Shared Lifetimes, Multigenerational Exposure, and Educational Mobility

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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Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Notes

  1. 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. 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. 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. 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. 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. 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. 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. 8.

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

References

  1. Alvaredo, F., Chancel, L., Piketty, T., Saez, E., & Zucman, G. (2018). World inequality report 2018. Cambridge, MA: Belknap Press of Harvard University Press.

    Google Scholar 

  2. Arias, E. (2014). United States life tables, 2010 (National Vital Statistics Reports Vol. 63, No 7). Hyattsville, MD: National Center for Health Statistics.

    Google Scholar 

  3. Arias, E., Curtin, L. R., Wei, R., & Anderson, R. N. (2008). U.S. decennial life tables for 1999–2001 (National Vital Statistics Reports Vol. 57, No 1). Hyattsville, MD: National Center for Health Statistics.

    Google Scholar 

  4. Armstrong, R. J. (1997). U.S. decennial life tables for 1989–91 (Vol. 1, No 1). Hyattsville, MD: National Center for Health Statistics.

    Google Scholar 

  5. Armstrong, R. J., & Curtin, L. R. (1985). U.S. decennial life tables for 1979–81 (Vol. 1, No. 1; DHHS Pub. No. (PHS) 85-1150-1). Washington, DC: U.S. Government Printing Office.

    Google Scholar 

  6. Bengtson, V. L. (2001). Beyond the nuclear family: The increasing importance of multigenerational bonds. Journal of Marriage and Family, 63, 1–16.

    Google Scholar 

  7. Bongaarts, J., Burch, T. K., & Wachter, K. W. (1987). Family demography: Methods and their application. Oxford, UK: Clarendon Press.

    Google Scholar 

  8. Carter, S. B., Gartner, S. S., Haines, M. R., Olmstead, A. L., Sutch, R., & Wright, G. (Eds.). (2006). Historical statistics of the United States. New York, NY: Cambridge University Press.

    Google Scholar 

  9. Centers for Disease Control and Prevention. (2014). Life tables. Accessed at http://www.cdc.gov/nchs/products/life_tables.htm

  10. Chan, T. W., & Boliver, V. (2013). The grandparents effect in social mobility: Evidence from British birth cohort studies. American Sociological Review, 78, 662–678.

    Google Scholar 

  11. Coale, A. J. (1965). Appendix: Estimates of average size of household. In A. J. Coale, L. A. Fallers, M. J. Levy, Jr., D. M. Schneider, & S. K. Tomkins (Eds.), Aspects of the analysis of family structure (pp. 64–69). Princeton, NJ: Princeton University Press.

    Google Scholar 

  12. Coale, A. J., Demeny, P., & Vaughan, B. (1983). Regional model life tables and stable populations (2nd ed.). New York, NY: Academic Press.

    Google Scholar 

  13. Coall, D. A., & Hertwig, R. (2010). Grandparental investment: Past, present, and future. Behavioral and Brain Sciences, 33, 1–59.

    Google Scholar 

  14. Daw, J., Verdery, A. M., & Margolis, R. (2016). Kin count(s): Educational and racial differences in extended kinship in the United States. Population and Development Review, 42, 491–517.

    Google Scholar 

  15. Elo, I. T., & Preston, S. H. (1996). Educational differentials in mortality: United States, 1979–1985. Social Science & Medicine, 42, 47–57.

    Google Scholar 

  16. Ferrie, J., Massey, C., & Rothbaum, J. (2016). Do grandparents and great-grandparents matter? Multigenerational mobility in the US, 1910–2013 (NBER Working Paper No. W22635). Cambridge, MA: National Bureau of Economic Research.

    Google Scholar 

  17. Goodman, L. A., Keyfitz, N., & Pullum, T. W. (1974). Family formation and the frequency of various kinship relationships. Theoretical Population Biology, 5, 1–27.

    Google Scholar 

  18. Greville, T. N. E. (1947). United States life tables and actuarial tables 1939–1941. Washington, DC: U.S. Government Printing Office.

    Google Scholar 

  19. Greville, T. N. E. (1975). United States life tables 1969–71 (DHEW Publication No. (HRA) 75-1150). Washington, DC: U.S. Government Printing Office.

    Google Scholar 

  20. Haines, M. R. (1989). American fertility in transition: New estimates of birth rates in the United States, 1900–1910. Demography, 26, 137–148.

    Google Scholar 

  21. Hällsten, M., & Pfeffer, F. T. (2017). Grand advantage: Family wealth and grandchildren’s educational achievement in Sweden. American Sociological Review, 82, 328–360.

    Google Scholar 

  22. Keyfitz, N. (1977). Applied mathematical demography. New York, NY: Springer.

    Google Scholar 

  23. Keyfitz, N. (1981). The limits of population forecasting. Population and Development Review, 7, 579–593.

    Google Scholar 

  24. Kitagawa, E., & Hauser, P. M. (1973). Differential mortality in the United States: A study in socioeconomic epidemiology. Cambridge, MA: Harvard University Press.

    Google Scholar 

  25. Knigge, A. (2016). Beyond the parental generation: The influence of grandfathers and great-grandfathers on status attainment. Demography, 53, 1219–1244.

    Google Scholar 

  26. Leopold, T., & Skopek, J. (2015). The demography of grandparenthood: An international profile. Social Forces, 94, 801–832.

    Google Scholar 

  27. Linder, F. E., & Grove, R. D. (1947). Vital statistics rates in the United States 1900–1940. Washington, DC: U.S. Government Printing Office.

    Google Scholar 

  28. Lotka, A. J. (1931). Orphanhood in relation to demographic factors. Metron, 9, 37–109.

    Google Scholar 

  29. Madoff, R. D. (2010). Immortality and the law: The rising power of the American dead. New Haven, CT: Yale University Press.

    Google Scholar 

  30. Maralani, V. (2013). The demography of social mobility: Black-white differences in the process of educational reproduction. American Journal of Sociology, 118, 1509–1558.

    Google Scholar 

  31. Mare, R. D. (1997). Differential fertility, intergenerational educational mobility, and racial inequality. Social Science Research, 26, 263–291.

    Google Scholar 

  32. Mare, R. D. (2011). A multigenerational view of inequality. Demography, 48, 1–23.

    Google Scholar 

  33. Mare, R. D. (2014). Multigenerational aspects of social stratification: Issues for further research. Research in Social Stratification and Mobility, 35, 121–128.

    Google Scholar 

  34. Mare, R. D., & Maralani, V. (2006). The intergenerational effects of changes in women’s educational attainments. American Sociological Review, 71, 542–564.

    Google Scholar 

  35. Mare, R. D., & Schwartz, C. R. (2006). Educational assortative mating and the family background of the next generation: A formal analysis. Riron to Hoho (Sociological Theory and Methods), 21, 253–277.

    Google Scholar 

  36. Mare, R. D., & Song, X. (2014). Social mobility in multiple generations (CCPR Working Paper Series PWP-CCPR-2016-014). Los Angeles: California Center for Population Research.

  37. Margolis, R. (2016). The changing demography of grandparenthood. Journal of Marriage and Family, 78, 610–622.

    Google Scholar 

  38. Margolis, R., & Wright, L. (2016). Older adults with three generations of kin: Prevalence, correlates, and transfers. Journals of Gerontology, Series B: Psychological Sciences and Social Sciences, 72, 1067–1072.

    Google Scholar 

  39. Martin, J. A., Hamilton, B. E., Osterman, M. J. K., Curtin, S. C., & Mathew, T. J. (2013). Births: Final data for 2012 (National Vital Statistics Reports Vol. 62, No. 9). Hyattsville, MD: National Center for Health Statistics.

    Google Scholar 

  40. Menken, J. (1985). Age and fertility: How late can you wait? Demography, 22, 469–483.

    Google Scholar 

  41. National Center for Health Statistics (NCHS). (2012). Health, United States, 2011: With special feature on socioeconomic status and health. Hyattsville, MD: NCHS.

    Google Scholar 

  42. Pfeffer, F. T. (2014). Multigenerational approaches to social mobility: A multifaceted research agenda. Research in Social Stratification and Mobility, 35, 1–12.

    Google Scholar 

  43. Pfeffer, F. T., & Killewald, A. (2017). Generations of advantage. Multigenerational correlations in family wealth. Social Forces, 96, 1411–1442.

    Google Scholar 

  44. Piketty, T. (2014). Capital in the 21st century. Cambridge, MA: Harvard University Press.

    Google Scholar 

  45. Prix, I., & Pfeffer, F. T. (2017). Does Donald need Uncle Scrooge? Extended family’s wealth and children’s educational attainment in the United States. In J. Erola & E. Kilpi-Jakonen (Eds.), Social inequality across generations: The role of compensation and multiplication in resource accumulation (pp. 112–135). Cheltenham, UK: Edward Elgar.

    Google Scholar 

  46. Rindfuss, R. R., Morgan, S. P., & Offutt, K. (1996). Education and the changing age pattern of American fertility: 1963–1989. Demography, 33, 277–290.

    Google Scholar 

  47. Rindfuss, R. R., & Sweet, J. (1977). Postwar fertility trends and differentials in the United States. New York, NY: Academic Press.

    Google Scholar 

  48. Rogot, E., Sorlie, P. D., & Johnson, N. J. (1992). Life expectancy by employment status, income, and education in the National Longitudinal Mortality Study. Public Health Reports, 107, 457–461.

    Google Scholar 

  49. Ruggles, S. (2012). The future of historical family demography. Annual Review of Sociology, 38, 423–441.

    Google Scholar 

  50. Ruggles, S. (2014). Big microdata for population research. Demography, 51, 287–297.

    Google Scholar 

  51. Sirken, M. G. (1964). United States life tables: 1959–61 (Public Health Service Publication No. 1252). Washington, DC: U.S. Department of Health, Education, and Welfare.

    Google Scholar 

  52. Sirken, M. G., & Carlson, G. A. (1954). United States life tables: 1949–51 (Vital Statistics—Special Reports, Vol. 41, Nos. 1–5). Washington, DC: U.S. Department of Health, Education, and Welfare.

    Google Scholar 

  53. Skopek, J., & Leopold, T. (2017). Who becomes a grandparent—and when? Education and fertility in multigenerational perspective. Demographic Research, 37, 917–928. https://doi.org/10.4054/DemRes.2017.37.29

    Google Scholar 

  54. Solon, G. (2018). What do we know so far about multigenerational mobility? Economic Journal, 128, F340–F352.

    Google Scholar 

  55. Song, X., & Campbell, C. D. (2017). Genealogical microdata and their significance for social science. Annual Review of Sociology, 43, 1–25.

  56. Song, X., & Mare, R. D. (2015). Prospective versus retrospective approaches to the study of intergenerational social mobility. Sociological Methods & Research, 44, 555–584.

    Google Scholar 

  57. Uhlenberg, P. (1996). Mortality decline in the twentieth century and supply of kin over the life course. Gerontologist, 36, 681–685.

    Google Scholar 

  58. Uhlenberg, P. (2009). Children in an aging society. Journals of Gerontology, Series B: Social Sciences, 64B, 489–496.

    Google Scholar 

  59. U.S. Census Bureau. (1921). United States life tables 1890, 1901, 1910, and 1901–1910. Washington, DC: U.S. Government Printing Office.

    Google Scholar 

  60. U.S. Census Bureau. (1975). Historical statistics of the United States: Colonial times to 1970 (Bicentennial ed., Part 2) Washington, DC: U.S. Government Printing Office.

  61. U.S. Census Bureau. (2014). Table A-1. Years of school completed by people 25 years and over, by age and sex: Selected years 1940 to 2014. Retrieved from https://www.census.gov/hhes/socdemo/education/data/cps/historical/

  62. Wachter, K. W., Hammel, E. A., & Laslett, P. (1978). Statistical studies of historical social structure. New York, NY: Academic Press.

    Google Scholar 

  63. Watkins, S. C., Menken, J. A., & Bongaarts, J. (1987). Demographic foundations of family change. American Sociological Review, 52, 346–358.

    Google Scholar 

  64. Wright, S. (1929). The evolution of dominance. American Naturalist, 63, 556–561.

    Google Scholar 

  65. Yahirun, J., Park, S., & Seltzer, J. A. (2018). Step-grandparenthood in the United States. Journal of Gerontology, Series B: Psychological Sciences and Social Sciences, 73, 1055–1065.

  66. Yang, Y., & Morgan, S. P. (2003). How big are educational and racial fertility differentials in the U.S.? Social Biology, 50, 167–187.

    Google Scholar 

  67. Zeng, Z., & Xie, Y. (2014). The effects of grandparents on children’s schooling: Evidence from rural China. Demography, 51, 599–618.

    Google Scholar 

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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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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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Keywords

  • Multigenerational exposure
  • Grandparents
  • Demographic change
  • Social mobility
  • Educational attainment