## Abstract

Recent decades have seen a significant decline in mid-pregnancy (“shotgun”) marriage, particularly among disadvantaged groups, which has contributed to increasing nonmarital birth rates. Despite public and political concern about this shift, the implications for parenting and child well-being are not known. Drawing on a sample of U.S. black and white mothers with nonmarital conceptions from the NLSY79, our study fills this gap. Using propensity score techniques to address concerns about selection bias, we found that mid-pregnancy marriages were associated with slightly better parenting quality relative to remaining single, although effect sizes were small and limited to marriages that remained intact at the time of child assessment. Mid-pregnancy marriages were not associated with improved children’s behavior or cognitive ability. These findings suggest that the retreat from mid-pregnancy marriage may contribute to increasing inequality in parenting resources for children.

## Introduction

In previous decades, nonmarital pregnancies in the United States were relatively common, yet nonmarital births were rare because of the normative expectation that unmarried pregnant couples would marry before the birth (Ellwood and Jencks 2004). Following Gibson-Davis et al. (2015), we adopt the terminology “mid-pregnancy marriages” to reference those marriages formed after conception but prior to birth. This norm has weakened over time, and mid-pregnancy marriages have declined sharply in recent decades. In the early 1960s, 60 % of women with nonmarital pregnancies married before the birth of their first child. By 2006–2010, only 5 % of single, noncohabiting, pregnant women entered into such marriages (Lichter et al. 2014).1 Declines in mid-pregnancy marriage are concentrated among historically disadvantaged populations, including women with low education and those who are black (England et al. 2013; Gibson-Davis and Rackin 2014). Indeed, qualitative research has suggested that many low- to moderate-income couples do not think that a nonmarital pregnancy is a sufficient reason to marry (Edin and Kefalas 2005; Sassler and Cunningham 2008). The shift away from mid-pregnancy marriage, which has contributed to increases in nonmarital birth rates (England et al. 2013; Zavodny 1999), is one example of the weakening link between marriage and childbearing.

The retreat from mid-pregnancy marriage has generated public and political nostalgia for norms about “legitimating” nonmarital pregnancies, partly because of an assumption that this type of marriage is beneficial for children. Given evidence that children living with both biological married parents fare better than children in other family structures (Amato 2005; McLanahan 2004; McLanahan and Sandefur 1994), some researchers and policymakers have inferred that marriage has a causal relationship with parenting and child well-being (Nock 2005) and that mid-pregnancy marriage will similarly benefit children.

This assumption is reflected in recent policy initiatives endorsing marriage as an effective strategy for improving the lives of economically disadvantaged single mothers and their children. For example, in 2010, Congress voted to provide \$75 million for eight healthy marriage promotion activities (U.S. Department of Health and Human Services 2014). One major initiative was the Building Strong Families program, which is a relationship skills program for low-income unmarried couples who had a baby within the past three months or who are expecting a baby (Brown 2010; Wood et al. 2014), thus (in the latter case) targeting couples who could potentially form mid-pregnancy marriages. Results from a random-assignment evaluation of this program, however, showed that the program had no effect on the likelihood that couples stayed together or got married (Wood et al. 2014).

Despite general consensus regarding the positive association between marriage and child well-being, disagreement remains as to whether the relationship is causal. Married-parent families differ from other family types in numerous ways, including educational and financial resources; and those selection factors, rather than marriage itself, may influence parenting behaviors and child well-being. Given that people who enter into mid-pregnancy marriages tend to have lower education and lower income than parents who married before conceiving a child (Zavodny 1999), it is possible that mid-pregnancy marriage itself does not benefit children.

Alternatively, marriage may be causally linked to parenting and child well-being but only for those with characteristics associated with selection into marriage, such as higher socioeconomic status (SES). In other words, the relationship may be causal via selection (Osborne and Palmo 2009), and the benefits of marriage may be differentially distributed according to these characteristics. For example, couples with high income and education may choose to marry in anticipation that pooling resources will amplify their advantages relative to not being married. Couples with lower SES may be unlikely to benefit from marriage if they do not have sufficient resources to share: marrying an unemployed partner is unlikely to stabilize a family’s financial resources. Thus, mid-pregnancy marriage possibly benefits only those more-advantaged couples whose characteristics also make them more likely to marry. Indeed, Ryan (2012) found that the benefits of marital birth for children’s cognitive development held only for those whose fathers’ human capital characteristics were associated with a high propensity to marry in the first place. Although that study considered the benefit of marital births, the current analysis focuses on the potential benefits of mid-pregnancy marriage.

The current study is the first to examine the implications for children of the demographic and normative shift away from mid-pregnancy marriages by evaluating the relationship among mid-pregnancy marriage, parenting quality, and child well-being. In doing so, we make three key contributions to the literature. First, scholarly research has overlooked the potentially unique role of mid-pregnancy marriage for children. If mid-pregnancy marriage predicts improved parenting and child outcomes relative to remaining single, decreasing rates of mid-pregnancy marriage among historically disadvantaged parents could amplify social inequality, thereby contributing to the increasingly diverging destinies of children from different social classes (McLanahan 2004). On the other hand, if mid-pregnancy marriages do not predict such outcomes, the decline in these relationships may not be cause for concern.

Second, we use propensity score techniques to account for the nonrandom selection into mid-pregnancy marriage. As already noted, mothers entering into such marriages differ in many ways from those who do not. Our methodological approach models selection into mid-pregnancy marriage, allows us to compare mothers with similar propensities of entering into mid-pregnancy marriage, and addresses some concerns about selection bias.

Finally, we examine heterogeneity in the benefits of mid-pregnancy marriage for children. Specifically, we assess whether mid-pregnancy marriage is associated with benefits only for children whose mothers are more advantaged and have a higher propensity to enter mid-pregnancy marriage, or instead whether the benefits extend to those who are unlikely to enter a mid-pregnancy marriage—the target population for policy interventions. We know of no other study that has taken a similar approach to studying heterogeneity in the benefits of mid-pregnancy marriage.

## Background

### Mid-Pregnancy Marriage

A small body of research has examined historical trends in and the demographic profile of mid-pregnancy marriages. Mid-pregnancy marriage has declined significantly over time, particularly among those with low levels of education and racial and ethnic minorities. Drawing on U.S. data from cohorts of women born between 1925 and 1959, England et al. (2012) found that declines in mid-pregnancy marriage were concentrated among less-educated black women. Studies using more recent U.S. data provide further evidence of socioeconomic stratification in mid-pregnancy marriage: the probability that a low-educated mother’s first child is born into a mid-pregnancy marriage declined by almost 60 % (from 12.5 % to 5.1 %) from the late 1980s to the 2000s (Gibson-Davis and Rackin 2014). At the same time, highly educated women were increasingly likely to enter mid-pregnancy marriages—from 1.2 % in the mid-late 1980s to 8.7 % in the mid-late 2000s (Gibson-Davis and Rackin 2014).

Other research has documented the characteristics of individuals with mid-pregnancy marriages, showing that such parents are advantaged compared with those who remained single after a nonmarital conception (Lichter et al. 2010; Manning 1993; Parnell et al. 1994; Rackin and Gibson-Davis 2012). For example, growing up in a nuclear family or with a strong religious background was associated with an increased likelihood of mid-pregnancy marriage relative to remaining single (Parnell et al. 1994; Uecker and Stokes 2008), and multiple studies have demonstrated a positive link between educational attainment and mid-pregnancy marriage among white couples but not black couples (Ginther and Zavodny 2001; Parnell et al. 1994; Zavodny 1999). Similarly, men’s earnings and employment were positively associated with mid-pregnancy marriage among white men but not black men (Zavodny 1999). Other studies examined the stability of mid-pregnancy marriages, with mixed findings (Ginther and Zavodny 2001; Rackin and Gibson-Davis 2012). Data from recent cohorts suggest that mid-pregnancy marriages were more likely to dissolve than pre-conception marriages but that these differences disappeared after other parental characteristics were controlled for (Rackin and Gibson-Davis 2012).

### Marriage and Children

Prior research suggests that marriage among biological parents is associated with better outcomes for children than single parenthood or cohabitation (Artis 2007; Brown 2004; Manning and Brown 2006). Family structure is also linked to parenting behaviors. Research has shown that single parents generally provide less supervision and are less emotionally supportive of their children compared with married parents (Astone and McLanahan 1991; McLanahan and Sandefur 1994; Thomson et al. 1992). The positive relationship between marriage and child well-being does not, however, extend to all types of marriage. Evidence suggests that children whose biological parents married after they were born did not experience the same benefits as those whose biological parents married before they were born (Heiland and Liu 2006; Osborne and Palmo 2009). This prior research suggests something unique about marriage prior to childbirth, or that individual characteristics associated with selection into pre-pregnancy marriage are uniquely linked to child well-being.

Research has indicated that linkages between marriage and child well-being may vary by race. Single parenthood is more prevalent among black mothers compared with those of other races; in 2011, almost 68 % of black women who gave birth were unmarried, compared with 26 % among non-Hispanic white women (Shattuck and Kreider 2013). At the same time, black single mothers may also have access to greater social resources outside the context of marriage than their white counterparts; Hill (1972) highlighted strong kinship ties among African American families, and Roschelle (1997) observed that caring for other people’s children has historically been a significant role for African American women. Indeed, studies have found that single parenthood was more strongly associated with reduced child well-being for white children compared with black children (Dunifon and Kowaleski-Jones 2002; Gil et al. 1998; McLanahan and Sandefur 1994; Thomas et al. 1996).

Several mechanisms may explain differences in child well-being across family structures (Amato 2005; Magnuson and Berger 2009). Marriage is associated with increased financial resources (Astone and McLanahan 1991; McLanahan and Sandefur 1994) and improves the economic well-being of children and single mothers (Lichter et al. 2003), which in turn predicts children’s overall well-being (Brooks-Gunn and Duncan 1997). Nonmarital childbearing is also linked with increased family instability and conflict. For example, children born to unmarried parents experience significantly more family structure changes compared with other children (Osborne and McLanahan 2007). Single mothers who marry have a higher risk of union dissolution than childless women who marry (Graefe and Lichter 2002; Williams et al. 2008), creating greater family instability for children, which in turn is linked to poorer outcomes for children (Brown 2006; Cavanagh and Huston 2006; Fomby and Cherlin 2007), especially among those from less-advantaged single-parent families (Wagmiller et al. 2010). Further, women with a premarital birth are more likely to report marital conflict than women who marry without a premarital birth (Timmer and Orbuch 2001), and parental conflict is linked to poorer child psychological well-being (Amato and Sobolewski 2001; Musick and Bumpass 1999; Musick and Meier 2010).

This study links biological parents’ relationship status at birth to later child and parenting outcomes, even if the parents do not remain partnered. The justification for this is twofold. First, we are interested in relationship status at birth because of the concern and resulting public investment targeting nonmarital childbearing. This is the point at which many programs and policies seek to intervene. Second, for those experiencing a nonmarital pregnancy, the relationship status at birth represents a key decision—whether to enter into a mid-pregnancy marriage—which sets the stage for later family structure trajectories because children born to single mothers experience greater instability later in life (Cavanagh and Huston 2006; Graefe and Lichter 2002; Williams et al. 2008). Therefore, understanding the implications of a decision made at the time of pregnancy identifies potential areas in which programs and policies might intervene, with possible long-term consequences.

### The Role of Selection Bias

Selection bias is a key issue when thinking about the linkages between mid-pregnancy marriage and child well-being. Two types of selection bias are possible: baseline bias and differential treatment effect bias (Morgan and Winship 2007). Baseline bias occurs when preexisting characteristics are associated with both marriage and child well-being. In this case, marriage itself may not directly confer benefits for children; rather, such outcomes may be due to the fact the most secure, healthy, and advantaged individuals are more likely to marry (Acs 2007; Hofferth 2005). Failure to account for baseline selection bias could bias associations between family structure and child well-being (McLanahan and Percheski 2008).

Differential treatment bias occurs when the linkages between marriage and child well-being vary across subgroups. Indeed, as noted earlier, the linkages between family structure and child well-being differ notably by race. Thus, marriage generally—and mid-pregnancy marriage specifically—may influence children differently, depending on their race.

Additionally, differential treatment bias may be associated with the propensity to enter into mid-pregnancy marriages. The current study examines whether the potential benefits for children of mid-pregnancy marriage vary for women who are more versus less likely to enter into this type of family structure. In other words, we evaluate whether the benefits of marriage are differentially distributed according to selection characteristics.

Our analytic approach, which explicitly considers the nonrandom selection of parents into mid-pregnancy marriages and allows for the possibility that mid-pregnancy marriage differentially influences children, sheds light on the larger implications of the retreat from mid-pregnancy marriage. More specifically, this approach allows us to examine whether mid-pregnancy marriage is associated with benefits for the children of those who are unlikely to enter this type of arrangement, which is informative for policy interventions targeted to unmarried parents who are unlikely to marry.

The goal of our study is to examine two research questions, using propensity score matching techniques to address issues of selection, and examining differences for white and black children separately. First, does mid-pregnancy marriage predict parenting and child well-being? And second, do the returns to marriage vary among those who are more versus less likely to enter mid-pregnancy marriages?

## Data

We use data from the National Longitudinal Survey of Youth 1979 (NLSY79), which is uniquely suited to investigate consequences of mid-pregnancy marriage for child outcomes. The NLSY79 is a nationally representative, longitudinal birth cohort study following individuals who were born between 1957 and 1964. Respondents were interviewed annually from 1979 through 1994 and biennially since. In 1986, the NLSY began biennial interviews of children born to female respondents of the NLSY79. The child sample is representative of children whose mothers were aged 14–22 in 1979. Although this cohort sample is not contemporary, it presents a rare opportunity to investigate the implications of the retreat from mid-pregnancy marriage among the cohort first experiencing it. Prior research found that the rise in nonmarital first births for the cohort of women born between the late 1940s and the early 1960s (which aligns with the NLSY79 sample) was primarily attributable to declines in mid-pregnancy marriage (England et al. 2013).

The NLSY79 has limitations as well. For example, results from the NLSY cohort may not be generalizable to contemporary populations. However, contemporary data sets do not allow one to link detailed information about parents, such as their marriage date and characteristics prior to childbirth, with assessments of their children. The NLSY79 is the most appropriate data set for our study because it allows us to examine a cohort that experienced a sharp decline in mid-pregnancy marriage yet has sufficient prevalence of mid-pregnancy marriage to support statistical analyses. The NLSY79, however, contains limited information about fathers, whose characteristics might have important implications for both selection into mid-pregnancy marriage and child well-being (Ryan 2012; Zavodny 1999). Further, it has no information about cohabitation among parents who had children prior to 1979 (approximately 11 % of our sample). Although cohabitation was not as common at that time as it is today, it is possible that we incorrectly classify some cohabiting couples as single. Despite these limitations, the NLSY79 is the most appropriate data to address the research questions posed here, which focus on the implications of mid-pregnancy marriage for children.

Our analytic sample consists of black and white mothers aged 14 to 25 who conceived their first child before their first marriage, as well as their firstborn children.2 We focus on mothers in this age range because they are most likely to have a nonmarital conception (Ventura 2009). Of the n = 12,686 total adult sample, our sample excludes 1,280 members of the NLSY’s military subsample (10 %); 5,579 men (44 %); 1,167 childless women (9 %); 1,377 women who were not aged 14–25 at first birth (11 %); 685 women who identified as a race or ethnicity other than white or black (5 %); 166 women whose start or end date of first marriage is missing (1 %); 980 women who were married eight months or more before their first birth (8 %); 24 women who were married and divorced before their first birth (<1 %); 95 women whose firstborn child never completed a child assessment (1 %); 30 women who never lived with their firstborn child at least half-time (<1 %); and 8 women whose children did not have valid data for any dependent variables in any year (<1 %).

Data are reshaped into person-year observations with 10 possible observations corresponding to years in which child well-being assessments were gathered: 1986, 1988, 1990, 1992, 1994, 1996, 1998, 2000, 2002, and 2004. This data structure allows us to examine all available child assessments and to include time-varying characteristics, such as the age of child at assessment and the number of children in the household. We remove 7,643 person-year observations without a completed child assessment (assessments were gathered for children up to age 16, and most children were not eligible for all 10 assessments) (59 %), 107 person-year observations when the child was not living with the mother at least part-time (1 %), and 45 person-year observations for which the child was missing data for all five dependent variables (<1 %).

The final analytic sample contains 1,288 unique respondents (n = 609 white mothers, n = 679 black mothers) and 5,155 person-year observations collected from 1986–2004. Complete data for all time-invariant variables included in the propensity score model were available for 85 % of our sample. Missing data were multiply imputed by chained equations (Royston 2004; Rubin 1987). We follow the strategy of “multiple imputation, then deletion” (MID), whereby respondents who were missing data on a dependent variable are included in the imputation but are ultimately excluded from the analytic sample (von Hippel 2007).

## Measures

### Dependent Variables

We assess mothers’ parenting quality using the cognitive stimulation and emotional support subscales of the Home Observation Measurement of the Environment-Short Form (HOME-SF) (Bradley and Caldwell 1984a,b), which were gathered from parents of children aged 0 to 14. These scales vary by age and combine interviewer observations and the mother’s report of the home environment. The cognitive stimulation battery asked questions such as, “How often do you get a chance to read to child?,” and “When your family watches TV, do you or (father) discuss programs with him/her?” The interviewer observations include items such as whether the child’s play environment was safe and the home was reasonably clean. The emotional support battery includes questions about spanking, child autonomy, and how the mother responded to tantrums. The interviewer observations include items such as whether the mother kissed or hugged the child, or conversed with the child. The total raw score for the HOME-SF is the sum of individual items, which varies by age group. There are no appropriate national norms available for these measures, but they are internally standardized to the full NLSY79 sample by age with a mean of 100 and standard deviation of 15 to allow comparison across children of different ages.

We assess child well-being with three dependent variables: (1) maternal reports of children’s behavior problems, (2) children’s math test scores, and (3) children’s reading comprehension scores. The Behavior Problem Index (BPI) was adapted from Achenbach and Edlebrock’s behavioral checklist (1981) and comprises 28 mother-reported questions regarding the child’s behavior and attitudes in the previous three months. Mothers rated each item using a three-point scale (often, sometimes, or not true); these ratings are dichotomized (1 = often or sometimes true, 0 = not true) and summed such that higher scores indicate more behavior problems. The score is then normed by age and sex to have a national mean of 100 and a standard deviation of 15. The BPI was administered for children ages 4 to 16.

Child cognitive development was assessed with the Peabody Individual Achievement Tests (PIAT) in math and reading comprehension. These assessments were administered to children ages 5 to 16. PIAT scores were normed by age in the late 1960s to a national mean of 100 with a standard deviation of 15. Both the PIAT mathematics and reading assessments are highly reliable and valid, as evidenced by their widespread use in the psychological and sociological literatures (Baker et al. 1993).

Note that our dependent variables were measured among children of different ages. Parenting quality was measured among mothers of children ages 0–14, children’s BPI was among children ages 4–16, and cognitive test scores were among children ages 5–16. Results were similar when the sample was limited to those ages with valid responses across all outcomes. Therefore, we present results for children of all ages to preserve sample size.

### Independent Variable

The key independent variable was an indicator of mid-pregnancy marriage. This measure is derived from the NLSY Fertility and Relationship History data file, which includes dates of marriage, divorce, and birth. Following prior research, we define mid-pregnancy marriage as a legal marriage that occurred 0–7 months before the child’s birth. To create the mid-pregnancy marriage variable, we compare the date of marriage with the date of birth: the variable is coded as 1 if the mother’s marriage date was 0–7 months before the child’s birth date. Because our sample is limited to women with nonmarital conceptions, the omitted category for this variable is young women who had a nonmarital conception and remained single at their first birth (that is, women who did not have a mid-pregnancy marriage, coded as 0).

Our analyses adjusted for selection factors associated with the mother’s characteristics and the mother’s home environment prior to the child’s birth, as well as child and household characteristics measured after the child’s birth. See Table 4 in the appendix for a complete list of variables included in the propensity score model and the weighted regressions.

### Mother’s Characteristics

Mother’s age at the birth of her first child is measured in years. Mother’s cognitive ability was measured in 1980 with the Armed Forces Qualification Test (AFQT). AFQT scores are normed by age and reported as a percentile. The Rotter Locus of Control Scale measures the extent to which individuals believe they have control over their lives (Rotter 1966). The scale indicates whether individuals had a high sense of internal control (i.e., feeling in control of their own lives through self-motivation or discipline) or external control (i.e., feeling little personal control and believing that fate or luck controls their lives). The scale was administered in 1979; scores range from 4 to 16, with higher scores indicating more external control.

### Mother’s Childhood Home Environment

Dichotomous variables indicate whether the mother was born in the South and whether she lived in a nuclear family (with her biological mother and father) at age 14. Mothers were asked to retrospectively report the religion in which they were raised, which was coded into four categories: (1) None/other (referent); (2) Roman Catholic; (3) Liberal Protestant, which includes Episcopalian, Methodist, or Presbyterian; and (4) Conservative Protestant, which includes Baptist, Lutheran, and unspecified Protestant. Lack of literacy material in the mother’s household at age 14 is represented with a dichotomous variable coded as 1 if the mother reported that nobody in the household received newspapers or magazines, or had a library card. A dichotomous variable also indicates whether the mother lived in an urban area at age 14 (coded 1 for town or city; coded 0 for country or farm area). Dichotomous variables indicate whether the child’s maternal grandmother was a teen mother, and the grandmother worked outside the house when the mother was age 14, and whether a foreign language was spoken in the mother’s household at age 14. Grandmother’s education is captured as the highest grade or year of regular school ever completed. Education is measured in years and ranges from 0 to 18; 0 indicates no education, and 18 indicates the sixth year of postsecondary education (college or graduate school).

### Child Characteristics

We also include child and household characteristics that were measured after the birth of the child. Child sex is represented with a dichotomous variable (coded 1 if child is male; coded 0 if child is female). Child low birth weight (LBW) indicates whether the child was 5.5 pounds or less at birth (coded 1 if the child weighed 5.5 pounds or less; coded 0 if the child weighed more than 5.5 pounds). The number of children in the household is a continuous measure of children age 18 or younger, and was collected at the time of the child assessment. Child’s age at assessment is measured in years and ranges from 0 to 16.

## Method

As noted earlier, women entering mid-pregnancy marriages likely differ from those who remain single in many ways, and these selection factors could be associated with child and parenting outcomes. To address this potential source of bias, we estimate propensity scores, which are conditional probabilities of selection into mid-pregnancy marriage, using logistic regression (Rosenbaum and Rubin 1983). In Eq. (1), D—the treatment variable—is equal to 1 for respondents who entered into mid-pregnancy marriages, and 0 for respondents who remained single. X is a vector of covariates associated with selection into mid-pregnancy marriage.
$logitD=α^+Xβ^+ε.$
(1)
For the second step of our analysis, we undertake a weighted regression analysis using propensity scores to derive the weights. We follow Morgan and Todd’s (2008) procedure for calculating weights using estimated propensity scores, $p^i$, which are the conditional predicted probabilities of mid-pregnancy marriage from Eq. (1). The estimated propensity scores are used to form three sets of weights: wi,ATE (Eq. (2a)), wi,ATT (Eq. (2b)), and wi,ATC (Eq. (2c)) (Morgan and Todd 2008:244).
$Fordi=1:wi,ATE=1p^i.Fordi=0:wi,ATE=11−p^i.$
(2a)
$Fordi=1:wi,ATT=1.Fordi=0:wi,ATT=p^i1−p^i.$
(2b)
$Fordi=1:wi,ATC=1−p^ip^i.Fordi=0:wi,ATC=1.$
(2c)

These weights allow us to estimate three different conditional average treatment effects. The weights for the average treatment effect (ATE) (Eq. (2a)) allow us to estimate the average effect of mid-pregnancy marriage across the entire sample (i.e., the difference in average outcomes between mid-pregnancy marriage and single). The ATE compares the well-being of children born to all mothers in mid-pregnancy marriages with the well-being of children born to all single mothers in the sample, controlling for other sociodemographic characteristics. The weights for the average treatment effect on the treated (ATT) (Eq. (2b)) allow us to estimate the average effect of mid-pregnancy marriage for those who have a high propensity for mid-pregnancy marriage. This estimate focuses on the difference in outcomes between mothers who had mid-pregnancy marriages and mothers who remained single but had a high propensity for mid-pregnancy marriage. In other words, we are approximating an unobservable counterfactual scenario: If a mother in a mid-pregnancy marriage had instead remained single, would there be differences in her parenting or the child’s well-being? The weights for the average treatment effect on the controls (ATC) (Eq. (2c)) allow us to estimate the average effect of mid-pregnancy marriage for those who have a low propensity of entering such marriages. Here, we examine the difference in outcomes between mothers who remained single and mothers who entered into mid-pregnancy marriage but had characteristics that predicted a low propensity of doing so. This approximates a slightly different counterfactual scenario: If a single mother had entered into a mid-pregnancy marriage, would there be differences in her parenting or the child’s well-being?

These weights make the treatment and control groups comparable in terms of sociodemographic characteristics, approximating an experimental design in which treatment (mid-pregnancy marriage) is randomly assigned. This method assumes that no additional confounding differences between mothers who enter mid-pregnancy marriages and mothers who stay single remain after we control for observed covariates. We assess balance in our data by estimating the average standardized mean differences between treatment and control groups for all covariates in the model (Morgan and Todd 2008; Rubin 1973). We also assess the standardized differences in standard deviations for continuous variables. A value of 0 indicates that the data are perfectly balanced. We experimented with model specification to achieve the best possible balance, adding interaction variables that are justified in light of past theory and research (Morgan and Todd 2008). In light of the literature documenting racial differences in the association between family structure and child well-being (Dunifon and Kowaleski-Jones 2002; Fomby and Cherlin 2007) and the large racial differences in our data in the prevalence of mid-pregnancy marriage, we perform all analyses separately for black and white respondents.3

Table 4 in the appendix presents results from our final propensity score models. Tables 5 and 6 in the appendix demonstrate that the ATE, ATT, and ATC weights derived from the propensity scores successfully balanced the data according to two criteria. First, the average standardized mean and standard deviation balance between treatment and control groups is significantly improved when we apply the weights (Table 5). Any remaining imbalance is addressed with supplemental parametric adjustment in the next phase of analysis, the weighted regressions (Morgan and Todd 2008). Second, there are no statistically significant differences between treatment and control groups when weighted with the ATE, ATT, or ATC weights (Table 4).

In the third stage of analysis, we estimated regressions using the propensity weights. In Eq. (3), Y is the child well-being outcome; D is the treatment variable; δ is the estimated effect of D on Y, adjusted for X; and X is a vector of observed variables that are thought to determine D and Y. We first estimate regressions by applying the ATE weights, estimating an average effect of mid-pregnancy marriage across the entire sample. We next assess causal effect heterogeneity by comparing the results from ATT and ATC weighted regressions. In other words, we compare the effect of mid-pregnancy marriage among children born to mothers who had a high propensity for mid-pregnancy marriage (ATT) with the effect of mid-pregnancy marriage among children born to mothers who had a low propensity for mid-pregnancy marriage (ATC).
$Y=α^+δ^D+Xβ^+ε.$
(3)

For all propensity-weighted regressions, we include the full set of covariates used to estimate the propensity scores, as well as supplementary covariates to further adjust for child’s characteristics that are unrelated to selection into mid-pregnancy marriage but might be associated with parenting and child well-being, such as the child’s age, child’s sex, whether the child had a low birth weight, and the number of children in the household under age 18. We adjust the standard errors to account for the fact that the child assessments are not independent. We restrict all models to the region of common support, which is the range of the propensity score for which there are respondents in both the treatment and control groups.

Propensity score weighted regression models such as those used here have several advantages over traditional ordinary least squares (OLS) regression. Such models are nonparametric and do not require assumptions about a linear relationship between the dependent and independent variables. Perhaps most significantly, such models provide a straightforward tool to address concerns about differential treatment effect bias and to examine causal effect heterogeneity.

Our approach also provides some advantages over traditional propensity score matching techniques. It provides a doubly robust method of balancing the data by incorporating covariates into both the propensity score and the weighted regressions, and therefore provides additional protection against model misspecification (Robins and Rotnitzky 2001). This method also facilitates a straightforward application of survey weights to account for the study’s complex sampling design and accommodates multiply imputed data. Finally, this approach allows us to take advantage of longitudinal data.

Nonetheless, our methodological approach also has some important limitations. This model can adjust only for differences in observable characteristics. Any unobservable characteristics—such as an individual’s sense of self-control, self-efficacy, or other genetic traits influencing mid-pregnancy marriage and child well-being—will bias our estimates. It is difficult to speculate on the direction of the bias, but these unobservable characteristics may operate similarly to other observable characteristics that are included in our models, such as age, cognitive test scores, and indicators of SES: individuals with more-favorable unobservable traits may be more likely to select into mid-pregnancy marriage and to have resources that are also associated with positive child well-being. Our results also rely on the correct specification of the propensity score model, which is vulnerable to the limitations of logistic regression. Despite these limitations, we are reassured by the fact that the propensity score model performs quite well in balancing the data.

## Results

Table 1 presents descriptive statistics by race and relationship status at birth (mid-pregnancy marriage or single). Consistent with prior research, mid-pregnancy marriage was extremely rare among black mothers: only 10 % of black women in our sample formed mid-pregnancy marriages, compared with more than one-half (53 %) of white women. Some noteworthy differences exist in terms of the characteristics that might be associated with selection into mid-pregnancy marriage. White mothers who entered such marriages have higher AFQT scores than those who remained single. They were also more likely to have lived with a nuclear family at age 14 (72 % vs. 56 %) and less likely to have lived in an urban area. Black mothers who entered mid-pregnancy marriages were slightly older, had higher AFQT scores, and had better-educated mothers compared with black mothers who remained single.

Unconditional descriptive statistics suggest that mid-pregnancy marriage is associated with higher quality parenting among both white and black mothers. Children born to mothers in mid-pregnancy marriages also reported better well-being on average compared to children born to single mothers. Specifically, children born to white mothers in mid-pregnancy marriages had fewer behavior problems and higher cognitive test scores than children born to white single mothers. Children born to black mothers in mid-pregnancy marriages also had higher reading comprehension scores than those born to single black mothers. These unconditional descriptive statistics do not account for any other characteristics that might be related to both selection into mid-pregnancy marriage and the indicators of well-being, however.

Our first research question asks whether mid-pregnancy marriage is associated with parenting and child well-being, controlling for other sociodemographic characteristics. Table 2 presents results from the ATE-weighted regressions predicting the relationship between mid-pregnancy marriage and these outcomes, separately for white and black women. Results suggest that mid-pregnancy marriage is associated with improved parenting quality, but not the metrics of child well-being examined here. Among whites, mid-pregnancy marriage is associated with a score on emotionally supportive parenting that is about 20 % of a standard deviation higher (b = 2.772, p < .01; SD = 14.201) and a score on cognitively stimulating parenting that is 19 % of a standard deviation higher (b = 2.664, p < .05; SD = 13.874). Among blacks, mid-pregnancy marriage is associated with a score on cognitively stimulating parenting that is about 23 % of a standard deviation higher (b = 3.558, p < .01; SD = 15.164), but the relationship between mid-pregnancy marriage and emotionally supportive parenting is not statistically significant at conventional thresholds (b = 2.570, p < .10).

Our second research question asks whether the returns to marriage vary among those who are more versus less likely to enter mid-pregnancy marriages. We answer this question by comparing ATT and ATC coefficients for mid-pregnancy marriage presented in Table 3 (full tables are available upon request). Recall that the ATT represents the effect of mid-pregnancy marriage relative to remaining single among mothers with a high propensity to enter this type of marriage, and the ATC represents the effect of mid-pregnancy marriage relative to remaining single among mothers with a low propensity to enter this type of marriage.

The ATT and ATC coefficients are statistically similar across all measures of parenting quality and child development for both white and black mothers. On balance, the results suggest that the relationship between mid-pregnancy marriage and parenting quality does not vary according to the mother’s propensity to form a mid-pregnancy marriage. In fact, Table 3 highlights the robustness of the relationship between mid-pregnancy marriage and higher quality parenting relative to remaining single among both white and black mothers and regardless of the propensity to enter into such marriages.

## Supplemental Analyses

Several sensitivity analyses assessed the robustness of our results. First, we examined whether the instability of mid-pregnancy marriages influenced our results. In our sample, 41 % of white mothers and 38 % of black mothers with mid-pregnancy marriages eventually divorced (as of the last date of child assessment). This instability might negate some of the benefits associated with mid-pregnancy marriage. Additional models included a dichotomous variable indicating whether the marriage dissolved by the time of the child assessment, as well as an interaction between mid-pregnancy marriage and dissolution, to examine whether the effect of mid-pregnancy marriage varies by relationship stability (results not shown but available on request). Results suggested that the positive association between mid-pregnancy marriage and higher-quality parenting was indeed limited to mid-pregnancy marriages that remained intact (as of the time of child assessment). Parenting quality among mothers in dissolved mid-pregnancy marriages was statistically similar to mothers who were single at the time of birth. Results from these supplemental models do not demonstrate linkages between mid-pregnancy marriage and child outcomes, even for mid-pregnancy marriages that remained intact at the time of child assessment.

Next, we examined whether our results were sensitive to the selected matching algorithm by comparing our results with those based on models using nearest-neighbor matching. Results from the nearest-neighbor matching are slightly weaker than those from the propensity-weighted regressions, particularly among blacks. Specifically, the coefficients for emotionally supportive and cognitively stimulating parenting reached the threshold of statistical significance in the propensity-weighted regression, but not in the nearest-neighbor matching. Nonetheless, the direction and magnitude of the coefficients are similar across both specifications. Because the methodological literature does not provide specific guidance on selecting a matching algorithm (Morgan and Winship 2007), we proceed with the propensity-weighted regression approach because it offers several benefits over nearest-neighbor matching for our study, as noted earlier.

## Discussion and Conclusion

The dramatic decrease in mid-pregnancy marriage has contributed to rising nonmarital birth rates, particularly among historically disadvantaged populations. However, the implications of this shift for children are not known. Our study fills this gap by estimating the associations among mid-pregnancy marriage, parenting quality, and child well-being. Employing propensity score techniques to address concerns about selection and to detect causal effect heterogeneity in the returns to mid-pregnancy marriage, our study yields three central findings. First, mid-pregnancy marriage is associated with slightly better parenting quality relative to remaining single among both white and black mothers. Second, despite better parenting quality, mid-pregnancy marriage is not associated with child well-being. Finally, we find no evidence of causal effect heterogeneity: we observe similar results among mothers with high propensities and those with low propensities to enter mid-pregnancy marriages.

Our finding that mid-pregnancy marriages are associated with slightly better parenting quality, even after accounting for a rich set of characteristics associated with selection into these marriages, is consistent with extant theory on family structure and parenting. For example, structural perspectives on marriage and parenting behavior hypothesize that marriage provides additional economic and emotional resources that increase parenting efficacy. Single mothers cannot rely on a spouse to share financial or parenting responsibilities, which limits the time available for child care and likely increases parenting stress (McLanahan and Percheski 2008; McLanahan and Sandefur 1994; Thomson et al. 1994). Empirical evidence for the link between family structure and parenting behavior is less clear, however, because of concerns about selection bias. Our findings are consistent with empirical research showing that single parents are less emotionally supportive, are less encouraging, and give harsher discipline compared with continuously married parents (Astone and McLanahan 1991; McLanahan and Sandefur 1994; Thomson et al. 1994). Although other research has suggested that some of this association may be attributed to parental characteristics that determine selection into marriage—such as maternal age, race/ethnicity, and education (Aronson and Huston 2004; Gibson-Davis 2008)—our study finds that this association persists even after we account for these characteristics, suggesting that the parenting benefits of marriage extend to mid-pregnancy marriage.

One important caveat to our findings about parenting quality is the small effect sizes (about 20 % of a standard deviation). Furthermore, our supplemental analyses suggest that the positive association between mid-pregnancy marriage and parenting is limited to marriages that were intact at the time of the child assessment. In light of the small effect sizes and the fragility of mid-pregnancy marriages, we interpret the positive association between mid-pregnancy marriage and parenting quality with caution.

Turning to child well-being, our results suggest that mid-pregnancy marriages are not any more advantageous than remaining single in terms of children’s behavior and cognitive test scores. Why did we not find an association between mid-pregnancy marriage and better child development, despite the association between mid-pregnancy marriage and higher-quality parenting? One explanation is that although the improvement in parenting quality for those entering mid-pregnancy marriage is statistically significant, it may not be substantively large enough to impact child development. It is also possible that parenting and child outcomes, at least as measured in household surveys, are independently, but not jointly, influenced by family structure. For example, Dunifon and Kowaleski-Jones (2002), also using NLSY data, found that single parenthood is associated with both parenting and child outcomes but that parenting behaviors do not account for the linkages between single parenthood and child well-being. Thus, mid-pregnancy marriage may influence mothers’ interactions with their children but not in ways that manifest themselves in detectable changes in these measures of child well-being.

Finally, we find that the relationship between mid-pregnancy marriage and child and parenting outcomes does not vary according to the mother’s propensity to form a mid-pregnancy marriage. This stands in contrast to Ryan (2012), who found that the benefits of a marital birth for children’s test scores and behavior problems confer only to those most likely to marry. Several differences between the two studies may explain this discrepancy. First, Ryan (2012) looked at all marital births rather than the subset of mid-pregnancy marriages. Perhaps the selection into marital births occurs along dimensions that matter more for child development than does the selection into mid-pregnancy marriage in particular. Second, Ryan used data containing a wide range of measures of fathers’ characteristics to classify families by their propensity to marry; perhaps our inability to measure fathers’ characteristics hinders our ability to detect heterogeneous returns to mid-pregnancy marriage. Given the scant literature on this topic, greater research examining heterogeneous returns to marriage for children is needed to better interpret these results.

Our study provides new evidence on the linkages between mid-pregnancy marriages and child well-being, but also has several limitations that highlight opportunities for future research. Some of these limitations are due to our use of the NLSY79, which is well-suited for our analyses in many ways but is limited in that it is not a contemporary sample. As mid-pregnancy marriage has become less common, the effect of this family structure on children may have shifted because of two factors: the changing composition of parents who form mid-pregnancy marriages and/or changes in the returns to mid-pregnancy marriage. The composition of mid-pregnancy marriages has likely changed as it has become increasingly rare (Gibson-Davis and Rackin 2014). As a result, mid-pregnancy marriage may have become more strongly associated with positive well-being given that it is increasingly composed of advantaged parents with other resources also contributing to child well-being (Lichter et al. 2014). The returns to mid-pregnancy marriage may have also shifted as well. As marriage has become more selective over time, the symbolic importance has increased (Cherlin 2004). Therefore, mid-pregnancy marriage might be more strongly associated with positive well-being because it has become a more distinctive marker of prestige or achievement for a couple with a nonmarital pregnancy. Thus, our results might provide a more conservative estimate of this association than those drawn from a contemporary sample.

We focus on the effects of relationship status at the mother’s first birth on child well-being among children ages 0–16, but because of limited sample sizes, we do not examine how these effects vary at different stages of child development. For instance, mid-pregnancy marriages may have stronger effects on child well-being when the children are younger and have prolonged exposure to the home environment. Also because of low sample sizes, we do not thoroughly examine how the stability or quality of mid-pregnancy marriages influences child well-being. Future research may be better able to disaggregate the effects of mid-pregnancy marriages that endured or dissolved. We also focus on the mothers’ characteristics and parenting behaviors, but fathers likely play a strong role in both selection into mid-pregnancy marriage and child well-being. Our data do not allow us to thoroughly measure fathers’ characteristics. Future research should examine the dual role of mothers and fathers in mid-pregnancy marriages. Finally, we cannot measure the relationship quality for those who did and those who did not marry, which is likely an important predictor of selection into mid-pregnancy marriage.

In summary, our study fills a gap in the literature by examining the relationship between mid-pregnancy marriage and child well-being. Although we find that mid-pregnancy marriage is associated with slightly better parenting quality relative to remaining single, we find no evidence that mid-pregnancy marriages are associated with better child behavior or cognitive test scores. Nonetheless, our findings suggest that the retreat from mid-pregnancy marriage may have implications for increasing inequality between children of different social classes. Over time, more-advantaged women have been increasingly entering into mid-pregnancy marriages, while less-advantaged women have been retreating from mid-pregnancy marriages (England et al. 2012; Gibson-Davis and Rackin 2014). This trend has potentially changed both the composition and the meaning of mid-pregnancy marriage as it has become more rare and distinctive. If mid-pregnancy marriage confers even small benefits in terms of parenting quality, this effect may compound the relative advantage of those who are increasingly likely to enter these marriages.

## Acknowledgments

An earlier version of this article was presented at the 2012 Annual Meeting of the Population Association of America, San Francisco, CA, and the 2012 Encore Conference sponsored by the Cornell Population Center. The authors thank the anonymous reviewers, Fenaba Addo, Michelle Frisco, Fran Goldscheider, Stephen L. Morgan, Emily Taylor Poppe, and Robert Wagmiller for their comments on earlier drafts of this article.

## Notes

1

Although the proportion of cohabiting pregnant women who married prior to the birth was greater, marital transitions among such women was still the minority experience, with only about 14 % entering into marriage prior to the birth (Lichter et al. 2014).

2

The NLSY79 has few Hispanic women who meet our sample criteria (n = 181). Therefore, we are unable to examine Hispanics in this study due to low sample size.

3

Propensity scores derived from the pooled sample (black and white respondents together) did not balance the data, which suggests that the selection mechanisms for mid-pregnancy marriage differ by race.

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