Child-raising cost and fertility from a contest perspective

Abstract

We model parents’ fertility and child-raising spending decisions as a Tullock contest with budget constraints and prizes that depend on relative efforts. We show that if the consequences of failure and the intensity of competition are sufficiently high, some potential parents forego having children in the resulting equilibrium. Moreover, parents having children prefer to have only one child and allocate all of their resources to raising that child rather than have multiple children. The equilibrium is consistent with the recent East Asian fertility experience and, more broadly, shows that competitive pressure, when combined with a high degree of inequality or poor social protection, can lead to an overaccumulation of human capital and low fertility.

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Notes

  1. 1.

    One exception to this strand of literature is Kalwij (2010), who concludes that cash grants affected the timing of the births but not the total fertility in Western Europe.

  2. 2.

    Although Singapore is located geographically in Southeast Asia, we consider it to be East Asian because of its culture. In addition, mainland China is excluded from the discussion since its legal restrictions on fertility make unclear the extent to which its low fertility is from parental choice or government-imposed.

  3. 3.

    While investigating the effects of risk-aversion on the contest participants’ effort levels, Skaperdas and Gan (1995) show that budget exhaustion can occur in equilibrium if certain conditions on the class of success probabilities and utility functions they consider are satisfied. In this paper, we have taken a different approach and allow the utilities to depend on relative effort levels, as we find it more compelling in the current context.

  4. 4.

    Clark (2017) provides a survey of the relevant empirical evidence.

  5. 5.

    Those observations are tempered somewhat in mainland China owing to its political system and the lingering effects of cultural revolution.

  6. 6.

    As shown in Fu and Lu (2012), that probability arises out of a noisy-ranking contest model in which contestants are ranked according to their effort multiplied by a noise term that follows an extreme value distribution. It also is equivalent to the “best-shot ranking rule”, in which contestants are ranked according to their best performance in a number of independent trials.

  7. 7.

    The expected number of successful children is normalized to be one in our model. Thus, rather than think of the parents in the model as representing the entire population, it may be more appropriate to view them as a peer group of parents whose children compete for one slot.

  8. 8.

    For example, Anderson and Kohler (2013), Iga (1981), Marginson (2011), Sorensen (1994) and Tan et al. (2016) all observe that a degree from a prestigious university is necessary, and often sufficient, for success in East Asia. Existing labor market studies also confirm those observations. Van der Velden et al. (2007) show that Japanese workers’ earnings are correlated strongly with the rankings of their alma maters, but not with family backgrounds or acquired competencies, while the opposite holds for the Netherlands. Lee and Brinton (1996) find that the university ranking is important for obtaining prestigious jobs in Korea, but having higher individual abilities than other students from the same university are not.

  9. 9.

    Attitudes in Canada are even more striking. A 2018 Ontario survey showed that only 15% of the public thought that a 4-years university degree is necessary for success (Ontario Institute for Studies in Education 2018).

  10. 10.

    A number of scholars have extended the standard Tullock framework to incorporate non-constant success and failure utilities. For example, \(v_s\) depends positively on total effort in Chung (1996) and either positively or negatively in Damianov et al. (2018). The two-competitor model of Chowdhury and Sheremeta (2011) allows success and failure utilities to depend linearly on the competitors’ efforts. In all-pay auctions, Kaplan et al. (2000) consider prizes that depend on the bidder’s own bid as well as her type, while Sela (2017) considers two-stage auctions in which the prize in the second stage depends on the bidder’s own bid in the first auction.

  11. 11.

    The OECD defines poverty relatively, as earning, inclusive of government transfers, less than or equal to 50% of the median income.

  12. 12.

    See, for example, Nohara and Sharp (2013) and Sugie (2017).

  13. 13.

    See, for example, (Baye et al. 1999) or Perez-Castrillo and Verdier (1992).

  14. 14.

    The conditions needed for concavity of \(P(c, {\hat{c}})\) are given in Proposition A.3 in the Appendix.

  15. 15.

    We believe that it is reasonable to assume that the modal parenting behavior in developed nations does sacrifice one child for the sake of giving another child a better chance to succeed.

  16. 16.

    Our reliance on stationarity requires group size N to be the same at all periods, which may not be ideal in a model of fertility. As an alternative, we may interpret stationarity as holding only locally. To be more precise, we fix a particular period t and investigate the equilibrium behavior of only the couples who make their decision in period t, treating the decisions of couples in periods \(t-1\) and \(t+1\) as fixed. Stationarity is then required only to hold between periods \(t-1\), t, and \(t+1\), which is more plausible because the gap between the periods presumably is short.

  17. 17.

    When \({{\bar{N}}} = 3\), \(\frac{\ln \left( 2+\frac{2}{{{\bar{N}}}-2}\right) }{\ln (2)} = \frac{\ln (4)}{\ln (2)} = 2\). It drops to 1.17 when \({{\bar{N}}}=10\) and continues to fall to 1 as \({{\bar{N}}} \rightarrow \infty\).

References

  1. Asian Development Bank. (2013). The social protection index: Assessing results for Asia and the Pacific. Manila: Asian Development Bank.

  2. Anderson, T., & Kohler, H.-P. (2013). Education fever and the East Asian fertility puzzle. Asian Population Studies, 9(2), 196–215.

    Google Scholar 

  3. Angrist, J., Lavy, V., & Schlosser, A. (2010). Multiple experiments for the causal link between the quantity and quality of children. Journal of Labor Economics, 28(4), 773–823.

    Google Scholar 

  4. Baye, M., Kovenock, D., & de Vries, C. (1999). The incidence of overdissipation in rent-seeking contests. Public Choice, 99(3/4), 439–454.

    Google Scholar 

  5. Becker, G. (1960). An economic analysis of fertility. In Universities-National Bureau (Ed.), Demographic and economic change in developed countries. Princeton: Princeton University Press.

    Google Scholar 

  6. Becker, G., & Lewis, H. G. (1973). On the interaction between the quantity and quality of children. Journal of Political Economy, 81(2), S279–S288.

    Google Scholar 

  7. Black, S., Devereux, P., & Salvanes, K. (2005). The more the merrier? The effect of family size and birth order on children’s education. Quarterly Journal of Economics, 120(2), 669–700.

    Google Scholar 

  8. Bray, M. (2013). Benefits and tensions of shadow education: Comparative perspectives on the roles and impact of private supplementary tutoring in the lives of Hong Kong students. Journal of International and Comparative Education, 2, 18–30.

    Google Scholar 

  9. Bray, M., & Kobakhidze, M. N. (2014). The global spread of shadow education: Supporting or undermining qualities of education? In D. B. Napier (Ed.), Qualities of education in a globalised world. Rotterdam: Sense Publishers.

    Google Scholar 

  10. Cáceres-Delpiano, J. (2006). The impacts of family size on investment in child quality. Journal of Human Resources, 41(4), 738–754.

    Google Scholar 

  11. Chan, H.-L., Liu, C.-Y., & Chau, Y.-L. (2011). Prevalence and association of suicide ideation among Taiwanese elderly: A population-based cross-sectional study. Chang Gung Medical Journal, 34(2), 197–204.

    Google Scholar 

  12. Che, Y.-K., & Gale, I. (1997). Rent dissipation when rent seekers are budget constrained. Public Choice, 92(1/2), 109–126.

    Google Scholar 

  13. Che, Y.-K., & Gale, I. (1998). Caps on political lobbying. American Economic Review, 88(3), 643–651.

    Google Scholar 

  14. Choe, M., & Retherford, R. (2009). The contribution of education to South Korea’s fertility decline to ‘lowest-low’ level. Asian Population Studies, 5(3), 267–288.

    Google Scholar 

  15. Chowdhury, S., & Sheremeta, R. (2011). A generalized Tullock contest. Public Choice, 147(3/4), 413–420.

    Google Scholar 

  16. Chung, T.-Y. (1996). Rent-seeking contest when the prize increases with aggregate efforts. Public Choice, 87(1/2), 55–66.

    Google Scholar 

  17. Chung, T., & Mallery, P. (1999). Social comparison, individualism-collectivism, and self-esteem in China and the United States. Current Psychology, 18(4), 340–352.

    Google Scholar 

  18. China Institute for Educational Finance Research - Household Survey (CIEFR-HS). (2017). 2017 China family education finance report. Beijing: Beijing University.

  19. Clark, A. (2017). Happiness, income and poverty. International Review of Economics, 64(2), 145–158.

    Google Scholar 

  20. Clark, A., Senik, C., & Yamada, K. (2013). The Joneses in Japan: Income comparisons and financial satisfaction. ISER Discussion paper No. 866.

  21. d’Addio, A., & d’Ercole, M. (2005). Trends and determinants of fertility rates in OECD countries: The role of policies. Paris: OECD Publishing.

    Google Scholar 

  22. Damianov, D. S., Sanders, S., & Yildizparlak, A. (2018). Asymmetric endogenous prize contests. Theory and Decision, 85(3/4), 435–453.

    Google Scholar 

  23. Doepke, M., & Zilibotti, F. (2017). Parenting with style: Altruism and paternalism in intergenerational preference transmission. Econometrica, 85(5), 1331–1371.

    Google Scholar 

  24. Drago, R., Sawyer, K., Shreffler, K., Warren, D., & Wooden, M. (2011). Did Australia’s baby bonus increase fertility intentions and births? Population Research and Policy Review, 30(3), 381–397.

    Google Scholar 

  25. European Commission (2010). Private household spending on education and training. Final project report

  26. Ermisch, J. (1988). Econometric analysis of birth rate dynamics in Britain. Journal of Human Resources, 23(4), 563–76.

    Google Scholar 

  27. Frejka, T., Jones, G., & Sardon, J.-P. (2010). East Asian childbearing patterns and policy developments. Population and Development Review, 36(3), 579–606.

    Google Scholar 

  28. Fu, Q., & Lu, J. (2012). Micro foundations of multi-prize lottery contests: A perspective of noisy performance ranking. Social Choice and Welfare, 38(3), 497–517.

    Google Scholar 

  29. Gauthier, A. (2016). Governmental support for families and obstacles to fertility in East Asia and other industrialized regions. In R. Rindfuss & M. Choe (Eds.), Low fertility, institutions, and their policies. Switzerland: Springer.

    Google Scholar 

  30. Gavious, A., Moldovanu, B., & Sela, A. (2002). Bid costs and endogenous bid caps. RAND Journal of Economics, 33(4), 709–722.

    Google Scholar 

  31. Goldstein, J., Sobotka, T., & Jasilioniene, A. (2009). The end of “lowest-low” fertility? Population and Development Review, 35(4), 663–699.

    Google Scholar 

  32. Iga, M. (1981). Suicide of Japanese youth. Suicide and Life-Threatening Behavior, 11(1), 17–30.

    Google Scholar 

  33. Jones, G., & Hamid, W. (2015). Singapore’s pro-natalist policies: To what extent have they worked? In R. Rindfuss & M. Choe (Eds.), Low and lower fertility: Variations across developed countries. Cham: Springer.

    Google Scholar 

  34. Jones, R., & Urasawa, S. (2014). Reducing the high rate of poverty among the elderly in Korea. OECD Economics Department Working Papers no. 1163.

  35. Kalwij, A. (2010). The impact of family policy expenditure on fertility in Western Europe. Demography, 47(2), 503–519.

    Google Scholar 

  36. Kaplan, T., Luski, I., Sela, A., & Wettstein, D. (2000). All-pay auctions with variable rewards. Journal of Industrial Economics, 50(4), 417–430.

    Google Scholar 

  37. Kim, K. K. (2010). Educational equality. In C. J. Lee, S. Y. Kim, & D. Adams (Eds.), Sixty Years of Korean Education. Seoul: Seoul National University Press.

    Google Scholar 

  38. Klumpp, T., & Polborn, M. (2006). Primaries and the New Hampshire effect. Journal of Public Economics, 90(6/7), 1073–1114.

    Google Scholar 

  39. Kwon, H.-J. (2001). Income transfers to the elderly in Korea and Taiwan. Journal of Social Policy, 30(1), 81–93.

    Google Scholar 

  40. Lee, J. (2008). Sibling size and investment in children’s education: An Asian instrument. Journal of Population Economics, 21(4), 855–875.

    Google Scholar 

  41. Lee, S., & Brinton, M. C. (1996). Elite education and social capital: The case of South Korea. Sociology of Education, 69(3), 177–192.

    Google Scholar 

  42. Lee, S., & Choi, H. (2015). Lowest-low fertility and policy responses in South Korea. In R. Rindfuss & M. Choe (Eds.), Low and lower fertility: Variations across developed countries. Cham: Springer.

    Google Scholar 

  43. Lee, S. K. (2011). Local perspectives of Korean shadow education. Reconsidering Development, 2(1), 1–22.

    Google Scholar 

  44. Lee, S. Y., & Ohtake, F. (2018). How conscious are you of others? ISER Discussion Paper No: Further evidence on relative income and happiness (p. 1022)

  45. Li, H., Zhang, J., & Zhu, Y. (2008). The quantity–quality trade-off of children in a developing country: Identification using Chinese twins. Demography, 45(1), 223–243.

    Google Scholar 

  46. Liu, J. (2012). Does cram schooling matter? Who goes to cram schools? Evidence from Taiwan. International Journal of Educational Development, 32(1), 46–52.

    Google Scholar 

  47. Marginson, S. (2011). Higher education in East Asia and Singapore: Rise of the confucian model. Higher Education, 61(5), 587–611.

    Google Scholar 

  48. McDonald, P. (2006). Fertility and the state: The efficacy of policy. Population and Development Review, 32(3), 485–510.

    Google Scholar 

  49. Megidish, R., & Sela, A. (2014). Sequential contests with synergy and budget constraints. Social Choice and Welfare, 42(1), 215–243.

    Google Scholar 

  50. Milligan, K. (2005). Subsidizing the stork: New evidence on tax incentives and fertility. Review of Economics and Statistics, 87(3), 539–55.

    Google Scholar 

  51. Nohara, Y., & Sharp, A. (2013). Japan’s elderly go on a petty crime spree: For many, benefits aren’t enough, families are gone, and hunger hurts. Bloomberg.

  52. OECD. (2015). Pensions at a glance 2017: OECD and G20 indicators. Paris: OECD Publishing.

  53. OECD. (2019). Society at a glance 2019: OECD social indicators. Paris: OECD Publishing.

  54. Ontario Institute for Studies in Education. (2018). Public attitudes toward education in Ontario 2018. Toronto: Ontario Institute for Studies. in Education.

  55. Perez-Castrillo, J. D., & Verdier, T. (1992). A general analysis of rent-seeking games. Public Choice, 73(3), 335–350.

    Google Scholar 

  56. Rosenzweig, M., & Wolpin, K. (1980). Testing the quantity–quality fertility model: The use of twins as a natural experiment. Econometrica, 48(1), 227–240.

    Google Scholar 

  57. Rosenzweig, M., & Zhang, J. (2009). Do population control policies induce more human capital investment? Twins, birth weight and China’s “one-child” policy. Review of Economic Studies, 76(3), 1149–1174.

    Google Scholar 

  58. Sela, A. (2017). Two-stage contests with effort-dependent values of winning. Review of Economic Design, 21(4), 253–272.

    Google Scholar 

  59. Skaperdas, S., & Gan, L. (1995). Risk aversion in contests. The Economic Journal, 105(431), 951–962.

    Google Scholar 

  60. Sorensen, C. W. (1994). Success and education in South Korea. Comparative Education Review, 38(1), 10–35.

    Google Scholar 

  61. Sorger, G., & Stark, O. (2013). Income redistribution going awry: The reversal power of the concern for relative deprivation. Journal of Economic Behavior and Organization, 86, 1–9.

    Google Scholar 

  62. Sugie, N. F. (2017). When the elderly turn to petty crime: Increasing elderly arrest rates in an aging population. International Criminal Justice Review, 27(1), 19–39.

    Google Scholar 

  63. Tan, P. L., Morgan, S. P., & Zagheni, E. (2016). A case for “reverse one-child” policies in Japan and South Korea? Examining the link between education costs and lowest-low fertility. Population Research and Policy Review, 35(3), 327–350.

    Google Scholar 

  64. Toulemon, L. (2011). Should governments in Europe be more aggressive in pushing for gender equality to raise fertility? The first “YES”. Demographic Research, 24, 179–200.

    Google Scholar 

  65. Tullock, G. (1980). Efficient rent-seeking. In J. Buchanan, R. Tollison, & G. Tullock (Eds.), Toward a theory of the rent-seeking society. College Station: Texas A&M Univ. Press.

    Google Scholar 

  66. van der Velden, R., van de Loo, P., & Meng, C. (2007). University and college differences in the returns to education in Japan and the Netherlands. In J. Allen, Y. Inenaga, R. Velden, & K. Yoshimoto (Eds.), Competencies, higher education and career in Japan and the Netherlands. Higher education dynamics (Vol. 21). Dordrecht: Springer.

    Google Scholar 

  67. White, K., & Lehman, D. (2005). Culture and social comparison seeking: The role of self-motives. Personality and Social Psychology Bulletin, 31(2), 232–42.

    Google Scholar 

  68. Whittington, L. A. (1992). Taxes and the family: The impact of the tax exemption for dependents on marital fertility. Demography, 29(2), 215–26.

    Google Scholar 

  69. Whittington, L. A., Alm, J., & Peters, H. E. (1990). Fertility and the personal exemption: Implicit pronatalist policy in the United States. American Economic Review, 80(3), 545–56.

    Google Scholar 

  70. World Bank (2006). Social safety nets in OECD countries. Social Safety Nets Primer Notes, No. 25. Washington, DC: World Bank.

  71. Yoon, S.-Y. (2016). Is gender inequality a barrier to realizing fertility intentions? Fertility aspirations and realizations in South Korea. Asian Population Studies, 12(2), 203–219.

    Google Scholar 

  72. Zhang, J., Quan, J., & van Meerbergen, P. (1994). The effect of tax-transfer policies on fertility in Canada. Journal of Human Resources, 29(1), 181–201.

    Google Scholar 

  73. Zhang, Y. (2013). Does private tutoring improve students’ National College Entrance Exam performance? A case study from Jinan, China. Economics of Education Review, 32(1), 1–28.

    Google Scholar 

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Acknowledgements

We have benefited greatly from discussions with Eric Fong, Qiang Fu, Li Gan, Mark Rosenzweig and Junsen Zhang. We would also like to thank the anonymous reviewers and William Shughart II for their valuable comments and editorial suggestions, as well as Weili Ding, Hanol Lee, Steven Lehrer, Eric Set and Fan Yang for their helpful comments on the earlier version. This paper was completed while Maxwell Pak was visiting NYU Shanghai, and he is grateful for their hospitality and financial support. Support from China National Natural Science Foundation (Grants #71403217 and #71874144) and China’s Ministry of Science and Technology (Grant #G20190023006) is also gratefully acknowledged.

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Xu, B., Pak, M. Child-raising cost and fertility from a contest perspective. Public Choice 186, 9–28 (2021). https://doi.org/10.1007/s11127-019-00751-y

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Keywords

  • Child-raising cost
  • Education
  • Fertility
  • Quantity–quality trade-off
  • Competition
  • Tullock contest

JEL Classification

  • D70
  • D91
  • I21
  • J13