The fertility integration of Mexican-Americans across generations: confronting the problem of the ‘third’ generation^*

* A previous version of this paper was presented at the 2012 European Population Association conference in Stockholm, Sweden.

ABSTRACT

The manner in which ‘third generation’ Mexican-Americans are identified, predicated on self-reported ethnic identity rather than grandparental nativity, is imprecise and potentially confounded with later generations. This study examines the degree to which this imprecision accounts for the stagnation found in many past studies of integration, including fertility integration. We use data from the study Immigration and Intergenerational Mobility in Metropolitan Los Angeles (IIMMLA), which includes questions on grandparental nativity, to construct a better-defined third generation. When IIMMLA data are aggregated into the commonly measured third-plus generation, the findings show a pattern of slow intergenerational-fertility integration, similar to previous research using the Current Population Survey or other data with third-plus generation measures. However, when we consider a third generation identified by grandparental nativity, evidence emerges of a faster fertility decline, bringing the third generation's fertility more in line with the native-born population as a whole. The results suggest that conclusions about integration based on third-plus generation measures should be regarded with greater scepticism and support efforts to include in surveys questions on grandparental nativity to enable the isolation of a genuine third generation among ethnic groups with immigrant origins.

KEYWORDS:

• Mexican-American
• fertility integration
• assimilation
• third generation

1. Introduction

Mexican migrants have been coming to the U.S. since at least the 1800s (Cardoso 1980), resulting in multiple generational groups in today's Mexican-origin population. Comparisons among these generational groups constitute a key element of research on immigrant integration, defined as convergence between the higher-generation members of the immigrant group and natives (National Academies of Sciences, Engineering, and Medicine 2016). Many recent studies making such comparisons for Mexican-Americans show lower levels of human capital and other attainment measures for third-plus generation Mexican immigrants relative to native-whites and even to second-generation Mexican-Americans (Livingston and Kahn 2002; Telles and Ortiz 2008; Zsembik and Llanes 1996). The integration of the Mexican-origin population is thus often viewed as lagging behind that of other groups that show stronger patterns of convergence. Some researchers attribute such apparently slower integration to ethno-racial discrimination against Mexican-Americans (Portes and Rumbaut 2001; Telles and Ortiz 2008). At the same time, studies of the Mexican-American second generation often document appreciable positive integration on such critical measures as schooling, income and family formation (Alba and Foner 2016; Alba and Nee 2003; Bean and Stevens 2003; Bean, Swicegood, and Berg 2000; Smith 2003; Waters and Jiménez 2005), suggesting at least the beginnings of notable integration among the children of Mexican immigrants and thus not overwhelming discrimination. These somewhat contradictory processes operating between the first and second generations and the second and third have given rise to accounts of generational decline (Gans 2007).

This apparent stagnation after the second generation is in many ways reminiscent of the experiences of earlier immigrant groups from Southern and Eastern Europe coming around the beginning of the twentieth century (Morgan, Watkins, and Ewbank 1994; Perlmann 2005). While the outcomes of later-generation members of these European groups and natives eventually converged (Alba 1985; Logan and Shin 2012), later-generation Mexican immigrants and their descendants appear not to be following this pattern. On fertility, for example, when comparing the third to the second generation, researchers have found smaller declines for the former compared with the latter (Bean, Swicegood, and Berg 2000; Frank and Heuveline 2005; Telles and Ortiz 2008). A similar pattern seems to occur for other factors (Bean et al. 1994; Eitle, Wahl, and Aranda 2009; Ewert 2009; Perreira, Harris, and Lee 2006; Telles and Ortiz 2008; Slack and Jensen 2007). Unfortunately, almost all of these studies have been unable to examine the third generation alone. Rather researchers have had to rely on a ‘third-plus’ generation grouping that consisted of the third, fourth, fifth or later generations (but for an exception, see Telles and Ortiz 2008).

This is problematic for several reasons. National-level and other large surveys like the U.S. Current Population Survey (CPS) contain questions only about whether the respondents and their parents are foreign-born. This information is lacking for grandparents. Consequently, for Mexican-Americans, it is necessary to approximate a ‘third’ generation by relying on questions regarding whether respondents say they are U.S.-born and Hispanic (and, if so, of Mexican origin), thus yielding a third-plus Mexican-American generation (Alba and Islam 2009; Emeka and Vallejo 2011; Visser 2014). But this grouping may be seriously flawed because it cannot reflect different generation-specific historical experiences (Jiménez 2010b). Moreover, it misses the experiences of many because of selective ‘ethnic attrition’, i.e. those of later-generation Mexican descent who ‘opt out’ of reporting that they are of Mexican origin, with this happening disproportionately among those of higher education (Duncan and Trejo 2007; Duncan and Trejo 2011; Lopez, Gonzalez-Barrera, and López 2017). This study is not subject to this bias because it draws on data that allow identification of a third-only generation via questions on the grandparental nativity. This yields a much improved third-only generation measure that may yield different conclusions about Mexican-fertility integration.¹

In what follows, we first introduce theoretical perspectives on integration and assess previous fertility integration research on the Mexican-origin population, as well as the degree of potential measurement problems that result from the way the third-plus generation has been defined. Then, we analyse data from the Immigration and Intergenerational Mobility in Metropolitan Los Angeles (IIMMLA) study (which provides a third-only generation measure), as well as CPS data (which provides a third-plus measure), to gauge the extent to which the IIMMLA data are representative of LA Mexican-Americans, as well as the extent to which the third-only and third-plus measures in the IIMMLA data yield different results about the generational pattern of Mexican-American fertility in Los Angeles. Descriptive and regression analyses are also conducted to ascertain how the cross-generational patterns of fertility levels change when we control for the influence of other factors. We end by discussing the implications of the findings for ideas about Mexican-American integration in the U.S.

2. Background and theory

One of the canonical theoretical perspectives on immigrant integration, as outlined in Milton Gordon's Assimilation in American Life (1964), envisions immigrants and their descendants moving through a series of stages, starting with their arrival as ‘newcomers’ and ending with their ‘entering the mainstream’ of society, with this process driven by both acculturation and structural assimilation dynamics (Bean, Brown, and Bachmeier 2015). Both optimistic revisions of this assimilation perspective (Alba and Nee 2003) and other more pessimistic theoretical approaches, such as segmented assimilation or racialisation (Portes and Zhou 1993; Telles and Ortiz 2008), have guided previous research on integration based on patterns of immigrant-group fertility.

2.1. Contemporary assimilation

Alba and Nee (2003) emphasise day-to-day decisions based on self-interest as working to produce integration-like effects as immigrants and natives cross boundaries and gradually become part of a new American ‘mainstream’. Across time and generation, immigrant groups thus acculturate and structurally assimilate across multiple dimensions, including such processes as childbearing, as immigrants from high-fertility countries adopt the host country's norms of smaller family sizes. The pace of assimilation processes among post-1965 Latino immigrant groups is also seen as buttressed by legal protections afforded by the civil rights movement, which, in theory, have expanded opportunities for immigrant structural integration. Adjustment of childbearing behaviours is a byproduct of both acculturation and structural incorporation.

Some researchers thus suggest, first, that Mexican immigrants and their descendants acculturate from pro-natalist (Erickson 1998) and pro-family (Bean, Curtis Jr, and Marcum 1977; Bean and Tienda 1988; Gonzales 2007; Hartnett and Parrado 2012) norms towards greater emphases on individualism, which is seen as encouraging smaller families (Lesthaeghe 2014; Lesthaeghe and Neidert 2006). These processes often involve shifts towards more egalitarian gender norms and ideology (Vasquez 2014) that facilitate reductions in family size. Second, structural integration through education and/or a career also delays and reduces fertility (Rindfuss, Morgan, and Offutt 1996), particularly among those coming from disadvantaged backgrounds (Brand and Davis 2011). This is supported by the work of Parrado and Morgan (2008), who in a synthetic-cohort approach show an intergenerational decline in fertility when comparing children-ever-born (CEB) among Mexican women by generation. They find stronger inverse relationships between educational attainment and fertility among Mexican-Americans than among non-Hispanic white women. The contemporary assimilation hypothesis thus leads us to expect that time and generation spent in the U.S. among Mexican-American women will be related to less childbearing.

2.2. Segmented assimilation

The assimilation model, however, has drawn criticism from those who argue that individual and structural characteristics of post-1965 immigrants reflect multi-trajectory, or segmented, integration processes (Portes and Bach 1985; Portes and Rumbaut 2001; Portes and Zhou 1993). They argue that the trajectories within different immigrant groups depend on whether those from a particular country come with high or low levels of human, cultural and social capital. These characteristics in turn interact with contexts of reception to produce either classic assimilation, upward assimilation sometimes with retained bi-culturalism or downward assimilation into a ‘rainbow’ underclass. Of various immigrant groups, Portes and Rumbaut (2001, 277) suggest that Mexicans are ‘the textbook example of theoretically anticipated effects of low immigrant human capital combined with a negative context of reception’ (italics theirs). They view such circumstances as involving exceptional risks for downward assimilation into a disadvantaged ‘native underclass’.

In follow-up papers (Haller, Portes, and Lynch 2011; Portes, Fernandez-Kelly, and Haller 2009), Portes and colleagues identify early childbearing, along with dropping out of school and having been incarcerated, as factors inducing downward assimilation among children of immigrants entering early adulthood. Other research on intergenerational-fertility integration also reports patterns outside the expectations of standard assimilation. Using cross-sectional data, Bean, Swicegood, and Berg (2000) and Frank and Heuveline (2005) found somewhat elevated childbearing from the second to the third-plus generation at the national level, while Hill and Johnson (2004) found a similar pattern in California. In their conclusion, Frank and Heuveline suggest that low returns to education and limited job opportunities among later-generation Mexican-American women reflect lower opportunity costs of childbearing. In one of the few studies able to use third-only generation data, Telles and Ortiz (2008) note that the third generation in LA and San Antonio shows slightly higher completed fertility than the second and fourth-plus generations, a result they attribute to increased awareness of racialisation among Mexicans-Americans and thus lower opportunity costs to fertility. Such results thus are consistent with the idea of little intergenerational progress in fertility and a lack of convergence with whites as a consequence of blocked mobility. This relatively higher fertility was also the case for blacks at the time of the IIMMLA survey in 2004 (Martin Joyce et al. 2017).

2.3. The measurement problem

To put these previous studies in context, most of them are in reality studies of an agglomeration of the third generation together with later generations and not exclusively the third generation. This larger third-plus-generation group includes all those born in the U.S. to U.S.-born parents who also identify themselves as Hispanic and of Mexican origin. The group comprises multiple generation groups (i.e. 3rd, 4th, 5th generation, etc.) and, because of ‘self-attrition’, contains only those who choose to self-identify as Hispanic and Mexican origin. The uniquely long history of Mexican migration to the U.S. means those in the third-plus generation cover a heterogeneous range of historical experiences in the U.S. (Jiménez 2010b). Many of the ancestors of older third-plus generation persons lived under colonial or Jim Crow-like conditions, while the offspring of more recent arrivals potentially benefited from the 1964 Civil Rights legislation (Alba and Nee 2003). Such different historical experiences can affect outcomes, with the families of those who arrived a few generations ago more likely entrenched in a cycle of poverty, while the ancestors of those third-generation members who arrived more recently were perhaps better positioned to take advantage of expanding opportunities and to capitalise on schooling (Rosenbaum and Rochford 2008), and thus perhaps more likely to show immigrant optimism (Kao and Tienda 2005, 1995), and to increase the prospects for upward mobility.

The third-plus generation is also subject to selection bias out of later-generation Hispanic/Mexican identity. Ethnic identity becomes increasingly fluid the further one is removed from the immigrant generation (Alba 1990; Waters 1990), making ethnic identification among later-generation Mexican-Americans a more variegated process. Mexican-Americans are a racially diverse group and span the phenotype spectrum from ‘indigenous’ to European characteristics (Jiménez 2010a; Murguia and Forman 2003). Intermarriage further influences the extent to which ethnic self-attrition occurs. The long history of migration from Mexico to the U.S. provides ample opportunities for intermarriage between non-Hispanic whites and those of Mexican origin (Bean and Stevens 2003; Bean and Tienda 1988; Lee and Bean 2010). Moreover, exogamy is selective of women, who are likely to adopt a non-Hispanic surname, and those with higher education (Cazares, Murguia, and Frisbie 1984; Duncan and Trejo 2007; Duncan and Trejo 2011).

Duncan and Trejo (2011, 2007) find that when Mexican females or males are married to non-Mexican spouses, they identify their children as Mexican origin only 64% and 71% of the time, respectively. Furthermore, attrition of a Mexican-American identity occurs more frequently among those with higher levels of education and higher English proficiency (Duncan and Trejo 2007), giving the appearance that integration progress has stalled in remaining third-plus generation respondents. Additionally, ethnic discrimination before 1964 gave the ancestors of the older third-plus generations greater incentive to select out of a Mexican identity if possible. Many of today's ‘true’ third generation have grown up in a time when a Mexican identity would be less of a hindrance for the opportunity and when multiculturalism is more valued than in the past (Alba and Nee 2003; Jiménez 2010b). This provides two potential mechanisms for why the third generation may differ from the fourth-plus generation. The fourth-plus generation may be more likely to reflect the legacies of earlier generations’ preferences for larger family sizes as a result of historical discrimination and limited upward mobility. Also, following the work of Duncan and Trejo, those who comprise the fourth-plus generation are more likely to be affected by selective self-attrition.

3. Data

3.1. IIMMLA data

Data for this study come from the 2004 IIMMLA survey. Los Angeles is a major U.S. immigration hub and has been the main receiving centre for generations of Mexicans (Bean, Brown, and Bachmeier 2015; Grebler, Moore, and Guzman 1970; Telles and Ortiz 2008). The Mexican-origin population comprises nearly six million people in Los Angeles, or about one-third of the metropolitan area's population and gives it, outside of Mexico City, the largest urban Mexican-origin conglomeration in the world (Bean, Brown, and Rumbaut 2006). With so many immigrants and multiple generations of native-born Mexican-Americans, Los Angeles provides an especially important location for studying processes of Mexican-American integration (Bean, Brown, and Bachmeier 2015).

The IIMMLA sample consists of a computer-assisted telephone interview of young adults aged 20–40 years old from multiple immigrant groups, with an oversampling of Mexican-Americans, especially in the second generation (Bean, Brown, and Bachmeier 2010; Bean, Brown, and Rumbaut 2006; Rumbaut, Massey, and Bean 2006). All Mexican-origin respondents were reached through random-digit dialling. To identify national origin, IIMMLA asked respondents about the country of birth as well as their parents’ and grandparents’ countries of birth. Of those initially contacted who were born in the U.S., the survey also asked whether they had any ancestors from outside the U.S. Because the survey obtained information about age-of-arrival in the U.S. among the foreign-born respondents, we distinguish a first generation group from a ‘1.5’ group. The former who came from Mexico at age 15 or older, while the latter arrived before age 15 and thus, were likely to have attended U.S. schools (Rumbaut 2004). The second generation is defined as those who were born in the U.S. with at least one parent born in Mexico. Since being raised in a household with two immigrants or one immigrant and one native may be very different, we also distinguish those with two foreign-born parents and those with one foreign-born and one U.S.-born parent (a 2.5 generation). Such distinctions, which encapsulate varying degrees of U.S. experience among parents, have been shown to matter for integration (Kalmijn 2010; Ramakrishnan 2004).

The third-only generation is defined as those who have two native-born parents and at least one grandparent born in Mexico. A further distinction could also be made based on how many grandparents were born in Mexico, but these groups are unreliably small and in any case show insignificant differences in childbearing between them, so they are included as part of a collective third-only generation measure. The fourth-plus generation consists of those who were born in the U.S. to U.S.-born parents and grandparents and who identify as having any sort of Mexican ancestry. Native-born persons who do not identify as Hispanic and whose parents were native-born, and who identify as white or black, are included in third-plus generation non-Hispanic white and black comparison groups, respectively. The sample consists of 68 first generation respondents, 135 1.5 generation respondents, 302 second-generation respondents, 87 third-generation respondents, 95 fourth-plus generation respondents, 213 black respondents and 200 white respondents. Table 1 compares the generation groups from IIMMLA and the CPS.

Table 1. Mexican-origin generation status definitions.

Generation status	Definitions
Panel A: IIMMLA
1st generation	Born in Mexico and arrived in the U.S. at age 14 or older
1.5 generation	Born in Mexico and arrived in the U.S. at age 13 or younger
2nd generation	Born in the U.S. with 1 or 2 Mexican-born Parents
3rd generation	Born in the U.S. with 2 U.S.-born parents; at least 1 Mexican-born grandparent
4th-plus generation	Born in the U.S. with 2 U.S.-born parents; all 4 grandparents U.S.-born; self-identifies as Mexican
3rd-plus generation	Group composed of aggregated 3rd and ‘4th-plus’ generation
Panel B: CPS
Generation Status	Definitions
1st generation	Born in Mexico and arrived in the U.S. at age 14 or older
1.5 generation	Born in Mexico and arrived in the U.S. at age 13 or younger
2nd generation	Born in the U.S. with 1 or 2 Mexican-born parents
3rd-plus generation	Born in the U.S. with U.S.-born parents; self-identifies as Mexican origin

Source: IIMMLA, 2004, and CPS-LA, June Fertility Supplement, 1998–2010.

3.2. CPS Data

To assess the representativeness of IIMMLA, we draw on the CPS June Fertility Supplement, biennially collected. To increase sample size and limit the effect of yearly fluctuations, we pool samples from 1998 to 2010. While capable of identifying those of Mexican background by a first, 1.5, second and 2.5 generation through respondent nativity, year of arrival and parental nativity, the CPS allows only for a self-identified adult third-plus generation. However, it has a considerable information on the topic of fertility among Mexican-origin females and has been used extensively in past studies (Bean, Swicegood, and Berg 2000; Frank and Heuveline 2005). Non-Hispanic white and black women provide native-born reference groups. The CPS sample is restricted women aged 20–40, the same age window as in IIMMLA.

To ensure equivalent geographies, the CPS data are from to the same five-county LA metro area as IIMMLA and will be referred to below as the CPS-LA subsample. The purpose of the CPS-LA and IIMMLA comparisons is twofold. Although fertility integration appears to stagnate and reverse when using the CPS at the national (Frank and Heuveline 2005; Bean, Swicegood, and Berg 2000) and California (Hill and Johnson 2004) levels, it needs to be established whether LA is exceptional. The CPS-LA data serve to gauge the representativeness of race and generation groups in IIMMLA. This is done to assess whether integration measures in IIMMLA are biased and whether similar patterns appear in other data.

4. Measures

4.1. Dependent variable

The dependent variable of focus is cumulative CEB, or the number of biological children a woman has had. IIMMLA asks whether the respondent is the parent of child/children under age 18 living in the household, and if so, how many. It also asks whether the respondent is the parent of a child under 18 who do not live in the household, and if so, how many. By combining these, we obtain the total number of biological children the respondent has who are under 18 years of age. Limiting the query to children under 18 entails a chance that some of the older respondents may undercount their fertility by omitting offspring who have already reached adulthood. To correct for this, we add an additional child to the fertility count for the 37 cases whose current age and age at first birth indicate a child to be 18 or older. This does not resolve the situation completely, since it is possible respondents had twin births or additional children who are over 18; however, very few cases have censored time frames long enough to make multiple births feasible. It should also be noted that each generation group has roughly the same frequency of respondents for whom this adjustment was needed, with each group having between four and eight respondents who fall into this category.

4.2. Independent variables

Both IIMMLA and the CPS collect information on the respondent's current age, marital status and educational attainment. Since the samples are of women across their reproductive years, controlling for age is necessary. Additionally, because childbearing tapers off at later ages, an age-squared term is included in the CEB regression analyses.

4.2.1. Education

Educational attainment is included in the regressions to adjust for differences in social structural standing. The variable is based on degree attainment and consists of less than high school, high school graduate, vocational training, some college, associate's degree, bachelor's degree, master's or doctoral degree. These have been aggregated into less than high school, high school degree/vocational training, some college/associate's degree, or college degree or more. Because of the non-linear effect of these different thresholds on fertility (Brand and Davis 2011), dummy variables are used. Both surveys also provide currently enrolled school status, which is included as a dummy variable.

4.2.2. Family status

Marital status is based on categories that include single (never married), married, cohabiting, divorced, separated and widowed. Both surveys provide a way to identify cohabiters; IIMMLA directly lists the option as a response to marital status, while the CPS-LA subsample permits identification of households in which a respondent is not currently married and lives with someone in a ‘relationship’. This method of identifying cohabiters in the CPS, however, is known to underestimate the prevalence of cohabitation (Kennedy and Fitch 2012). This disparity is replicated in the present study, with cohabiters accounting for 9% of respondents in IIMMLA, but only slightly more than 1% in the CPS-LA. Divorced, separated and widowed are aggregated into one category. The measures of educational attainment and family characteristics attempt to capture differences in cultural or structural incorporation among the Mexican-origin generation groups, non-Hispanic whites and blacks.

5. Methods

We first present the demographic characteristics of the IIMMLA sample. Next, we estimate a series of negative binomial regressions using county fixed effects to assess whether having an improved third-generation measure influences our understanding of Mexican-fertility integration. County fixed effects are employed to help control for the effects of sorting that may occur due to unobserved characteristics. Negative binomial regression models are conducted on the ordinal CEB measure. The negative binomial distribution is preferred to the Poisson because of potential overdispersion and its predictive accuracy. Specifically, we estimate the following equation:(1) $\text{ln( }\mu )=x_{ij}\beta +{\epsilon }_{ij},$(1) where the log of the mean is assumed to be a linear function of the independent variables, β is a parameter to be estimated for person i in county j and exp(ϵ) is a random error term assumed to have a gamma distribution with a mean of 1 and a variance of α. These estimates predicted conditional childbearing controlling for differences in age and age² (Model 1), education attainment and current school enrolment (Model 2), marital status, number of siblings, spouse characteristics and intermarriage (Model 3), and finally a full model that includes all covariates (Model 4).²

Then, the IIMMLA and the CPS-LA samples are compared to gauge the representativeness of IIMMLA and to assess whether the findings might have broader applicability, which would be doubtful if they were different. In this comparison, cohabitation and never married are combined in IIMMLA due to the limitation of CPS variables available. The surveys are pooled and the variables are compared by race and generation status. Specifically, CEB is examined across surveys by race and generation to assess whether fertility integration patterns in LA are unique from those observed at the nation and state levels (Bean, Swicegood, and Berg 2000; Hill and Johnson 2004; Ellis and Almgren 2009) and whether the groups in IIMMLA, particularly the aggregated ‘third-plus’ generation, are similar to those captured in a nationally representative survey. A different ‘third-plus’ generation could be due to the survey capturing a distinct third generation as a result of using questions on ancestry rather than self-identification. The analyses show if different patterns of intergenerational integration are found when disaggregating the third-only from a ‘fourth-plus’ generation, thus shedding light on how problematic the widespread use of a ‘third-plus’ generation category may be for conclusions about cross-generational integration.

6. Analysis and results

Table 2 presents descriptive information on the IIMMLA data for Mexican-origin females as well as native-born white and black females. For comparison purposes, the 3rd-plus, 3rd-only and 4th-plus generations are included to provide a sense of how different the 3rd-plus and 3rd-only fertility levels are. If no other data than 3rd-plus generation data were available, the descriptive information would be expected to show acculturation and structural integration from the first into the 1.5 and second generations, but little or no difference from the second to the third-plus generation on educational attainment and marital behaviours. Although the 3rd-plus generation sample is slightly older, their average CEB is 1.4, no different from that of the second generation, implying the same degree of integration when using the ‘plus’ measure. However, with the more precisely measured third-only generation, clearer evidence of further integration into the third generation emerges for childbearing, as well as for educational attainment and family characteristics. Although these characteristics do not converge with those of non-Hispanic whites, intergenerational fertility into the third generation declines to 1.2 CEB, as one would expect under cross-generation integration (Alba, Jiménez, and Marrow 2014). Thus, clear evidence emerges that the use of third-plus generation data masks increased integration in childbearing. The disaggregated ‘fourth-plus’ generation shows a notably higher CEB of 1.5 as well as educational attainment and more negative family characteristics. In the fourth-plus generation, low levels of educational attainment and intermarriage, combined with higher fertility, provide evidence of selective attrition. Such a pattern has often previously been interpreted as reflecting lack of integration (Portes, Fernandez-Kelly, and Haller 2009; Telles and Ortiz 2011), but here we see that it is in all likelihood more a consequence of selective attrition (arguably itself an integration process) rather than mobility blockage.

Table 2. Means and proportions for key variables for Mexican-origin, non-Hispanic white and black women in greater Los Angeles, ages 20–40.

Variables	1st gen.	1.5 gen.	2nd gen.	3rd+ gen.	3rd gen.	4th+ gen.	Black	NH White
Number of children	2.2	1.7	1.4	1.4	1.2	1.5	1.5	1.0
Age	31.0	29.1	27.6	29.2	30.2	28.3	30.8	30.7
Education
Less than HS	0.74	0.28	0.11	0.12	0.10	0.13	0.12	0.04
HS/VoTech	0.15	0.32	0.31	0.29	0.24	0.34	0.21	0.15
Some college	0.03	0.27	0.43	0.41	0.46	0.37	0.47	0.36
Bachelor's degree plus	0.09	0.13	0.15	0.18	0.20	0.17	0.21	0.45
Enrolled in school	0.02	0.13	0.17	0.15	0.15	0.15	0.11	0.18
Marital status
Married	0.60	0.45	0.40	0.43	0.44	0.44	0.25	0.45
Divorced	0.09	0.1	0.14	0.12	0.10	0.13	0.15	0.12
Cohabiting	0.13	0.14	0.08	0.11	0.10	0.12	0.06	0.09
Single	0.18	0.3	0.38	0.34	0.36	0.32	0.54	0.36
Intermarried	0.02	0.05	0.07	0.25	0.34	0.17	0.03	0.12
Number of siblings	5.4	4.4	3.8	3.4	3.4	3.3	4.1	2.7
N	68	135	302	157	87	95	200	213

Source: IIMMLA, 2004.

We next present a series of negative binomial regression models comparing fertility across these groups. The aim of the analysis is twofold; first, to view how fertility incorporation differs when a third-plus generation versus a third and fourth-plus generation is available. To highlight this difference, results from models using the disaggregated generation groups are presented, but include a line for the third-plus generation that was taken from parallel models. Although some small variations exist between analyses due to an extra degree of freedom, they are otherwise identical and have no impact on the other groups or the other independent variables. The second goal is to test whether this improved measure leads to evidence of convergence of childbearing behaviours with whites, and, if not, whether this is due to remaining differences in either structural assimilation or acculturation.

Table 3 presents incidence rate ratio coefficients from a series of negative binomial regression on fertility incorporation for IIMMLA. The appropriate interpretation of the IRR coefficient would be, for a coefficient of 1.2, that a one-unit change on that factor yields 20% higher average CEB. The models include, in addition to race, ethnicity and generation status, age and age² (Model 1), educational attainment and current school status (Model 2), marital status and family background characteristics (Model 3) and, finally, these factors together (Model 4) (full regression output provided in Appendix). Model 1 displays how our understanding of fertility incorporation is imprecise when research is limited to using third-plus generation category. Although there is some evidence of converging fertility patterns using the third-plus generation category, with family size differences falling from 116% higher than whites for the first generation to 94% higher for the 1.5 generation, 81% for the second generation and 55% for the third-plus generation (Model 1), once the third-only and the fourth-plus generations are disaggregated, there is evidence of intergenerational progress that would otherwise remain hidden. While third generation Mexicans-Americans have 35% more children than the white reference group, the fourth-plus generation report having 76% more.³ Alternative Model 1 specifications that use the third generation as the reference group shows that such women have significantly lower childbearing than the first, 1.5, second and fourth-plus generations. Despite this additional realised fertility decline, convergence with the third generation and whites is not found in Model 1.

Table 3. Negative binomial regressions of fertility on independent variables, women ages 20–40, in Los Angeles.

	Model 1	Model 2	Model 3	Model 4
Race/generation status
1st generation	2.16**	1.27†	1.62**	1.13
	(0.26)	(0.16)	(0.21)	(0.15)
1.5 generation	1.94**	1.4**	1.52**	1.26*
	(0.21)	(0.15)	(0.18)	(0.14)
2nd generation	1.81**	1.45**	1.53**	1.39**
	(0.18)	(0.14)	(0.16)	(0.14)
3rd-plus generation	1.55**	1.26*	1.35**	1.2†
	(0.16)	(0.13)	(0.15)	(0.12)
3rd generation	1.35*	1.13	1.22	1.09
	(0.18)	(0.15)	(0.16)	(0.14)
4th-plus generation	1.76**	1.38**	1.49**	1.31*
	(0.21)	(0.16)	(0.19)	(0.16)
Non-Hispanic White	Ref.	Ref.	Ref.	Ref.
Black	1.53**	1.27*	1.56**	1.44**
	(0.16)	(0.13)	(0.19)	(0.15)
Additional controls
Age	Y	Y	Y	Y
Educational Attainment	N	Y	N	Y
Currently enrolled in school	N	Y	N	Y
Marital status	N	N	Y	Y
Siblings	N	N	Y	Y
Intermarried	N	N	Y	Y
County fixed effects	Y	Y	Y	Y
Observations	1100	1100	1100	1100
Pseudo R-squared	0.09	0.13	0.13	0.16

Source: IIMMLA, 2004.

*p < .05.

**p < .01.

†p < .10.

Differences in education characteristics (Model 2) account for a large proportion of the differences between white and Mexican or black women. However, a significant difference still remains between the white reference group and the 1.5, second, third-plus and fourth-plus generations along with black women, indicating that factors above and beyond this measure of socioeconomic status are producing high childbearing. The third generation, notably, is no longer significantly different from whites when controlling for education, with only a 13% larger family size, indicating only weak, if any, cultural preferences for larger family sizes. However, when we look at third-plus generation data, we see statistically significantly higher fertility, at 26% above the white reference group. The first generation, as well, is no longer significantly different from whites, but given their low levels of education, with almost 75% of the sample reporting less than a high school education and 15% more reporting only a high school education, controlling for education is bound to have a large impact on their fertility.

Model 3 controls for marital behaviours and family status. The diminished differences between Mexican-origin and white women indicate these factors also contribute to the elevated childbearing of Mexican women, though not for black women, for whom the difference with white women slightly increases (1.53 vs. 1.56). This is to be expected, as Mexican women marry at earlier ages, grow up in larger families, and are less likely to be married to a white partner, all of which are associated with increased family size. These variables have the largest impact among first-generation women, and diminish with each successive generation category. When controlling for marital status and family background, the difference between white and black females changes only marginally. This is due in part to the observed higher levels of black childbearing outside of marriage. The covariates mostly operate in expected ways, although those in cohabiting relationships report roughly identical fertility levels to those of married women.

Model 4 includes controls for both educational attainment and family characteristics. This shows that, despite controlling for education and family status characteristics, the fertility of the 1.5, second and fourth-plus generation, and black women is significantly higher than that of whites. Again, if we were limited to third-plus generation data, we would conclude that the third-plus generation has higher fertility than native-whites; but, with the more accurate measure, we see that the third-only is no different from whites. While the third generation has fertility that is roughly 9% greater than white women, the fourth-plus generation reports fertility that is 31% higher, and this latter figure is significantly different form whites. The intergenerational progress and distinctive childbearing behaviour of Mexican-American women relative to black women do not support segmented assimilation or racialisation perspectives.

6.1. IIMMLA and CPS-LA comparison

Table 4 presents descriptive information comparing the IIMMLA and CPS-LA samples. On the measure of CEB, the race and generation groups compare reasonably well except for the second generation. The third-plus generation in IIMMLA is not significantly different from its CPS-LA counterpart, suggesting the above results are not driven by a biased sample. After controlling for mean age differences between the second and third-plus generations, there is a lack of intergenerational progress and a slight increase in the CEB between second and third-plus generations, as has been found at the national and California state levels (Bean, Swicegood, and Berg 2000; Frank and Heuveline 2005; Telles and Ortiz 2008). The second generation in IIMMLA, however, is slightly biased in respect to its fertility. Additional analyses were undertaken to ascertain whether this was the result of differences in other factors, but the fertility of second-generation IIMMLA respondents remained significantly higher even after controlling for education.

Table 4. Comparison of results for IIMMLA and CPS-LA samples.

		Mexican-origin generation				Black	NH White
		1st	1.5	2nd	3rd-plus
Demographic
Mean children	IIMMLA	2.2	1.7	1.4^a*	1.4	1.5	1.0
Ever born^b	CPS-LA	2.2	1.7	1.1	1.5	1.4	1.0
Mean age^c	IIMMLA	31.0	29.2	27.6	29.2	30.8	30.7
	CPS-LA	31.7	29.7	27.2	29.9	30.1	30.9
Education (proportions)
Less than HS^d	IIMMLA	0.74*	0.28	0.11†	0.12	0.12	0.04
	CPS-LA	0.65	0.33	0.15	0.15	0.10	0.05
HS/VoTech	IIMMLA	0.15	0.32	0.31	0.29	0.21*	0.15*
	CPS-LA	0.23	0.37	0.3	0.34	0.26	0.21
Some College	IIMMLA	0.03†	0.27	0.43	0.41	0.47	0.36
	CPS-LA	0.09	0.22	0.41	0.37	0.43	0.36
Bachelor’s degree	IIMMLA	0.09*	0.13	0.15	0.18	0.21	0.45*
or more	CPS-LA	0.03	0.08	0.14	0.14	0.21	0.38
Family status (proportions)
Married4	IIMMLA	0.60	0.45†	0.40	0.44	0.25	0.45
	CPS-LA	0.70	0.54	0.37	0.46	0.27	0.47
Divorced	IIMMLA	0.09	0.10	0.14*	0.12	0.15	0.12
	CPS-LA	0.08	0.09	0.09	0.1	0.11	0.10
Cohabiting	IIMMLA	0.13	0.14	0.08	0.11	0.06	0.09
	CPS-LA	0.01	0.02	0.01	0.01	0.02	0.01
Single	IIMMLA	0.18	0.30†	0.38*	0.34**	0.55	0.36*
	CPS-LA	0.21	0.36	0.54	0.43	0.61	0.42
Observations	IIMMLA	68	135	302	182	213	200
	CPS-LA	989	317	600	406	385	1505

Source: IIMMLA, 2004, and CPS-LA June Fertility Supplement, 1998–2010.

^aRemains significant even when controlling for differences in marital status.

^bNegative binomial regression; comparisons between surveys include control for age.

^cRobust regression.

^dDifferences estimated using a series of logistic regressions.

*p < .05.

**p < .01.

†p < .10.

That the third-plus generations are similar between samples has certain implications, namely that using ancestry rather than self-identification to identify a third-plus generation does not change the identified sample. Under a strong form of identity out-selection (a fourth-plus measure), it would be expected that those who do not identify as Hispanic and Mexican, and so would not appear in the CPS-LA, might nonetheless have been captured in IIMMLA because of its use of ancestry, as has been the case elsewhere (Emeka and Vallejo 2011; Visser 2014). Since attrition from the sample of people who self-identify as Mexican is selective of more highly educated people, who tend to have fewer children (Duncan and Trejo 2007; Duncan and Trejo 2011), restoring these people to the sample should make the IIMMLA and CPS-LA samples appear similar, and they are. This comparison, of course, cannot measure the pervasiveness of self-attrition, only that using ancestry for the third-plus generation rather than self-identification does not seem to change the captured sample. A second implication is that the results from IIMMLA using an aggregated third-plus generation would be expected to replicate the CPS-LA.

7. Summary

The findings of this paper repeatedly point toward problems in using imprecise third-plus generation measures. If IIMMLA yielded only a third-plus generation measure, and that were all we had used, our findings would have replicated many previous studies and drawn more pessimistic conclusions about integration than seem warranted by the more refined results shown here. With the more precise third-only generation measure, greater convergence on intergenerational fertility emerges. Furthermore, Mexican-American third generation women show childbearing behaviour distinctive from that of blacks. Convergence with whites appears when controlling for differences in either educational attainment or family status, indicating it is social status, rather than mobility blockage, that results in increased childbearing. The emergent pattern of fertility decline points towards the support of an integration rather than a downward assimilation or racialisation model, at least through the third generation.

That the aggregated third-plus generation in IIMMLA compares reasonably well to CPS-LA third-plus generation supports the idea that was an improved third-only measure available in the CPS-LA, the findings from IIMMLA would likely be replicated. This has both theoretical and practical implications. Theoretically, it implies a more positive effect of integration experiences than has been found elsewhere. This calls into question previous negative findings on third generation Mexican-fertility integration, as well as those for other dimensions of incorporation. Although there is an ongoing debate about whether intergenerational mobility or convergence with whites at the third generation represents evidence of assimilation (Alba, Jiménez, and Marrow 2014; Telles and Ortiz 2011), our findings suggest there are substantial mobility and convergence that are often missed because of data aggregated only as a third-plus generation. Practically, current population estimates for Mexicans in LA may be overestimating the future growth of the third generation. Perhaps this would be inconsequential if this group were a small fraction of the Mexican-origin population, but the third-plus generation currently accounts for about 30% of the group, a figure that will only increase as the children of immigrants who arrived in the 1980s and 1990s enter into adulthood and bear the third generation. Accurately measuring this group will become increasingly vital to properly assess demographic outcomes and integration processes.

Though this study improves upon previous ones by relying on more precise questions to identify third-only generation Mexican-American women, some issues remain. Though we have criticised the use of a ‘plus’ generation, we are forced to rely on such an approach to delineate a fourth-plus generation, because so few respondents would know much about their great-grandparents or beyond. This leaves us able only to speculate the cause of the higher fertility found in the fourth-plus generation. Also, though LA has the largest Mexican-origin community in the U.S., and therefore is an important context to study, it may also be unique for the very same reason. Finally, though the IIMMLA and CPS-LA samples are reasonably comparable, the childbearing of the second generation in IIMMLA remains higher than the CPS-LA in a way that is not explained by additional controls.

Ideally, future studies would have more surveys available to them with information on grandparent nativity, theoretically allowing for a greater investigation into the experiences of Mexican-Americans on several dimensions of integration, particularly in more geographic areas and in cases where past research has found stagnation and reversal, including in school behaviour (Ewert 2009), educational attainment (Bean et al. 1994; Perreira, Harris, and Lee 2006), under employment (Slack and Jensen 2007), or incarceration, suicide, drug and alcohol use (Peña et al. 2008). Such data are hard to collect, however, because respondents may not know the birthplaces of grandparents. Studies nonetheless need to consider future potential sources of within-group heterogeneity that might bias results and conclusions (Alba, Jiménez, and Marrow 2014; Aradhya et al. 2016; Aradhya, Scott, and Smith 2017; Jiménez, Fields, and Schachter 2015).

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Christopher D. Smith http://orcid.org/0000-0002-1909-9245

Notes

* A previous version of this paper was presented at the 2012 European Population Association conference in Stockholm, Sweden.

1 Analyses of CPS data focusing on generational patterns of the characteristics of children 17 or under can derive a third-only generation by selecting the children of U.S.-born respondents who have at least one foreign-born parent. This technique works for children's outcomes, as assessed by offspring who remain in the parent's household, and permits cross-generational comparisons (e.g. Jiménez, Park, and Pedroza 2017).

2 We also estimated alternative Poisson and zero-inflated models, and the results were virtually identical across the different approaches. Results available from the authors by request.

3 The reader should note that each column of Table 3 presents results for two regression models together, one containing the third-plus generation measure and the other containing this measure broken into its two parts, one for the third-only group and the other for a fourth-plus group. We present the coefficients for the effects of the three coefficients coming from two separate models in one column in Table 3 both to save space and to make it easier for the reader to compare them.

Appendix Full results from negative binomial regressions of fertility on independent variables, women in Los Angeles, ages 20–40

	Model 1		Model 2		Model 3		Model 4
Race/generation status
1st generation	2.16	**	1.27	†	1.62	**	1.13
	(0.26)		(0.16)		(0.21)		(0.15)
1.5 generation	1.94	**	1.4	**	1.52	**	1.26	*
	(0.21)		(0.15)		(0.18)		(0.14)
2nd generation	1.81	**	1.45	**	1.53	**	1.39	**
	(0.18)		(0.14)		(0.16)		(0.14)
3rd-plus generation	1.55	**	1.26	*	1.35	**	1.20+	†
	(0.16)		(0.13)		(0.15)		(0.12)
3rd generation	1.35	*	1.13		1.22		1.09
	(0.18)		(0.15)		(0.16)		(0.14)
4th-plus generation	1.76	**	1.38	**	1.49	**	1.31	*
	(0.21)		(0.16)		(0.19)		(0.16)
Non-Hispanic white	Ref.		Ref.		Ref.		Ref.
Black	1.53	**	1.27	*	1.56	**	1.44	**
	(0.16)		(0.13)		(0.17)		(0.15)
Age
R’s Age	1.79	**	1.83	**	1.62	**	1.65	**
	(0.11)		(0.11)		(0.1)		(0.1)
Mean-centered Age^2	0.99	**	0.99	**	0.99	**	0.99
	(0.0)		(0.0)		(0.0)		(0.0)
Educational Attainment
Less than HS	-		1.54	**	-		1.54	**
			(0.12)				(0.13)
HS/VoTech	-		1.21	**	-		1.18	*
			(0.08)				(0.08)
Some College/Associates degree	-		Ref.		-		Ref.
Bachelor's degree or more	-		0.61	**	-		0.65	**
			(0.06)				(0.06)
Enrolled in school	-		0.62		-		0.7	*
			(0.11)				(0.11)
Family Background
Married	-		-		Ref.		Ref.
Divorced/separated	-		-		0.86	*	0.84	*
					(0.07)		(0.06)
Cohabiting	-		-		1.06		1.0
					(0.09)		(0.07)
Single	-		-		0.44	**	0.43	**
					(0.04)		(0.04)
Siblings
None	-		-		Ref.		Ref.
One	-		-		1.5	†	1.56	*
					(0.31)		(0.31)
Two	-		-		1.38		1.37
					(0.28)		(0.27)
Three	-		-		1.63	*	1.57	*
					(0.33)		(0.31)
Four or more	-		-		1.79	**	1.6	*
					(0.34)		(0.3)
Intermarried	-		-		0.87		1.0
					(0.09)		(0.1)
Observations	1100		1100		1100		1100
Pseudo R-squared	0.09		0.13		0.13		0.16

Source: IIMMLA, 2004.

^† p < .10.

* p < .05.

** p < .01.