0.985 (0.107)	1.374* (0.190)	1.211 (0.131)	1.246*** (0.059)	0.982 (0.035)	1.552*** (0.062)
State population	0.993 (0.018)	1.067*** (0.020)	0.995 (0.012)	0.999 (0.011)	1.048** (0.019)	0.993 (0.008)
Proportion foreign-born	4.107 (13.530)	0.187 (0.636)	3.219 (5.883)	1.580 (2.330)	6.252 (15.460)	4.788* (3.707)
Medicaid expenditure	1.015*** (0.004)	0.988* (0.005)	1.006* (0.003)	1.001 (0.002)	0.990** (0.003)	0.998 (0.001)
Unemployment rate	1.003 (0.009)	1.021 (0.014)	1.000 (0.007)	1.018* (0.008)	1.012 (0.011)	1.002 (0.003)
TANF benefits	0.974 (0.030)	1.009 (0.037)	1.015 (0.019)	1.012 (0.022)	1.008 (0.034)	1.016 (0.015)
Poverty rate	0.984 (0.008)	0.991 (0.005)	0.995 (0.005)	0.988*** (0.003)	0.995 (0.005)	1.001 (0.003)
Minimum wage	1.012 (0.018)	1.047** (0.017)	0.974 (0.016)	1.011 (0.012)	1.025* (0.012)	0.984 (0.015)
State governor democrat	0.990 (0.026)	0.951 (0.032)	0.978 (0.017)	1.016 (0.022)	1.003 (0.035)	1.002 (0.011)
Prop legislators democrat	1.051 (0.271)	0.970 (0.280)	1.007 (0.173)	0.909 (0.171)	0.757 (0.184)	1.042 (0.137)
Percent uninsured	0.989 (0.011)	1.001 (0.009)	0.994 (0.006)	0.990 (0.007)	1.002 (0.011)	0.993 (0.005)
TANF for non-qualified children	0.912* (0.037)	0.898*** (0.027)	1.045 (0.034)	0.983 (0.021)	1.039 (0.032)	1.119*** (0.030)
Medicaid for undocumented pregnant women	1.053 (0.028)	0.947 (0.028)	1.029 (0.053)	0.980 (0.052)	0.948 (0.033)	0.984 (0.024)
N	1,001,776	1,001,776	1,001,776	4,104,491	4,104,491	4,104,491

Notes: All models contain state and year fixed effects.; Standard errors in parentheses

^*p < 0.05

^**p < 0.01

^***p < 0.001. Estimates based on the state-year cells shaded grey in Table 1 reflecting the adoption of the 2003 birth certificate revision.

Table 2A:

Odds Ratios from Individual-level Logistic Regression Models Predicting Infant Health for Native-born White Mothers

	Low birth weight Model (1)	Pre-term birth Model (2)	Small for gestational age Model (3)
Universal E-Verify	1.120*** (0.030)	1.148*** (0.035)	0.990 (0.013)
Public E-Verify	1.102*** (0.021)	1.128*** (0.024)	1.005 (0.009)
High School	0.736*** (0.012)	0.872*** (0.016)	0.719*** (0.012)
Some College	0.577*** (0.011)	0.777*** (0.015)	0.554*** (0.010)
College or more	0.413*** (0.010)	0.609*** (0.015)	0.433*** (0.012)
Maternal Age (reference group: 18-21)
21-24	1.124*** (0.011)	1.016** (0.006)	1.130*** (0.009)
25-34	1.305*** (0.016)	1.096*** (0.009)	1.170*** (0.014)
35-44	1.771*** (0.022)	1.431*** (0.015)	1.286*** (0.014)
Married	0.706*** (0.013)	0.783*** (0.013)	0.727*** (0.012)
Male	0.831*** (0.004)	1.138*** (0.003)	0.969*** (0.003)
Birth Order (reference group: 1st)
2nd	0.646*** (0.007)	0.893*** (0.010)	0.658*** (0.009)
3rd	0.674*** (0.009)	0.981 (0.014)	0.659*** (0.010)
4th or higher	0.744*** (0.017)	1.116*** (0.027)	0.648*** (0.014)
State total population (1,000,000s)	0.982* (0.008)	1.008 (0.012)	0.992 (0.008)
Proportion foreign-born	0.309 (0.357)	1.003 (1.384)	0.724 (0.419)
Medicaid expenditure ($1,000,000,000)	1.005* (0.002)	0.996 (0.002)	0.998* (0.001)
Unemployment rate	1.005 (0.003)	1.008 (0.006)	0.997 (0.002)
TANF benefits ($100)	1.009 (0.020)	1.021 (0.020)	1.015 (0.016)
Poverty rate	0.995 (0.003)	0.997 (0.003)	1.001 (0.002)
Minimum wage	1.001 (0.004)	1.007 (0.005)	0.993** (0.002)
State governor democrat	0.971 (0.015)	0.951** (0.018)	1.012 (0.008)
% of state legislators democrat	1.062 (0.163)	1.190 (0.195)	1.168* (0.073)
% uninsured	0.987*** (0.004)	0.991 (0.006)	1.000 (0.003)
TANF for non-qualified children	0.965* (0.014)	1.013 (0.019)	0.963*** (0.007)
Medicaid for undocumented pregnant women	0.970* (0.014)	0.959 (0.029)	1.018 (0.011)
N	10,828,653	10,828,653	10,828,653

Notes:

⁽¹⁾All models contain state and year fixed effects. Standard errors in parentheses. Estimates based on the state-year cells shaded grey in Table 1 reflecting the adoption of the 2003 birth certificate revision.

^*p < 0.05

^**p < 0.01

^***p < 0.001

Table 3A:

Odds Ratios from Individual-level Logistic Regression Models Including Interactions Between E-Verify Policy and Nativity Group

	Top quartile of undocumented probability distribution versus Native-born White			All foreign-born women from top 25 sending countries versus Native-born White
	Low Birth Weight	Preterm Birth	Small for Gestational Age	Low Birth Weight	Preterm Birth	Small for Gestational Age
	Model (1)	Model (2)	Model (3)	Model (1)	Model (2)	Model (3)
Immigrant (vs native-born)	0.657*** (0.029)	0.943 (0.043)	0.676*** (0.026)	0.894*** (0.019)	0.936*** (0.016)	0.981 (0.019)
Universal E-Verify	1.122*** (0.029)	1.151*** (0.037)	0.993 (0.011)	1.131*** (0.033)	1.154*** (0.041)	1.003 (0.013)
Immigrant *Universal E-Verify	1.022 (0.053)	1.020 (0.035)	0.988 (0.035)	0.934 (0.043)	0.984 (0.026)	0.961 (0.034)
Public E-Verify	1.100*** (0.021)	1.125*** (0.023)	1.006 (0.009)	1.109*** (0.021)	1.130*** (0.022)	1.011 (0.010)
Immigrant*Public E-Verify	0.978 (0.022)	0.991 (0.027)	0.963 (0.026)	0.936 (0.038)	1.005 (0.040)	0.970 (0.030)
Maternal educational attainment
High school	0.760*** (0.010)	0.882*** (0.012)	0.747*** (0.011)	0.867*** (0.021)	0.923*** (0.009)	0.856*** (0.021)
Some college	0.589*** (0.010)	0.786*** (0.012)	0.571*** (0.009)	0.706*** (0.029)	0.836*** (0.013)	0.688*** (0.028)
College or more	0.419*** (0.010)	0.616*** (0.013)	0.446*** (0.012)	0.522*** (0.027)	0.659*** (0.014)	0.571*** (0.033)
Maternal age
21-24	1.091*** (0.015)	0.990 (0.009)	1.092*** (0.016)	1.046* (0.019)	0.969** (0.011)	1.047* (0.019)
25-34	1.254*** (0.023)	1.055*** (0.012)	1.106*** (0.024)	1.164*** (0.026)	1.018 (0.013)	1.018 (0.029)
35-44	1.711*** (0.026)	1.378*** (0.016)	1.213*** (0.023)	1.582*** (0.029)	1.346*** (0.016)	1.071* (0.033)
Married	0.726*** (0.014)	0.795*** (0.013)	0.747*** (0.013)	0.756*** (0.017)	0.807*** (0.012)	0.783*** (0.019)
Male	0.839*** (0.003)	1.141*** (0.004)	0.978*** (0.003)	0.852*** (0.007)	1.146*** (0.007)	0.995 (0.008)
Birth Order
2nd	0.647*** (0.007)	0.900*** (0.010)	0.660*** (0.008)	0.650*** (0.006)	0.907*** (0.010)	0.658*** (0.008)
3rd	0.671*** (0.008)	0.986 (0.014)	0.652*** (0.009)	0.666*** (0.007)	0.994 (0.011)	0.638*** (0.011)
4th or higher	0.730*** (0.015)	1.121*** (0.025)	0.633*** (0.011)	0.719*** (0.010)	1.127*** (0.020)	0.621*** (0.012)
Non-Hispanic white	1.095* (0.039)	1.007 (0.039)	0.986 (0.033)	1.100* (0.050)	0.923*** (0.013)	1.095* (0.043)
Non-Hispanic black	1.693*** (0.230)	1.459*** (0.121)	1.305*** (0.104)	1.757*** (0.108)	1.319*** (0.034)	1.425*** (0.071)
Non-Hispanic other	0.949 (0.109)	1.395* (0.201)	1.186 (0.122)	1.764*** (0.109)	1.079* (0.036)	2.186*** (0.147)
State population	0.986 (0.009)	1.020 (0.013)	0.989 (0.008)	0.996 (0.008)	1.028 (0.015)	0.993 (0.008)
Proportion foreign-born	0.426 (0.509)	0.840 (1.257)	0.851 (0.479)	0.453 (0.504)	1.567 (2.56)	1.311 (0.705)
Medicaid expenditure	1.005** (0.002)	0.995* (0.002)	0.998 (0.001)	1.004* (0.002)	0.994** (0.002)	0.997** (0.0010)
Unemployment rate	1.005 (0.003)	1.009 (0.006)	0.997 (0.002)	1.009* (0.004)	1.010 (0.006)	0.999 (0.002)
TANF benefits	1.007 (0.019)	1.018 (0.021)	1.018 (0.014)	1.010 (0.019)	1.015 (0.021)	1.018 (0.014)
Poverty rate	0.994 (0.003)	0.996 (0.003)	1.000 (0.002)	0.994 (0.003)	0.996 (0.003)	1.000 (0.002)
Minimum wage	1.002 (0.005)	1.011* (0.005)	0.992* (0.003)	1.001 (0.005)	1.009 (0.006)	0.992* (0.004)
State governor democrat	0.972 (0.015)	0.949** (0.018)	1.009 (0.007)	0.979 (0.016)	0.961 (0.022)	1.006 (0.007)
Prop legislators democrat	1.061 (0.160)	1.158 (0.190)	1.146* (0.066)	1.072 (0.163)	1.099 (0.184)	1.159* (0.073)
Percent uninsured	0.987*** (0.004)	0.992 (0.006)	0.999 (0.003)	0.988** (0.004)	0.994 (0.007)	0.998 (0.003)
TANF for non-qualified	0.964* (0.014)	1.009 (0.016)	0.969*** (0.007)	0.970* (0.013)	1.014 (0.020)	0.988 (0.008)
Medicaid for undocum. pregnant women	0.976 (0.014)	0.957 (0.026)	1.017 (0.015)	0.973 (0.017)	0.955 (0.030)	1.008 (0.013)
N	11,830,429	11,830,429	11,830,429	14,933,144	14,933,144	14,933,144

Notes: All models contain state and year fixed effects.; Standard errors in parentheses

^*p < 0.05

^**p < 0.01

^***p < 0.001

Estimates based on the state-year cells shaded grey in Table 1 reflecting the adoption of the 2003 birth certificate revision.

Table 4A:

Coefficients from Aggregated State-Level OLS Regressions Predicting the Percentage of Births to Married Mothers and More Educated Mothers

	Top Quartile of Undocumented Probability Distribution		All women from Top 25 Sending Countries		Native-born White Mothers
	% Births to Married Mothers	% Births to Mothers with High School or More	% Births to Married Mothers	% Births to Mothers with High School or More	% Births to Married Mothers	% Births to Mothers with High School or More
	Model (1)	Model (2)	Model (3)	Model (4)	Model (5)	Model (6)
Universal E-Verify	−0.051 (1.349)	1.364 (0.856)	−0.255 (0.558)	0.571 (0.626)	−0.859** (0.315)	0.774** (0.279)
Public E-Verify	0.142 (0.983)	−1.073 (0.623)	−0.178 (0.407)	−0.908* (0.456)	−0.977*** (0.230)	−0.163 (0.203)
State population	−2.039* (0.800)	−1.201* (0.507)	−0.846* (0.331)	−0.866* (0.371)	−0.166 (0.187)	−0.084 (0.165)
Proportion Foreign-born	−87.700 (87.95)	27.90 (55.81)	−49.090 (36.030)	−228.500*** (40.380)	−8.698 (20.340)	22.650 (18.000)
Medicaid expenditure	0.326* (0.162)	−0.203 (0.103)	0.024 (0.067)	−0.099 (0.075)	0.026 (0.038)	−0.131*** (0.034)
Unemployment rate	0.568 (0.355)	−0.165 (0.225)	0.095 (0.147)	−0.061 (0.165)	−0.013 (0.083)	−0.007 (0.073)
TANF benefits	−2.525* (1.181)	−1.956** (0.750)	0.393 (0.489)	−0.968 (0.549)	0.362 (0.276)	−0.007 (0.245)
Poverty rate	0.067 (0.244)	−0.005 (0.155)	−0.023 (0.101)	0.079 (0.113)	−0.031 (0.057)	−0.002 (0.050)
Minimum wage	0.436 (0.563)	−0.591 (0.357)	−0.077 (0.233)	0.066 (0.261)	0.0495 (0.132)	0.159 (0.117)
State governor democrat	−0.189 (0.894)	0.055 (0.567)	0.728 (0.370)	1.297** (0.415)	0.193 (0.209)	0.274 (0.185)
Prop legislators democrat	4.389 (8.555)	−1.788 (5.429)	0.123 (3.541)	−5.268 (3.969)	−0.295 (1.999)	−1.024 (1.769)
Percent uninsured	−0.190 (0.380)	0.186 (0.241)	0.335* (0.157)	0.418* (0.176)	−0.146 (0.0887)	0.057 (0.078)
TANF for non-qualified	2.070 (3.897)	−2.613 (2.473)	1.305 (1.614)	0.568 (1.810)	0.590 (0.911)	−0.0300 (0.807)
Medicaid for undocum. pregnant women	0.545 (1.598)	0.520 (1.014)	0.323 (0.662)	0.955 (0.742)	−0.253 (0.374)	0.150 (0.331)
Constant	87.710*** (10.98)	30.460*** (6.968)	74.890*** (4.549)	39.890*** (5.098)	76.680*** (2.568)	83.190*** (2.273)
N	217	217	220	220	220	220

Notes: All models contain state and year fixed effects.; Standard errors in parentheses

^*p < 0.05

^**p < 0.01

^***p < 0.001

Estimates based on the state-year cells shaded grey in Table 1 reflecting the adoption of the 2003 birth certificate revision.

All state control variables lagged by one calendar year to align with the timing of most conceptions

Appendix 2: Derivation of Probabilities

In this paper, we are interested in understanding how the probability of being undocumented according to a previously estimated proxy measure relates to key outcomes. Let D denote documentation status (either documented or undocumented). We have information on four characteristics which we denote X₁, X₂, X₃, and X₄. We are interested in calculating ****p(D|X₁, X₂, X₃, X₄). By Bayes rule we have

$$p(D\mid X_1,X_2,X_3,X_4)=\frac{p(X_1,X_2,X_3,X_4\mid D)p(D)}{p(X_1,X_2,X_3,X_4)}$$

If we assume that the characteristics are conditionally independent, we can write

$$p(D\mid X_1,X_2,X_3,X_4)=\frac{p(X_1\mid D)p(X_2\mid D)p(X_3\mid D)p(X_4\mid D)p(D)}{p(X_1,X_2,X_3,X_4)}.$$

Using the definition of conditional probability this can be rewritten as

$$p(D\mid X_1,X_2,X_3,X_4)=\frac{p(D\mid X_1)p(X_1)}{p(C)}\cdot \frac{p(D\mid X_2)p(X_2)}{p(D)}\cdot \frac{p(D\mid X_3)p(X_3)}{p(D)}\cdot \frac{p(D\mid X_4)p(X_4)}{p(D)}\cdot \frac{p(D)}{p(X_1,X_2{X}_3{X}_4)}$$

Finally, we can re-write this as:

$$p(D\mid X_1,X_2,X_3,X_4)\propto \frac{p(D\mid X_1)p(D\mid X_2)p(D\mid X_3)p(D\mid X_4)}{[p(D)]}$$

From this we can estimate the probability of being undocumented (Undoc) versus documented (Doc) according to the previously estimated proxy measure as

$$p(\text{Undoc}\mid X_1,X_2,X_3,X_4)=\frac{\text{Pr}(\text{Undoc}\mid X_1)\mathit{Pr}(\text{Undoc}\mid X_2)\text{Pr}(\text{Undoc}\mid X_3)\text{Pr}(\text{Undoc}\mid X_4)}{(C_1+C_2)\cdot [\text{Pr}(\text{Undoc}){]}^3}$$

where

$$C_1=\frac{\text{Pr}(\text{Undoc}\mid X_1)\text{Pr}(\text{Undoc}\mid X_2)\text{Pr}(\text{Undoc}\mid X_3)\text{Pr}(\text{Undoc}\mid X_4)}{[\text{Pr}(\text{Undoc}){]}^2}$$

and

$$C_2=\frac{\text{Pr}(\text{Doc}\mid X_1)\text{Pr}(\text{Doc}\mid X_2)\text{Pr}(\text{Doc}\mid X_3)\text{Pr}(\text{Doc}\mid X_4)}{[\text{Pr}(\text{Doc}){]}^2}.$$