What is the relationship between industrial change and black family structure in the past 40 years?

1This model is crude because it only allows factors reflected in socioeconomic transition rates or demographic rates to influence future income distributions. Period-specific shifts in supply or demand may change these distributions. Mismatches between model-projected and observed distributions suggest that period-specific forces are more important than intergenerational mechanisms in shaping these distributions.

2Like others (Musick and Mare 2004; Preston 1974), I examine a “demographic” fertility effect. I assume that fertility’s importance stems from the number of children born to each group, not the association between fertility and mobility. This assumption is plausible; evidence suggests that additional siblings have no negative causal effect on children’s educational or economic outcomes (Angrist, Lavy, and Schlosser 2010; Black, Devereux, and Salvanes 2005; Caceres-Delpiano 2006; Guo and VanWey 1999). Parents may adjust to family-size increases without harming children’s attainment (e.g., by reducing leisure-related consumption).

3When there is no socioeconomic persistence, black children’s disproportionate entrance into lower-class families does not shape the future socioeconomic distribution of black adults. Conversely, when there is no mobility, fertility differences completely determine the ultimate distribution. All settle in the highest-fertility class, although such convergence may take many generations.

4The CPS excludes institutionalized individuals. Rising incarceration increasingly excludes economically marginal men from household surveys, understating black-white male wage inequality (Western 2006). Biases are much smaller here than in analyses of men’s wages, for two reasons. First, I study total family income (including women’s wages and non-wage income rarely accruing to prison-bound men [e.g., Aid to Families with Dependent Children]) and include unemployed men (whose exclusion understates wage inequality). Second, I study men and women together and women alone, never men alone. Although female incarceration grew, the proportion of women incarcerated remains small, meaning effects on complete distributions are small. Women-only samples should not suffer meaningful bias.

5Family incomes could be compared without using discrete categories. However, the categorical approach allows the continuity and change models to produce comparable results while capturing differential asymmetries in black and white children’s intergenerational mobility. In contrast, mobility measures using continuous income (intergenerational correlations or elasticities) obscure differential upward and downward mobility.

6One concern with excluding taxes involves the Earned Income Tax Credit (EITC), whose refunds through the tax system have grown since its 1975 introduction. However, including imputed EITC income (both estimated by the Census Bureau and calculated through the NBER’s TAXSIM module) generates results very similar to those presented here. EITC effects concentrate around the poverty line, as transfers are generally small (less than $1,800 in 2007, on average [Meyer 2010]). The tax credit pushes families out of poverty but does not appear to meaningfully alter black-white family income inequality trends that account for differences across the distribution, not only the bottom.

7Income distributions shifted upward and widened since 1968 (McCall and Percheski 2010). However, black and white mean family incomes grew at the same rate; income redistribution across quintiles also evolved similarly (U.S. Census Bureau 2010). Consequently, alternative analyses using fixed-income boundaries (permitting broadly shared or differentially distributed income growth to redistribute the population across income groups) produce nearly identical results to analyses using variable-boundary quintiles (constraining one-fifth of the population to occupy each group). I study quintiles because they address racial stratification scholars’ central concern with relative group positions, and they are easier to interpret. Results are robust to this choice.

8Using Casper and Cohen’s (2000) adjusted POSSLQ procedure for identifying cohabitors, I repeated the analysis including unmarried and married partners. These results are very similar, although inequality declines slightly less when including cohabitors. Cohabitation increased more quickly among whites than among blacks, leading to racial convergence in this family structure (Bumpass and Lu 2000), but black-white family income inequality is larger within cohabiting families than within married families (Manning and Lichter 1996). I focus on marriage due to evidence of significantly less stability and potentially less financial sharing within cohabiting families than within married families (Smock 2000). However, findings do not hinge on this decision.

9Formally, DKL=∑j=15pWjlog2(pWjpBj) where pWj and pBj are white and black adults’ probabilities of falling into family income quintile j. DKL captures the weighted average difference between the distributions’ log likelihoods, weighted by the importance of each mass point in the white income distribution. Generally, DKL is not symmetric, but my results are not sensitive to the reference distribution. Switching the distributions when calculating DKL leaves the conclusions unchanged.

10When disaggregating by family structure in addition to quintile and age, I separate the stably married from those who were not. Comparing results from models ignoring versus incorporating marital status reveals how racial differences in family-structure persistence (and its interaction with income) shape racial inequality trends. The two family groups used in the intergenerational analysis differ from the four family groups used in the change analysis (which distinguishes families by marital status and parental status). In the intergenerational analysis, only parents contribute to the future population. Intergenerational models include group-specific fertility rates to account for different reproductive propensities.

11Formally, top-row cell entries in the age-by-quintile analysis are PR,t(Yc = j | Yp = k)×f a,k,R,t. PR,t(Yc = j | Yp = k) is the probability that children of race R born in year t will attain adult income Yc in quintile j, given parental income Yp in quintile k; fa,k,R,t is the fertility rate of women age a, quintile k, and race R in year t. Other projections incorporate children’s marital status, Uc, and parents’ marital status, Up in two ways: assuming that marital status and income persist either independently or jointly. Formally, these assumptions correspond to cell entries PR,t(Yc = j | Yp = k)×PR,t(Uc = s | Up = l)×fa,k,l,R,t and PR,t(Yc = j,Uc = s | Yp = k,Up = l)×fa,k,l,R,t.

12Time-varying models permit the possibility that the chain will not converge to a unique equilibrium distribution.

13I use parents’ marital status and income quintile when their children were teens to predict these children’s marital status and income quintile in adulthood. Because of data sparsity, to populate time-varying transition matrices I use parametric smoothing across birth cohorts to predict cohort-specific transition rates.

14I use two fertility data sources because each supplements the other’s weaknesses. The NVS provides more accurate estimates because it draws on administrative reports of all births; the Census relies on survey reports of children living with their mothers. However, in the years required for this analysis, the NVS distinguishes fertility only by race. The Census permits calculations of age-specific fertility by race, marital status, and income quintile.

15Formally, between-group entropy is HRbt=∑g=1GpRglog2(1pRg), where pRg is the probability of a member of race R falling into family type g. Within-group entropy is HRwg=∑j=15pRg,jpRglog2(pRgpRg,j), where pRg,j is the probability of a member of race R and group g falling into quintile j.

16To cleanly decompose demographic and economic components, I do not adjust income for family size. Adjusting confuses demographic trends in family composition with economic trends in total income when examining within-family type distributions. Moreover, in intergenerational analyses, size-adjusting mixes fertility, marriage, and labor-supply decisions. Nevertheless, results using size-adjusted income mirror results reported here, with two noteworthy deviations. First, black-white inequality’s original level and decline are larger when size-adjusting, as African American families were larger but shrunk faster than white families. Second, the role of demographic change is slightly smaller when size-adjusting, because married-couple families’ relative well-being declines.

17Table 1 displays Bartholomew’s indices, which summarize children’s probabilities of switching income quintiles, weighing large moves more heavily than small moves. Higher values indicate more mobility. Formally, IBarth=15∑k=15∑j=15pkj∣k-j∣, where pkj represents children’s probability of moving from quintile k to quintile j.

18The raw data suggest that African American income mobility may have declined, as black families became more likely to maintain economic advantages (see Table 1). However, the change was not large enough to be detected statistically, nor to shape predicted inequality trends. This finding aligns with other PSID analyses, which uncover little evidence of significant mobility changes (Hertz 2007; Lee and Solon 2009).

19Family income mobility patterns are similar across the women-only and two-sex samples, suggesting that the projection models’ focus on women (to account for sex-specific fertility and mortality rates) should not affect the results’ generalizability.

20Models assuming perfect mobility predict almost zero racial inequality (Figure 6, row 9). Perfect mobility rates alter predicted income distributions more among blacks than among whites; observed black mobility is farther from the perfect counterfactual. Perhaps surprisingly, eliminating transmission differences via extreme persistence also generates low predicted black-white inequality (Figure 6, row 12). This is because complete immobility eliminates African Americans’ substantial downward mobility. In the short run, the distributions do not become bottom-heavy, as they do when using observed mobility. (In the long run under this model, fertility drives population redistribution; all migrate to the highest-fertility group, that is, low-income married women.)

21Like Preston (1974), I find small fertility effects on predicted racial inequality. Theoretically, black women’s steeper class-fertility gradient (especially among the unmarried; see Figure S2 in the online supplement) could perpetuate inequality by over-representing children in poor families; low-income, single African American mothers have proportionately more children, and proportionately fewer highly educated African American women marry (Bennett, Bloom, and Craig 1989). Consistent with this hypothesis, factual fertility rates (allowing racial differences) predict higher (and more accurate) inequality levels than do counterfactual rates using white fertility for both races (see Figure 6). However, compared to income and family-structure effects, fertility effects are small. Relatively high mobility offsets relatively small fertility differences (see also Mare 1997). Surprisingly, Census fertility data (which differentiate by class, marital status, and race) project somewhat less racial inequality than do NVS data (which differentiate only by race); thus, NVS data generate better predictions (comparing panels, Figure 6). This is because married women’s fertility rates far exceed unmarried women’s (the married population dominates when mixed with the unmarried), and racial differences in the class-fertility gradient are small among married women (creating greater racial convergence). Nevertheless, Census- versus NVS-based projections are fairly similar, again suggesting small fertility effects.

22These results also highlight the importance of gender differences in work and pay in maintaining racial inequality. Rising wages among black women (particularly among black mothers) helped reduce inequality over time, but reliance on these wages still maintains substantial black-white family income inequality, because women generally earn less than men and mothers earn less than women without children.

Page 2

Bartholomew’s Index of Intergenerational Family Income Mobility by Race, Parents’ Marital Status, and Cohort