Abstract
Chapter 2 described the conceptual and methodological foundations of the Child and Youth Well-Being Index (CWI). The question now becomes: What can the CWI and its component time series tell us about the well-being of America’s children and its changes (improvements and deteriorations) over time? Related to this are questions, such as what are the properties of the CWI?, how robust is it?, how does it relate to data on the subjective well-being of children and youth? and how can the CWI be used to study and anticipate changes in well-being? This chapter addresses these questions.
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Notes
- 1.
Observed values for most of the basic social indicator time series identified in Table 2.1 of Chap. 2 are available from the base years through 2008. In a few cases, however, this is not the case. In order to compute the values of our composite indices through 2008, we therefore estimated best-fitting autoregressive integrated moving average
(ARIMA) time series models (Yaffee 2000) for these series (as described in the Appendix to this chapter) and projected the values for those series for 2008 (and, in a few cases, for 2007).
- 2.
Only the overall child poverty rate is used in our composite well-being indices. However, the family-structure-specific time series shown in Fig. 3.2 are displayed in order to provide further information and to verify that trends exhibited in the population-specific time series are similar to those in the overall poverty rate series.
- 3.
Bianchi (1996) found that, by the mid-1990s, more unmarried women with dependent children were working than in previous decades. Also, since 1980, nonmarital childbearing rates have increased more rapidly for nonteen women compared to that of teens, and in the 1990s, birth rates for older women have continued to rise, whereas teen birth rates have been falling (Martin et al. 2006). In addition, research using Panel Study in Income Dynamics data indicates that older, single childbearing women are more likely to work before and after giving birth (Foster et al. 1998).
- 4.
- 5.
For the construction of domain-specific composite indices, we include the prevalence rate of children with any form of health insurance coverage in the family economic/material well-being index, as indicated in Table 2.1. In brief, we treat this basic indicator primarily as an index of the command a child’s family has over material resources.
- 6.
Again, only the overall single-parent prevalence rate time series is used in our composite indices of child and youth well-being. The female- and male-specific rates are included in Fig. 3.5 to provide evidence of consistency of the trends over time.
- 7.
Recall that many of the basic indicator time series identified in Table 2.1 are available in age-disaggregated form, as, for example, the mortality series exhibited in Fig. 3.6. In the construction of our domain-specific and overall composite indices of child and youth well-being, however, we aggregate the mortality series across all ages 1–19 in order not to give extra weight to age specificity for these series as compared to other series that are available only for broad age groups. Similar comments apply to other Key Indicators for which sets of age-specific data are available.
- 8.
The relationship of the availability of such medical technology to socioeconomic status has been documented by Gortmaker and Wise (1997).
- 9.
The obesity time series in Fig. 3.8 follow the definition first established in 1977, revised in 2000 (Kuczmarski et al. 2002), and renamed (see Kreb et al. 2007). That is, obese is defined as a body mass index (BMI) at or above the sex-specific 95th percentile BMI cutoff points calculated at 6-month intervals for children ages 6 through 11 from the 1963–1965 National Health Examination Survey (NHES) and for adolescents ages 12 through 17 from the 1966–1970 NHES. Age is at time of examination at mobile examination centers in the NHES. The obesity time series in Fig. 3.8 were linearly interpolated for intervening years from the waves of the NHANES: 1971–1974, 1976–1980, 1988–1994, 1999–2000, 2001–2002, 2003–2004, 2005–2006, and 2007–2008.
- 10.
Even taking into account the fact that the scale of the graph does not show the fine detail of changes in the birth rate for the 10–14 age group, the changes are smaller than those for the 15–17 age group.
- 11.
Because of the lack of uniform definitions, reporting standards, and general incompleteness of official reports, we do not include a statistical series on child abuse and neglect as part of the CWI. Note, however, that the National Crime Victimization Survey, the source of data on the rate of violent crime victimization in Fig. 3.9, includes violent crime victimizations by family members in its definition of victimizations. Furthermore, studies have shown that a separate time series of those family victimizations reported in the NCVS covaries over time very closely with the total violent crime victimization series shown in Fig. 3.9. Thus, it can be concluded that violent crime victimizations wherein the perpetrator was a parent or other family member have declined since 1975 along with violent crime victimizations as a whole.
- 12.
The years for which the time series in Fig. 3.11 are interpolated to annual dates were noted earlier.
- 13.
Since presidential elections occur on a 4-year cycle, the time series in Fig. 3.12 is interpolated for the intervening years in order to be consistent with the annual time series format of the other indicators in our index. For years beyond the most recent presidential election, we fix the voting percentage at the level of the last election so that this time series does not influence the index values in off-years.
- 14.
- 15.
In order to compute numerical values of the international best-practice composite index, we use the best-practice US values for those indicators in Table 3.1 for which comparable data cannot be found for other countries.
- 16.
We have not been able to disaggregate one indicator, the rate of children and adolescents living in families with incomes below the poverty line, by age to more specificity than the ages 6–17 range. Therefore, in order to capture trends in the poverty rate overtime (which likely are quite similar for the childhood and adolescence/teenage categories), we include this indicator in both the childhood and adolescence/teenage groups of indicators in Table 3.2.
- 17.
Data limitations prevent us from including two other race/ethnic groups, namely, Native Americans and Asian Americans, in the analyses reported in this section. Almost none of the basic social indicator time series used in constructing our indices are available in annual time series for these two groups.
- 18.
Chapter 4 of this volume extends these race/ethnic group analyses in various ways.
- 19.
The race/ethnic-group-specific domain indices of child and youth well-being are based on 27 of the 28 basic indicator series identified in Table 2.1. One Key Indicator, the rate of violent crime offending, is not included due to a lack of specificity regarding Hispanic ethnicity.
- 20.
Graphs of the unadjusted domain-specific indices of well-being for both African-American and Hispanic children/youths exhibit more overtime variability than found in the graphs for white children/youths. This is consistent with the presence of more statistical variability in the databases (often sample surveys) from these smaller populations. To reduce the year-to-year variability in these indices so that trends can be more easily seen, we applied 3-year moving averages to the domain-specific and composite indices for all three race/ethnic groups. The resulting smoothed time series are plotted in Figs. 3.20, 3.21, and 3.22.
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Appendix. Description of Arima Models
Appendix. Description of Arima Models
In order to calculate the composite CWI for the most recent calendar years, it is necessary to have values of all of the component 28 Key Indicators. Some of the data series for the indicators are slower to be published than others, e.g., those based on vital statistics data sources. For these time series, it is necessary to produce one- or two-time-period-ahead forecasts to bring them up to date. Accordingly, we have studied the time series properties of all of the indicators using autoregressive integrated moving average (ARIMA) statistical models (see, e.g., Granger and Newbold 1997; Yaffee 2000).
For each of the 28 time series, conventional ARIMA time series model estimation and selection methods produced the best-fitting models described in the Table 3.A.1 below. The models are denoted in the standard ARIMA(p ,d, q) triplet form, where p gives the order of the autoregressive (AR) part of the best-fitting model (if any), d gives the order of differencing of the time series necessary to produce stationarity (i.e., to eliminate long-term time trends so that the mean of the time series is zero and its variance is constant), and q gives the order of the moving average (MA) part of the model. The order of differencing of a time series necessary to produce stationarity is generally indicative of the nature of the long-term trend in the level of the series. For instance, a time series that exhibits a general linear trend of increase or decrease usually requires only first-order differencing (d = 1) to achieve stationarity. On the other hand, a time series that shows an increase followed by a decrease, or vice versa, usually requires second-order differencing (d = 2) to produce stationarity.
Because these are relatively slow moving annual time series, their ARIMA properties generally are relatively simple. Many of the time series take the form of ARIMA(0, 1, 1) models, that is, the time series are best fit by first-order moving average models after first-order differencing. These are termed integrated moving average models of order d = 1 and q = 1, i.e., IMA(1, 1) models, and may be written:
where Y t denotes the value of the time series in year t, e t is a white noise error term (i.e., is an independently distributed random variable with a mean of zero and a constant variance), and θ is a coefficient measuring the extent to which the error or innovation in time period t − 1 is added to the error term in period t to determine the change in Y from time period t − 1 to time period t. Such models are equivalent to exponential smoothing models (Granger and Newbold 1997, p. 172). Several others of the series take the form of ARIMA(0, 2, 2) models, time series that are best fit by second-order moving averages after second differencing. These models correspond to what are termed Holt-Winters extensions of exponential smoothing models (Granger and Newbold 1997, pp. 164–712). The third pattern observed in Table 3.A.1 is ARIMA(0, 2, 1) models, which are intermediate between the (0,1,1) and (0,2,2) models.
All of these models imply that, after long-term trends are eliminated from the data, the best short-term forecasts of the series place great weight on the last one or two observed values of the series or equivalently the innovations/changes corresponding thereto. In practice, we have found that the resulting projections are, indeed, relatively accurate for one or two periods ahead of the most recently available observed data.
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Land, K.C., Lamb, V.L., Meadows, S., Zheng, H., Fu, Q. (2012). The CWI and Its Components: Empirical Studies and Findings. In: Land, K. (eds) The Well-Being of America's Children. Children’s Well-Being: Indicators and Research, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4092-1_3
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