Single-parent households and mortality among children and youth

Social Science Research xxx (2016) 1e10

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Single-parent households and mortality among children and youth Paul R. Amato*, Sarah E. Patterson Department of Sociology, Pennsylvania State University, 211 Oswald Tower, University Park, PA 16801, United States

a r t i c l e i n f o

a b s t r a c t

Article history: Received 14 January 2016 Received in revised form 23 August 2016 Accepted 28 September 2016 Available online xxx

Although many studies have examined associations between family structure and child outcomes, few have considered how the increase in single-parent households since the 1960s may have affected child mortality rates. We examined state-level changes in the percentage of children living with single parents between 1968 and 2010 and state-level trends in mortality among children and youth (age 19 or younger) in the United States. Regression models with state and year fixed effects revealed that increases in single parenthood were associated with small increments in accidental deaths and homicides. © 2016 Published by Elsevier Inc.

Keywords: Single-parent households Child mortality Accidents Suicides Homicides Fixed effects models State-level data

1. Introduction The current study is based on two well-known trends. First, the percentage of children living in single-parent households in the United States has more than tripled since the middle of the 20th century, rising from 9% in the early 1960s to 28% in 2014 (Child Trends, 2015). Second, research shows that children living in single-parent households have more mental and physical health problems than do children living in two-parent households (Amato, 2005; Brown, 2010). If the connection between single parenthood and children's health is at least partly causal, then the growth of single-parent households may have negatively affected the general level of children's health in the general population. Our goal was to see if the growth of single parenthood in the United States since the 1960s was associated with an increase in child and youth mortalitydan infrequently studied outcome in this literature. To address this issue, we combined state data on child mortality from the Centers for Disease Control (CDC) with data on the percentage of children living with single parents from the American Community Survey (ACS), the Current Population Survey (CPS), and the U. S. Decennial Census. We then conducted a state-level analysis of mortality rates between 1968 and 2010 using statistical models with state and year fixed-effects, interactions between state and time, and controls for time-varying variables that might produce spurious associations.

* Corresponding author. E-mail addresses: [email protected] (P.R. Amato), [email protected] (S.E. Patterson). http://dx.doi.org/10.1016/j.ssresearch.2016.09.017 0049-089X/© 2016 Published by Elsevier Inc.

Please cite this article in press as: Amato, P.R., Patterson, S.E., Single-parent households and mortality among children and youth, Social Science Research (2016), http://dx.doi.org/10.1016/j.ssresearch.2016.09.017

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1.1. Background We focus on three causes of child mortality: unintentional injuries, homicides, and suicides. Plausible reasons exist for thinking that each type of mortality might be elevated for children in single-parent households. As we explain below, this may occur because (on average) single-parent households, compared with two-parent households, (1) are more socially and economically disadvantaged, (2) involve less parental monitoring and supervision, (3) include more everyday stress (for children as well a parents) due to financial insecurity and parent union instability (Amato, 2005). Unintentional injuries are the leading cause of death for children in the United States, and more children die each year from accidents than from all diseases combined (Borse et al., 2008). Most fatal accidents occur in the home and yard, and a lack of parental supervision is often a contributing factor (Breysse et al., 2004; Morrongiello and Schell, 2010; Scheidt et al., 1995). Compared with married parents, single parents are more constrained in the amount of time they can devote to monitoring their children's activities. Moreover, parents who are under stress, either from chronic financial pressure or interpersonal problems, tend to adopt a less involved style of parenting (Crnic and Low, 2002). Indeed, time budget studies show that children in single-parent households spend less time with parents and receive less supervision than do children in two-parent households (Kahlil et al., 2014). In addition, many single parents and their children live in crowded, substandard housingdsettings in which accidental injuries are more common (Breysse et al., 2004; Durkin et al., 1994). Several studies have shown that children from single-parent households are more likely than children from two-parent households to be seriously injured in accidents, both in the United States (Dawson, 1991; Durkin et al., 1994) and in England (O'Connor et al., 2000). Nepomnyaschy and Donnelly (2015) found that children living with single mothers in the United States were more likely to be injured than were children living with two biological parents, but this difference no longer was statistically significant after controlling for a variety of demographic and economic variables. Irrespective of these findings, whether children living with single parents are disproportionately likely to die from accidents has not been investigated. Homicide is the fourth-leading cause of death among children age 1e14 and the third-leading cause of death among youth age 15e24 (Centers for Disease Control and Prevention, 2014). Indeed, children age 12e17 are more than twice as likely as adults to be the victims of serious violent crime (Sickmund and Puzzanchera, 2006). Youth from single-parent households may be at increased risk of homicides because they are more likely than those from two-parent households to be involved in delinquent activities (Anderson, 2002). Many criminologists assume that the well-established correlation between family structure and delinquency is due primarily to the limited parental supervision available in many single-parent households (Sampson and Groves, 1989). Involvement in delinquent activities, in turn, increases the risk that youth will be assaulted or murdered (Raine et al., 1996; Lauritsen et al., 1992). Consistent with these observations, studies have shown that youth from single-parent households have an elevated risk of being homicide victims in Sweden (Weitoft et al., 2003) and the United States (Winpisinger et al., 1991). Suicide is the second-leading cause of death among children age 10e14 as well as youth age 15e24 (Centers for Disease Control and Prevention, 2014). The 2013 national Youth Risk Behavior Survey revealed that 17% of high school students had seriously considered suicide in the past 12 months, and 8% had attempted to commit suicide (Swahn and Bossarte, 2007). Depression in children and youth (a major risk factor for suicide) is linked with interpersonal problems in the family, including harsh or emotionally disengaged parenting, chronic discord between parents, and a history of unstable and unpredictable family and household relationships (Cicchetti and Toth, 1998). These problems tend to be more common in singleparents families and, presumably for this reason (at least in part), children in single-parent households have an elevated risk of becoming depressed (Amato, 2005). Consistent with this reasoning, studies have shown that children living with single parents are especially likely to think about or attempt suicide in New Zealand (Donald et al., 2006; Fergusson et al., 2000) and the Netherlands (Kienhorst et al., 1990). A large-scale longitudinal study in Sweden found that youth (boys as well as girls) living with single parents were more likely to commit suicide than were youth living with two parents (Weitoft et al., 2003). Similarly, a study from Denmark found a link between parental divorce and completed suicide among children and youth age 10e21 (Agerbo et al., 2002). Whether a similar link between single-parent households and youth suicide exists in the United States is unknown. In addition to the individual mechanisms discussed in this section, state- or community-level factors also may have implications for understanding the links between single parenthood and child mortality. Communities or states with large concentrations of single parent households, for example, may have higher levels of social disorganization, weaker social networks, and less social capitaldall of which might increase children's health problems. Indeed, contextual studies (using multilevel modeling) have shown that children in communities with many single parent households are more likely to exhibit a variety of behavioral and health problemsdirrespective of their own family characteristics (Hoffmann, 2006; Osgood and Chambers, 2000; Thorlindsson et al., 2012).

1.2. The current study Although children living in single-parent households appear to be at greater risk for mortality, most of the studies on this topic have been conducted outside of the United Statesdmainly in Western Europe and New Zealand. Because single parents in the United States differ from their European counterparts on a variety of social and economic characteristics (Gornick and Please cite this article in press as: Amato, P.R., Patterson, S.E., Single-parent households and mortality among children and youth, Social Science Research (2016), http://dx.doi.org/10.1016/j.ssresearch.2016.09.017

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€ntti, 2011), it is difficult to generalize from Europe to the American context. New research is necessary to determine whether Ja a link between single parenthood and child mortality exists in the United States. Because child mortality is an uncommon outcome, it cannot be studied easily with individual-level survey data. This topic can be studied, however, with data aggregated to the state level. State-level data have been used to test many hypotheses about families, including hypotheses involving single parenthood and children's academic achievement (Amato et al., 2015), unemployment and divorce (Amato and Beattie, 2011; Hellerstein and Morrill, 2011), divorce and suicide (Breault, 1986), economic conditions and birthrates (Matthews et al., 1997), family planning services and teen births (Yang and Gaydos, 2010), father-absent families and voting patterns (Monson and Mertens, 2011), and marriage education and family demographics (Hawkins et al., 2013). The current study falls within this well-established research tradition. Analyzing aggregate data at the state level makes it possible to determine if the increase in single parenthood in the United States since 1968 was associated with changes in child mortality in the general population. This goal differs from most previous studies in this literature, which have examined links between family structure and outcomes for individual children. The current study attempts to answer the question, “Has the increase in single parenthood been accompanied by an increase in child mortality?” rather than, “Do children living with single parents have a higher probability of dying than children living with two parents?” A risk of using aggregate data, of course, is the ecological fallacy: Associations observed at the aggregate level may not hold at the individual level. Aggregate-level data have a compensating advantage, however. Because most genetic and personality traits change slowly at the societal level, aggregate-level data are less susceptible to many forms of selection bias than are individual-level data (Amato and Beattie, 2011). Although we should be cautious about drawing causal inferences with aggregate data, it is still of theoretical and practical interest to know whether the rise in single parenthood in the United States was accompanied by an increase in child mortality. We know of only one study on this topic that relied on aggregate-level data. Durkin et al. (1994) found that the percentage of single-parent households in census tracts in Manhattan, New York was positively associated with the incidence of child injuries from accidents, assaults, and gunshots, controlling for income, education, crowding, and unemployment. Because the Durkin et al. study was cross-sectional, it could not determine if increases in single-parent households were associated with increases in potentially fatal child outcomes. The current study goes beyond the Durkin et al. (1994) study by using longitudinal, national data and examining child deaths from multiple causes. Although our focus is on accidents, homicides, and suicides, we also include data on deaths from neoplasms (the 2nd most common cause of child mortality between 1968 and 2010). Unlike accidents, homicides, and suicides, there is no clear theoretical reason why children living in single parent households should have an elevated risk of dying from neoplasms. For this reason, including data on mortality from this cause provides a check on the validity of our results. We relied on children and youth age 0e19 in our analyses. We included 18 and 19 year olds to make our family structure variables consistent with the CDC's mortality age groupings. Although individuals age 18 and 19 are legally adults, most continue to live at home and are at least partly dependent on their parents. The 2010 American Community Survey (the last year in our data file) indicates that 65% of 18e19 years olds lived at home with parents, including 24% who lived with single parents. Moreover, childhood family structure predicts a variety of psychological and behavioral outcomes among young adult offspringdeven those who no longer live at home with parents (Amato and Booth, 1997). Because only within-state variation over time is included in our fixed effects models, we implicitly control for all timeinvariant differences between states, including relatively stable legal, cultural, and political traits (e.g., consistently red versus blue states). Moreover, our use of year fixed effects controls for historical events (period effects) that affect all states similarly, such as national recessions, presidential elections, and changes in federal legislation. We also included interactions between state and time to capture linear and quadratic trends in state-level characteristics that may influence child mortality, with the slopes of the trends allowed to vary across states (Friedberg, 1998). These procedures adjust for autoregressive trends and control for a large number of unobserved time-varying factors within states. In supplementary models we also explicitly controlled for several time-varying factors, including race, ethnicity, parents' education, and poverty. Race, ethnicity, and education are related to the likelihood of becoming a single parent (Kreider and Elliott, 2009) as well as to the likelihood of child mortality (Blakely et al., 2003; Durkin et al., 1994) and, hence, could produce a spurious association between the two trends. Poverty increases the risk of becoming a single parent as well as the risk that children will die before reaching adulthood. Of course, poverty can be a consequence as well as a cause of single parenthood, so its status in a causal model is ambiguous. Nevertheless, this procedure allows us to see if changes in family structure are related to changes in child mortality independently of poverty. Blakely et al. (2003) found that living with a single parent was associated with an increased risk of child mortality (from all causes) in New Zealand, but the association no longer was statistically significant after controlling for socioeconomic status. 2. Data and methods 2.1. Mortality Data on child fatalities between 1968 and 2010 came from the CDC's Wide-Ranging Online Data for Epidemiologic Research (WONDER), an online database for underlying cause of death (United States Department of Health and Human Services (US DHHS), 2014). The database includes annual mortality counts for all U.S. counties based on death certificates. The data were produced by the National Center for Health Statistics (NCHS), which provides standard forms and procedures Please cite this article in press as: Amato, P.R., Patterson, S.E., Single-parent households and mortality among children and youth, Social Science Research (2016), http://dx.doi.org/10.1016/j.ssresearch.2016.09.017

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for the uniform registration of deaths in each state. The database allows for deaths to be downloaded and categorized by age, year, and cause of death according to the International Classification of Diseases (ICD-10) death codes. We looked at child deaths (ages 0e19) from all causes as well as accidents, homicides, suicides, and neoplasms. We relied on the raw counts provided by the CDC and calculated mortality rates as the number of deaths per 100,000 people age 0e19 in each state (and the District of Columbia) in each year. To deal with missing observations for particular states in particular years, we relied on simple listwise deletion in the main analysis and multiple imputation in a supplementary analysis. 2.2. Household family structure Data on children's living arrangements in each state (and the District of Columbia) between 1968 and 2010 came from the ACS, the CPS and the U.S. Decennial Census, depending on the year. These data were downloaded through the Integrated Public Use Microdata Series USA (Ruggles et al., 2010). We focused on children and youth (age 0e19) and classified them into single-parent households if they lived with a mother or a father (either biological or adoptive) but not both. We also included a variable to reflect the percentage of children living with neither parent. Children in all households with two parents (two biological parents, two adoptive parents, one biological parent and a step-parent) served as a combined reference category. We did not distinguish between two-parent households on the basis of parents' marital status (married or cohabiting) or gender in the main analysis, although we did in a supplementary analysis, as described later. 2.3. Control variables To control for race-ethnicity, we included two variables to reflect the percentage of children and youth (0e19) who were Black or Hispanic. Parental education was a four-category variable based on the percentage of mothers with resident children age 0e19 (1) without high school degrees, (2) with high school degrees, (3) with some college or postsecondary education, and (4) with college degrees. Because these percentages add to 100, the percentage in any one category can be determined from the percentages in the other three. Consequently, all four categories could not be entered simultaneously into a regression equation, and it was necessary for one category to serve as the omitted reference group in the analysis. Mothers without high school degrees served this purpose. (These mothers were included in the analysis but do not appear as a separate category in the regression tables.) Finally, we included the percentage of children and youth (0e19) living below the federal poverty line. All variables were weighted and aggregated to the state level in each year. 2.4. Estimation approach We used pooled time series regression analysis with fixed state and year effects to estimate the statistical models. The data file included one observation for each state in each year beginning in 1968 and concluding in 2010. We adopted the econometric model for state-level data outlined by Friedberg (1998) for this purpose. (For another application of this model, see Hellerstein and Morill, 2011). The statistical model is shown in the following formula.

Child mortalityst ¼ b0 þ b1 * single parentst þ b2 * no parentst þ b3 * STATEs þ b4 * YEARt þ b5 STATEs * time þ b6 STATEs * time2 þ ust

In this formula, child mortality is the mortality rate (deaths per 100,000 children) in states in yeart. Single parent refers to the percentage of children living in households with single parents (in states in yeart), whereas no parent refers to the percentage of children living in households with neither parent (in states in yeart). STATE is a vector of state fixed effects, and YEAR is a vector of year fixed effects. State fixed effects involved a series of dummy variables, one for each state minus one. Year fixed effects involved a series of dummy variables, one for each year between 1968 and 2010 minus one. The full model includes interactions between states and time (year) and between states and time squared. These terms capture trends (linear and quadratic) in state-level characteristics that may influence child mortality. Because the statistical models includes only within-state change, the regression coefficients can be interpreted as the estimated effect of residual changes in the independent variables on residual changes in the dependent variables. Our estimates are based on within-state deviations in single parenthood and child mortality in specific years from general period trends at both the national and state levels. 3. Results 3.1. Descriptive trends Trends in single parenthood (weighted by state population size) are shown in the top panel of Fig. 1. Children living with single parents increased steadily from 1968 to 201, as did children living without either parent. The bottom panel shows trends in child mortality rates. Note that the crude death rate from accidents declined from 36.5 in 1968 to 11.0 in 2010. Trends Please cite this article in press as: Amato, P.R., Patterson, S.E., Single-parent households and mortality among children and youth, Social Science Research (2016), http://dx.doi.org/10.1016/j.ssresearch.2016.09.017

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Fig. 1. The percentage of children and youth (age 0e19) living in single-parent households and in households with neither parent by year.

in homicides and suicides were less straightforward. The crude homicide rate rose from 2.1 in 1968 to 7.2 in 1993 and then declined slightly, whereas the crude suicide rate rose from 1.3 in 1968 to 3.2 in 1988 and then declined. Despite these fluctuations, homicides and suicides remained higher in 2010 than they had been in 1968. Deaths from neoplasms declined more or less continuously (but gradually) during this period. As an example of these trends, we describe Pennsylvania, a state that represents the country reasonably well. Between 1968 and 2010, the share of children living with single parents increased from 12% to 31%, whereas the share of children living with no parents increased from 4% to 8%. In 1968, there were 1328 accidental deaths and 315 deaths from neoplasms. These numbers correspond to child mortality rates of 30.86 and 7.32, respectively. By 2010, the mortality rates for accidents and neoplasms had decreased to 11.89, and 2.26, respectively. In contrast, in 1968 there were 76 homicides and 44 suicides, which correspond to child mortality rates of 1.77 and 1.02, respectively. By 2010, these rates were higher at 3.09 and 2.83, respectively. Taken together, Figs. 1 and 2 demonstrate that child mortality from accidental injuries declined while the percentage of children living with single parents increased. At first glance, these contrary trends suggest that the increase in single parenthood could not have had problematic consequences for mortality due to accidentsdthe most common cause of child deaths. Nevertheless, these variables could be positively associated in a fixed effects framework if child mortality declined more slowly in states that had the largest increases in single parenthood. Because fixed effects models are based on deviation scores, states can have positive deviation scores if their rate of decline is less than the mean of all states. If these same states also have greater than average increases in single parenthood, then the association between variables can be positive despite the fact that the overall level of mortality is declining.

3.2. Regression results Table 1 (top panel) shows the results from three ordinary least squares (OLS) regression analyses with child mortality from accidents serving as the dependent variable. The regression models are weighted by population size (number of children 0e19 in each state in each year) so that larger states contribute more to the analysis than smaller states. Model 1 (the baseline model) reveals that the percentage of children living with single parents was negatively and significantly associated with child accident mortality. This result is consistent with the trends shown in Figs. 1 and 2, that is, child mortality from accidents decreased during the same years that single parenthood increased. With the state and year fixed effects added in Model 2, however, the coefficient became positive and significant. The coefficient for single parenthood continued to be significant (although reduced in magnitude) in Model 3 with the state  time interactions included. Specifically, these results indicate that a one-point increase in the percentage of children living with a single parent was associated with 0.05 additional accidental deaths for every 100,000 children. The percentage of children living with neither parent was positive and significant in Models 1 and 2, although the association declined to non-significance in Model 3. The R squared values were generally high, but this is not uncommon when using fixed effects models with aggregate-level data. Table 1 (bottom panel) shows the corresponding results with child mortality from homicides serving as the dependent variable. Model 1 reveals that the percentage of children living with single parents was positively and significantly associated with child homicides. The association between variables became weaker in Model 2 (with the state and year fixed effects) and weaker still in Model 3 (with the state  time interactions). Nevertheless, in the final and most stringent analysis, the b coefficient remained positive and statistically significant. Specifically, the b coefficient indicates that a one-point increase in the percentage of children living with single parents was associated with an increase of 0.03 homicides per 100,000 children. Please cite this article in press as: Amato, P.R., Patterson, S.E., Single-parent households and mortality among children and youth, Social Science Research (2016), http://dx.doi.org/10.1016/j.ssresearch.2016.09.017

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Fig. 2. Child mortality rates (deaths per 100,000 people age 0e19) from the four common causes by year.

Table 1 Fixed effects regression of child mortality rates from accidents and homicides on the percentage of children (0e19) living with single parents and no parents: 1968e2010.

Accidents % Single parent % No parent Intercept R squared Homicides % Single parent % No parent Intercept R squared

Model 1 (baseline)

Model 2 (þyear and state fixed effects)

Model 3 (þstate  time interactions)

1.05*** (0.03) 1.73*** (0.09) 36.10 (0.73) 0.50

0.08** (0.03) 0.34*** (0.05) 18.63 (1.41) 0.94

0.05* (0.03) 0.07 (0.05) 30.12 (1.46) 0.97

0.11*** (0.01) 0.03 (0.03) 1.49 (0.23) 0.11

0.08*** (0.01) 0.08* (0.04) 1.73 (0.57) 0.69

0.03* (0.01) 0.02 (0.04) 3.10 (0.20) 0.80

Note: Table values are unstandardized b coefficients with robust standard errors in parentheses. Sample size (states x years) is 1910 for accidents and 1802 for homicides. *p < 0.05; **p < 0.01; ***p < 0.001.

Although the coefficient for the percentage of children living with neither parent was significant in Model 2, it was not significant in the most stringent model (Model 3).

Table 2 Fixed effects regression of child mortality rates from suicides and all causes on the percentage of children (0e19) living with single parents and no parents: 1968e2010.

Suicides % Single parent % No parent Intercept R squared Neoplasms % Single parent % No parent Intercept R squared

Model 1 (baseline)

Model 2 (þyear and state fixed effects)

Model 3 (þstate  time interactions)

0.01 (0.004) 0.01 (0.01) 2.58 (0.13) 0.00

0.04*** (0.01) 0.01 (0.01) 4.40 (0.57) 0.58

0.01 (0.01) 0.002 (0.01) 5.78 (0.55) 0.80

0.16*** (0.01) 0.03* (0.01) 7.71 (0.15) 0.56

0.004 (0.01) 0.01 (0.01) 1.79 (0.36) 0.87

0.01 (0.01) 0.01 (0.01) 3.13 (0.42) 0.88

Note: Table values are unstandardized b coefficients with robust standard errors in parentheses. Sample size (states x years) is 1796 for suicides and 1828 for neoplasms. *p < 0.05; **p < 0.01; ***p < 0.001.

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The results for children mortality due to suicides are shown in Table 2 (top panel). Model 1 reveals that the percentage of children living with single parents was not associated with child suicides. The association between variables became positive and significant in Model 2 but declined to non-significance in Model 3. Nevertheless, it is worth noting that the Model 3 coefficient for single parenthood and suicide approached significance (p ¼ 0.06)da trend consistent with our earlier reasoning and the results for accidents and homicides in Table 1. Correspondingly, the percentage of children not living with either parent was not significant in any model. Table 2 (bottom panel) shows the results for total child mortality from neoplasms. The association between single parenthood and child mortality was negative and statistically significant in Model 1. This association, however, declined and was no longer significant in Models 2 and 3. Correspondingly, the coefficient for the percentage of children living with neither parent was negative and significant in Model 1 (consistent with Figs. 1 and 2) but failed to attain significance in subsequent models. In addition to looking at specific causes of death, we also conducted an analysis using the mortality rate based on child deaths from all causes. An analysis (not shown) comparable to Model 3 (Tables 1 and 2) yielded b coefficients of 0.16 (SE ¼ 0.07, p < 0.05) for the percentage of children living with single parents and 0.15 (SE ¼ 0.14, ns) for the percentage of children living with no parents. Presumably, the association between single parenthood and overall mortality was driven largely by deaths from accidents and homicides. Indeed, with deaths from accidents and homicides subtracted from the total mortality rate, the resulting association no longer was statistically significant (b ¼ 0.08, SE ¼ 0.05, ns). 3.3. Alternative specifications We conducted a series of alternative specifications to determine the stability of our results. Overall, these analytical variations indicated that the results reported in Tables 1 and 2 were generally robust across different analytic procedures. First, although the models in Tables 1 and 2 implicitly controlled for a large number of unobserved variables, we added several demographic control variables (as described in the methods section) to the equations. These results appear in Table 3 and should be compared with the final columns of Tables 1 and 2. Consistent with the earlier results, these analyses revealed that the percentage of children living with single parents was positively and significantly associated with deaths due to accidents and homicides but not to deaths due to suicides and neoplasms. Indeed, the coefficient for single parents and mortality from accidents became somewhat larger in magnitude (0.09 versus 0.06) with the demographic controls in the model. Similarly, the association between living with neither parent and accident mortality became larger and statistically significant with the demographic controls in the model. (The results for poverty were counter-intuitive, and we return to these findings in the discussion.) Second, we considered the possibility that outliers might have influenced our results. Washington D.C., in particular, consistently had the highest percentage of children living with single parents along with some of the highest child mortality rates. Excluding this influential case, however, yielded results that were essentially identical to those reported in Tables 1e3. Third, we conducted a series of unweighted analyses, with each state carrying the same weight, irrespective of population size. These analyses yielded results that were similar to those reported in Tables 1e3, except that the estimated effects of single parenthood were somewhat larger. Fourth, we conducted analyses in which the percentage of children living in singleparent households was lagged by 1 through 10 years. Single parenthood was associated with child mortality from accidents and homicides when the data were lagged by 1e5 years but not when the lags were of longer durations. These results suggest that the estimated effects of increases in single parenthood were largely felt within the first five years and then began to dissipate. Fifth, we conducted new analysis with bootstrapped standard errors. Although the standard errors increased modestly, all significant results were replicated. Sixth, although children living with stepparents are of interest, it is not possible to identify all stepparents from the available information in the data sets (Minnesota Population Center, 2014). As a result, an unknown number of children

Table 3 Fixed effects regression of child mortality rates on the percentage of children (0e19) living with single parents and no parents with demographic controls: 1968e2010.

% Single parent % No parent % Black % Hispanic % Mom high school % Mom some college % Mom college grad % Poverty Intercept R squared

Accidents

Homicides

Suicides

Neoplasms

0.09** (0.03) 0.11* (0.05) 0.08* (0.32) 0.09* (0.04) 0.01 (0.01) 0.05 (0.01) 0.01 (0.02) 0.15 *** (0.02) 20.38 (1.87) 0.97

0.04** (0.02) 0.01 (0.04) 0.00 (0.02) 0.07* (0.03) 0.02* (0.01) 0.01 (0.01) 0.01 (0.01) 0.02 (1.41) 3.06 (2.12) 0.80

0.01 (0.01) 0.002 (0.01) 0.01 (0.01) 0.01 (0.01) 0.001 (0.01) 0.003 (0.005) 0.01 (0.01) 0.01 (0.01) 12.44 (2.83) 0.80

0.01 (0.01) 0.01 (0.01) 0.01 (0.01) 0.002 (0.01) 0.001 (0.004) 0.002 (0.005) 0.002 (0.01) 0.01 (0.01) 3.99 (1.14) 0.88

Note: Table values are unstandardized b coefficients with robust standard errors in parentheses. All models include state and year fixed effects and interaction terms between state and time and between state and time squared. Sample sizes (states x years) are 1910 for accidents, 1802 for homicides, 1796 for suicides, and 1828 for neoplasms. *p < 0.05; **p < 0.01; ***p < 0.001.

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classified as living with two parents were living with a parent and a stepparent. We attempted to deal with this issue by creating a dummy variable for stepparent households that we were able to identify. This step effectively removed identified stepfamilies from the omitted comparison group of two-parent households. With the new stepparent variable in the model, the results closely mirrored those from Tables 1e3. Seventh, we conducted analyses with a dummy variable added for twoparent households in which parents were unmarried. This was accomplished by incorporating the marital status of the mothers in two-parent householdsda variable that was available in all years. With this variable in the model, the omitted comparison group consisted of two-parent married couple households. All of the key findings in Tables 1e3 were replicated in the new specification. Moreover, the variable for cohabiting couple households was not significantly related to any outcome. Finally, we relied on multiple imputation rather than listwise deletion to deal with missing data. Analyses based on five replications yielded results that were substantively identical to those reported in Tables 1e3. In general, missing data did not appear to bias the results of the main analysis. 4. Discussion Was the rise in the percentage of single-parent households since the 1960s associated with an increase in child mortality in the United States? Our analysis indicates that within-state increases in the percentage of children living with single parents were associated with increases in children's mortality from accidents and homicides but not from suicides. (Nevertheless, the results for suicide were in the same direction and approached significance.) These results are consistent with previous research on child accidents (e.g., Dawson, 1991) and child homicides (e.g., Weitoft et al., 2003) but not with previous work on child suicides (e.g., Agerbo et al., 2002). We also showed that the rise of single parent households was not linked with neoplasms or overall child mortality net of accidents and homicides. This finding is not surprising, given that there is no clear theoretical reason why single parenthood should be linked with neoplasms or other causes of child mortality other than accident, homicides, and suicides. It would be premature, however, to assume that the increase in single parenthood between 1968 and 2010 caused an increase in child mortality. After all, our analysis may have excluded one or more time-varying variables that are causally prior to single parenthood as well as to child mortality. In the United States, the growth of single parent households was bound up with many other trends, including changes in men's and women's employment, growing economic and social inequality, mass incarceration, and changes in welfare policy. It is difficult to sort out the independent effects of single parenthood when so many factors are changing at the same time. Despite this cautionary qualification, it is useful to ask how big the estimated effects are in the present study. In 2010, the last year in our data set, there were approximately 83.2 million people between the ages of 0 and 19 in the United States. Using this number and the b coefficients from models with all fixed effects, state  time interactions, control variables, and weights for population size (Table 3), a one-point increase in the percentage of children (ages 0e19) living with single parents would be associated with an additional 75 deaths from accidents and 33 deaths from homicides. To put this in perspective, there were 13,897 deaths in this age group recorded in the CDC data for 2010, so these additional cases represent less than a one percent increase in mortality. Although any increase in child deaths is nontrivial, our estimate of 108 cases is small in absolute terms and, for example, considerably less than the 390 children (ages 0e14) who drown in swimming pools in the United States every year (Gipson, 2012). Although not the main focus of the current study, the percentage of children living with neither parent was associated with increases in accidents, but only with controls for race, ethnicity, maternal education, and poverty (Table 3). Comparatively little attention has been given to children living with neither parent, presumably because their numbers are relatively small. Despite this lack of attention, however, children living without parents score lower than other children on a variety of measures of adjustment, achievement, and wellbeing (Scott et al., 2013). Using the b coefficients from Table 3 and the number of children (ages 0e19) in the United States in 2010, a one-point increase in the percentage of children living without parents would be associated with an additional 92 accidental deaths. These suggest that living without parents is a small but nontrivial risk factor for child mortality. With respect to the control variables (shown in Table 3), the percentage of Black children in the population was positively related to accidental deaths, and the percentage of Hispanic children was positively related to accidental deaths and homicides. These trends are consistent with the assumption that minority status is a risk factor for a variety of problematic child health outcomes, including some forms of mortality. Maternal education, in contrast, was not related to child mortality. Child poverty was negatively related to deaths from accidents in Table 3da counter intuitive finding. The association between poverty and child mortality from accidents in a model without state and year fixed effects was positive, as one would expect (b ¼ 0.14, SE ¼ 0.04, p < 0.01). This result suggests that the positive bivariate association between poverty and child mortality may have been due to unobserved characteristics of states and years, although it is not clear what these might be. Nevertheless, our analysis suggests that child mortality from accidents decreased in years when states experienced increases in poverty. Although speculative, if increases in poverty are due to declines in employment (single parents moving out of the labor force or decreasing their work hours), then a corresponding increase in child supervision (because single parents are in the home for more hours) could account for small decrements in child mortality. Moreover, many poor parents cannot afford to own and drive automobiles, and vehicle deaths are a common source of fatal accidents for children. The current study is limited in many respects. We could not distinguish as clearly as we would have liked between households with two biological parents and households with stepparents. Moreover, our analysis may have excluded one or Please cite this article in press as: Amato, P.R., Patterson, S.E., Single-parent households and mortality among children and youth, Social Science Research (2016), http://dx.doi.org/10.1016/j.ssresearch.2016.09.017

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more time-varying variables that affected our independent as well as our dependent variables, resulting in spurious associations. (Of course, the same concern applies to all non-experimental studies of social trends.) It is also possible that our measure of single parenthood is a marker for being disadvantaged more generally, and it is this general pattern of disadvantage (rather than single parenthood per se) that places children at risk of mortality. Associations between family structure and child mortality also are likely to vary with child gender, age, and race or ethnicity, although exploring these variations was beyond the limits of the current study. Despite these limitations, the current study is one of the few to consider how changes in family structure may have affected child outcomes at the societal rather than the individual level. Our study suggests that the increase in single-parent households in the United States since the 1960s was linked with a small increase in child mortality from accidents and homicides. Additional studies that use individual-level data are needed to replicate and clarify this finding, although large samples will be required, given that child mortality is a relatively uncommon outcome. New studies that dig more deeply into variations by child age, gender, race, and ethnicity also would make useful contributions to our understanding of a topic of continuing public interest. Acknowledgements This research was supported by funding from the Eunice Kennedy Shriver National Institute of Child Health and Human Development to the Population Research Institute at The Pennsylvania State University for Population Research Infrastructure (R24 HD041025) and Family Demography Training (T-32HD007514). References Agerbo, E., Nordentoft, M., Mortensen, P.B., 2002. 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