Short-Term and Long-Term Educational Mobility of Families: A Two-Sex Approach


We use a multigenerational perspective to investigate how families reproduce and pass their educational advantages to succeeding generations. Unlike traditional mobility studies that have typically focused on one-sex influences from fathers to sons, we rely on a two-sex approach that accounts for interactions between males and females—the process in which males and females mate and have children with those of similar educational statuses and jointly determine the educational status attainment of their offspring. Using data from the Panel Study of Income Dynamics, we approach this issue from both a short-term and a long-term perspective. For the short term, grandparents’ educational attainments have a direct association with grandchildren’s education as well as an indirect association that is mediated by parents’ education and demographic behaviors. For the long term, initial educational advantages of families may benefit as many as three subsequent generations, but such advantages are later offset by the lower fertility of highly educated persons. Yet, all families eventually achieve the same educational distribution of descendants because of intermarriages between families of high- and low-education origin.

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  1. 1.

    We use terms “family” and “family line” to refer broadly to social organization consisting of not only parents and offspring but also all descendants from a common ancestor.

  2. 2.

    We take a prospective approach in which we examine the transmission of educational status from the perspective of the grandparent generation. This approach is different from the more common retrospective approach that asks respondents about the characteristics of their parents and grandparents. For further discussions on the distinction between the two approaches and methods that reconcile the two approaches, see Song and Mare (2015).

  3. 3.

    Our model assumes independence of education and age. A refinement of the two-sex model may include age structure of the population, duration of marriages, polygamous mating rules, and differential demographic outcomes by age groups (Keyfitz 1972). A model with age structure incorporates the effects of marriage and fertility timing effects, fertility levels by age groups, and marriage squeezes caused by period fertility fluctuations and sex-ratio imbalance at older ages.

  4. 4.

    Family Identification Mapping System is a tool developed by the PSID to create intergenerational linked samples (

  5. 5.

    This linking method yields a larger sample from a prospective method that links PSID respondents from the first generation to the second and third generations because only a subset of the parents and grandparents of the third generation are themselves PSID respondents.

  6. 6.

    By focusing on families with four grandparents, we are excluding those with some grandparents omitted, which tend to be single-parent families. In other research, we examine the implications of single parenthood for the potential effect of grandparents on grandchildren (Song 2016). In that research, the results show that the net association between grandparent and grandchild educational attainment is weaker in single-parent families.

  7. 7.

    To check the robustness of our analyses on assortative mating, we also examined a sample restricted to the most recent marriage of individuals. Results are similar to those presented in this article.

  8. 8.

    Tabulations of the characteristics of our PSID samples by selected characteristics are available from the authors upon request.

  9. 9.

    We do not control for race in our analyses because we are unable to examine racial and educational assortative mating jointly, given the sample size.

  10. 10.

    Whereas Hertel and Groh-Samberg also used the PSID, they relied on patrilineal lineages. We provide a more complete two-sex model that includes all four grandparents, both parents, and sons and daughters.

  11. 11.

    In analyses not shown here, we also found heterogeneity in assortative mating within the same education groups of husbands and wives by their fathers’ and mothers’ education. In particular, educational matching is most likely to occur between males and females who themselves, as well as their parents, are in the same or adjacent education groups. Tables for these analyses are available from the authors on request.

  12. 12.

    Model specifications and test results are available from the authors on request.

  13. 13.

    This result is documented in tables for two-generation assortative mating not shown here but available from the authors on request.

  14. 14.

    The number of generations that it takes for the two-sex model to converge to its equilibrium depends on population size. When the population size is large, it takes longer for all families to be connected to each other through marriages.


  1. Bartholomew, D. J. (1982). Stochastic models for social processes (3rd ed.). New York, NY: Wiley.

  2. Behrman, J., & Taubman, P. (1985). Intergenerational earning mobility in the United States: Some estimates and a test of Becker’s intergenerational endowments model. Review of Economics and Statistics, 67, 144–151.

    Article  Google Scholar 

  3. Beller, E. (2009). Bringing intergenerational social mobility research into the twenty-first century. American Sociological Review, 74, 507–528.

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Bernheim, D. B., & Bagwell, K. (1988). Is everything neutral? Journal of Political Economy, 96, 308–338.

    Article  Google Scholar 

  6. Bessa-Gomes, C., Legendre, S., & Clobert, J. (2010). Discrete two-sex models of population dynamics: On modelling the mating function. Acta Oecologica, 36, 439–445.

    Article  Google Scholar 

  7. Blau, P. M. (1977). Inequality and heterogeneity: A primitive theory of social structure. New York, NY: Free Press.

  8. Blau, P. M., & Duncan, O. D. (1967). The American occupational structure. New York, NY: Wiley.

  9. Bloome, D. (2014). Racial inequality trends and the intergenerational persistence of income and family structure. American Sociological Review, 79, 1196–1225.

    Article  Google Scholar 

  10. Bol, T., & Kalmijn, M. (2015). Grandparents’ resources and grandchildren’s schooling: Does grandparental involvement moderate the grandparent effect? Social Science Research, 55, 155–170.

    Article  Google Scholar 

  11. Caswell, H. (2001). Matrix population models: Construction, analysis, and interpretatio (2nd ed.). Sunderland, MA: Sinauer Associates.

  12. Caswell, H., & Weeks, D. E. (1986). Two-sex models: chaos, extinction, and other dynamic consequences of sex. American Naturalist, 128, 707–735.

    Article  Google Scholar 

  13. Chan, T. W., & Boliver, V. (2013). The grandparent’s effect in social mobility: Evidence from British birth cohort studies. American Sociological Review, 78, 662–678.

    Article  Google Scholar 

  14. Cherlin, A. J., & Furstenberg, F. F. (1986). The new American grandparent: A place in the family, a life apart. New York, NY: Basic Books.

  15. Clark, G. (2014). The son also rises: Surnames and the history of social mobility. Princeton, NJ: Princeton University Press.

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

    Article  Google Scholar 

  17. DeLeire, T., & Kalil, A. (2002). Good things come in threes: Single-parent multigenerational family structure and adolescent adjustment. Demography, 39, 393–413.

    Article  Google Scholar 

  18. Duncan, O. D. (1966). Methodological issues in the analysis of social mobility. In N. J. Smelser & S. M. Lipset (Eds.), Social structure and mobility in economic development (pp. 51–97). Chicago, IL: Aldine.

  19. Erikson, R., & Goldthorpe, J. H. (1992). The constant flux: A study of class mobility in industrial societies. Oxford, UK: Clarendon Press.

  20. Erola, J., & Moisio, P. (2007). Social mobility over three generations in Finland, 1950–2000. European Sociological Review, 23, 169–183.

    Article  Google Scholar 

  21. Featherman, D. L., & Hauser, R. M. (1978). Opportunity and change. New York, NY: Academic Press.

  22. Fernández, R., & Rogerson, R. (2001). Sorting and long-run inequality. Quarterly Journal of Economics, 116, 1305–1341.

    Article  Google Scholar 

  23. Goldstein, D. B. (2008). Jacob’s legacy: A genetic view of Jewish history. New Haven, CT: Yale University Press.

  24. Goodman, L. A. (1953). Population growth of the sexes. Biometrics, 9, 212–225.

  25. Hertel, F. R., & Groh-Samberg, O. (2014). Class mobility across three generations in the U.S and Germany. Research in Social Stratification and Mobility, 35, 35–52.

    Article  Google Scholar 

  26. Hodge, R. W. (1966). Occupational mobility as a probability process. Demography, 3, 19–34.

    Article  Google Scholar 

  27. Hout, M. (1983). Mobility tables. Beverly Hills, CA: Sage Publications.

  28. Hout, M. (1988). More universalism, less structural mobility: The American occupational structure in the 1980s. American Journal of Sociology, 93, 1358–1400.

    Article  Google Scholar 

  29. Jæger, M. M. (2012). The extended family and children’s educational success. American Sociological Review, 77, 903–922.

    Article  Google Scholar 

  30. Kalmijn, M. (1991a). Status homogamy in the United States. American Journal of Sociology, 97, 496–523.

    Article  Google Scholar 

  31. Kalmijn, M. (1991b). Shifting boundaries: Trends in religious and educational homogamy. American Sociological Review, 56, 786–800.

    Article  Google Scholar 

  32. Keyfitz, N. (1968). Introduction to the mathematics of population. London, UK: Addison-Wesley Publishing Company.

  33. Keyfitz, N. (1972). The mathematics of sex and marriage. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, 4, 89–108.

    Google Scholar 

  34. Lam, D. (1986). The dynamics of population growth, differential fertility, and inequality. American Economic Review, 76, 1103–1116.

    Google Scholar 

  35. Lee, J. Z., & Campbell, C. D. (1997). Fate and fortune in rural China: Social organization and population behavior in Liaoning. Cambridge, UK: Cambridge University Press.

  36. Lee, J. Z., & Wang, F. (1999). One quarter of humanity: Malthusian mythology and Chinese realities. Cambridge, MA: Harvard University Press.

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

    Article  Google Scholar 

  38. Mare, R. D. (1991). Five decades of educational assortative mating. American Sociological Review, 56, 15–32.

    Article  Google Scholar 

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

    Article  Google Scholar 

  40. Mare, R. D. (2000). Assortative mating, intergenerational mobility, and educational inequality (Working Paper CCPR-004-00). Los Angeles: California Center for Population Research.

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  43. 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 

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

  45. Matras, J. (1961). Differential fertility, intergenerational occupational mobility and change in the occupational distribution: Some elementary interrelationships. Population Studies, 15, 187–197.

    Article  Google Scholar 

  46. Matras, J. (1967). Social mobility and social structure: Some insights from the linear model. American Sociological Review, 32, 608–614.

    Article  Google Scholar 

  47. Møllegaard, S., & Jæger, M. M. (2015). The effect of grandparents’ economic, cultural, and social capital on grandchildren’s educational success. Research in Social Stratification and Mobility, 42, 11–19.

    Article  Google Scholar 

  48. Musick, K., & Mare, R. D. (2004). Family structure, intergenerational mobility, and the reproduction of poverty: Evidence for increasing polarization? Demography, 41, 629–648.

    Article  Google Scholar 

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

    Article  Google Scholar 

  50. Piketty, T. (2014). Capital in the twenty-first century. Cambridge, MA: Harvard University Press.

  51. Pollak, R. A. (1986). A reformulation of the two-sex problem. Demography, 23, 247–259.

    Article  Google Scholar 

  52. Pollak, R. A. (1987). The two-sex problem with persistent unions: A generalization of the birth matrix-mating rule model. Theoretical Population Biology, 32, 176–187.

    Article  Google Scholar 

  53. Pollak, R. A. (1990). Two-sex demographic models. Journal of Political Economy, 98, 399–420.

    Article  Google Scholar 

  54. Preston, S. H. (1974). Differential fertility, unwanted fertility, and racial trends in occupational achievement. American Sociological Review, 39, 492–506.

    Article  Google Scholar 

  55. Preston, S. H., & Campbell, C. D. (1993). Differential fertility and the distribution of traits: The case of IQ. American Journal of Sociology, 98, 997–1019.

    Article  Google Scholar 

  56. PSID Main Interview User Manual: Release 2013. (2013). Ann Arbor: Institute for Social Research, University of Michigan.

  57. Qian, Z. (1997). Breaking the racial barriers: Variations in interracial marriage between 1980 and 1990. Demography, 34, 263–276.

    Article  Google Scholar 

  58. Qian, Z. (1998). Changes in assortative mating: The impact of age and education, 1970–1990. Demography, 35, 279–292.

    Article  Google Scholar 

  59. Qian, Z., & Preston, S. H. (1993). Changes in American marriage, 1972 to 1987: Availability and forces of attraction by age and education. American Sociological Review, 58, 482–495.

    Article  Google Scholar 

  60. Ruggles, S. (2007). The decline of intergenerational coresidence in the United States, 1850 to 2000. American Sociological Review, 72, 964–989.

    Article  Google Scholar 

  61. Schnore, L. F. (1961). Social mobility in demographic perspective. American Sociological Review, 26, 407–423.

    Article  Google Scholar 

  62. Schoen, R. (1981). The harmonic mean as the basis of a realistic two-sex marriage model. Demography, 18, 201–216.

    Article  Google Scholar 

  63. Schoen, R. (1988). Modeling multigroup populations. New York, NY: Plenum Press.

  64. Schwartz, C. R. (2010). Earnings inequality and the changing association between spouses’ earnings. American Journal of Sociology, 115, 1524–1557.

    Article  Google Scholar 

  65. Schwartz, C. R. (2013). Trends and variation in assortative mating: Causes and consequences. Annual Review of Sociology, 39, 451–470.

    Article  Google Scholar 

  66. Schwartz, C. R., & Mare, R. D. (2005). Trends in educational assortative marriage from 1940 to 2003. Demography, 42, 621–646.

    Article  Google Scholar 

  67. Sewell, W. H., & Hauser, R. M. (1975). Education, occupation, and earnings: Achievement in the early career. New York, NY: Academic Press.

  68. Silverstein, M., & Marenco, A. (2001). How Americans enact the grandparent role across the family life. Journal of Family Issues, 22, 493–522.

    Article  Google Scholar 

  69. Song, X. (2016). Diverging mobility trajectories: Grandparent effects on educational attainment in one- and two-parent families. Demography, 53, 1905–1932.

  70. Song, X., & Mare, R. D. (2015). Retrospective versus prospective approaches to the study of intergenerational social mobility. Sociological Methods and Research, 44, 555–584.

    Article  Google Scholar 

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

    Article  Google Scholar 

  72. Warren, J. R., & Hauser, R. M. (1997). Social stratification across three generations: New evidence from the Wisconsin Longitudinal Study. American Sociological Review, 62, 561–572.

    Article  Google Scholar 

  73. Wightman, P., & Danziger, S. (2014). Multigenerational income disadvantage and the educational attainment of young adults. Research in Social Stratification and Mobility, 35, 53–69.

    Article  Google Scholar 

  74. Zeng, Z., & Xie, Y. (2014). The effects of grandparents on children’s schooling: Evidence from rural China. Demography, 51, 599–617.

    Article  Google Scholar 

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We are grateful to Cameron Campbell, Hal Caswell, Thomas DiPrete, Mark Handcock, Benjamin Jarvis, Sung Park, Judith Seltzer, Florencia Torche, Shripad Tuljapurkar, and the Demography reviewers and editors for their valuable suggestions. Earlier versions of this article were presented at the Biodemography Workshop at Stanford University, May 6–8, 2013; the spring meeting of ISA Research Committee on Social Stratification (RC28), Trento, Italy, May 16–18, 2013; and the annual meeting of the American Sociological Association, August 10–13, 2013, New York City. The authors received support from the National Science Foundation (SES-1260456) and benefited from facilities and resources provided by the California Center for Population Research at UCLA (CCPR), which receives core support (R24-HD041022) from the Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD).

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Song, X., Mare, R.D. Short-Term and Long-Term Educational Mobility of Families: A Two-Sex Approach. Demography 54, 145–173 (2017).

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  • Educational mobility
  • Multigenerational
  • Two-sex model
  • Assortative mating