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Shared Lifetimes, Multigenerational Exposure, and Educational Mobility

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Demography

Abstract

In this article, we report analyses of the effects of fertility and mortality trends on the mutual exposure of grandparents and grandchildren and their consequences for multigenerational processes of social mobility in the United States from 1900 to 2010. Using historical vital statistics and stable population models, we report systematic analyses of grandparent-grandchild exposures from both prospective (grandparent) and retrospective (grandchild) perspectives. We also estimate exposure levels and trends specific to education levels of grandparents and grandchildren and decompose the overall trend into the effect of changing mortality, fertility level, and fertility timing. We show that changes in mutual exposure of grandparent and grandchild generations may have contributed to an increasing association between grandparents’ and grandchildren’s educational attainments.

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Notes

  1. Parents’ education refers to father’s years of schooling if grandparents are from the paternal side; otherwise, it refers to mother’s years of schooling.

  2. Haines (1989) did not provide separate estimates for 1900 and 1910. We use the midpoint method to estimate TFR in 1900 and 1910.

  3. Specifically, we estimate m(x) ∝ N(Ar, σ2), within the range of x ∈ [15,45] for woman and [15,60] for men. We assume that the mean age of childbearing (Ar) and the variance of age of childbearing (σ2) are the same for men and women given that the Census Bureau provides these estimates only for females. Specifically, because \( GRR={\int}_{\upalpha}^{\upbeta}m(x) dx \), we estimate m(x) = GRR ∙ ψ(Ar, σ2, α, β; x), where \( \uppsi \left({A}_r,{\upsigma}^2,\upalpha, \upbeta; x\right)=\frac{\upphi \left({A}_r,{\upsigma}^2;x\right)}{\Phi \left({A}_r,{\upsigma}^2;\upbeta \right)-\Phi \left({A}_r,{\upsigma}^2;\upalpha \right)} \) if α < x < β, and ϕ(⋅) and Φ(⋅) refer to the probability density function and the cumulative distribution function of a normal distribution, respectively.

  4. Specifically, the relationship of the intrinsic growth rate and the age-specific fertility and mortality schedules follows \( {\int}_0^t{e}^{- rx}l(x)m(x) dx=1 \), where r is the intrinsic growth rate, and t is the maximum age in the population.

  5. We assume that the GRR for the first education group in 1900 is proportional to the GRR for the second education group in 1920 with a constant c, where c = GRR1900 / ∑iGRRedu = i ∣ year = 1920 ∙ P(edu = i | year = 1900).

  6. Because of interaction between mortality and fertility levels, the fertility effect would be bigger if we fixed the mortality level at a lower level (e.g., the level of 1950) than observed in Fig. 2, panel a. The results are included in Tables A6 and A7 of the online appendix.

  7. The estimated fertility effect becomes larger when we fix mortality at a lower level (e.g., the level of 1950) than that shown in Fig. 2, panel b. Again, this implies that the effects of fertility and mortality are not additive; instead, their interaction affects the trend in exposure.

  8. It is also possible to obtain estimates for grandchildren whose grandparents differ in their levels of education.

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Acknowledgments

This research was supported by the National Science Foundation (SES-1260456). The authors also benefited from facilities and resources provided by the California Center for Population Research (CCPR) at UCLA, which receives core support (P2C-HD041022) from the Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD). Earlier versions of this article have been presented at the 2015 RC28 Conference at the University of Pennsylvania; the 2016 ASA annual meeting in Seattle, Washington; the 2016 PAA annual meeting in Washington, DC; the 2017 ISA-RC28 Spring Meeting in Cologne, Germany; the Demography Workshop at the University of Chicago; the Demography and Inequality workshop organized by the European Consortium for Sociological Research in Berlin, Germany; and the Office of Population Research at Princeton University. We thank Cameron Campbell, Hal Caswell, Irma Elo, Anette Fasang, Michael Hout, Giovanna Merli, John Murphy, Judith Seltzer, Kazuo Yamaguchi, and numerous seminar participants for helpful discussions and comments, and Xia Zheng for outstanding research assistance.

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  1. Department of Sociology, University of Chicago, 1126 E. 59th Street, Chicago, IL, 60637, USA

    Xi Song

  2. Department of Sociology, University of California, Los Angeles, 264 Haines Hall, 375 Portola Plaza, Los Angeles, CA, 90095-1551, USA

    Robert D. Mare

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Song, X., Mare, R.D. Shared Lifetimes, Multigenerational Exposure, and Educational Mobility. Demography 56, 891–916 (2019). https://doi.org/10.1007/s13524-019-00772-8

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