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Child-raising cost and fertility from a contest perspective

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

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

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

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

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

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

  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. 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. 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 \({{\bar{N}}} \rightarrow \infty\).

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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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  1. Research Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu, 610074, Sichuan, China

    Bing Xu & Maxwell Pak

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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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