## Abstract

The prevalence, consequences, and unequal distribution of parental and own incarceration in the United States are well documented. However, much of our knowledge of the reach of the carceral state into family life is focused on incarceration of a parent, romantic partner, or child, to the exclusion of other important relationships. Using data from the Family History of Incarceration Study, a nationally representative survey of U.S. adults (N = 2,029), this study introduces novel descriptive measures that provide a more comprehensive picture of the demography and racially unequal distribution of family incarceration: degree, generational extension, and permeation. This analysis shows that Black adults in the United States are not only more likely to have experienced family incarceration but are also more likely to have had more family members incarcerated (5.3 members vs. ≤2.8 members for adults of other racial/ethnic groups) and to have had family members from more generations ever incarcerated (1.7 generations vs. ≤1.1 generations for those of other groups). Further, the stability of these estimates across model specifications underscores the importance of interrogating long-standing approaches to the analysis of linkages between race, the criminal legal system, and family life and the investigation of racialized systems and social inequality more broadly.

## Introduction

Nearly half of all residents of the United States have ever had an immediate family member incarcerated (Enns et al. 2019). Black residents are substantially more likely than residents of other racial/ethnic groups to have had a family member incarcerated (Enns et al. 2019; Wildeman 2009) or to have been incarcerated themselves (Enns et al. 2019; Pettit and Western 2004). Further, experiences of one's own incarceration and that of one's family members are linked to adverse outcomes in virtually all domains of well-being across the life course (e.g., Foster and Hagan 2007; Wakefield and Wildeman 2014). These features of incarceration situate it as a core component of racial inequality and stratification in the United States (e.g., Alexander 2012; Roberts 2004; Wakefield and Uggen 2010; Wildeman and Muller 2012; Wilson 1987).

The central role of mass incarceration as part of the landscape of U.S. inequality includes its intersection with family life. Incarceration has the potential to put tremendous pressure on families, straining social and financial resources (e.g., Bruns 2020; Green et al. 2006), restructuring social roles and responsibilities (e.g., Braman 2004; Nurse 2002; Turney 2014), and adding logistical and emotional challenges to family relationships during and after incarceration (e.g., Comfort 2008; Gurusami 2019; Waller and Swisher 2006). Incarceration is also linked to family life through its impacts on core demographic processes. For example, a growing scholarship has explored whether and how incarceration shapes fertility (e.g., Cancian et al. 2016), mortality (e.g., Pridemore 2014; Wildeman and Muller 2012), and family instability (e.g., Sykes and Pettit 2014; Wildeman et al. 2016).

However, examinations of incarceration and family life have two characteristics that limit our understanding of the demographic contours of family incarceration. First, prior analyses focus nearly exclusively on relationships centered in the White, upper-middle-class construct of the nuclear family (e.g., Coontz 1992; Letiecq 2019; Nelson 2014). This work focuses on immediate family—parents, partners, and children—to the exclusion of other relationships that may be equally or more important to a person's social world (e.g., Amorim 2019; Eriksen and Gerstel 2002; Meek 2008) and without consideration of how family size and composition may be related to differential risks of family incarceration.1 A second limitation to analyses of family incarceration is their focus on prevalence (e.g., Enns et al. 2019). As descriptions of the reach of the carceral state, prevalence estimates of family incarceration are certainly more informative than measures limited to current incarceration. However, prevalence measures effectively flatten experiences of family incarceration, obscuring differences in numbers of family members incarcerated, generations of family impacted, and other ways in which this experience might vary. The focus to date on immediate family and prevalence in the study of mass incarceration may therefore yield an incomplete understanding of the impacts of this policy regime, potentially underestimating racial inequalities in the reach and consequences of family incarceration (Chung and Hepburn 2018; Lee et al. 2015; Wildeman and Wakefield 2014).

This study uses nationally representative data from the Family History of Incarceration Study (FamHIS) to examine racial/ethnic inequalities in the depth and distribution of incarceration in families of U.S. adults. I introduce three new descriptors of family incarceration to look beyond prevalence and beyond parents, partners, and children: degree (number of family members), generational extension (horizontal, upward, or downward generation), and permeation (number of generations). This descriptive analysis sheds light on previously unexamined dimensions of inequality in family incarceration exposure. I find that in addition to being more likely to experience family incarceration, Black adults experience substantially greater degree and permeation of family incarceration than adults in other racial/ethnic groups. Further, disparities between Black and non-Black adults in family incarceration prevalence, degree, generational extension, and permeation are statistically distinguishable even after accounting for key correlates of family configuration and criminal legal system contact.

## Background

In an era of persistently high rates of incarceration in the United States (Walmsley 2018), researchers have documented the reach of the carceral state into life outside jail and prison walls (Braman 2004; Clear 2007; Lerman and Weaver 2014). This work focuses primarily on the incarceration of parents, romantic partners, and children (e.g., Comfort 2008; Foster and Hagan 2015; Wildeman 2009; Wildeman and Wakefield 2014) and has found that their incarceration has the potential to reshape the tempo, structure, and tenor of family and daily life (e.g., Arditti et al. 2003; Comfort 2016; Miller 2021).

Parent, partner, and child incarceration have also been found to be consistently and negatively associated with well-being over the life course (e.g., Arditti 2012; Wakefield and Uggen 2010; Wildeman et al. 2018). Incarceration of these relations is associated with lower levels of school engagement and attainment (e.g., Cho 2009; Hagan and Foster 2012; Haskins 2014) and higher risks of relationship instability (e.g., Turney 2014, 2015), infant mortality (e.g., Wildeman 2012), and poor adult health (e.g., Lee et al. 2014), for example. The racially unequal distribution of parent, partner, and child incarceration across the population, coupled with these multifaceted negative associations, positions incarceration as a core component of family inequality in the United States (e.g., Patillo et al. 2004; Wildeman and Wang 2017).

### Beyond Partners, Parents, and Prevalence

However, there are some critical limitations to our current understanding of this dimension of family inequality. First, as previously mentioned, the scholarship is constrained by its focus on social relationships construed to be most central to one's life (i.e., parents, romantic partners, and children; Wildeman and Muller 2012). So far, this limited view of the family, combined with the absence of appropriate quantitative data, has made it difficult or impossible to detail incarceration of relations beyond the immediate or nuclear family.2 This focus on biological proximity effectively privileges familial relationships and norms predominantly held by the White middle to upper class (Coontz 1992; Roberts 2002; Smith 1993). In doing so, prior analyses have taken a prescriptive approach, perhaps inadvertently, defining the relationships assumed to be most consequential for those “left behind” by their incarceration (Wildeman and Wakefield 2014:372, 375).

Yet, families include relations other than parents, partners, and children, and relationships with these other individuals are also important correlates of well-being and outcomes over the life course (e.g., Cross 2020; Hall and Crowder 2011; Turney 2014; Youngblut et al. 2015). Siblings, for example, influence one another's well-being in childhood and can later serve as sources of support in adulthood (e.g., Brody 1998; White and Riedmann 1992). Grandparents and other relations—particularly grandmothers and aunts—often serve as primary or secondary caregivers and as critical sources of in-kind support in families (e.g., Gerstel 2011; Jaeger 2012).

Additionally, prior work documenting variation in family and support networks across racial/ethnic groups and family configurations (e.g., single-parent families) found that people who are more likely to have extended family centrally involved in daily life (e.g., Sarkisian 2007; Sarkisian and Gerstel 2012) are of the same social groups that are disproportionately likely to experience family incarceration (Enns et al. 2019). Family demographic research would suggest that the impacts of incarceration of family members other than parents, partners, or children may be more severe for Black persons and families, who are simultaneously at higher risk of carceral contact (Enns et al. 2019; Pierson et al. 2020) and more likely to be close to, receiving support from, or living with extended family (e.g., Benin and Keith 1995; Cross 2018; Erola et al. 2018; Moore 1990). Family disruption and strain linked to incarceration could therefore be related to inequality in at least two ways: through unequal distribution and unequal impact.

Further, recent estimates show that the incarceration of family members other than partners, parents, and children is common. Sibling incarceration (27%) is 1.5 times to twice as common as parental (18%), partner (14%), or child incarceration (12%) (Enns et al. 2019). Moreover, analysis of these other types of family carceral contact finds that these experiences are unequally distributed, with individuals identifying as Black disproportionately and more likely to be exposed (Boen et al. 2022; Enns et al. 2019). To date, many analyses drawing on data on extended family incarceration use that information in attempts to account for “family effects” or supposed predispositions to criminality, rather than as a type of carceral contact itself (e.g., Besemer et al. 2018; Buhller et al. 2018; Harding et al. 2017; Norris et al. 2021).

A second limitation to current understanding of family incarceration in the United States is the focus to date on prevalence, and particularly, as noted above, prevalence of parent, partner, and child incarceration. This focus on prevalence may mask other key differences in incarceration risk and exposure. Just as families vary in size, structure, and composition (e.g., Cross 2018; Fomby and Cherlin 2007; Perkins 2017; Swartz 2009), the structure and distribution of incarceration within families also likely vary in important ways.

To illustrate the impact of these limitations, consider two hypothetical individuals, one whose father was incarcerated and a second whose father and aunt were incarcerated. The most common contemporary approaches to studying family incarceration would capture the fact that both individuals have had family incarcerated, but not differences in the number of family members ever incarcerated or differences in the relationships affected. Indeed, predominant approaches that focus on immediate family would entirely fail to capture the aunt's incarceration in this example.

Without a more comprehensive understanding of the configurations of incarceration within families and how these vary across racial/ethnic groups (or not), description and analysis of family incarceration are susceptible to oversimplification of the experience and potential misidentification of the outcomes and effects of carceral contact. Put in technical terms, without a better handle on the heterogeneity of family incarceration, the experience of having one relation incarcerated is measured as similar or as having similar “effects” as having a family with multiple generations of incarceration exposure.

### Detailing Family Incarceration: Social Network and Family Demographic Approaches

In this study, I examine racial/ethnic inequality in exposure to family member incarceration using measures beyond prevalence. For this task, conceptual tools commonly leveraged in family demographic and social network analyses are especially useful. The family is, after all, a social network (e.g., Bott 1957; Chung and Hepburn 2018; Stack 1974), one with sociocultural and legal definitions (e.g., Bea and Poppe 2021). The conceptualization of families as social networks and incarceration as a shock that moves through them is central to our understanding of incarceration as a mechanism of inequality (e.g., Haynie et al. 2018; Mowen and Visher 2016; Wakefield 2016; Wildeman and Wakefield 2014). Here, I provide new detail about family incarceration in the United States and racial/ethnic inequalities therein by combining family demographic tools, a social network perspective on the family, and an eye to the racialized effects of incarceration on families. To do so, I describe family incarceration using race/ethnicity-specific estimates of the prevalence, degree (number of family members), generational extension (same, older, or younger generation), and permeation (number of generations) of incarceration in families of adults. I use regression analysis to account for variation in family and life course contexts (e.g., parental status) and other socioeconomic and demographic characteristics and contexts that are understood to be correlates of exposure to family incarceration.

Given the racialized history of the criminal legal system in the United States (Beckett and Western 2001; Miller 2013; Muller 2012; Thompson 2020), I anticipate that these new descriptors of family incarceration will provide additional detail about racial disparities in family incarceration that prevalence measures cannot capture. Indeed, prevalence estimates may mask other critical dimensions of inequality related to incarceration, namely, the profundity and intensity with which incarceration reverberates through family systems. Existing knowledge of family and household diversity suggests multiple plausible hypotheses about racial/ethnic differences in family incarceration. Accounting for dimensions of social variation related to, but not wholly distinct from, race and racism in the United States might partially explain anticipated racial/ethnic differences in family incarceration. On the other hand, it is possible that social organization in the United States is so profoundly racialized that any racial/ethnic differences in family incarceration are not further clarified by incorporating information about other dimensions of social life linked to family structure and composition or criminal legal system contact.

## Data, Measures, and Methods

### The Family History of Incarceration Study

This analysis uses data from the Family History of Incarceration Study, a nationally representative survey of noninstitutionalized adults residing in the United States in 2019. These data were the basis for the first-ever estimates of the prevalence of family incarceration in the country (Enns et al. 2018; Enns et al. 2019). The FamHIS is based on the AmeriSpeak panel operated by the National Opinion Research Center (NORC) at the University of Chicago (NORC 2019) and has features that make it uniquely appropriate for studying family incarceration at a national scale. The FamHIS sample is a probability-based sample drawn from a respondent panel that oversamples adults from age and racial/ethnic groups often underrepresented in survey data (Dennis 2016). Additionally, the survey was administered in both English and Spanish and through web and phone response options, mitigating potential nonresponse and social desirability bias (Dennis 2016).

The FamHIS survey instrument includes a set of roster-based items about family incarceration that respondents experienced at or before the time of survey. The survey was designed to minimize respondent fatigue/satisficing and recall and social desirability bias by itemizing family incarceration information early in the survey, preceded by an opinion item that asks about respondents' confidence in their local criminal justice system. Prior to collecting information about incarcerated relations, the FamHIS also walked respondents through a general family roster to prime recall of family relationships and to ease the respondent into these more detailed questions (Enns et al. 2018). These features are in line with best practices for survey-based social network data collection (Fischer and Bayham 2019; Paik and Sanchagrin 2013).

The survey opens with a screening item that asked a baseline sample of 4,041 respondents recruited from the NORC AmeriSpeak panel whether they had ever had any immediate family members incarcerated in a jail or prison for at least one night (Enns et al. 2019). At the conclusion of this screening module, all 1,808 respondents who reported any immediate family incarceration and a random 1,009-person sample from the remaining 2,233 respondents who did not report any immediate family incarceration were recruited to participate in the rest of the survey. The survey went on to ask about respondents' own jail or prison incarceration as well as that of their extended family.

With this design, 2,817 respondents (70% of the screener respondents) were ultimately asked about own and immediate and extended family incarceration over the course of the survey. To define the analytic sample, I took additional steps to exclude individuals missing information necessary for the analysis. This resulted in the exclusion of two respondents who were not assigned sampling weights because they skipped nearly the full survey (Enns et al. 2019:2); those who did not provide information about family incarceration (n = 718); and those missing any sociodemographic information required for the analyses (n = 18).3

Table 1 presents a statistical description of the final analytic sample of 2,029 respondents. The characteristics of the analytic sample are nearly identical to those reflected in benchmark data, illustrating its representativeness. The sole observed difference between the analytic sample and comparison data is in the distribution of respondents across metropolitan and nonmetropolitan areas. In the analytic sample, most respondents were from metropolitan areas (88%), whereas that was the case for 42% in comparison data. Supplementary analyses drawing on imputed information for the 786 of the 2,815 respondents excluded owing to missing data show that the imputed and analytic samples are nearly identical; a statistical comparison of the full FamHIS sample, the analytic sample used here, and the imputed sample is presented in Table A1 of the online appendix.

### Family Incarceration

The FamHIS survey collected information about immediate family incarceration in two ways. First, respondents were asked a general question about immediate family incarceration, introduced as a “screening item”:

Many people have been held in jail or prison for a night or more at some point in their lives. Please think about your immediate family, including parents; brothers; sisters; children; and your current spouse, current romantic partner, or anyone else you have had a child with. Please include step, foster, and adoptive family members. Confidentially and for statistical purposes only, have any members of your immediate family, NOT including yourself, ever been held in jail or prison for one night or longer? (Enns et al. 2018; Enns et al. 2019)

Those who responded affirmatively were asked for additional detail: the number of family members ever incarcerated and the respondents' relationships to them. To encourage recollection of all relations while mitigating respondent fatigue, the survey moved through the following relationships using a roster: mother, father, brother, sister, son, daughter, spouse/romantic partner, and nonpartner coparent. Specifically, respondents were asked:

You mentioned a moment ago that a member of your immediate family has been held in jail or prison for one night or longer. How many people from the following groups have ever been held in jail or prison for one night or longer? Include step, foster, and adoptive family members. (Enns et al. 2018; Enns et al. 2019)

After this initial set of questions about immediate family incarceration, those who went on to complete the full survey were asked about extended family incarceration with the following question:

Now we would like you to think about any other, more extended, family members you feel close with who are not included in the earlier groups. As far as you are aware, have any of those other family members you feel close with ever been held in a jail or prison for a night or more at some point in their lives? (Enns et al. 2018; Enns et al. 2019)

As with immediate family, the survey then proceeded to a relationship-specific roster that asked,

How many people in each group have ever been held in jail or prison for one night or longer? (Enns et al. 2018; Enns et al. 2019)

The respondent was asked about grandparents, grandchildren, cousins, aunts/uncles, nieces/nephews, godparents, mothers/fathers-in-law, sisters/brothers-in-law, and “other family.” Finally, respondents were asked if they themselves had ever been incarcerated in jail or prison for at least one night.

Using this information, I constructed descriptors of U.S. adults' exposure to family incarceration: the prevalence of family incarceration, previously estimated in other work using the FamHIS (Enns et al. 2019; Sundaresh et al. 2020), and three new descriptors of family incarceration: degree, generational extension, and permeation. The set of three measures describing the prevalence of family incarceration indicates whether a respondent ever had immediate, extended, and any (immediate or extended) family incarcerated for more than one night, using separate measures for each of the three types of family incarceration. To provide further insight into variation in the intensity of exposure, I use a measure of the degree of family incarceration. Drawn from social network methods, the term “degree” refers to an individual or social unit's total number of network ties (Wasserman and Faust 2009:100). Here, degree is conceptualized as a tie to the carceral state and measured as the total number of family members ever incarcerated for at least one night, reporting totals for immediate, extended, and any family.

To explore variation in the structure of incarceration through family systems, I use two additional measures: generational extension and permeation. The term “extension” draws from family demographic language used to describe the inclusion of nonimmediate family in living arrangements or households (e.g., Angel and Tienda 1982; Glick et al. 1997; Sarkisian et al. 2007). Generational extension of family incarceration is captured here using a set of three dichotomous measures: horizontal extension, or the incarceration of anyone of the same generation as the respondent (sibling, cousin, sibling-in-law, spouse/romantic partner, coparent); downward extension, or incarceration of anyone in a generation below the respondent (child, niece/nephew, grandchild); and upward extension, or the incarceration of anyone who is of a generation above the respondent (parent, aunt/uncle, parent-in-law, grandparent, godparent).

Finally, permeation of family incarceration reports the number of generations in a respondent's family that have had any incarceration, including that of the respondent. The FamHIS measures of family incarceration include 16 family relation types. These relational categories span up to five generations of a respondent's family, extending two generations below (e.g., grandchild) to two generations above the respondent (e.g., grandparent). Therefore, my measure of family incarceration permeation ranges from a minimum of zero (no family ever incarcerated) to a maximum of five generations (family members incarcerated in two generations below, in two generations above, and in the same generation as the respondent).

To contextualize the analyses discussed later, it is important to consider the ways in which the FamHIS measures of family incarceration are unique. Indeed, these survey items are distinct from many other survey measures of family incarceration in three ways that make them both broader and more specific: response eligibility, relationship range, and duration. Unlike other surveys that ask about incarceration, the FamHIS asks about incarceration regardless of other potentially precedent criminal legal encounters. The crime module of the 1997 National Longitudinal Survey of Youth (NLSY97; Bureau of Labor Statistics, U.S. Department of Labor 2019), for example, asks respondents about incarceration conditional on earlier-stage criminal legal involvement (e.g., conviction, sentencing). Because the FamHIS does not, these data can capture confinement at all stages of system contact, including pretrial detention, and allow for the uncertainty of processes leading to incarceration that often characterize the experience (Walker 2022).

In addition to capturing a broader range of relationships than those in other surveys that inquire about family incarceration (e.g., Add Health; Harris 2018; see also, Wildeman et al. 2016), the FamHIS is also more specific. These data, as described previously, itemize rosters of family relationships and also detail the duration and facility types of incarceration to be considered. The FamHIS measures specify incarceration spells of “one night or longer” and incarceration spells “in jail or prison,” mitigating ambiguity and resultant inconsistency across respondents about whether an incarceration spell “counts” (Enns et al. 2018; Enns et al. 2019), while also discounting incarceration spells of less than a day in duration. Combined, these differences suggest that the FamHIS would produce higher estimates of family incarceration prevalence, but in large part owing to an intentionally broader definition of the numerator, rather than measurement error. Indeed, these measures may even underestimate overall levels of carceral contact because of exclusion of incarceration spells of less than a day.

### Respondent Characteristics and Contexts

This study seeks to expand understanding of racial/ethnic inequality in family incarceration. Therefore, a key measure is that of respondent's race/ethnicity. FamHIS's two measures of race/ethnicity use six mutually exclusive categories in one (Asian, Black, Hispanic, other, White, and two or more racial/ethnic groups) and five in the other (American Indian/Alaska Native, Black, Hispanic, other, White). I combine these measures, creating four mutually exclusive categories of self-identified race and ethnicity: Black, Hispanic, White, and multiracial or other racial/ethnic group. Further disaggregation was not possible owing to small cell sizes that rendered models inestimable.

One's exposure to family incarceration is shaped, in part, by life course experiences that impact one's family ties, structures, and living arrangements. For example, the likelihood of experiencing a spouse's incarceration is directly linked to whether one was ever married. The models account for measures of life course experiences and contexts that shape family and household relationships, and therefore, the number and types of family members potentially incarcerated. These covariates are continuous measures of respondents' age (in years) and household size (number of household members); a categorical measure of partnership history/status (previously married and not living with a spouse/partner, living with a spouse/partner, never married and not living with a spouse/partner); and dichotomous measures of parental status (whether the respondent has children) and nativity (born outside the United States).4

Family life and risks of criminal legal system contact are also gendered (Braman 2004; Daly 1989). Women are slightly more likely than men to have ever had any immediate family members incarcerated (Enns et al. 2019) and are often tasked with the work of maintaining familial ties with loved ones who are behind bars and supporting formerly incarcerated relations as they transition back into civilian life upon release (Arditti et al. 2003; Braman 2004; Comfort 2008). The analysis therefore includes a dichotomous measure of respondent gender noting whether the respondent identifies as male or female.5

Risks of criminal legal system contact also vary spatially, with uneven risks of imprisonment and trends in incarceration and carceral expansion across the United States (Eason 2017; Kang-Brown and Subramanian 2017). The models therefore also account for respondents' region of residence (Northeast, Midwest, South, West) and whether they live in a metropolitan area. Socioeconomic contexts are also strong correlates of incarceration risk (Pettit and Western 2004; Western and Muller 2013; Wildeman 2009). Therefore, the analysis uses categorical measures of respondents' educational attainment (no high school education, high school degree or equivalent, some college, bachelor's degree or more) and household income ($0–$24,999; $25,000–$49,999; $50,000–$74,999; $75,000–$99,999; \$100,000+). Finally, because interviewer effects are known potential sources of bias and unreliability in name generator survey items such as those in the FamHIS (Fischer and Bayham 2019; Paik and Sanchagrin 2013), I account for respondents' survey mode (phone survey with a live interviewer vs. web survey).

### Analytic Approach

This comprehensive descriptive analysis begins with a statistical summary of family incarceration exposure of noninstitutionalized adults. I then proceed by estimating nested regression models that examine racial/ethnic differences in the prevalence, degree, generational extension, and permeation of family incarceration, accounting for increasingly comprehensive sets of measures of characteristics and contexts correlated with one's family structure and risks of carceral contact. I estimate separate regression models for each racial/ethnic group and begin by estimating characteristics of family incarceration as functions of respondents' race/ethnicity and survey mode (Model 1). The three subsequent specifications account additionally for respondents' life course characteristics (Model 2), geographic context (Model 3), and socioeconomic context (Model 4), with discussion of the results focusing on comparisons across racial/ethnic groups. Variation with respect to social characteristics and contexts often treated as independent of race—such as socioeconomic status, marital status, and residential context—are themselves components of racialized life and racism (e.g., Faber 2020; Ray 2019; Sewell 2016; Williams and Collins 1995). Therefore, these regression adjustments, rather than “controlling away” predictors of family incarceration, serve to situate this analysis in relation to prior scholarship investigating race and incarceration in the United States.

Associations between racial/ethnic group and prevalence and generational extension of family incarceration are estimated using logistic regression models, accounting for the binary form of those measures. Models for the continuous measure of degree of family incarceration are specified as linear regressions and for the count measure of permeation of family incarceration as Poisson regressions. All analyses apply sampling weights that account for the FamHIS sampling design and unequal eligibility for participation in the full survey and benchmark the FamHIS sample to the U.S. noninstitutionalized adult population.

## Results

The statistical snapshot presented in Table 2 presents an unadjusted summary of family incarceration exposure in the analytic sample, overall and by racial/ethnic group. Forty percent of adults have ever had immediate family incarcerated, 34% have ever had extended family incarcerated, and over half of adults have ever had any family incarcerated (52%). On average, U.S. adults have had two or three family members incarcerated for at least one night. Additionally, horizontal (same generation) family incarceration is the most common (44%) of the three types of generational extension of family incarceration experienced. Thirty percent and 19% experienced upward and downward extension of family incarceration, respectively.

Adults who are Black are substantially more likely to experience both immediate and extended family incarceration and likely to experience more intensive exposure to family incarceration than those of other racial/ethnic groups. For example, on average, White respondents report having 0.75 immediate and 1.17 extended family members ever incarcerated, while those numbers are more than twice as high among those who are Black (2.11 immediate and 3.20 extended family members).

These unadjusted estimates of the prevalence, degree, generational extension, and permeation of family incarceration provide a detailed illustration of the reach of incarceration and racial/ethnic inequality therein. My analysis now turns to a series of nested multivariate regression models to further explore the racialized nature of this adverse exposure. These models allow for a comparison of race/ethnicity-specific estimates of the prevalence, degree, generational extension, and permeation of family incarceration while incorporating variation in other characteristics, experiences, and contexts previously identified as correlates of family diversity and carceral contact.

### Prevalence of Family Incarceration

Estimated associations from models that incorporate only information about respondents' race/ethnicity and survey mode show great variation in the prevalence of immediate, extended, and any family incarceration across racial/ethnic groups (Table 3, Model 1). Models 2–4, although adding substantial detail about respondents' characteristics and social contexts, tell a story that is virtually identical to that of the baseline model. Indeed, even after adjusting for measures that describe life course characteristics (age, gender, parental status, partnership/cohabitation history and status, household size; Model 2), spatial context (region, metropolitan area; Model 3), and socioeconomic context (educational attainment, household income; Model 4), the racial/ethnic disparities estimated in Model 1 remain statistically distinguishable and stable in magnitude across specifications.

According to estimates from the fully adjusted models (Model 4), individuals who identify as Black are substantially more likely than adults of all other racial/ethnic groups to have experienced the incarceration of a family member, whether focusing on immediate family, extended family, or both immediate and extended family. Sixty percent of Black adults have experienced an immediate family member's incarceration, 53% have experienced extended family incarceration, and 74% have experienced either of those events. Alongside this stark Black–non-Black disparity, it is also notable that at least one third of adults in each racial/ethnic group have experienced immediate family incarceration. The adjusted proportions of adults who have experienced extended family incarceration are greater than three in 10 in all groups (Table 3, Model 4).

Individuals identifying as Asian, American Indian/Alaska Native, or of another racial/ethnic group (combined because of prohibitively small cell sizes) have the lowest predicted probabilities of immediate (33%), extended (31%), and any family incarceration (44%). However, these estimates should be interpreted with caution. Prevalence estimates for those in the “other” category are not statistically distinguishable from those describing the experiences of White or Hispanic adults and represent an aggregation of members of racial/ethnic groups with distinct historical and contemporary contexts of criminalization and apprehension (e.g., Franklin 2013; Hall and Simkus 1975).

### Degree of Family Incarceration

Prevalence is but one way to describe the reach of incarceration and its variation across racial/ethnic groups. The next set of models estimates associations between race/ethnicity and degree, or the number of family members ever incarcerated for at least one night. Models that adjust only for respondents' race/ethnicity and survey mode reveal substantial racial disparities in the degree of family incarceration experienced. As observed for the models of prevalence, estimates of degree of family incarceration are remarkably stable across models (see online appendix Table A3a). This is true for all subsequent analyses; therefore, the remaining discussion of results focuses on estimated associations from the fully adjusted models (Model 4), with full model results presented in the online appendix (see Tables A3a, A4a, and A5a).

As shown in Figure 1, the fully adjusted models of degree of family incarceration estimate that, on average, U.S. adults have had one immediate family member, 1.5 extended family members, and 2.5 family members of any relation incarcerated. Turning now to race/ethnicity-specific estimates, the importance of looking beyond prevalence when examining carceral contact in family life is immediately evident. This descriptor of family incarceration allows us to see that in addition to being substantially more likely to have ever experienced family incarceration, Black adults are likely to have experienced a higher degree of family incarceration, or a greater number of family members ever incarcerated. This is true even after adjusting for characteristics that are mechanically associated with family size, such as parental and partnership status, which shape the “risk pool” of family members who could have been incarcerated (Figure 1 and online appendix Table A3a).

On average, White adults have had fewer than one immediate family member, 1.2 extended family members, and 1.9 immediate or extended family members ever incarcerated. Among those of Hispanic ethnicity, adults have had 1.1 immediate family members, 1.7 extended family members, and 2.8 family members of any relation incarcerated, although these estimates were not statistically distinguishable from those for respondents in the other racial/ethnic group. Again, Black adults' experiences contrast sharply with those in all other groups: on average, Black adults have had 2.1 immediate family members, 3.2 extended family members, and 5.3 family members of any relation incarcerated.

### Generational Extension of Family Incarceration

Taking a demographic perspective, we can also consider potential variation in the structure of incarceration within family systems. I explore this using three descriptors of generational extension of family incarceration: horizontal (e.g., cousin), upward (e.g., aunt), and downward (e.g., grandchild) extension. Adjusted associations between race/ethnicity and generational extension of family incarceration are presented in Figure 2 and online appendix Table A4a. The fully adjusted models show that horizontal family incarceration—of siblings, cousins, coparents, or romantic partners—is the most common generational extension of family incarceration experienced overall. Forty-four percent of adults have experienced family incarceration through horizontal extension, 30% through upward extension, and 19% through downward extension.

Family incarceration through horizontal extension is also the most prevalent type of generational extension of family incarceration experienced among Black, other race/ethnicity, and White adults. Again, race/ethnicity-specific estimates reveal substantial between-group differences in magnitude that remain constant across models. Two thirds of Black adults (66%) have ever experienced family incarceration through horizontal extension, a statistically distinguishably higher adjusted proportion than that of White adults (39%). Among adults of Hispanic ethnicity, 49% have experienced family incarceration through horizontal extension, but this proportion is not statistically distinguishable from the share of Hispanic adults who have experienced family incarceration through upward extension (i.e., 49% [95% confidence interval = 40%–58%] vs. 34% [95% confidence interval = 26%–42%]).

Proportions of individuals reporting upward or downward family incarceration, though lower than the proportions reporting horizontal extension, are still substantial. Upward family incarceration is the second most commonly experienced generational extension of family incarceration for all racial/ethnic groups. Approximately half of Black respondents (49%) reported experiencing upward family incarceration, along with about one third of Hispanic adults (34%) and adults of another race/ethnicity (31%), and one quarter of White adults (26%). Differences between estimates for Black adults and adults identifying as White or of other racial/ethnic groups are statistically distinguishable. Other pairwise comparisons do not reveal statistically distinguishable differences.

Finally, downward family incarceration is the least prevalent type of generational extension for all racial/ethnic groups, but again, it is substantially and statistically more common for those identifying as Black. Eighteen percent of White adults, 14% of Hispanic adults, 13% of those in the other racial/ethnic group, and 34% of Black adults report having had a child, nephew/niece, grandchild, or godchild incarcerated.

### Permeation of Family Incarceration

Finally, to further detail the reach of family incarceration, I estimate associations between racial/ethnic categories and the permeation of incarceration through family systems, measured as the number of generations in which a respondent has had ever-incarcerated family members (Figure 3 and online appendix Table A5a). Consistent with the picture of the racialized nature of carceral contact presented so far, these analyses show that family incarceration permeates deeper into the families of Black adults than those who are White, of Hispanic ethnicity, or in the other racial/ethnic group (Figure 3). Black adults have had an average of 1.7 generations with any family incarceration, a statistically higher number of generations than for those who are Hispanic (1.1 generation) or White or in another racial/ethnic group (<1.0 generation). No other pairwise comparisons of the permeation of family incarceration revealed statistically distinguishable differences.

## Discussion

Unequal risks of criminal legal system contact and its consequences are well documented (Foster and Hagan 2015; Massoglia and Pridemore 2015; Wakefield and Uggen 2010). However, without a more detailed demography of family incarceration, we risk misunderstanding and misestimating the reach of mass incarceration, its effects on families, and the potential impact of interventions intended to lower incarceration rates, numbers of incarcerated persons, and consequences of incarceration (Chung and Hepburn 2018; Enns et al. 2019; Wildeman and Wakefield 2014). This investigation provides new detail about racial/ethnic inequality in carceral contact in the United States, summarized here in three points. First, unadjusted estimates show that family incarceration is not only prevalent, but also deeply embedded through families. On average, a noninstitutionalized U.S. adult has had 2.5 family members ever incarcerated and 1.1 generations in which a family member has been incarcerated.

Second, for Black adults, the likelihood of family incarceration and the degree, generational extension, and permeation of family incarceration far exceeds that of other racial/ethnic groups. On average, a Black adult has had 5.3 family members incarcerated and 1.7 generations with family members who have been incarcerated. Third, estimated racial/ethnic inequalities in the degree, generational extension, and permeation of incarceration do not change with incorporation of additional information about adults' characteristics and contexts. There is a tendency to interpret analyses that integrate measures of correlates of race as “controlling” for differences to create a race-neutral vacuum for comparison (e.g., Gillborn et al. 2018; Stewart 2008:116–119). However, the striking stability in estimated disparities in family incarceration observed here provides additional evidence of the overwhelming salience of race for criminal legal system contact and the inextricably racialized nature of sociodemographic and economic contexts in the United States (e.g., Ray 2019; Reskin 2012; Sewell 2016).

Although this study provides important and novel population-based detail about the demography of family incarceration in the United States, my estimates come with important limitations, including challenges shared with other survey research on racialized institutional contact and race and family life (e.g., Geller et al. 2016; Pettit 2012). First, the data's underrepresentation of U.S. adults in nonmetropolitan areas could mean that these estimates are biased, although it is unclear whether that implies overestimation or underestimation of the prevalence, degree, generational extension, and permeation of family incarceration and racial disparities therein. Recent expansion of incarceration in rural places (Eason 2017; Kang-Brown and Subramanian 2017) means that if people living in rural areas are likely to have family members incarcerated locally, these estimates potentially underestimate family incarceration. This could be all the truer for Hispanic adults, who are more likely to be surveilled and detained as part of immigration enforcement, a component of carceral expansion in the rural United States (Arriaga 2017; Menjívar et al. 2018; National Research Council 2014:61–64; Pickett 2016). Second, my inability to produce estimates for Asian, Pacific Islander, Alaska Native, and American Indian persons owing to prohibitively small cell sizes is a major limitation. The aggregation of these racial/ethnic groups in an “other” category combines racial/ethnic groups with starkly different histories of contact with the carceral state (Beckett and Evans 2015; Franklin 2013; Hall and Simkus 1975; Madley 2019).

Third, the FamHIS data are nationally representative of U.S. adults in households, meaning that the sample systematically misses those who are institutionalized, including incarcerated adults (Pettit 2012). Evidence of the clustering of carceral contact, shown here and in prior work (e.g., Lee et al. 2015; Wildeman and Wakefield 2014), suggests that those not represented in these analyses as a result of the FamHIS design may be more likely to have ever-incarcerated family members than noninstitutionalized adults. Additionally, I cannot be certain that respondents considered all family, living or deceased, coresident or not, in completing the survey. Although it is likely that respondents were able to report on incarceration of their closest family members, the measures of family analyzed here, even though broadly inclusive, may not capture incarceration of more distant relations. As extended family networks are generally larger than immediate family networks, the finding that the prevalence of immediate family incarceration is greater than that of extended family incarceration is surprising (40% vs. 34%; Table 2). This may be due to respondents' incomplete knowledge of the incarceration histories of more distant relations.

Relatedly, it is possible that these estimates are impacted by the same racial/ethnic differences in family life that motivate this study's investigation of the demography of family incarceration. The FamHIS captures a greater range of relationships than many other data sets on family incarceration. However, racial patterning in family structure and change (Amorim et al. 2017; Cross 2018) may mean that respondents of different racial/ethnic groups are differentially likely to be knowledgeable of the incarceration status and histories of the relationships enumerated in the FamHIS. Additionally, differences in the inclusion of nonbiological and nonlegal relations in defining family may mean that the FamHIS rosters of relationships are unequally effective in capturing respondents' “doing” of family (Naples 2001:31–33; Smith 1993). The greater prevalence of “fictive” or “chosen” family among those who are American Indian/Alaska Native, Black, or of Hispanic ethnicity suggests that my measures of the prevalence, degree, extension, and permeation of incarceration are, too, potentially limited by labels used to itemize these relationships (Letiecq 2019; Nelson 2014; Smith 1993).

Finally, interviewer or survey mode effects, as well as social desirability bias and resultant underreporting of family incarceration, may also pose threats to my conclusions. To explore potential social desirability bias and survey mode effects, I estimated models that do (main analyses) and do not (supplementary analyses) control for survey mode. This exercise shows that estimated prevalence, degree, extension, and permeation of family incarceration and racial/ethnic disparities therein remain identical across both sets of models. This comparison stems some of the concern about the potential impact of social desirability bias on my findings.6

However, if social desirability bias in measurement of family incarceration is statistically correlated with race/ethnicity or family structure and composition, my conclusions would still be vulnerable to misestimation. The stigma of criminal legal system contact (Brew et al. 2022; Sugie and Turney 2017), racially disproportionate likelihoods of that experience, and evidence of higher likelihoods of nonresponse among minoritized social groups (Klein et al. 2011; Tomaskovic-Devey et al. 2006) suggest potential underreporting of family incarceration. This underreporting may be more severe among those who are Black, are Hispanic, or have lower incomes or educational attainment, all of which are also correlates of incarceration (Western and Pettit 2010). These may lead to my underestimation of racial/ethnic disparities in family incarceration prevalence, degree, generational extension, and permeation.

A look beyond the scope of this analysis highlights important considerations for future investigation. The substantial racial heterogeneity and inequality in family incarceration identified here lead to questions about potentially heterogeneous effects of incarceration across relationships. For example, is parental incarceration necessarily more consequential for one's well-being than the incarceration of a sibling, aunt, or friend? Future work that can build on the descriptors of family incarceration that I present here may be fruitful for answering such questions and other investigations of the consequences of state involvement in family life. Examples of tools that could be leveraged for this include social network and social psychological measures of the significance, quality, and conditions of social ties (e.g., valued graphs, frequency of interaction, closeness) (Bearman and Parigi 2004; Brashears 2014; Burt 1984; Wasserman and Faust 2009) and household, family, and network rosters (Marsden 1987; Tach and Cornwell 2015).

My findings also motivate additional areas for investigation that are more epistemic in nature, interrogating how we study race, racism, and racialization, as well as family and criminal legal system contact. The utility and validity of estimated effects of incarceration are often evaluated vis-à-vis analysts' ability to account for selection (Wakefield and Uggen 2010; Wildeman 2020).7 This generally takes the form of statistical controls for racial/ethnic identity or local population composition, as well as characteristics and contexts conceptualized as distinct from race but related to criminal legal system contact. However, details about the racialized demography of family incarceration presented in this study further underscore the necessity of critical evaluation of the inclusion of statistical controls in analyses of incarceration and its unequal form, function, and consequences. What does it mean to estimate effects of incarceration “net of” race/ethnicity and family characteristics when this may ultimately control away disparities in carceral contact that are central to U.S. incarceration, such as those described here? What does it mean to model population dynamics and well-being as functions of incarceration rates while “controlling for” racial/ethnic composition when the elevated degree, extension, and permeation of incarceration in Black families are themselves part of population inequality?

This analysis details the demographic characteristics and structure of family incarceration in the United States, offering new information about the multifaceted nature of racial/ethnic inequality at the intersection of carceral and family life. In addition to confirming the disproportionate burden of incarceration for Black lives identified previously (Alexander 2012; Enns et al. 2018; Roberts 2004; Wildeman 2009), these estimates provide new measures and information about the unequal and racialized creep of the carceral system into family life and family histories.

## Acknowledgments

The author thanks Mariana Amorim, Megan Doherty Bea, Peter Enns, Hedwig Lee, Jennifer Hickes Lundquist, Joya Misra, Mark Pachucki, Anthony Paik, Donald Tomaskovic-Devey, and Christopher Wildeman, as well as anonymous editors and reviewers, for their thoughtful feedback on early versions of this work.

## Notes

1

See Chung and Hepburn (2018), Enns et al. (2019), Goldman (2020), Lee et al. (2015), Meek (2008), Sirois (2020), and Wildeman and Wakefield (2014), and journalistic coverage in Lantigua-Williams (2016), for some key exceptions.

2

This point is also made by others, including Chung and Hepburn (2018), Enns and colleagues (2019), Lee and colleagues (2014), and Wildeman and Wakefield (2014).

3

Twenty-one of the excluded respondents were missing information on both family incarceration and sociodemographic measures required for the regression analyses.

4

The FamHIS data also include a family roster that could presumably be used to determine respondents’ family size. However, examination of the data indicates that those measures do not reliably capture the size of respondents’ families. For example, respondents sometimes reported having no family members of a certain type but then reported having had relations of that type incarcerated (Enns et al. 2019). Therefore, I elected not to use those measures.

5

Although this problematically conflates gender with sex, I use this terminology to be consistent with the language used in the FamHIS survey instrument.

6

The main analyses, which adjust for survey mode, are presented in Table 3, Figures 13, and Tables A3a, A4a, and A5a of the online appendix. The supplementary analyses, which do not adjust for survey mode, are presented in Tables A2, A3b, A4b, and A5b of the online appendix.

7

A deeper discussion of causal estimation of family incarceration effects is beyond the scope of this study. See work by Billings (2018), Cho (2009), Dobbie et al. (2018), and Norris and colleagues (2021) for examples of such analyses and Wildeman (2020) for a discussion.

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