## Abstract

Changes in parental romantic relationships are an important component of family instability, but children are exposed to many other changes in the composition of their households that bear on child well-being. Prior research that focused on parental transitions has thus overlooked a substantial source of instability in children’s lives. I argue that the instability in children’s residential arrangements is characterized by household instability rather than family instability. To evaluate this thesis, I use the 1968–2015 waves of the Panel Study of Income Dynamics and time-varying methods for causal inference to test the independent effects of different types of changes in household composition on educational attainment. Experiencing changes involving nonparent, nonsibling household members has a significant negative effect on educational attainment that is similar in magnitude to that for children who experience changes involving residential parents. Measures of parental changes miss the nearly 20 % of children who experience changes involving household members other than parents or siblings. By showing that changes in nonparental household members are both common and consequential experiences for children, I demonstrate the value of conceptualizing the changes to which children are exposed as a product of household instability, rather than simply family instability.

## Introduction

Family structure, especially whether children live with a single parent or two parents, has long been of interest to researchers estimating the effects of family characteristics on children’s outcomes. This research tradition has generally concluded that children growing up with a single parent are at a disadvantage in many domains relative to children who grow up with two parents (McLanahan and Sandefur 1994; McLanahan et al. 2013). More recently, research in family sociology has acknowledged the dynamic nature of family structure: children who end up living with single parents often experience the departure of a parent from a two-parent home and may also experience the arrival of a new parental figure (Beck et al. 2010; Cavanagh 2008; McLanahan 2011; Mitchell 2013). This new focus on instability argues that it is disruption and change in family structure rather than type of family structure that is detrimental to children’s well-being. Research on family instability thus tends to define instability in terms of changes in parental romantic relationships: dissolution, repartnering, or churning among parents and their partners.

I argue for the substantive importance of changes in household composition beyond parents and parents’ partners as an indicator of volatility in children’s lives. Despite the substantial literature documenting the effects of parental divorce and repartnering on children’s outcomes, relatively few studies have considered whether changes in household composition beyond parents are consequential for children’s well-being. To overcome this limitation, I use data from the Panel Study of Income Dynamics (PSID) to track changes in children’s households involving relatives and nonrelatives during childhood and adolescence and estimate the effect of these changes on their educational attainment—specifically, their likelihood of graduating from high school and enrolling in postsecondary education.

Using inverse probability of treatment (IPT) weighting and marginal structural models that facilitate the estimation of causal effects, I find that entries into and exits from children’s households of parents and nonparents are common and consequential for children’s educational attainment. Nonparents include extended family members, such as grandparents, aunts, uncles, and cousins, as well as nonrelatives. Children who experience changes involving parents are less likely to graduate from high school, and children who experience changes involving parents or changes involving nonparent, nonsibling household members are less likely to enroll in postsecondary education compared with children who experience no such changes in household composition, net of controls for family structure. My findings also demonstrate that the effect of changes in household composition differs by race, with negative effects found for white but not black children. I conclude by encouraging future research on family instability to pursue a more expansive definition of instability beyond parents and their partners, reflecting more of the changes in households that children experience.

## Background and Motivation

Two strands of research motivate this study. The first is the literature on family instability, which has generally found that family structure changes are disruptive to children’s lives. This literature has almost exclusively used parental separation/divorce and repartnering to predict children’s short- and long-term outcomes without incorporating other changes in children’s households. The second strand of research explores multigenerational and extended family households, documenting children’s exposure to these living arrangements and the associations between these arrangements and children’s outcomes. These studies, however, have mostly conceptualized multigenerational and extended family households as a static characteristic and have rarely acknowledged the instability associated with these arrangements. I consider changes in children’s household composition that result from parents and nonparents leaving or entering their households.

### Parental Relationship Dissolution and Repartnering

Research focused on children’s coresident parents has found that experiencing parental divorce is associated with negative outcomes in childhood, in adolescence, and across generations. Children who experience parental divorce while they are in elementary school have lower math and reading scores, worse social skills, and more negative internalizing and externalizing behavior, on average, than children who do not experience parental divorce (Kim 2011). Experiencing parental divorce as a child is associated with early home-leaving and nonmarital childbearing in adolescence (Cherlin et al. 1995). The negative consequences of divorce may extend across generations because divorce in one generation is associated with lower educational attainment, marital discord, and weaker relationships with parents in subsequent generations (Amato and Cheadle 2005). These studies focused on identifying the effect of experiencing one change in family structure on later outcomes for children.

Other research has considered family structure as a dynamic process unfolding over childhood and adolescence and potentially involving multiple transitions among parents and parental figures. Studies of the cumulative effects of family structure changes showed that repeated transitions in family structures are particularly harmful to children’s development and well-being. Among younger children, exposure to repeated family structure changes is associated with lower school engagement, externalizing behavior, and negative relationships with teachers and peers (Cavanagh and Huston 2006; Fomby and Cherlin 2007; Fomby and Osborne 2010; Lee and McLanahan 2015; McLanahan 2011). Experiencing multiple transitions in family structure is associated with lower educational attainment, early home-leaving, nonmarital childbearing, depression, delinquency, and drug use among adolescents (Aquilino 1996; Brown 2006; Cavanagh 2008; Wu 1996). These findings of negative effects of family structure transitions increase our understanding of the negative effect of family structure itself, suggesting that disruptions in family structure associated with single parenthood are consequential for children, rather than the status of living with a single parent.

### Multigenerational and Extended Families

A separate literature has considered multigenerational and extended family households and the association between these types of family structures and children’s outcomes. Living in multigenerational households is more common among single mothers than among two-parent families (Cohen and Casper 2002; Pilkauskas 2012), and research on multigenerational and extended family households acknowledges the role that these multi-adult households can play for families in need of economic or other support (Bengtson 2001). Infants living with grandparents in a variety of family structures (married parents, cohabiting parents, single parents) generally score better on cognitive tests than infants living in the same family structures without grandparents (Sun and Li 2014). Among older children, those living with never-married single mothers and grandparents are more likely to graduate from high school, more likely to enroll in college, and less likely to smoke or drink than youth living with two married parents, cohabiting parents, or single mothers alone (DeLeire and Kalil 2002). Research comparing children living with single parents and children living with single parents and grandparents has shown that children living with grandparents may have access to more economic resources than their counterparts living with single mothers (Mutchler and Baker 2009). White children in this arrangement have more cognitive stimulation at home and score better on reading recognition tests (Dunifon and Kowaleski-Jones 2007). Children living with grandparents also may be exposed to lower parenting quality, from parents and grandparents, and more familial conflict (Chase-Lansdale et al. 1994; Harvey 2015). These studies compared children living with grandparents and children who do not live with grandparents; they found that coresidence with grandparents can be positive or negative for children depending on the circumstances, but these studies did not estimate whether changes in household composition involving grandparents are positive or negative for children.

Just as scholars of family instability have come to understand family structure as a dynamic rather than a static characteristic, multigenerational and doubled-up households have been shown to be characterized by a great deal of instability (Pilkauskas 2012). In a national sample, more than 60 % of multigenerational households experienced some change in composition within one year, and more than 90 % of such households changed within five years (Glick and Van Hook 2011). These rates of change are substantially higher than the rates of change experienced by children living with parents alone.

Moving beyond point-in-time coresidence with extended family members, some research has estimated the short-term consequences for children of instability among grandparents and other related and unrelated coresident adults. In some cases, changes in household composition involving grandparents or other adults appear to be beneficial: very young children of single mothers who gain a coresident grandparent or a biological parent had a higher rate of cognitive growth than did children living in many stable family structures (Sun and Li 2014). Transitions of grandparents and other adults into and out of a child’s household are associated with early childhood cognitive outcomes independent of parental relationship transitions. These changes are negatively associated with cognitive outcomes among white and African American children but positively associated with cognitive outcomes among Latino children (Mollborn et al. 2012). These studies considered short-term early childhood cognitive outcomes, and the effect of household transitions on longer-term outcomes—like those I consider here—may follow a different pattern. Mollborn et al. (2012) considered transitions among parents, grandparents, and other adult relatives, addressing the omission of nonparent changes in household composition in this literature. By the authors’ own admission, however, the short-term cognitive outcome that they examined has only a tenuous connection to longer-term outcomes. The work of Mollborn and colleagues is foundational in considering children’s coresidence with and instability involving extended family members. In this study, I build on their work by estimating the effect of changes in household composition on longer-term outcomes using a causal inference technique.

Together, these two lines of research point to four general conclusions that motivate the analysis in this study. First, parental relationship dissolution and repartnering matter for children’s outcomes. Changes in family structure involving parents are generally associated with negative cognitive, emotional, and behavioral outcomes. Second, extended family or multigenerational coresidence is associated with resources available to children at home. These can be (1) economic resources, if doubling-up is a strategy for addressing low incomes and high housing costs; or (2) parenting and supervisory resources, if grandparents or other adults provide childcare. Third, children living in multigenerational and extended family households likely experience many changes in household composition given the instability of these arrangements. And fourth, changes in household composition involving extended family members are associated with short-term cognitive outcomes.

Because of the evidence that these changes are associated with short-term outcomes, research on longer-term outcomes should incorporate changes in household composition into measures of disruptions in children’s lives. I use a method designed to facilitate causal inference to estimate the effect of changes in household composition during childhood on two longer-term outcomes: high school graduation and postsecondary enrollment. To accomplish this, I track changes in the presence of parents and other members of children’s households over 17 years and categorize children based on their experience of changes in household composition. Research on child outcomes should account for transitions experienced by children living in doubled-up and extended family households, integrating changes involving extended family and nonrelatives into the literature focused on changes among parents and their partners. If changes involving extended family members and nonrelatives are as disruptive to children as changes involving parents, then research that does not consider the broader household roster is potentially missing changes that could be important for predicting children’s success in school and beyond and underestimating the total costs to children of change in their residential arrangements. I show that the primary focus of prior research on parents and parents’ romantic partners misses many changes to which children are exposed, and I argue that these changes in household composition reflect disruption in children’s developmental contexts that could have lasting consequences.

### Differences by Race and Ethnicity

Research estimating the effect of changes in household composition on children’s outcomes must also consider heterogeneity by race and ethnicity. The distribution of family structure types differs by race; in 2012, 55 % of black and 31 % of Hispanic children in the United States lived with a single parent, compared with 21 % of white and 13 % of Asian children (Vespa et al. 2013). Multigenerational and extended family households represent a relatively small share of family households overall, but 3 % of white-headed family households were multigenerational, compared with 6 % of Asian-headed family households and 8 % of households with a black or Hispanic head (Vespa et al. 2013).

Multigenerational households have high rates of change, so differences in the share of children living in multigenerational households by race and ethnicity could also mean that children in different racial and ethnic groups are exposed to different rates of changes in household composition. Varied prevalence by race/ethnicity in children’s exposure to changes in household composition may also lead to variation by race/ethnicity in the effects of these transitions. If changes in household composition are a less normative experience among white children, these changes could be more disruptive in their lives. These children may feel more stigma about a parental divorce or an uncle coming to live with them, for example, and they could have fewer social and emotional resources to draw on in adjusting to the change. The types of changes may matter. If black children experience more changes involving extended family members whereas white children predominantly experience changes involving parents and their romantic partners, the effects of changes in household composition could differ by race. I show that more children experience changes involving nonparent, nonsibling household members than experience changes involving parents, which is particularly evident among black children. I proceed to estimate whether there are different effects of these changes in household composition by race.

Research focused on parental transitions has suggested that the effects of transitions may differ by race. Repeated family structure transitions are associated with higher externalizing scores among white children but not black children (Fomby and Cherlin 2007), and they are more strongly associated with earlier onset of sexual activity among white adolescents than among black adolescents (Fomby et al. 2010). Changes among coresident extended family members in early childhood have negative associations with short-term cognitive outcomes among white and African American children and positive associations with the same outcomes among Latino children (Mollborn et al. 2012).

### Importance of Education as an Outcome

High school graduation is an important outcome in its own right and also predictive of many other socioeconomic characteristics. Completing high school is associated with lower unemployment rates (Rumberger 1987). High school graduation or an equivalency degree is necessary for postsecondary educational attainment, which is in turn associated with better labor market outcomes. Increased schooling is also positively associated with income earned and wealth acquired over time (Oreopoulos 2007; Rumberger 1987). Beyond employment and income, higher educational attainment is associated with better health (Freudenberg and Ruglis 2007), marriage (Copen et al. 2012; Goldstein and Kenny 2001), and marital stability (Martin 2006). Nonmarital childbearing is more common among women who have less than a high school education than it is among women with more education (Upchurch et al. 2002).

High school graduation and postsecondary enrollment are important as measures of education and as indicators of the likelihood of other later-life socioeconomic characteristics and outcomes. I hypothesize that changes among household members—including parents, extended family members, and nonrelatives—reduce the likelihood of high school graduation and postsecondary enrollment. The literature considering parental relationship dissolution and repartnering proposes a series of theoretical mechanisms connecting parental relationship changes to children’s well-being. These include socioemotional and cognitive work to readjust to a new family structure, stress associated with conditions that precede and follow the change, worsened parent-child relations, exposure to conflict between parents and partners, and disruptions in social support networks as a result of family change (Amato and Keith 1991; Coleman et al. 2000; Fomby and Cherlin 2007). Some of these proposed mechanisms are applicable to children’s experience of changes in household composition involving grandparents and other extended kin and nonkin as well. In particular, if the entry of nonparents into a child’s household is a strategy to address economic hardship (Mutchler and Baker 2009), a negative effect of household change could result from stress associated with material deprivation and the disruption required to address it. Parents who are adjusting to new roles in a household that expands to include other relatives or nonrelatives may have less energy to focus on their children. Further, children may be exposed to conflict between parents and other adults, especially related to “house rules” and methods of childrearing (Harvey 2015). Finally, when a relative or nonrelative leaves a child’s house, that child may experience a disruption in social support provided by the departing individual and that individual’s network.

I connect the literatures on family instability and extended family households and test the hypothesis that changes in household composition involving nonparents affect children’s longer-term outcomes—namely, their educational attainment. In addition to advancing theory on family and household instability, I address methodological limitations of prior research through a causal inference technique employing IPT weighting and marginal structural models.

## Data

I use data from the PSID to measure how changes in household composition experienced during childhood and adolescence affect the likelihood of high school graduation and postsecondary enrollment. The PSID began in 1968 as a nationally representative sample of approximately 4,800 families containing more than 18,000 individuals (PSID 2017). The survey has interviewed these families and their descendants since 1968, annually between 1968 and 1997, and biennially since 1997. The PSID is a large nationally representative survey that includes many waves, following children from the time they are very young through the transition to adulthood and the formation of their own households. I use data from the 1968 wave through the 2015 wave of the study. I construct complete household rosters at each wave of data collection for the 6,554 children who are continuously present in a responding PSID household from age 1 to 17 years. My outcome models are limited to the 5,981 individuals who are present in or reported by a PSID household at age 20, when I measure educational attainment, and for whom I have complete household roster data from ages 1 to 17. I present results from the full sample in addition to results limited to children living with white or black heads of household. The Latino and immigrant subsamples of the PSID do not include a large enough sample of Latino children followed continuously throughout childhood to allow me to present results limited to Latino children. My analyses are weighted to account for sample selection and attrition.

This analysis relies on identifying how people entering and leaving children’s households are related to those children. Constructing household rosters and identifying every household member’s relationship to every other household member is a laborious process. The PSID does not include a household relationship matrix that indicates each household member’s relationship to all other members. Rather, it includes a variable indicating every household member’s relationship to the head of household. The individual-level data also include parent pointers if an individual’s mother or father resides in the same household. I use the relationship to the head and parent pointer variables to identify relationships between children and heads of household and to infer relationships between children and other household members. In the 1968 survey wave, the relationship to head variable has eight values: (1) head (self); (2) wife; (3) child; (4) sibling; (5) parent; (6) grandchild or other child relative; (7) other, including adult relatives; and (8) spouse of head who moved out or died in the year prior to the interview. Coding relationships to children in the household entails logically inferring relationships based on the child’s relationship to the head of household. The first step is using the parent pointers to identify children’s coresident mothers and fathers. After parents are assigned, I use the relationship to head variable to link individuals. For example, if Household Member 4 is listed as the head’s brother and the focal child is listed as the head’s child, then I assume that Household Member 4 is the child’s uncle. If a child does not live with a parent, I use the relationship to head variable to determine both the child’s relationship to the head of household (e.g., grandchild) and the child’s relationship to other household members. To highlight the contribution of nonparents to changes in household composition, I collapse these relationships into two groups: (1) parents (biological, adoptive, and stepparents); and (2) nonparent, nonsibling household members (including extended family members and nonrelatives).

Over time, the relationship to head variable expanded to include many additional values, allowing more specific relationships to be identified. Starting in the 1983 survey, the relationship to head variable includes 33 values capturing members of the head’s immediate family, extended family, in-laws, cohabiting partners, and nonrelatives. Later years of the survey also include parent pointers, so the first step in identifying children’s relationships to other household members remains the same. After parents are identified, I use the relationship to head variable in the later years of the survey the same way I use it for the earlier years. The main difference in the later years is that it is possible to more precisely identify children’s relationships to in-laws and cohabiting partners of the head of household. After assigning specific relationships between children and household members, I collapse these relationships into the same two categories of parents and nonparent, nonsibling household members. In general, I categorize in-laws as other relatives and cohabiting partners and their family members as nonrelatives (see Table A1 in the online supplement for relationship assignment to categories). I categorize cohabiting partners of parents as nonrelatives rather than as parents because cohabiting partners are not classified consistently across waves of the PSID. Before 1983, they appear in the survey simply as nonrelatives (I return to this decision later).

## Methods

My goal is to estimate the effect of household instability in childhood and adolescence on the probability of high school graduation and postsecondary enrollment. Conventional regression methods with baseline control variables are not sufficient for this type of research question because they do not allow me to account for time-varying confounding between my main independent variable (changes in household composition) and other predictors of high school graduation. For example, living in a household with income below the poverty line during childhood is associated with a lower likelihood of graduating from high school (Duncan and Murnane 2011) and a higher likelihood of experiencing changes in household composition independent of other characteristics (Mollborn 2016). If I do not account for time-varying poverty status during childhood and adolescence in my models estimating the effect of changes in household composition on high school graduation, I would attribute any independent effect of poverty on high school graduation to changes in household composition. Conversely, if I control for time-varying covariates, such as poverty status and homeownership, I would fail to capture the indirect effect of changes in household composition on high school graduation that operate through these covariates.

One solution to this dilemma is to use marginal structural models and IPT weighting to explicitly account for time-varying covariates (Robins et al. 2000). These models address bias from time-varying covariates, such as income, that can influence and be influenced by time-varying treatments—in this case, changes in household composition. In essence, the models adjust for these confounding factors that occur prior to the current household composition (and therefore may be determinants of current household composition) and do not adjust for the values of the same confounders that come after the current household composition (and therefore may be its consequences). As in standard regression models, marginal structural models using IPT weighting assume no unmeasured confounding conditional on the covariates included in the prediction and outcome models (Robins et al. 2000). To interpret the results of these models as causal estimates, the models must include all confounding factors.

The first step in this process is creating IPT weights. I use each child’s exposure to household composition change in the prior wave, baseline covariates, and prior wave time-varying covariates to predict the probability of the observed type of household change the child experienced in the current wave. Using four logistic regression models, I predict the probability of experiencing one of four mutually exclusive types of household change: (1) change involving only a parental figure; (2) change involving only a nonparent, nonsibling household member; (3) change involving both a parent and other household member; and (4) no change.1 I take the inverse of the predicted probability of the observed household change and use that to weight each child’s contribution to a pseudo-population in which household change in each period is independent of prior confounding variables, making it unnecessary to control for time-varying confounders in the final regression model because they are accounted for by the weight.

I use a stabilized IPT weight to achieve narrower confidence intervals because IPT weights tend to be highly variable (Robins et al. 2000).2 To create a stabilized weight, I predict the probability of the observed type of household change experienced by each child, using exposure to household change in the prior wave and time-invariant baseline covariates, omitting time-varying covariates from the prior wave. I calculate the stabilized weight by multiplying this second predicted probability by the inverse of the first predicted probability. This is shown in Eq. (1):
$swi=∏t=117PEt=etiE¯t−1=e¯t−1iX0=x0PEt=etiE¯t−1=e¯t−1iX¯t−1=x¯t−1i.$
1

In each period (t), I estimate the probability of the actual type of household change experienced by the child (eti), given the history of both household changes ($e¯t−1i$) and other confounders, such as poverty status and homeownership in the prior wave ($x¯t−1i$). After I have a predicted probability from each wave that the child is observed, I multiply these probabilities across waves to create the final stabilized IPT weight. The models used to predict changes in household composition and create the IPT weights include baseline characteristics of the child, household, and head of household. Child-specific baseline characteristics include indicators for sex (female = 1), whether the child lives with married parents, whether the head of household is the child’s parent (vs. a nonparent relative or nonrelative), and whether the child has a sibling (a proxy for birth order). Baseline, in this instance, is the year of the child’s entry into the survey, which happens around the time of the child’s birth, ranging from 1968 to 1999. For the head of household, I control for sex, race/ethnicity (indicators for black, Hispanic, and other race, with white as the reference category), age, educational attainment (indicators for less than high school, some college, and bachelor’s degree or more, with high school diploma as the reference category), employment status (indicators for unemployed and retired/disabled, with employed as reference), marital status (single, widowed/divorced/separated, with married as the reference category), and current region of residence. I also include a number of household-level baseline characteristics: whether the home is owned, rented, or neither; household income (five categories based on quintile cut points in the national income distribution); an indicator for household income falling below the poverty line; household size; and number of children in the household. I cluster standard errors by household to account for multiple observations per household.

My unit of analysis is an individual child, and characteristics of his or her household could change substantially across waves as the composition of his or her household changes across waves. Therefore, to predict household change experienced before the current wave, I include prior wave time-varying measures of many of the same characteristics measured and included at baseline: whether the child’s parent is head of household; the household head’s sex, age, education, employment, marital status, and region of residence; household size; homeownership; income and poverty status; number of children; and age of youngest child. I include baseline but not time-varying indicators for the household head’s race/ethnicity because there is very little variation across waves. Even if the household head changes because the original head moves out or the child lives with a different family member, the race/ethnicity of the head is nearly constant.

After I construct the stabilized IPT weight, I use this weight to run weighted logistic regression models with high school graduation and postsecondary enrollment as the outcome, as shown in Eq. (2):
$logitIPT−weightedPYi=1=α+γ1p+γ2o+γ3b+x0β.$
2

I categorize children by the type of household changes they experienced from ages 0 to 17: change among parental figures only (p); change among nonparent, nonsibling household members only (o); changes among both parents and nonparents (b); and no such changes. My main predictor variables are indicators for membership in the first three categories, with no changes as the reference category. Coefficients for these variables represent estimated causal effects of exposure to household changes on high school graduation or postsecondary enrollment, conditional on the assumption that all confounders are measured and included in the model. In addition to these three dummy variables, my weighted logistic models control for the baseline variables from the prediction model (x0) because using stabilized weights reintroduces correlation between the household composition variables and the baseline covariates.

## Results

Table 1 presents survey-weighted baseline descriptive statistics for the sample of individuals for whom I observe the outcome of high school graduation, pooled across all waves of the PSID. The table presents characteristics of the individuals’ households and heads of household (typically their parents) and themselves, for the full sample and separately among white children (approximately 80 % of the sample) and black children (14 %). Reporting these descriptive statistics separately by race emphasizes the different household contexts white and black children experience during childhood. Just under one-half of the children in the sample are female. Most (92 %) white children lived with married parents at baseline (soon after the child’s birth), compared with 43 % of black children. (Children living with two parents, with one parent, and with no parents are all included in my sample.) In terms of outcomes, 86 % of white children graduated from high school, and 50 % enrolled in postsecondary education; corresponding figures for black children are 74 % and 29 %, respectively. Of the approximately 6,000 individuals in the analytic sample, 12 % overall lived in a household headed by a female at baseline, but nearly one-half of black children lived in a female-headed household at birth. Six of 10 white children lived in households owned by the household head, and a similar proportion of black children lived in rented households. At baseline, about 6 % of white children had household incomes below the poverty line, while 39 % of black children lived in impoverished households. The average household size was just over four people for white children and just over five people for black children.

At baseline, 13 % of children in the sample lived with an extended family member and/or a nonrelative. Racial differences in household composition are evident here: 8 % of white children and 37 % of black children had nonparent, nonsibling coresidents. Overall, approximately 8 % of children lived with a grandparent at baseline; more than 5 % of children lived with aunts, uncles, and/or cousins; and just over 1 % lived with a nonrelative (including cohabiting partners of parents and their relatives).

Table 1 also presents statistics on changes in household composition across childhood and adolescence. I categorize children into four mutually exclusive categories based on their experiences of household change. Nearly one-half (48 %) of the children in the sample experienced no change among a parent or a nonparent, nonsibling household member in the first 17 years they were observed by the PSID. Fifteen percent experienced at least one change involving a parent entering or leaving their household but no changes among other relatives or nonrelatives, and 17 % experienced at least one change involving a nonparent, nonsibling household member but none involving a parent. The nonparent, nonsibling household members include other relatives, such as grandparents, aunts, uncles, and cousins; they also include nonrelatives, such as cohabiting partners of the household head, friends, or boarders. Among children for whom I can always distinguish cohabiting partners of parents from other nonrelatives (those entering the survey in 1983 or after), only 7 % of children in the sample who experienced changes involving only nonparent, nonsibling household members experienced changes only among cohabiting partners of parents.3 Thus, only 47 of 667 children would be categorized differently if I had a separate category for cohabiting partners of parents. (I return to the implications of this choice in the section titled Supplementary Analyses.) The remaining 20 % of children in the full sample experienced changes involving both parents and other household members before age 17. These two changes could have happened simultaneously in the same wave of the survey, or they could be separated by many years and waves. This fourth category includes children who have experienced two different types of changes in their household composition.

Figure 1 presents children’s exposure to changes in household composition in a different and revealing manner. Figure 1 shows the weighted cumulative percentage of children who experienced changes in household composition involving their parents and the percentage of children who experienced changes involving nonparent, nonsibling household members during childhood and early adolescence (up to age 17). This figure is limited to children for whom I can track and display annual changes in household composition (i.e., those who entered before 1981 and were observed annually for 17 years before the PSID switched to biennial data collection in 1997). Among these children, 35 % experienced at least one change involving parents during childhood, and 36 % experienced at least one change involving nonparent, nonsibling household members.

The seventh and eighth rows of Table 1, under Cumulative Percentage of Children Exposed to Change, show equivalent statistics for the full sample, and the findings are similar: 33 % of children experienced a change involving parents, and 36 % experienced a change involving other household members. Disaggregating by race reveals that nearly one-half of black children and approximately one-third of white children experienced a change involving parents. Furthermore, 70 % of black children experienced a change involving other household members, compared with just under 30 % of white children.

These cumulative percentages may appear to be at odds with the proportion of children in each category of household change shown above them in Table 1. Recall that the statistics under Household Change Category report mutually exclusive categories of household change, and Fig. 1 and the cumulative percentage statistics demonstrate overall exposure to change. Some of the 33 % of children experiencing a change involving parents are also among the 36 % of children experiencing a change involving nonparents: they fall into the change in parents and nonparents category under Household Change Category. The mutually exclusive categories indicate that the 17 % of children who experienced changes involving only nonparents are missed in measures of family instability focused on parents, while the cumulative percentages demonstrate that not accounting for changes in household composition involving nonparents results in overlooking changes affecting nearly 40 % of children overall and 70 % of black children.

The descriptive analyses show how common changes in household composition are, and the multivariate analyses presented next examine the characteristics that predict exposure to changes in household composition and the effects of these changes on educational attainment. Results from the prediction models used to estimate the IPT weights show that in general, living with married parents at baseline, with a more-educated head of household, and in a home that is owned and not rented is associated with more stability in household composition during childhood. Experiencing a change in household composition at one wave is highly predictive of experiencing the same type of change in a subsequent wave. Complete results from these models are shown in the online supplement.

Table 2 presents the results from the IPT-weighted logistic regressions. I present results from a regression on the full sample and then show results from regressions that include an interaction between household change and race (comparing white children and black children). In the full sample, experiencing changes in household composition involving one’s parents or experiencing changes in household composition involving parents and nonparent, nonsibling household members is associated with a significant reduction in the odds of graduating from high school, by between 30 % and 40 % (coefficients for all variables in the model shown in Table A2 in the online supplement). This is net of baseline family structure and family structure in the prior wave because these are accounted for by the baseline controls and IPT weight. All three of the coefficients for household change are significantly negative in the model predicting postsecondary enrollment in the full sample: experiencing changes involving only parents, changes involving only nonparents, or changes involving parents and nonparents are significantly associated with substantially reduced odds of enrolling in postsecondary education.

Disaggregating the sample into the two main racial groups represented in the PSID suggests that the effects of changes in household composition may be worse among white children than among black children. Table 2 shows that among white children, changes involving parents, changes involving nonparents, and changes involving both parents and nonparents are all significantly associated with reduced likelihood of high school graduation and postsecondary enrollment. Figs. 2 and 3 plot the average predicted probability of high school graduation and postsecondary enrollment among white children in the four categories of household change.4 White children experiencing no change in parents or other nonsibling household members have a predicted probability of high school graduation of 87 %. The predicted probability drops to 82 % among white children experiencing changes involving parents only, to 83 % among those experiencing changes involving only nonparents, and to a low of 81 % among children who over the course of childhood experienced changes involving parents and nonparents. The difference in predicted probability by household change is starker for postsecondary enrollment: white children experiencing no changes have a predicted probability of postsecondary enrollment of 51 % compared with 40 % among white children who before age 17 experienced household changes involving parents and nonparents.

Among black children, however, the findings are different. Experiencing changes involving parents does not significantly predict high school graduation, and the coefficient for changes involving nonparents is positive and marginally significant. The marginally significant and negative association of changes involving nonparents with high school graduation among white children is significantly different than the estimated positive association among black children (p < .05). This holds in the model predicting postsecondary enrollment: the association with changes involving nonparents is significantly negative among white children and not significantly different from 0 among black children. These results suggest that changes involving grandparents, other extended family members, and unrelated household members are significantly worse for white children than for black children.

### Supplementary Analyses

I conduct a number of supplementary analyses that increase my confidence in my results. Some readers may be concerned about my decision to categorize parents’ cohabiting partners as nonrelatives rather than as parental figures. As I noted earlier, less than 10 % of children who experienced changes only among nonparent, nonsibling household members experienced changes only among cohabiting partners of parents. I conduct a supplemental analysis reclassifying these children as experiencing changes involving parents instead of changes involving nonparents, and the results for postsecondary enrollment do not change (shown in Table A3 in the online supplement). Classifying parents’ cohabiting partners as parents supports a stronger argument for differences by race in the model predicting high school graduation. In the models presented in Table 2, the coefficients for other change are significantly different by race; in these supplemental models, the coefficients for both parent change and nonparent change are significantly different by race.

I use a different specification in my outcome model than is common in recent research employing marginal structural models. These models are typically used to measure duration effects, and the outcome models use a count of time spent in a certain condition, or an average measure of exposure, to predict the outcome of interest. The equivalent specification in my case would be to sum all changes in household composition that children experience during their first 17 years and use those counts as predictors of educational attainment. Using this specification assumes that the number of changes has a linear relationship with educational attainment—that the first change involving parents, for example, would have an equivalent effect as the second or third change involving parents, which is not necessarily predicted by prior research and theory. This alternative specification as a model with count variables instead of categorical variables returns negative coefficients for changes involving parents, nonparents, and both parents and nonparents. Results from models with counts as independent variables are shown in Table A4 in the online supplement. All the significant and negative coefficients in Table 2 are also negative in Table A4 (see the online supplement): some are large in magnitude, but not all reach conventional levels of significance.

Another option addressing the linearity assumption would be to create a series of indicator variables that account for thresholds in the number of changes by type of change. I present two such specifications in the online supplement and show that my main conclusions are unchanged.

In general, research on family instability has moved away from categorical conceptualizations of instability such as the one I present here. Although my categorization of exposure to household change does not explicitly account for the number of changes children experience, as a count or threshold model could, it is representative of the amount of volatility that children experience in their households and captures meaningful differences in household instability. In my sample, children who experience change only among parents are, on average, exposed to fewer changes over time than are children who experience change involving only other household members. Children who experience changes involving both parents and other household members are exposed to the most change in household composition over time. I control for baseline family structure in the models predicting educational attainment, and the weights I construct account for family structure during childhood, increasing my confidence that I am measuring an effect of changes in household composition. The correct way to specify household instability is probably not dichotomous or categorical, but it is also probably not linear. We do not know the true functional form of how changes in household composition are related to children’s outcomes. In the main text and online appendices, I present four approaches to measuring household instability, and all support similar inferences.

The online supplement presents six additional tests: (1) results from logit models not weighted with the IPT weight (i.e., weighted with the survey weight alone); (2) race-specific stabilized IPT weights; (3) heterogeneity by class; (4) differences across time; (5) different categorical specifications of household change; and (6) differences by the timing of change during childhood. None of these models come to substantively different conclusions than those presented in the main text.

## Discussion

My findings show that changes in household composition involving parents and nonparents are consequential for children’s educational attainment and, in turn, their well-being. I demonstrate the value of conceptualizing the changes in developmental environments to which children are exposed as a product of broader changes in household composition, rather than family instability as traditionally understood. Informed by previous research on family instability and multigenerational households, this article contributes to both literatures by accounting for household changes that children experience beyond parents and their partners and by capturing the dynamic nature of extended family living arrangements. Further, I include in my measure of change household members not related to the child, acknowledging the contributions of nonrelatives to household instability.

I use inverse probability of treatment (IPT) weighting and marginal structural models to reduce bias as a result of selection into household structure and changes. These models improve upon ordinary least squares models by addressing time-varying confounding variables, but they still rely on assumptions in order to interpret the results as causal effects. In particular, these models assume that all the characteristics that predict household change and are also associated with educational attainment are included as covariates in the prediction models that I use to estimate the weights. I include a number of characteristics of the individual child, head of household, and household in these models, but perhaps other characteristics—such as health problems of household members, housing characteristics beyond tenure, and characteristics of family members outside the household—independently predict household change. I use this method as an attempt to estimate causal effects, and I am explicit in this aim (see Hernán 2018), but readers should keep in mind the assumptions required to interpret my estimates as causal effects and potential threats to validity.

Changes among household members do not appear to affect all children equally: the effects of changes involving nonparents on high school graduation and postsecondary enrollment differ significantly by race. Why might this be? As discussed earlier, family structures differ by race. A larger share of black children compared with white children live with single parents (Sarkisian and Gerstel 2004; Vespa et al. 2013), and children living with single mothers are more likely than children living with two parents to live in doubled-up and multigenerational households (Cohen and Casper 2002; Pilkauskas 2012).

In fact, the types of household change that children in my sample experienced differ substantially by race. Overall, 48 % of the sample experienced no change among parents or other nonsibling household members. Among whites, 55 % experienced no change, but this statistic was only 17 % among blacks. A smaller share of blacks was exposed to changes among parents only compared with whites (11 % versus 16 %, respectively). And a larger share of blacks was exposed to changes among other household members (33 %, compared with 14 % for whites) and changes among both parents and other household members (39 %, compared with 16 % for whites). Black children are thus less likely than white children to experience changes involving only parents but are more likely than white children to experience any change involving a parent. Exposure to changes in household composition is less common among whites than among blacks and could perhaps be a more disruptive change in the lives of white children if they are less familiar with the experience and less equipped to adjust to the change. Recent research on the heterogeneous effects of divorce supports this hypothesis: the negative effect of parental divorce on high school graduation and postsecondary educational attainment appears to be limited to children with the lowest propensity to experience parental divorce (Brand et al. 2017).

Other possible explanations could account for the differences by race. For example, high school graduation and postsecondary enrollment rates differ by race. In my sample from the PSID, 86 % of white children graduated from high school, and 50 % enrolled in postsecondary education. Corresponding figures for black children were only 74 % and 29 %, respectively. Perhaps among blacks, those children who are most susceptible to disruption from household changes are already not graduating from high school or enrolling in postsecondary education for some other reason. The disruption from household change may not move the needle.

I conceptualize changes in household composition as indicators or markers of volatility in the lives of children. Perhaps changes in household composition are a better indicator of volatility among white children than among black children if these changes are more common among blacks and potentially have less stigma attached to them. The developmental contexts of white children and black children likely differ, on average, in other ways that could explain why a change in household composition may be more disruptive to white children. For example, black children are exposed to very different neighborhood environments than white children, living in more disadvantaged, impoverished, and violent contexts, on average (Perkins and Sampson 2015; Quillian 2003). Black children are also much more likely than white children to experience the incarceration of fathers and extended family members (Chung and Hepburn 2018), which could prompt many different types of household composition change by removing parents from the household and pushing other relatives to join the household to provide resources and care. Some evidence shows that black children are less negatively affected by family structure transitions because they have greater social protection—that is, support from other kin—and face greater socioeconomic stress (Fomby et al. 2010). In sum, these differences suggest that exploring heterogeneous effects, by race and other characteristics, in future research would be worthwhile. Relying on the PSID limits my analysis to exploring differences between white and black children, but future work should consider additional racial/ethnic groups as well.

The advantage of using the PSID to track changes in household composition is that the study follows individuals over a long period, providing household rosters every year or two years. The disadvantage is that some residential arrangements are much shorter-lived, occurring between waves, and these entrances and exits are not captured by an annual or biennial survey. Compared with an annual survey, data collected every four months by the Survey of Income and Program Participation (SIPP) show 20 % more changes in household composition, but the SIPP panels of two and a half to four years do not permit the estimation of long-term effects (Perkins 2017).

In conclusion, by showing that changes in nonparental household members are both common and consequential for children, this article contributes to the literatures on family instability and multigenerational households by broadening the conceptualization of family instability to incorporate changes among other members of children’s households. That changes involving other household members and changes involving parents have similar effects on postsecondary enrollment suggests that prior research that has not accounted for other household members provides an incomplete understanding of how changes in children’s families and developmental environments matter for their longer-term outcomes. Research focused narrowly on instability among parents misses household changes among the 17 % of children who experienced a change among nonparent, nonsibling household members during childhood but not among parents. Prior research on family instability characterizes these children as having stable households, which could understate the consequences of disruption because children with parental instability are being compared with a mixed group of those with and those without other types of changes.

I also make a methodological contribution by using time-varying methods to facilitate causal inference to show that changes in parental and nonparental figures matter for children’s educational attainment. This overall finding masks heterogeneity by racial group because the negative effect of changes in household composition is limited to white children. Among black children, the causal effects are not significant.

This topic is ripe for further research. Scholars studying the causes and consequences of family instability for children should account for the facts that many children who are categorized by conventional measures of family instability as having stable homes in reality experience meaningful changes in household composition, and that many children who experience changes involving parents experience additional changes involving nonparents. Are some changes beneficial for children, despite the negative average effect presented here? Perhaps experiencing sequential or multiple changes involving parents or nonparents amplifies the disruption associated with household change. In addition, changes involving two household members may have different effects if the changes occur at the same time versus being separated by a year or more. We might expect a significant interaction between two types of changes only if they occur at the same time.

It would be worthwhile to give more attention in future work to how different specifications of change affect outcomes differently. For example, future work should expand the categories of change modeled here to consider the number and type of changes as well as changes among adult household members versus the entry and exit of children, given that the age of household members could have meaningful implications for resources available to children. I categorize cohabiting partners of parents as nonrelatives in this analysis for the sake of consistency across survey waves. Separating the effects of changes involving short-term versus long-term cohabitors could be a worthwhile direction for future research. A holistic approach to studying the effects of changes in household composition on children’s outcomes is supported by recent research introducing the concept of developmental ecologies that suggests that the effects of repeated exposure among young children to changes in coresident maternal romantic partners and grandparents on kindergarten outcomes vary by the socioeconomic resources available in, and health risks posed by, children’s families, homes, and environments (Mollborn 2016). Future research should take a more holistic view of families and households to more accurately represent change and volatility in children’s lives and estimate how experiences in childhood predict later-life outcomes.

## Acknowledgments

An earlier version of this article was presented at the 2017 annual meeting of the Population Association of America in Chicago, IL. For excellent comments and guidance, I gratefully acknowledge Kathryn Edin, Alexandra Killewald, Ann Owens, Robert J. Sampson, Daniel Schneider, and Bruce Western. Matthew Arck helped with formatting. Any errors are my own. This research was supported by the Joint Center for Housing Studies of Harvard University and a Harvard University grant from the Multidisciplinary Program in Inequality & Social Policy. The collection of Panel Study of Income Dynamics data used in this study was party supported by the National Institutes of Health under Grant No. R01 HD069609 and the National Science Foundation under Award No. 1157698.

## Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Notes

1

I can observe children who enter the survey between 1968 and 1980 every year given the PSID’s annual data collection from 1968 until 1997. I include in my sample children who entered the survey after 1980 and remained in the survey until age 17, but I do not observe them every year because the PSID switched to biennial data collection in 1997. I use four logistic regression models to predict the four mutually exclusive types of household change rather than a multinomial logistic regression model because the multinomial model does not allow me to account for the variation in the length of time between observations (annual vs. biennial) both within children and between children in my prediction models; specifically, Stata does not allow the use of the offset option in multinomial models to account for different exposure time. Using a multinomial logistic regression model produces similar results (available upon request).

2

The unstabilized IPT weights that I estimate range from 1.21 to 1.15 × 1016 (with a standard deviation of 1.46 × 1014), whereas the stabilized weights range from 0.002 to 1.92 × 108 (SD = 2,372,773). This range demonstrates that the stabilized weights include both very small and very large numbers, so for analysis, I truncate the weights at the 5th and 95th percentile, resulting in a stabilized weight that ranges from 0.10 to 2.34 (SD = 0.54).

3

Although 7 % of children in this category experienced changes involving only cohabiting partners of parents, 8 % of children in this category experienced at least one change involving a cohabiting partner of a parent. Thus, 92 % of children in this nonparent, nonsibling change category experienced a change involving an extended family member or nonrelative who is not a cohabiting partner of a parent. Among the 788 children who experienced changes involving both parents and other household members, 27 % experienced at least one change involving a cohabiting partner of a parent. Cohabiting partners of parents are thus not responsible for the majority of nonparent changes to which children are exposed. Cohabiting partners are not even responsible for most changes involving nonrelatives. Fewer than one-half of the nonrelative changes experienced by children entering the survey after 1983 involved cohabiting partners.

4

These predicted probabilities are calculated using the Stata margins command with estimates from the stabilized IPT–weighted outcome model and interacting category of household change with race (white vs. black).

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