The role of migration on family formation trajectories Evidence from - - PDF document

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The role of migration on family formation trajectories

Evidence from the United States Andrés Felipe Castro Torres1 Ph.D. candidate in Demography & Sociology University of Pennsylvania

1 Introduction

Understanding differences in demographic outcomes across migration status groups is a pressing demand for contemporary societies. Even if migration rates level off in the near future, current stocks of migrant populations will be of significant relevance in shaping contemporary societies. One overlooked dimension of migrant’s characteristics is their trajectories of family formation and dissolution. While the timing and level of family formation events–e.g. fertility rates and ages at first birth and marriage–have received considerable attention in the migration literature, the full trajectory of family formation and dissolution events among migrants has not been studied. Insofar as the family was a fundamental institution for modern societies during the 20th century and has remained as such in the run of the 21st, understanding its pat- terns of formation and dissolution is a key question for sociological research. More so when it comes to understand the connection between social stratification system, family formation pathways and how migrant populations are (or are not) affected by this con-

• nection. The patterns of household formation and childbearing are correlated with the

structure of social stratification systems in a two-way relationships. Differential access to services, information and opportunities lead to divergent outcomes in the timing and prevalence of family formation and dissolution events. Moreover, these differences have been found to contribute sustaining socioeconomic difference across certain categories of people (McLanahan & Percheski 2008, McLanahan 2009, Greil et al. 2011).

1Contact: candres@sas.upenn.edu

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The family experienced fundamental changes during the second half of the 20th cen- tury within countries of the Americas (Furstenberg 2014). First, there has been an overall delay in the transitions to the first birth and the first marriage along with increases in the prevalence of cohabitation (Hayford et al. 2014, Pesando et al. 2016). Second, in- creasing marital instability has lead to larger variability in the unfolding of individual’s life-course after the first transitions (Cherlin 2005). Third, substantial differences be- tween socioeconomic status groups in the patterns and the timing of family formation have increased (Furstenberg 2008). All these changes interact with the diversification of migration streams to the US during the second half of the 20th century (Organization of American States 2011). This papers is an attempt to look jointly at these three processes by comparing the sequences of family formation/dissolution events of two ten-year birth cohorts of US-born and foreign born women; and their associations with socioeconomic characteristics. Differences across different migration status on fertility and marriage outcomes has been largely studied (Parrado 2015). Yet, few studies have looked at full trajectories of family formation and dissolution events. A family formation trajectory (FFT) is under- stood as the whole set of births, marriages and marriage dissolution that happen to woman during her life. Under this perspective the focus changes from the timing to first-events to life trajectories which seldom constitute the conceptual unit of analysis in demographic research (Billari 2001). This paper explores how migrants’ FFT differ from those of the native-born population in the US from three perspectives. First, it assess the overall level of heterogeneity in FFT

• ver age across three populations: native-born women, foreign born women and foreign

born women who arrived to the US after age fifteen. Second, it clusters FFT trajectories within each population to describe the patterns of childbearing and family formation in each group. Third, it compares the associations between socioeconomic and demographic characteristics and the clusters of FFT in the three populations.

2 Theoretical background

The diversification of migration streams all over the world has translated into substantial heterogeneity in family and fertility outcomes among immigrant populations (Kulu & Milewski 2007, Kulu & Hannemann 2016). Racial, ethnic and socioeconomic disparities in the timing of childbearing are reinforced by these demographic dynamics in virtually all developed countries (Frejka & Sardon 2006, Sullivan 2005). Yet, no assessment of 2

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the variability after the first transition (to parenthood and to partner-hood) has been conducted in a comparative way between migrant and non-migrants. Since the classical study of Goldberg (1953) on fertility and internal migration in the UK, several studies have tested competing hypothesis about the relationship between migration and fertility for different countries. These studies include the US (Parrado & Morgan 2008, Parrado 2011), Canada (Adserà & Ferrer 2014), Spain (Castro-Martín & Rosero-Bixby 2011), Italy (Mussino & Strozza 2012), France (Toulemon & Mazuy 2004), the United Kingdom (Dubuc 2012, Robards & Berrington 2015), Germany (Mayer & Riphahn 2000, Schmid & Kohls 2009, Milewski 2010), Sweden (Andersson 2004) and Es- tonia (Kulu 2005). Results are mixed in terms of the magnitude and the direction of the association between the migration experience and fertility; both aspects (magnitude and direction) are found to depend at least on the context of reception, the country

• f origin and the age at migration. Despite these mixed results, negative and positive

correlations between migration and fertility seem to be the consequence of the tempo- ral disruption caused by the migration experience, i.e. the fundamental changes that happen to immigrant’s life-courses before, during and after migration. These changes include modifications of the fertility/marriage schedule due to the absence of the partner (Lindstrom & Saucedo 2002). Most of the research in this area focuses on the timing of the first birth/marriage or

• n age-specific fertility rates comparing foreign-born and native-born women. However,

individuals’ lives include more than one event and the accumulation of these events is the basis of aggregate demographic dynamics such as complete fertility, marriage prevalence and marriage stability (Ryder 1965). The complete history of births, unions and disso- lutions constitutes an important unit of analysis in order to understand the connection between migration and fertility/family outcomes. As argued by Billari (2001) ’[...] by focusing on the time-to-event, researchers may miss a general overview of life-courses, thus failing to adopt a ’holistic’ perspective that sees life courses as one meaningful con- ceptual unit’ (p. 440). This is not to say that ’time-to-event’ approaches are inherently wrong, but to emphasize the complementarity of trajectory-based approaches as posited by Aisenbrey & Fasang (2010). Studying family/fertility outcomes among migrant populations has several method-

• logical challenges. They are mostly related with the difficulty of identifying a proper

counter-factual for migrant women and with the bias associated with period indicators that do not account for the age at migration (Toulemon & Mazuy 2004, Parrado 2011). From a technical point of view, conditioning on migration to study subsequent events may 3

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underestimate the prevalence before the move (Hoem 2014). A cohort approach avoids potential biases of period and time-to-event approaches for two reasons. First, measures of cohort fertility do not suffer from period bias. Second, by taking the complete sequence of events it is possible to study conditions before and after

• migration. In addition, it provides a complete picture of the life-course of cohorts and

its relationship with aggregate demographic outcomes. Hence, the study of the complete spell of individuals’ events over their reproductive ages constitutes an innovate approach to understand family formation differentials. This approach has been proved useful to understand labor market events as well a many other questions of sociological interest (Abbot 1995, Pailhe et al. 2013, Fasang & Raab 2014). In sum, a comparison of cohorts’ trajectories of marital status and fertility can im- prove our understanding of the association between migration and the dynamics of family

• formation. Focusing on cohorts’ trajectories can help us reconcile the mixed results the

literature has produced so far and provide a holistic understanding of both individual behavior and aggregate demographic outcomes.

3 Methods

This paper uses three statistical techniques: (1) sequence analysis (SA), cluster analysis (CA) and multinomial logistic models (MLM). SA techniques are use to measure dis- similarity levels across individual trajectories of family formation. Hierarchical cluster tecniques are used to identify typical trajectories of family formation and dissolution. Fi- nally, MLM are used to examine the associations between socioeconomic characteristics and the typical family pathways derived from the cluster analysis. 3.1 Sequence Analysis To compare sequence of categorical states (e.g. single, married, divorced) it is neces- sary to measure the dissimilarity between pairs of sequences. A measure based on the comparison of sequences’ features is typically used to assess between-sequences proxim- ity/similarity. As complex objects, sequences can be compared in several dimensions. In the social sciences, there are at least five aspects in which sequences can be compared: (1) experienced states (including features to account for the relative proximity between states), (2) distribution of the states, (3) timing of events, (4) duration of states and (5) sequencing (Studer & Ritschard 2016b). There is not distance measure that can account for all the dimensions simultaneously. Typically, distance measures neglect one aspect 4

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when fully account for another. Researchers need to select one approach based on the research question of interest. Perhaps because of the relatively recent application of SA to sociological research, there are both skepticism on its usefulness (Wu 2000) and optimism on its future development and potential contributions (Abbot & Tsay 2000, Aisenbrey & Fasang 2010, Fasang & Liao 2014, Aisenbrey & Fasang 2017). Most of the criticism against SA have been focused on the use of Optimal Matching (OM) to construct distance measures. Classic OM techniques do not account for four out of five socially meaningful aspects in which sequence can be

• compared. Moreover, OM requires the definition of substitution-, deletion- and insertion-

costs (often termed as edit-operation costs), which do not have a meaningful sociological interpretation by themselves (Elzinga & Studer 2015). Despite these critiques, most of the initial studies that used SA relied on OM to measure dissimilarity among sequences. In response to these critiques, recent studies have developed alternative ways for computing distance measures that are more sensitive to the five aspects and do not depend on edit

• perations (see Studer & Ritschard (2014) for an overview of distance measures). These

studies have provided three important improvements. First, alternative OM-based distance measures have been proposed to better account for the timing of events by using age-specific information (Lesnard 2010). Coined as dynamic Hamming matching (HAM), this particular OM variant is highly sensitive to the timing of the event as the edit-operation costs are based on age-specific transition

• matrices. This variant is particularly appealing to study family formation events as the

timing of events is a crucial–not unique–feature of family dynamics. Second, they have introduced a sub-sequence-based distance measure that incorpo- rates: differences in the sequencing of the events (i.e. the order in which events take place

• ver the life-course), the timing and the duration of the events (i.e. when do events take

place and how long do individual remain in a given state), and the potential proximity between states (i.e. the fact that some states can be similar to others). The general approach proposed by these authors is called Sub-sequence Vector Representation (SVR) (Elzinga & Studer 2015). SVR measures are more sensitive to the ordering of the events than to their timing. Third, these studies have conducted simulations to assess the sensitivity of different distance measures to the above mentioned five aspects. Results from these studies show the high level of flexibility of both OM-based (including HAM) and SVR approaches with respect to alternative distance measures (Studer & Ritschard 2016b). Yet, the criticism against OM on the lack of sociological sense of edit-operation costs remains. 5

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As an emerging/alternative technique SA requires somehow validation before their results can be fully considered as evidence of social dynamics with some explanatory

• power. Concerns about the validity of SA arise from the fact that the researcher has

to select a metric and the parameters associated to it. This selection could seem rather arbitrary as it does not depend on the nature of the variable–like in the case of regression

• analysis. To overcome this issue I will use two different approaches. most of the time I

will present results based on the HAM distance as it became obvious, at some point, that giving more weight to the timing of the events leads to more homogeneous cluster with a more direct sociological meaning than the clusters derived from the SVR approach. 3.1.1 Distance measures The two approaches to measure between-sequences distances are: the dynamic Hamming matching (HAM) based on age-specific transition matrices, and a SVR-based metric with a between-state similarity matrix calculate from overall transitions rates. Under a HAM approach, the distance between two sequences is proportional to the effort necessary to transform one sequence into another. Sequence’s transformation is performed via three fundamental edit operations: substitution, deletion and insertion. Each of these operations has an associated cost and the sum of all cost involved in the transformation of one sequence into another constitute the total transformation cost. The lower the total transformation cost the higher the similarity/proximity between a pair of

• trajectories. As all sequences in this paper have the same length, there is no need for

deletion and insertion costs. Substitution costs are based on age-specific transition probabilities. The substitution cost between two different states i and j is inversely related to the observed transition probability as presented in equation 1. SCa(i, j) = c − [p(Sa = i|Xa−1 = j) + p(St = j|St−1 = i)] (1) SCa(i, j) stands for the substitution cost between states i and j at age a (a = 15, 16, . . . , 39), S represents a random variable for the states of the sequence and c is a constant with the upper bound for the costs (i.e. the substitution cost for two states with zero observed transitions). I set c = 2 as the theoretical maximum value for each transition probability is one. Comparative studies have shown that, in the absence of deletion and insertion cost, results are robust to the selection of c (Robette & Bry 2012). This set of matrices is used to compute the minimum total transformation cost for 6

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each pair of sequences in the sample. All minimum costs are organized in a matrix which is called distance or dissimilarity matrix. Under a SVR approach the distance between a pair of sequences depends on the number (and length) of common sub-sequences. A sub-sequence is any sequence of equal

• r shorter length than the sequences in the analysis. Each sequence is represented as a
• vector. The positions of the vector correspond to all possible sub-sequences, from those of

length one (single states) to full sequences (sequence of the same length of the sequences in the analysis). For instance, in a sequence with three states (a, b, c) the set of all possible sub- sequences is: (a, b, c, aa, bb, cc, ab, ac, bc, ba, ca, cb, abc, cba, bac, cab, acb, bca). To construct the sub-sequence vector representation of a given sequence, a value of one is assigned to the vector’s position if the sub-sequence in that position is present in the sequence and zero is assigned otherwise. The sub-sequence vector representation X and Y of the sequences S1 = ab and S2 = bc are display in table 1. TABLE 1 AROUND HERE The binary representation for the presence of a sub-sequence can be extended to ac- count for the number of times a sub-sequence appear within a sequences and for the length

• f the sub-sequence. Typically, short sub-sequences such as those of length one can be

disregarded as they may be consider as of little influence in individuals’ life course. When sequences are represented in this way, equation 2 can be used to count the number sub- sequences that are unique to each sequence. This number can be taken as a dissimilarity measure. d(X, Y ) =

• i

|xi − yi|2

• = X′(M)X + Y ′(M)Y − 2X′(M)Y

(2) Where d is the dissimilarity between the sequences represented by vectors X and Y , i is a index for the vector positions and M is a squared matrix for between states similarities (Studer et al. 2011). Hence, an SVR distance measure requires two parameters. First, a function that weights shared spells based on their length. Second, a states’ proximity matrix, i.e. a matrix which entries are proportional to the similarity between all the states of the sequence. The logic behind first parameter is that a pair of sequences that share the same state during ten years are more similar than a pair of sequences that share the same state during 7

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less than ten years. Moreover, in some contexts, sharing a state for a very short time can be unimportant; for example, in contexts of low prevalence of cohabitation, short spells of

• ne year of cohabitation before marriage can be disregarded as they do not translate into

fundamental changes in individuals’ family trajectories. These two features are achieved by using a concave function as in equation 3 L(a) = (a − k − 1)p (3) L represents the weighted level of similarity associated to a shared spell of length a, k represents the minimum length of the spells that are included in the measurement, and p a factor to give more weight to longer spells (p > 0). For this paper I selected k = 2, i.e. I did not include spells of length one, and p = 2. As for the states’ proximity matrix, I use the between-state transition rates as a measure of between-state similarity. This approach has two important advantages. First, it accounts for the most neglected dimension of similarity between sequences, i.e. the fact that some states are closer to others. Second, it depends on the data since it is derived from transitions rates. In contrast to the use of transitions rates to determine edit-operation costs, the use of transitions rates as measures of states’ proximity have a sociological sense in the context of family formation events. Higher transitions rates from cohabitation to marriage than from cohabitation to divorce (indeed, by definition this latter transitions are null) signal the higher proximity between cohabitation and marriage than between cohabitation and divorce. Hence, two distance matrices are computed in this paper: one using the HAM approach with age-specific transition probabilities. Another one using and SVR approach with the two parameters explained above. I use the library seqdistOO from the R package to construct the sequences and compute the distance matrices (Studer & Ritschard 2016a). These two matrices constitute the main input for both the discrepancy analysis and the cluster analysis. 3.1.2 Discrepancy analysis of state sequences Discrepancy is a measure of between-individual variability in the sequence states. If all women are in the same state in given age range (say, 15 to 19) discrepancy will be zero. Conversely, if women experience divergent states over this time window (e.g. some get married, have a child, start cohabiting, etc.) discrepancy will increase. As the SVR distance measure I used includes a set of parameters for states’ similarity, lower 8

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discrepancy levels can also be associated to women experiencing similar states. In short, age specific discrepancy levels reflect how divergent are family formation events in a window time (four years in this case). Studer et al. (2011) proposed a framework to assess discrepancy levels across sub- populations (defined by categorical variables) inspired in the principles of the classic Analysis of Variance (ANOVA). These authors show that the fundamental decomposition

• f the total sum of squares into between- and within-sum of squares in ANOVA, holds

for distance matrices. Hence, three statistics can be computed to assess the level of association (pseudo − F), the proportion of explained discrepancy (pseudo − R2) and the the level of homogeneity (Levene − like) across the categories of a nominal variable (e.g. race/ethnicity, migration status, educational attainment, etc.). The statistical significance

• f these three quantities can be assessed via permutation tests. These three statistics can

be computed for specific window-times over age. Hence it is possible to evaluate how they vary over the life course. Additionally, authors extended the bivariate ANOVA to a multifactor ANOVA that allows to evaluate the simultaneously more than one categorical variable. These proce- dures were implemented using the library TraMineR of the R package (Studer & Ritschard 2016b). 3.2 Cluster analysis Clusters were identified using agglomerative hierarchical clustering (HC) implemented in the R package WeightedCluster (Studer 2013)2. I preferred this technique over non- hierarchical clustering for three reasons. First, hierarchical clustering does not require the specification of the number of groups, i.e. the researcher can select the number of groups based on the clustering structure of the data. Second, hierarchical clustering permits the construction of classifications threes which permit the comparisons of clustering structure across sub-populations (native-born vs foreign-born). Third, hierarchical clustering tend to be more stable as it does not depend on initial conditions. I used the a pseudo−R2 to measure the proportion of the discrepancy explained by the clusters as a measure for the goodness of the clustering (Studer et al. 2011). The marginal increase of this quantity serves to set a cutoff point in the selection of the numbers of groups to analyze. Given that the SVR metric includes more features than the HAM metric, it is expected that the pseudo − R2 for clusters based on the SVR metric would be lower than the pseudo − R2 for clusters based on the HAM.

2Specifically I used the function hclust using Ward’s methods

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3.3 Explanatory variables of multinomial logistic models I use multinomial logistic models to correlate typical trajectories of family formation with socioeconomic characteristic. These models predict the likelihood of belonging to one specific trajectory with respect to the reference cluster. The reference cluster was chosen based on two interrelated criteria. First, the reference cluster represents the normative condition for the oldest birth cohort in the sample–e.g. fertility around 2 children per woman along with ordered transitions (first marriage then childbearing) and low preva- lence of marital dissolution. Second, the reference cluster ought to be among the largest clusters–i.e. it should represent the most common family pathway among the oldest co-

• hort. Consequently, the odds ratios from the multinominal models can be interpreted as

deviations from a normative/majority-type family pathway. MLM were used only among two sub-populations: native-born women and immigrant women (as defined above). The reference cluster for each sub-population will be fully described in the results section. All models were fitted using replicated weights to account for the sampling design. I used the library survey from the R package (Lumley 2004, 2010) to set the sampling design and computed the replicated weights, and the function multinom from the library nnet to fit the multinomial models (Venables & Ripley 2002). Next subsection describes the rational for variable selection and the hypothesis associated to them. 3.3.1 Timing of education Using retrospective information on the dates of graduation from high school and college I constructed two categorical variables that reflect the timing of educational attainment. The first category of both variables includes women who did not graduate from high school and did not graduate from college, respectively. The second category includes women who graduated ’on time’, that is, below a normative age. For high school graduation I choose 20 years and for college I choose 24 years. Finally, all women obtaining each degree after these two ages were grouped in the last category. The second category of these two variable was selected as the reference category for the MLM. This category represents the ’normative’ timing of an educational pathway. Hence, the odds ratios can be interpreted in terms of factors contributing to deviation from a standard/normative life course. I expect to find strong associations between non- normative educational pathways and non-normative family pathways. 10

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3.3.2 Race and ethnicity I rely on the racial and ethnic classification provided by the NSFG. This survey distin- guishes four racial/ethnic categories: Non-Hispanic White (NH White), Non-Hispanic Black (NH Black), Hispanic and Non-Hispanic Other. The reference group for this variable was NH White as they represent the majority

• f the population in the US. This is not the case among foreign-born women, yet for

comparability purpose I kept the same reference group in both populations. I expect to find strong and statistically significant coefficients for racial/ethnic groups among the native-born women. These coefficients should be consistent with the literature

• n the prevalence and timing of family formation events by race, and their association with

inequalities in socioeconomic conditions across these groups. For foreign-born women, I expect to find weaker–and non-statistically significant associations–between race/ethnicity and family pathways. 3.3.3 Religion and birth cohort These two variables account for the family background and the macro-conditions in which women lived during their reproductive ages. For religion, the category Protestant was selected as the reference category following a similar rational as for the timing of education and race and ethnicity, i.e. the normative and most-prevalent category among the oldest

• cohort. Teh other categories for religion are: Non-religious, Catholic and Other.

Based on their year of birth women were grouped into two birth cohorts. The first one includes women that were born between 1950 and 1959 (1950-60) and the second women includes women that were born between 1960 and 1975 (1960-75). Sample size prevents me from further disaggregation. Hence, all these variable permits me to assess the associations between socioeconomic and family background characteristics and typical family formation pathways. The selec- tion of reference categories as explained above allows me to interpret the odds ratios from MLM as the likelihood of deviating from a standard-normative trajectory taken from the

• ldest cohort.

4 Data

I use five waves of the National Survey of Family Growth (NSFG) from 1995 to 2013-

• 15. The NSFG is a national representative survey that collects retrospective information

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• n marriages, marriage dissolution, fertility and education among other aspects. This

particular feature makes the NSFG an ideal source to study individual life-courses. It

• versampled Black and Hispanic women in the more recent waves which provides a fairly

large number of observations of foreign born women. I restricted the sample to women age 39 and above in order to reconstruct the sequence of live births, unions, marriages and marriage-dissolution from age 15 to age 39. Women in this analytical sample were born between 1950 and 1975. Table 2 displays the sample sizes by race/ethnicity, migration status and birth cohort. All the analysis were conducted separately for native-born and foreign-born women. TABLE 2 AROUND HERE I use the age at migration to analyze subgroups of foreign-born women typically distin- guished in the migration literature. The 1.5 generation (1.5-gen, henceforth) are foreign- born women who arrived to the US before age 15. Women who arrived to the US after this age are considered as immigrants. The guiding hypothesis for this distinction is that the association between socioeconomic conditions and family pathways is stronger among native-born women compared to foreign-born. Moreover, I expect the strength of the association to be weaker among immigrant women. To reconstruct the sequence of events I use the reported dates for the first cohabitation, all live births, all marriages and all marriage dissolution. I recoded marital status into five categories (single, cohabiting, married, separated and remarried). Parities of three children and more were collapsed into one single category (3+). Hence, the sequences

• f family pathways have 20 possible states, I refer to these 20 states as the alphabet of

the sequence. Figure 8 displays the first ten sequences from the data set. Five colors are used to differentiate marital status while the intensity of the color serves to differentiate parity levels as recommended by Fasang & Liao (2014). Even thought births, marriages and divorces can be observed after age 39, more than 95% of these events occurred before this age which makes me confident about the consistency of the results. Note that event though in sequences number eight and ten in figure 8 women have a similar age at first birth (19 and 18 respectively) and similar complete fertility (3+), they display divergent trajectories of family pathways. Sequence number eight displays three years of single motherhood between ages 19 and 21 followed by seven years of marriage, a second child at age 23 (within the marriage), then a separation at age 29 along with a third

• child. In contrast, sequence number ten display no single motherhood; instead, the first

birth and the first marriage happened at the same time (age 18). This woman separated 12

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when she was 25 and she got remarried at age 31, finally at age 35 this woman had a third child. This example reflects the potential of studying sequences as a complement to the study the timing of first marriage and birth. To be sure sequences of family formation trajectories are much more complex than transition-ages and consequently our explanatory power will be lower. Among the 6,315 native-born women there were 5,023 unique sequences of family

• pathways. Among the 267 1.5-gen women and the 989 immigrant women there were 250

and 903 unique sequences, respectively. All sequences have the same length (25 years) and appropriated sample weights were used in all the analysis. Standard errors were estimated using the sample design of the NSFG with standardized weights.

5 Results

5.1 Lower discrepancy levels among immigrant women Discrepancy levels on family pathways increase linearly over age until the early twenties for all three migration status groups (refer to Figure 8). After age 20 discrepancy levels

• ff and remains flat at least until age 35 the last age for which discrepancy levels are

computed in this study. Noticeably, discrepancy levels for women who migrated after age 15 are lower than those of native-born women at all ages. 1.5-gen women 15 display intermediate discrepancy levels. The lower discrepancy levels among migrant women cpmared to the native-born women

• ver the life course are associated with two different dynamics. First, between ages 15

and 25, lower discrepancy is associated with the higher proportion of single and child- less women among immigrants than among native-born. Second, after the late twenties discrepancy among native-born women slightly increases due to the increase in the pro- portion of separated and remarried women. In contrast, separation and remarriage are less prevalent among migrant women. In other words, marital stability among migrant women contributes to the homogeneity of family pathways after age 25 (refer to figure 9 in the Appendix). This shifting dynamic is captured by the pseudo − R2 which peaks at age 18, then decreases until age 25 and increases onwards towards it highest level at age 35. FIGURE 8 AROUND HERE Among native-born women differences in discrepancy levels between NH White women and all other racial/ethnic groups are concentrated between ages 15 and 25. After age 13

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25, all racial/ethnic groups display similar discrepancy levels. Moreover, within each racial/ethnic group discrepancy levels are associated with different dynamics. Increas- ing discrepancy levels among NH Black women before age 25 are associated with early marriage and cohabitation along with a high prevalence of single motherhood. After age 25 the prevalence of single motherhood stabilizes but the proportion of separated women increases steadily. Among Hispanic women discrepancy grows rapidly between age 15 and 25 due to early transitions to marriage and first birth. After age 25 the increasing preva- lence of separation keeps discrepancy flat among Hispanic women. For NH white women discrepancy levels increase more slowly over age than in other racial/ethnic groups. Be- fore age 25, slow growth in discrepancy levels is associated with delayed transitions to marriage and motherhood. After age 25, discrepancy levels grow faster among NH white women than among other groups mainly because of the increasing prevalence of remar-

• riage. Discrepancy levels for women classified as NH Other resemble those of Hispanic

women except that they display a higher prevalence of single motherhood (refer to Figure 9 in the Appendix). The right panel in figure 8 confirms that discrepancy levels among immigrant women are lower than those of native-born women at all ages for all racial/ethnic groups. Three additional aspects of the racial/ethnic disparities in discrepancy levels among immigrant women are worth to mention. First, discrepancy increases over age among immigrant women at a lower pace compared to native-born. Second, racial disparities are larger among immigrant than among native-born women (higher pseudo−R2). Third, compared to native-born women, discrepancy levels among immigrants are much lower at ages before the mean at at migration. At least three explanations can be offered for these differences in discrepancy levels by migration status. First, higher homogeneity among immigrants can be associated to selection into emigration, i.e. people who decided to migrate have similar marital and fertility preferences. Second, selection into return migration, i.e. those with divergent– relative to the context of reception–family preferences are more likely to return. Third, the migration experience disrupts individuals’ lives leading to a delay in the transitions to marriage and first birth. Delayed transitions then translate into less time to experience diverse family states (remarriage and children within a second marriage). Given the nature of the data at hand, none of these explanation can be directly proven. 14

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5.2 School timing and the weakening of background characteristics among immigrants Despite the higher levels of homogeneity in family pathways among immigrants, the ex- planatory power of socioeconomic variables on their family trajectories is lower than on native-born’s trajectories. Table 3 displays the pseudo − R2 along with the p-value for the pseudo − F test of a multifactor analysis applied to the distance matrices of different population sub-groups. TABLE 3 AROUND HERE The total proportion of explained discrepancy varies by migration status, while the full model explains 1.8% of the dissimilarity among native-born women, it explains 2.9 and 3.4% among foreign-born women and women who migrated after age 15, respec-

• tively. Among these two sub-population groups, the full mode includes non-statistically

significant terms. Race/ethnicity and education are significantly associated with family trajectories for all three sub-groups. However, neither religion nor birth cohort are significantly associated with family trajectories among foreign born women and women who migrated after age

• 15. Noticeably, the significance level of race/ethnicity is marginal among women who

migrated after age 15 (p-value=0.065). In demonstrating a weakening of the association between family formation and both religion and birth cohort these results suggest the potential disruptive nature of the migration experience. 5.3 Typical trajectories of family formation and dissolution Table 4 and 5 show the proportion of explained discrepancy for different numbers of groups for native-born women and foreign-born women, respectively. For comparative purposes these proportion were computed using both metrics SVR and HAM. TABLE 4 AROUND HERE I decided to analyze nine clusters of family pathways for three reasons. First, the proportion of explained discrepancy by this number of groups largely surpasses the pro- portion of explained discrepancy in the multifactor models for both native- and foreign- born women. Whereas multifactor models explain less than 4% of the total discrepancy in all cases, nine clusters explain more than 15% of the total dissimlarity. These propor- tions must be evaluated in relative terms depending on the complexity (i.e. the number 15

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• f sequence’s aspects included in the distance measure) of the metric. The SVR met-

rics implemented here accounts for more aspects than the HAM; hence the proportion of explained discrepancy must be higher for the HAM metric than for SVR given a fixed number of groups. TABLE 5 AROUND HERE Second, the marginal increase in the explained dissimilarity rapidly diminish below 10% after eight clusters which implies little gains by selecting more than nine clusters. Third, given sample sizes more than nine groups will affect the statistical power of sub- sequent analysis, in particular the multinomial models (refer to figure 9 in the Appendix for a graphic comparison of the clustering structure derived from both distance measures by migration status and race/ethnicity). Among native-born women, similar fertility levels can be associated with divergent dynamics in terms of family formation and dissolution. The nine typical trajectories of family formation among native-born women comprise five fertility levels from childless women to women with an average of 3.5 children ever born (refer to figure 8. Fertility levels below one are associated with two divergent dynamics, one of high marital stability (C2) and the other one of virtually no marital stability (C3). By age 39 all women in cluster 3 are either separated of remarried. Both clusters are characterized by the late

• nset of childbearing.

TABLE 8 AROUND HERE Fertility levels of around one child are associated with high marital stability and a wide range in the age at first marriage. Average fertility levels are linked to two different marital dynamics: marital stability (C5) and marital instability along with a high prevalence of remarriage (C6). All women in cluster 6 separated at some point, half of them remarried and the other half stayed single. A particular group of women with slightly above fertility level (C7) is characterized by the early and high prevalence of single motherhood. Finally, fertility levels above three children per women have also a divergent dynamic in terms of marital stability. Most of the women in cluster 8 are married by age 25 and they stay married until age 39. Some of the nine typical family pathways among immigrants resemble those of the native born women. Some other, instead, have no equivalent cluster among the native- born population. The index plots for these nine trajectories are displayed in figure 8. There is no cluster of childless women among the foreign-born who migrated after age 15. 16

SLIDE 17

The lowest fertility level among foreign born women occurs in cluster 1. It is associated with a late onset of cohabitation followed by marriage (bottom part of the index plot) and early onset of single motherhood (top part of the index plot). Even though there is a cluster with a similar fertility level among native-born women (C2), its characteristics do not resemble that of C1 among foreign-born women. While low fertility among native-born women occurs in context of universal marriage, among foreign-born women low fertility seems to be associated with low prevalence and late marriage. Fertility levels around one child per woman are both associated with marital stability among foreign-born women (C2 and C3). Two fundamental distinctions lay behind this similar fertility level. First, transitions to marriage and childbearing occurs, on average, six years later among women in cluster 2 compared to women in cluster 3. Second, only 64% of women in cluster 2 had a children whereas all women in cluster 3 have at least

• ne child.

Three different clusters among native born women have close-to-average fertility levels. These three clusters differ in the timing of the transitions, the order between the first birth and the first marriage and the prevalence/stability of the marriages. In C4 the first child

• ccurs within marriage at relatively late ages. In contrast, the first child tends to happen

before marriage among women in cluster 5. Moreover, the prevalence of marriage is lower among women in C5 compared to women in C4 and C6. Finally, women in C6 get married and have the first child earlier in life and their marriages are stable. Whereas the main distinction between the two clusters of average fertility among native-born women was marriage stability, among foreign-born women the timing of events adds one important distinction. Clusters 7, 8 and 9 are somehow unique as they have different fertility levels. Tran- sitions to first birth, marriage and marriage dissolution occur early in life among women in cluster 7. Additionally, among women in C7 all first marriages ended up dissolved, and 64% of these women remarried. There is no comparable cluster to C7 among the native-born women. In contrast, C8 among foreign-born women is similar to C8 among the native-born population. Rapid transitions to higher parity levels within stable mar- riages characterize women’s family pathways in this group. Finally, the highest fertility level is observed in cluster 9. Women in this cluster have the lowest mean ages at first marriage and first birth. 34% of the marriages of these women ended up dissolved, and none o them remarried. 17

SLIDE 18

5.4 Relatively stable fertility, delayed transitions and changes/divergence in family path- ways Small differences in complete fertility and the timing of family formation events across migration status groups contrast with the diversity of family pathways and the differences in the predictive power of socioeconomic factors. Table 8 presents the summary of two different models predicting three outcomes. The first model has the interaction between birth cohort and place of birth. The second model interacts the birth cohort with the migration status distinguishing women who migrated before and after age 15. The three predicted outcomes are: children ever born (CEB), age at first birth (AFB) and age at first marriage (AFM). TABLE 8 AROUND HERE Across the two birth cohorts of native born women, complete fertility has remained constant at levels around two children per woman. As for foreign-born women, fertility declined over the two cohorts. Immigrant women born between 1950-60 had on average 0.4 more children more than native-born women of the same birth cohort (reference group). In contrast, complete fertility among younger immigrant women (1960-75 birth cohort) is not statistically different from that of the 1950-60 native-born cohort. For the age at first birth, the younger cohort of native-born women had the first kid, on average, one year later than native-born women from the first cohort (reference group). None of the two cohorts of foreign-born women had a statistically significant difference in the mean age at first birth with respect to the reference group. Similarly– compared to the 1950-60 birth cohort of native-born women–the age at first marriage

• nly differ for the second cohort of native-born women, who got married two years later,
• n average. Together these results point to stable fertility levels, delayed transitions and

small differences among migration status groups. Yet, family formation pathway differ

• vastly. This result can be further described by taking complete fertility as a weighted

average of complete fertility across the clusters of family formation. Tables 6 and 7 display the distribution of women across the clusters of family formation trajectories by birth cohort for native-born and foreign-born women respectively. For native-born women, the largest increase in the share of women across cohorts

• ccurred in cluster 7. Women in this cluster tend to get married after the first birth

for which this cluster constitute a non-normative sequence of family formation events. Instead, a normative sequence of family formation events is depicted by cluster 5 which have the largest share of women among the 1950-60 birth cohort. It is precisely this cluster 18

SLIDE 19

the one that experienced the largest decline in the share of women. Together, these two changes are consistent with previous studies on the weakening of the traditional family. As for the other positive changes, cluster 2 excel by its 36% increase in the proportion

• f women among the second cohort of study. This clusters constitute the modal state

among the 1960-75 birth cohort which is consistent with previous studies on the delaying

• f transitions to childbearing and marriage among younger people.

Despite the high prevalence of marriage and marriage stability in this cluster, only 43% of the women had at least one child. Finally, cluster 4 also grew across cohorts. Two main aspects distinguish this cluster from cluster 2: earlier marriage and higher prevalence of childbearing. Yet complete fertility among these women is below the average, for which the contribution of this group to aggregate fertility is negative. Hence, based on the largest absolute changes in women distribution across cohorts, stable complete fertility among native-born women seems to be associated with increas- ing divergence on family formation trajectories in three complementary ways. First, im- portant increases in above-average fertility groups characterized for single motherhood. Second, declining prevalence of average fertility levels among traditional-stable families, and third increasing prevalence of trajectories with delayed transitions to childbearing and marriage along with low fertility levels. For women who migrated after age 15 stability in complete fertility levels is linked to different dynamics compared to those occurring among native-born women. The largest absolute decrease and increase in cluster’s size occurred in clusters of slightly above- average fertility (C5 and C6). Cluster 5 became the modal trajectory among the younger cohort, whereas cluster 6 became a one of the smallest clusters among the same group of

• women. In contrast to native-born women, the traditional-stable family trajectory (two

children within marriage) became more prevalent among immigrant women. This changes are reinforced by the 27% increase in size in cluster 4 which is also characterized by stable marriage, yet with a higher mean age at first birth and first marriage than women in cluster 6. Cluster with above-fertility levels either decreased in size (C7 and C9) or remained stable (C8). Clusters with around one child per woman experienced the smallest changes in terms of size across the two cohorts. Finally, cluster 1–the cluster with the lowest fertility among immigrant women– grew 32% which contributed to keep fertility at average levels over time. Hence, based on the largest absolute changes in clusters’ sizes across cohorts of foreign born women, stable complete fertility in this population is associated with a concentration 19

SLIDE 20

• f women in trajectories that led to average fertility levels (C4 and C5). Changes in

clusters with high and low fertility are smaller and balance each other out. 5.5 Multinomial-logistic models predicting the clusters For the native-born population cluster number 5 was selected as the reference catego- ryAmong foreign-born women, these two criteria do not align. The largest cluster in the 19650-60 birth cohort (C8, 16% of women) displays above-average fertility (3.5 children per woman). The second largest cluster (C6, 15.3%) displays, instead, close to average fertility (2.3 children per woman) and high marital stability. Given the small difference in the proportion of women in the 1950-60 birth cohort between these two clusters, C6 was chosen as the reference group for the immigrant population. 5.5.1 Native-born women All clusters of family pathways among native-born women display statistically significant associations with socieconomic and demographic variables (refer to table 9). TABLE 9 AROUND HERE The cluster of childless and unmarried women is negatively associated with not having bachelor degree (0.44). In other words, family pathways characterized by sporadic and non-permanent cohabitation spells over the life course are more common among educated women than among women without bachelor degree. Hispanic women are more likely to be in this cluster compared to NH White women. In terms of religion, this cluster seems to be uncommon among protestant women; instead catholic women and women from other religions are 1.7 and 7.7 times more likely to follow this path, respectively. Low fertility pathways (C2 and C3) are positively associated with delayed acquisition

• f bachelor degree (After 24). Yet, women without bachelor are less likely to follow C2

trajectory and are more likely to follow C3. The main difference between these two tra- jectories are the prevalence of marital dissolution and remarriage along with the timing of family formation events. While only 19% of women in C2 experienced marital dissolution and 5% of them remarried afterward; almost all women in C3 were separated or divorced by age 35 (98%); 75% of these women went into a second marriage. In sum, family path- ways of delayed transitions, stable marriages and low fertility are more common among educated women. In contrast, early transitions, unstable marriages and low fertility are more likely to be followed by women without bachelor degree. 20

SLIDE 21

Compared to NH white women, Hispanic women are less likely ’to deviate’ from the normative pattern of family formation and follow low-fertility pathways. Instead, NH Black women are 2.1 times more likely than NH Whites to be in cluster 2. As for reli- gion, all religion groups are positively associated with C2 and C3. These association are stronger among cluster 2, especially among non-religious women and women who classified themselves in the category ’Other’. As for cluster 1 to 3 (below average fertility), women without bachelor degree are less likely to be in C4 than women who graduated from college before age 24. Compared to NH White women, Hispanic women and NH Black women are less and more likely to be in cluster 4, respectively. All religion categories different from Protestant are positively associated with this cluster. Deviations from average fertility levels within stable marriages (C5) to average fertility levels within unstable marriages and high prevalence of remarriage (C6) are positively associated with not having a bachelor degree and pertaining to the NH Other racial

• group. Catholic women are less likely to pertain to cluster 6 compared to protestant

women. Cluster 7–slightly above average fertility levels and high prevalence of single motherhood–displays similar associations as those observed for C6-women in terms of education and race/ethnicity. NH Other women and women without bachelor degree are more likely to follow this pattern. In terms of religion, women form all religious groups are more likely to follow C7-pattern than protestant women. For the two clusters of high fertility (C8 and C9), associations with with the timing

• f education diverge. In the case of C8 both not having a BA degree and getting a BA

degree after age 24, make women less likely to pertain to this cluster. In contrast, these two associations are positive and greater for C9. Yet, only the coefficient for not having a BA degree is statistically significant. As for the clusters of low fertility and average fertility, education is positively associated with of marital stability (C2, C5 and C8). In terms of racial/ethnic groups, Hispanic women are more likely to follow both pat- terns of high fertility. Only non-religious women and women of other religions are more likely to be in the last cluster. The fact that all coefficients associated with the younger cohort (1960-75) are positive (six are statistically significant) signals the increasing divergence in family pathways across

• cohorts. In other words, all ’non-normative’ clusters are more prevalent than C5 among

youngest women of this study. 21

SLIDE 22

5.5.2 Immigrant women Table 9 display a summary of the multinomial model for immigrant women. Among this population, not having a BA degree is associated with a lower probability of following all

• f the three trajectories of below-average fertility (C1 to C3). Yet, this association is not

statistically significant for cluster 3. There are not statistically significant associations between racial groups and low-fertility clusters of family trajectories, except for cluster 3. Compared to NH White women, Hispanic women are morel likely to pertain to cluster 3. As for religion, only two associations are statistically significant. Catholic women are less likely to be in cluster 1 and women of other religion are less likely to be in cluster 2. TABLE 10 AROUND HERE Deviations from the normative trajectory of family formation among immigrant women with average fertility levels are represented in clusters 4 and 5. C4-women differ from the normative trajectory because they experience delayed transitions to marriage (on average six years later than women in cluster 6) and to childbearing (on average, seven years later than C6-women). Women without BA degree are less likely to belong to this cluster, whereas Hispanic and NH Other women are more likely to pertain to this group, compared to NH White women. There seems to be no statistically significant associations among religious groups and this cluster. Women from C5 are instead characterized by a lower marriage prevalence along with a high prevalence of single motherhood, compared to C6. Being in this clusters is nega- tively associated with graduating from college after age 24 and being catholic. No other socioeconomic characteristic is significantly correlated with the likelihood of being in this particular cluster. For clusters of above-average fertility there are almost none statistically significant associations between the clusters of family formation trajectories and socioeconomic vari-

• ables. Only NH-Other women are more likely to pertain to cluster 9. This lack of associ-

ations along with lower heterogeneity support the hypothesis of the migration experience as capable of weaken the links between family pathway and socioeconomic conditions. the estimated coefficients for the younger cohort are all positive and most of them sta- tistically significant (five out of seven). These results suggest–as for native-born women– an increase in the diversification of family trajectories from the normative pattern in the 1950-60 birth cohort. 22

SLIDE 23

6 Conclusions

At the aggregate level, family formation trajectories among immigrant women are less heterogeneous than those of the native born population over the whole life course. This finding contrasts with the higher level heterogeneity observed among migrants in other dimensions/behaviors. It is expected that a pool of women from different countries, who have migrated for multiple reasons to a new place, with or without their families, were much more heterogeneous compared to individuals in the host society. This does not seems to be the case for the trajectories of family formation and family dissolution. This phenomena is observed starting at age 20, i.e. four years below the median age at migration, and remained until age 39. Hence, mechanisms of selection into migration and conditions in the context of reception seem to be at play in reducing FFT’s heterogeneity. More generally, to the extent that social expectations on the timing of FFT’s events exist in both host- and origin- societies, a time-consuming (disruptive) experience such as the migration experience, can only reduce heterogeneity, as individuals engaged in such experience had less time and opportunity to make choices. This could happen either by anticipation –if individuals knew they wanted to migrate and therefore accelerated their FFT; or afterward, once they have migrated and need to cope with social expectations. Noticeably, this results does not seems to be driven by the fact that Hispanic women constitute the large majority of the immigrant women studied in this paper. Indeed, among immigrant women, Hispanic ones display the highest heterogeneity, yet lower than that of the native-born. The associations between FFTs and socioeconomic and demographic characteristics are weaker among immigrant women than among native-born. In other words, the role of the social stratification systems (the joint distribution of SES characteristics associated with women’s position in the US society) in shaping FFTs differ by migration status. The patterns of FFT among foreign-born women in general are less affected by these

• characteristics. Less so are the FFTs of immigrant women as defined here–women who

migrated after age 15. These results support the socialization hypothesis that states that early processes of socialization within the family and the cultural environment in the country of origin are more relevant in shaping family outcomes among the first generation

• f migrants. Among the same cohorts in Latin American societies cohabitation was more

prevalent than in the US; similarly, marriage was more stable and the role of religion seemed to be less determinant for family pathways than it is for US-born and 1.5-gen women. Yet, this is just an speculation given that this paper did not examine FFTs 23

SLIDE 24

among women in the origin countries. A fundamental exception for this weakening of the association between FFT and SES variables is the timing of education. The strong and statistically significant association between the timing of getting a high school and BA degree and family pathways is consis- tent across the three sub-populations–native-born, 1.5-gen and immigrant women. Since the association holds for both 1.5-gen and immigrant women, the place of obtaining the BA degree seems less important than the mere fact of spending time going to school. Noticeably, FFT are less homogeneous among highly educated women which is consistent with the secondary-socialization (after the family) role of the educational system. The process of clustering family formation trajectories by migration status reveals substantial differences between the two populations: native-born and immigrant women. Several unique family formation pattern were identified among native-born women with-

• ut having a correspondent one among immigrant women. Permanent celibacy and child-

lessness was a pattern among native born women, and it was not found among the foreign

• born. Similarly, below-average-fertility, average-fertility and above-average-fertility lev-

els among native-born women occur among women with stable and unstable marriages; these six patterns emerged as typical trajectories of FFT in this population. In contrast,

• nly above-average fertility levels are associated with marital instability among immigrant
• women. Finally, single-motherhood appears to be a typical trajectory only among native

born women. As for the immigrant women, a pattern of either delayed or early transitions to first marriage and first birth, along with rapid transitions to higher order births in stable marriages, was observed in a unique way among this population. Another key difference refers to the overall higher fertility among the foreign born population across the four fertility regimes that this research found. This difference is compensated by the distribution of women over fertility regimes, which leads to similar aggregate levels of fertility across the two population. Moreover, the stability of complete fertility levels over time also finds an explanation in the changes of these marginal distri-

• butions. However, this explanation varies by migration status. Among immigrant women,

fertility remained constant across cohorts due to an increase in the share of women in low- and average-fertility regimes; along with a decreased in the share of women in high fertility

• regimes. Among the native born population, complete fertility remained constant mainly

due an increase in the proportion of women in slightly-above-average and below-average fertility regimes compensated by a decrease in the two groups if higher fertility. Despite stability of complete fertility around two children per woman over time and 24

SLIDE 25

across migration-status groups, the dynamics of family formation trajectories differ across cohorts and by nativity status. In other words, aggregate reproduction levels are constant despite changes and differences in FFT over time and across populations. I termed this phenomena relative independence–similarity in differences. This relative independence does not imply that these two phenomena are unrelated. On the contrary, evidence presented here suggests the necessity of studying these demographic processes jointly. Within each cluster of FFT, fertility and marriage dynamics were closely tied; it is the changes in the distribution of women over cluster what have preserved fertility in the above mentioned level. In a multivariate framework the predictive power of socioeconomic variables (except for the timing of educational attainment) on FFT is higher among the native born pop- ulation as compared to immigrant women. The well-documented protective associations

• f religion and race on marital stability are observed among native-born women.

In- stead, among foreign born, the relationship between these two variables and FFT is not straightforward. The importance of identifying similarities and differences on FFT across population and individuals relies on the fact that the accumulation of events (multiple marriages and/or multiples births) or the permanency within steady states (durable marriages or low parity levels) over the life-course can have divergent implications for both men and women forming families and for their offspring. This is an area that requires both theoretical and methodological development as the complexity of individual life-courses has proven to be higher than the conceptual and methodological tools at hand. Moreover, this research has also shows the limitation of an immigration perspective, that is, the inherent limitation of looking a FFTs among the selected women that stayed in the US. Looking at the same cohort of women who returned to their countries of origin and women who did not migrated, is a pressing necessity to improve our understanding

• f the meaning of the findings presented here.

25

SLIDE 26

7 Tables

26

SLIDE 27

Table 1: Sub-sequence vector representation for two sequences

Sequence a b c aa bb cc ab ac bc ba ca cb abc cba bac cab acb bca S1 = X 1 1 1 S2 = Y 1 1 1

27

SLIDE 28

Table 2: Sample size by race/ethnicity, migration status and birth cohort for women ages 39 and above - NSFG 1995-2015

Race/ Migration status ethnicity Native-born Migrated <15 Migrated <15 Total Birth cohort 1950-60 1960-75 1950-60 1960-75 1950-60 1960-75 NH White 1724 2517 42 44 36 82 4445 Hispanic 147 390 30 91 142 440 1240 NH Black 572 814 7 17 29 79 1518 NH Other 40 107 3 32 50 130 362 Total 2483 3828 82 184 257 731 7565

28

SLIDE 29

Table 3: Summary measures for a multifactor ANOVA for the SVR distance measure by migration status

Native-born Foreign-born Age.Mig>15 Variable F R2 p-value F R2 p-value F R2 p-value Race/ethnicity 0.144 0.006 0.000 0.015 0.007 0.036 0.007 0.009 0.065 Bachelor degree 0.252 0.007 0.000 0.021 0.007 0.001 0.012 0.009 0.001 Religion 0.066 0.003 0.000 0.013 0.006 0.138 0.006 0.006 0.547 Birth cohort 0.093 0.001 0.000 0.007 0.001 0.996 0.003 0.001 0.993 Total 0.145 0.018 0.000 0.021 0.029 0.000 0.010 0.034 0.000

29

SLIDE 30

Table 4: Proportion of explained dissimilarity for different numbers of clusters among native-born women by race/ethnicity using two distance measures

Number of Native-born NH white NH Black Hispanic clusters SVR HAM SVR HAM SVR HAM SVR HAM 4 0.139 0.184 0.165 0.193 0.091 0.180 0.113 0.179 5 0.162 0.222 0.193 0.229 0.108 0.218 0.128 0.215 6 0.178 0.249 0.208 0.261 0.124 0.253 0.158 0.251 7 0.190 0.272 0.228 0.286 0.139 0.283 0.172 0.279 8 0.206 0.295 0.244 0.308 0.150 0.310 0.190 0.301 9 0.223 0.319 0.260 0.329 0.161 0.336 0.209 0.325 10 0.237 0.337 0.273 0.349 0.172 0.355 0.232 0.348 11 0.248 0.353 0.287 0.368 0.183 0.370 0.242 0.366 12 0.259 0.367 0.299 0.385 0.194 0.386 0.258 0.383

30

SLIDE 31

Table 5: Proportion of explained dissimilarity for different numbers of clusters among foreign-born women by race/ethnicity using two distance measures

Number of Foreign-born NH white NH Black Hispanic clusters SVR HAM SVR HAM SVR HAM SVR HAM 4 0.208 0.194 0.182 0.236 0.180 0.212 0.192 0.197 5 0.235 0.234 0.242 0.282 0.232 0.255 0.220 0.231 6 0.255 0.262 0.274 0.319 0.270 0.288 0.240 0.263 7 0.277 0.288 0.297 0.348 0.298 0.322 0.259 0.289 8 0.297 0.310 0.322 0.370 0.326 0.350 0.275 0.304 9 0.314 0.332 0.344 0.392 0.351 0.378 0.293 0.323 10 0.327 0.348 0.365 0.414 0.369 0.404 0.303 0.340 11 0.336 0.366 0.385 0.432 0.398 0.426 0.314 0.352 12 0.347 0.379 0.406 0.450 0.420 0.447 0.324 0.364

31

SLIDE 32

Table 6: Marginal distribution for clusters of family formation trajectories by birth cohort

Birth cohort Absolute Relative Cluster 1950-60 1960-75 change change C1-0 6.6 6.5

• 0.1

0.98 C2-0.7 11.6 15.8 4.2 1.36 C3-0.9 13.4 10.4

• 3.0

0.78 C4-1.6 11.5 13.5 2.0 1.17 C5-2 16.8 11.4

• 5.4

0.68 C6-2.1 11.1 9.1

• 2.0

0.82 C7-2.6 6.6 13.4 6.8 2.03 C8-3.6 13.5 12.1

• 1.4

0.90 C9-3.6 9.0 7.8

• 1.2

0.87

32

SLIDE 33

Table 7: Marginal distribution for clusters of family formation trajectories by birth cohort

Birth cohort Absolute Relative Cluster 1950-60 1960-75 change change C1-0.6 6.5 8.6 2.1 1.32 C2-1.1 10.3 11.0 0.7 1.07 C3-1.2 7.4 7.2

• 0.2

0.97 C4-2.1 8.1 10.2 2.2 1.27 C5-2.2 12.0 19.2 7.2 1.60 C6-2.3 15.3 7.3

• 8.0

0.48 C7-2.9 13.2 12.0

• 1.2

0.91 C8-3.5 16.0 16.0

• 0.0

1.00 C9-4.4 11.1 8.5

• 2.6

0.77

33

SLIDE 34

Table 8: OLS estimates for prevalence and timing of family formation events

CEB AFB AFM CEB AFB AFM Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 1960-75 0.042 1.107∗∗∗ 2.076∗∗∗ 0.043 1.080∗∗∗ 2.063∗∗∗ (0.038) (0.214) (0.411) (0.037) (0.216) (0.411) Foreign born 0.386∗ 0.666 0.497 (0.144) (0.466) (0.430) 1960-75:Foreign born −0.020 −0.368 0.010 (0.172) (0.712) (0.658) AgeMig<15 −0.024 0.015 −0.192 (0.154) (0.692) (0.615) AgeMig>15 0.539∗∗ 0.674 0.570 (0.161) (0.412) (0.521) 1960-75:AgeMig<15 0.207 −0.559 0.589 (0.151) (0.862) (1.084) 1960-75:AgeMig>15 −0.111 −0.112 −0.012 (0.193) (0.694) (0.742) Constant 1.876∗∗∗ 23.555∗∗∗ 22.112∗∗∗ 1.875∗∗∗ 23.573∗∗∗ 22.123∗∗∗ (0.027) (0.116) (0.279) (0.026) (0.118) (0.279) N 7,565 6,127 6,279 7,565 6,127 6,279 Log Likelihood −14,612.440 −20,813.710 −20,788.900 −14,605.140 −20,811.170 −20,788.590 AIC 29,232.880 41,635.420 41,585.800 29,222.270 41,634.340 41,589.180

∗p < .05; ∗∗p < .01; ∗∗∗p < .001

34

SLIDE 35

Table 9: Summary of multinomial logistic model on family formation trajec- tories of native-born women (Ref: Cluster 5-2.0)

Covariate C1-0 C2-0.7 C3-0.9 C4-1.6 C6-2.1 C7-2.6 C8-3.6 C9-3.6 Bachelor degree (Before 24) No BA degree 0.44

∗∗∗

0.42

∗∗

1.50

∗

0.43

∗∗∗

3.64

∗∗

3.01

∗∗∗

0.98

∗∗

11.86

∗∗∗

After 24 1.84 2.14

∗∗

2.27

∗∗

1.11 3.32 3.11 0.88

∗∗

2.88 Race/ethnicity (NH White) Hispanic 1.72

∗∗∗

0.80

∗∗

0.85

∗

0.84

∗∗∗

2.22 2.98 2.36

∗∗∗

2.15

∗

NH Black 5.01 2.14

∗∗∗

1.45 1.29

∗∗∗

1.84 15.34 2.58 3.94 NH Other 2.24 0.98 0.39 1.08 1.10

∗∗

5.40

∗∗

0.79 2.02 Religion (Protestant) No religion 4.93 3.01

∗∗∗

1.86

∗

1.85

∗

1.59 2.38

∗∗∗

0.99

∗∗∗

1.87

∗∗∗

Catholic 1.71

∗∗∗

1.72

∗∗∗

1.06

∗∗∗

1.22

∗∗∗

0.68

∗∗∗

1.69

∗∗∗

1.06 0.88 Other 7.68

∗

5.55

∗∗

3.68 2.38 1.74 2.92

∗∗∗

4.73 3.98

∗∗∗

Birth cohort (1950-1960) 1960-75 1.09

∗∗∗

1.64

∗∗∗

1.05

∗∗∗

1.50

∗∗∗

1.13

∗∗∗

2.88 1.24

∗∗∗

1.18

35

SLIDE 36

Table 10: Summary of multinomial logistic model on family formation trajec- toris of foreign-born women (Ref: Cluster 5-2.0)

Covariate C1-0.6 C2-1.1 C3-1.2 C4-2.1 C5-2.2 C7-2.9 C8-3.5 C9-4.4 Bachelor degree (Before 24) No BA degree 0.14

∗∗

0.20

∗∗

0.16 0.31

∗∗∗

0.70 2.69 0.82 4.91 After 24 0.22 0.34

∗

0.16 0.61 0.44

∗∗

1.93 0.48 0.08 Race/ethnicity (NH White) Hispanic 1.69 0.85 2.18

∗∗

1.03

∗∗∗

3.78 5.36 1.53 4.33 NH Black 18.80 8.25 3.65 5.52 22.38 29.01 5.33 6.96 NH Other 2.18 2.38 2.22 1.18

∗∗

2.37 1.37 2.13 1.16

∗∗

Religion (Protestant) No religion 1.08 2.88 2.21 1.06 0.81 1.46 0.67 0.08 Catholic 0.81

∗∗∗

1.46 0.71 1.24 0.55

∗∗

1.37 1.20 0.78 Other 0.27 0.80

∗∗∗

0.47 0.36 0.48 0.21 0.33 0.02 Birth cohort (1950-1960) 1960-75 2.49

∗∗∗

2.00

∗∗

1.86

∗∗∗

3.01 2.63

∗∗∗

1.93 2.20

∗∗∗

1.58

36

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8 Figures

Figure 1: Ten family formation pathways from the National Survey of Family Growth

Age 15 17 19 21 23 25 27 29 31 33 35 37 39 2 3 4 5 6 7 8 9 10

20−State alphabet of family pathways Single−0 Single−1 Single−2 Single−3+ Cohabiting−0 Cohabiting−1 Cohabiting−2 Cohabiting−3+ Married−0 Married−1 Married−2 Married−3+ Remarried−0 Remarried−1 Remarried−2 Remarried−3+ Separated−0 Separated−1 Separated−2 Separated−3+

37

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Figure 2: Discrepancy levels and proportion of explained discrepancy over age by migration status and racial/ethnic groups

15 20 25 30 35 0.0 0.1 0.2 0.3 0.4 0.5

Age Discrepancy

Migration status AgeMig<15 AgeMig>15

• US. born

R2 0.0000 0.0010 0.0020 0.0030 15 20 25 30 35 0.0 0.1 0.2 0.3 0.4 0.5

Age

Native−born Hispanic NH White NH Black NH Other R2 0.000 0.005 0.010 0.015 0.020 15 20 25 30 35 0.0 0.1 0.2 0.3 0.4 0.5

Age

Foreign−born Hispanic NH White NH Black NH Other R2 0.00 0.01 0.02 0.03 0.04 0.05

pseudo−R2

38

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Figure 3: Cumulative proportion of women by state of family formation tra- jectory over age by cluster - Native-born women

C1−0

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C2−0.7

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C3−0.9

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C4−1.6

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C5−2

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C6−2.1

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C7−2.6

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C8−3.6

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C9−3.6

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

39

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Figure 4: Cumulative proportion of women by state of family formation tra- jectory over age by cluster - Women who migrated after age 15

C1−0.6

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C2−1.1

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C3−1.2

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C4−2.1

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C5−2.2

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C6−2.3

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C7−2.9

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C8−3.5

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

C9−4.4

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

40

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9 Appendix

Figure 5: Marginal distribution of family states over age by migration status

• US. born

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

AgeMig<15

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

AgeMig>15

Age Proportion 15 17 19 21 23 25 27 29 31 33 35 37 39 0.0 0.2 0.4 0.6 0.8 1.0

41

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Figure 6: Marginal distribution of family states over age by race/ethnicity among native-born women

NH White

Age Proportion 15 18 21 24 27 30 33 36 39 0.0 0.2 0.4 0.6 0.8 1.0

Hispanic

Age Proportion 15 18 21 24 27 30 33 36 39 0.0 0.2 0.4 0.6 0.8 1.0

NH Black

Age Proportion 15 18 21 24 27 30 33 36 39 0.0 0.2 0.4 0.6 0.8 1.0

NH Other

Age Proportion 15 18 21 24 27 30 33 36 39 0.0 0.2 0.4 0.6 0.8 1.0

42

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Figure 7: Marginal distribution of family states over age by race/ethnicity among foreign-born women

NH White

Age Proportion 15 18 21 24 27 30 33 36 39 0.0 0.2 0.4 0.6 0.8 1.0

Hispanic

Age Proportion 15 18 21 24 27 30 33 36 39 0.0 0.2 0.4 0.6 0.8 1.0

NH Black

Age Proportion 15 18 21 24 27 30 33 36 39 0.0 0.2 0.4 0.6 0.8 1.0

NH Other

Age Proportion 15 18 21 24 27 30 33 36 39 0.0 0.2 0.4 0.6 0.8 1.0

43

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Figure 8: Proportion of explained discrepancy (R@) and marginal in increase in R2 for different number of clusters by migration status and race/ethnic groups

10 20 30 40 50 0.0 0.2 0.4 0.6 0.8 Numbers of groups Pseudo−R2 Distance metric SVR HAM 10 20 30 40 50 0.0 0.1 0.2 0.3 0.4 Numbers of groups Marginal increase in R2 Native−born NH White NH Black Hispanic NH Other 10 20 30 40 50 0.0 0.2 0.4 0.6 0.8 Numbers of groups Pseudo−R2 Distance metric SVR HAM 10 20 30 40 50 0.0 0.1 0.2 0.3 0.4 Numbers of groups Marginal increase in R2 Foreign−born NH White NH Black Hispanic NH Other

44

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Table 11: Timing and prevalence of family formation events by clusters - Native born women

Cluster Children Mean age at first Percent ever experiencing ever born Birth Marriage Divorce Divorce Marriage Birth Remarriage C1 0.01 39.4 39.6 39.5 0.3 11.2 0.7 0.0 C2 0.70 34.7 30.0 36.3 18.9 92.4 43.5 4.8 C3 0.92 26.1 21.2 25.6 98.6 100.0 70.9 72.3 C4 1.62 29.1 25.0 36.7 19.3 100.0 100.0 4.8 C5 2.02 23.6 21.4 38.3 9.1 100.0 100.0 1.6 C6 2.08 21.2 19.9 26.0 100.0 100.0 100.0 68.1 C7 2.56 21.4 30.0 32.6 28.4 46.2 100.0 16.2 C8 3.56 22.1 22.2 38.0 14.8 100.0 100.0 1.5 C9 3.58 18.4 18.8 25.5 100.0 100.0 100.0 64.4

45

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Cluster Children Mean age at first Percent ever experiencing ever born Birth Marriage Divorce Divorce Marriage Birth Remarriage C1 0.63 36.1 36.7 38.5 6.6 52.3 47.3 1.6 C2 1.05 33.8 29.1 37.2 10.6 100.0 64.2 2.4 C3 1.19 27.0 23.8 39.5 16.1 100.0 100.0 0.6 C4 2.06 28.4 25.8 39.1 12.1 100.0 100.0 0.0 C5- 2.16 24.8 27.7 29.8 46.6 69.2 94.9 34.7 C6 2.25 21.4 20.2 38.5 13.1 100.0 100.0 6.1 C7 2.93 20.2 19.4 26.2 100.0 100.0 100.0 64.8 C8 3.54 24.0 23.3 38.4 14.7 100.0 100.0 2.8 C9 4.41 18.4 19.9 35.8 36.4 100.0 100.0 10.2

Table 12: Age migration > 15 46

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