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“Backslanted X” fertility dynamics and macroeconomics


A large number of pairs of countries exhibit a dynamic pattern in which: (1) Fertility in both countries declines across time; (2) initially, one country has a higher fertility and a lower per-capita income than the other; and (3) in time, as per-capita incomes converge, fertility rates in the poorer country become lower than in the richer one. This article documents the prevalence of such dynamics and offers a theoretical model in which these dynamics emerge endogenously. Assuming differences in the degree of utility substitution between consumption and rearing children across countries generates all three components of these dynamics.

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  1. Appendix A presents several additional figures showing such dynamics among different pairs of countries.

  2. For theoretical articles that study the dynamics of fertility treating it as an endogenous variable and analyzing its dynamics within a dynamic macroeconomic framework, see for example, Becker et al. (1990), Galor and Weil (1996, 2000), Galor and Moav (2002), and Moav (2005).

  3. Several studies have come near the “Backslanted X” fertility dynamics when dealing with the reversal of the relationship between fertility and female labor participation among OECD countries. This relation was negative until the beginning of the 1980s but has turned positive since. See for example, Del Boca (2002), Adserà (2004), and Apps and Rees (2004). Some of these studies merely document this reversal, and others also provide explanations for the recent positive link, but none of them tries to explain the transition from the previous negative link to the current positive one.

  4. Several articles, e.g., Galor and Weil (2000), do find that income effects may generate a positive link between per-capita output and fertility. This positive relation, however, is limited to the early stages of growth and therefore is not relevant to the current article.

  5. See for example, Barro and Becker (1989) who studied the large country case, unlike the simpler case analyzed here, and restricted themselves therefore to an analysis of the dynamics around the steady state.

  6. As was discussed in the introduction, an important part of the schooling costs spring from secondary schooling tuition, which is government financed in most countries during the past few decades, and the forgone earnings of uneducated young individuals. Thus, not assuming that the cost of a unit of education increases with the growth in incomes (an assumption taken, for example, by Dahan and Tsiddon 1998 and Maoz and Moav 1999) is merely a simplification. A version of the current article, where the price of education is an increasing concave function of the adults’ income that yields the same qualitative results, is available from the author.

  7. τ t represents the amount of schooling a child gets. The only reason why it is interpreted as time is to create, as simple as possible, a mechanism of diminishing returns to investment in education. Such a diminishing returns mechanism is important for generating output convergence as under the simplifying assumptions of this model human capital accumulation is the sole source of growth.

  8. The purpose of assuming that rearing children costs the parents’ time is to make the (alternative) cost of rearing children positively correlated with the per-capita income in the economy. Alternative assumptions leading to this property are possible too. One simple such alternative, that would not change the equations of the model at all, would be to assume that rearing children requires some services, such as medical services or schooling. As the economy grows, the human capital of the suppliers of these services increases, making these suppliers more efficient in doing each specific task. On the other hand, this progress also adds more and more new tasks to these services. Assuming that these two contradicting effects on the suppliers’ time required to raise a single child balance one another, making this time fixed at z, the cost of rearing each single child in a period would still be zI t .

  9. Note that τ t is independent of α. This is not an important result but merely a by-product of the simplifying assumptions of a log-linear utility function and a time cost that is linear in n t .


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I thank Oded Galor, Moshe Hazan, and two anonymous referees for their most valuable help. I also would like to thank seminar participants in the Universities of Haifa and Jerusalem and at the S.E.D. 2006 convention for their helpful comments.

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Correspondence to Yishay D. Maoz.

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Responsible editor: Junsen Zhang

Appendix A

Appendix A

Fig. 3
figure 3

Total fertility rates (TFR) in several selected countries. Source: World Bank data

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Maoz, Y.D. “Backslanted X” fertility dynamics and macroeconomics. J Popul Econ 21, 159–172 (2008).

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  • Fertility
  • Human capital
  • Economic growth

JEL Classification

  • J11
  • J13
  • O40