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Fertility versus productivity: a model of growth with evolutionary equilibria

Foreman-Peck, James and Zhou, Peng 2020. Fertility versus productivity: a model of growth with evolutionary equilibria. Journal of Population Economics 10.1007/s00148-020-00813-2

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We develop a quantitative model that is consistent with three principal building blocks of Unified Growth Theory: the break-out from economic stagnation, the build-up to the Industrial Revolution, and the onset of the fertility transition. Our analysis suggests that England’s escape from the Malthusian trap was triggered by the demographic catastrophes in the aftermath of the Black Death; household investment in children ultimately raised wages despite an increasing population; and rising human capital, combined with the increasing elasticity of substitution between child quantity and quality, reduced target family size and contributed to the fertility transition. We develop a unified growth (UG) model (Galor and Weil 2000; Galor and Moav 2002; Galor 2011) that closely fits a wide range of data for the English economy. In addition to explaining the break-out from the Malthusian trap, the model provides an explanation for the fertility transition and the magnitudes of the various contributions to this change. Human capital accumulation is the endogenous key driver of these transitions.Footnote 1 Two fundamental mechanisms determine this accumulation. First, negative population growth (particularly that triggered by the Black Death) selects for the removal the portion of the population whose preferences render them “less fit.” Second, major mortality events both raise surviving child costs and eliminate agents with lower willingness to choose smaller families with high child quality.Footnote 2 We show that the data imply an increasing trade-off between child quantity and quality, with the elasticity of substitution between quantity and quality rising as extreme mortality impacts. As this elasticity increases, the Malthusian demand for number of children responds less to higher wages, and the negative effect of human capital growth on the demand for children becomes stronger. These effects are conducive to economic growth because they increasingly constrain population expansion and enhance human capital formation. Generation-specific mortality rates in our model reflect how life phases are affected differently; in particular, child death rates are higher than those of younger adults. Our model predicts that a fall in child mortality boosts target numbers of children (simply due to higher survival rates) but, in contrast to adult mortality, has no impact on investment in child “quality.” The model offers three explanations required by UG that are consistent with the data. The first is that escape from the Malthusian trap in England was triggered by the demographic catastrophes of the fourteenth and fifteenth centuries.Footnote 3 After these great mortality shocks, contrary to expectations, interest rates and skill premia did not return to their previous levels despite subsequent population growth and increasing land scarcity (Van Zanden 2009, p. 162). In our model, the economy attains new, non-Malthusian equilibria, as lower mortality induces more investment in children and young people, as well as greater savings. Contributors to these equilibria are Malthus’ preventive checks: higher age among females in their first marriage, and female childlessness (Hajnal 1965). The second explanation is that, in line with Malthus’ scheme, the long-term increasing productivity from human capital accumulation raised the demand for children, boosting the population. Unlike Malthus’s model, however, here, driven by household choice, productivity and accumulation eventually offset diminishing returns from population growth, and real wages begin to rise—just as they did in the Industrial Revolution. We show that, for England, an economic growth process was in place for a long period before the effect on average living standards became strongly apparent.Footnote 4 The third explanation is that, after the Industrial Revolution, the economy experienced a fertility transition because generalized child costs rose strongly. Both were propelled by human capital–driven technical progress rooted in family decisions and the rising elasticity of substitution between child costs and child quality. The demand for children increases with wage growth but by less as the elasticity of substitution rises. The generalized cost of child quality does not rise as much as that of child quantity because the supply of human capital expands with falling adult mortality. The shift in relative cost (of quantity against quality) lowers target family size. The rise in child cost is principally due to the increasing wage and the spread of family-financed schooling, which lowers both target family size and crude birth rate (CBR). Greater schooling implies falling child labor opportunities, another contributor to the reversal of intergenerational transfers.Footnote 5 Female literacy and the male–female wage premium play a smaller role in the decline of both CBR and net family size. Econometric analyses (Crafts 1984; Tzannatos and Symons 1989) present exogenous changes in generalized English child costs and quality as transition explanations without longer period ambitions. Their identification is weaker than in our model.Footnote 6 We explicitly derive these generalized costs and explain their movements. Unified growth theories (UGTs) have modeled fertility transitions as consequences of either technological progress that alters the quality/education-fertility trade-off or mortality decline (see Galor (2012) for a survey and Doepke (2005) for a model driven by mortality decline). In the present paper, both mechanisms play a part. In our model, technological change driven by human capital accumulation raises child costs. Ultimately, both these costs and human capital accumulation reduce fertility. This resembles the process discussed by Galor and Weil (2000); however, unlike them, we do not assign a positive role to population growth in technological progress because Crafts and Mills (2009), who studied the English population specifically, found no evidence for it. An alternative is to model technological change with two sectors, as done by Dutta et al. (2018). Their technological advances have different effects depending on the sector in which they primarily occur; agricultural advances boost population, whereas improvements in the non-agricultural sector enhance per capita incomes. Technological change alters relative prices and thus could make food more expensive, which would mean a higher cost of raising children. Strulik and Weisdorf (2008) hypothesized that such a price change triggered the fewer children of the English fertility transition—a hypothesis that we test in the present paper. The paper’s theoretical contribution is to show how key time-varying parameters can explain very long-term economic growth. This is achieved by explicitly building into our model preferences endogenous to mortality shocks. In contrast to evolutionary models with two types of individuals (Galor and Moav 2002; Galor and Michalopoulos 2012), the present model postulates a distribution of types. Our model also differs from others in its evolutionary path—a continuous spectrum of steady states, not transitional dynamics. A merit of this approach is that it allows for greater flexibility in modeling and fitting the data.Footnote 7 To simulate the effects of the many processes identified in the historical literature on the English economy, the present model includes a specific auxiliary component and a structural component, providing generalizable knowledge of growth in a unified fashion. Like Bar and Leukhina (2010), we postulate that, in England, the reduction in adult mortality improved knowledge transmission and thus became a force behind the ultimate rise in output per capita. The geographical march of the fourteenth-century plague shows that the resulting extreme mortality shocks were exogenous to the English economy. We note that the intensity and frequency of these mortality shocks diminished with the success of Western European quarantine regulations from the early eighteenth century (Chesnais 1992, p. 141). Such a decline in mortality would be exogenous to the English economy, even though it may have been endogenous to Western Europe as a whole. In UG models, mortality is often assumed to be endogenous. Voigtländer and Voth (2013a) postulated that death rates could increase with income, due to urbanization. In de la Croix and Licandro’s (2012) model, because of a parental trade-off between their own human capital investment and the time spent rearing children, during the fertility transition, richer cohorts have additional incentives to invest in childhood development. This ensures falling mortality, along with fertility. Strulik and Weisdorf (2014) specified a two-sector UG model in which a higher survival probability causes parents to nourish their children better. This specification is the opposite of the “negative sibship size” effect described by Brezis and Ferreira (2016), which alters the Beckerian quality–quantity trade-off. The closeness of our model to the English data, facilitated by the seven overlapping generations structure, suggests that the assumption of exogenous mortality is more appropriate for England. The remainder of the paper is organized as follows: Section 1 sets out the components of the model, including the overlapping generations, the evolution in response to extreme mortality shocks, the household choice, Malthusian constraints, and the shock structure. Because the nonlinearities of the full model rule out closed-form solutions, the properties of a restricted version of the model are discussed, and the time paths of the generalized costs of children and child quality are then predicted in Section 2. Section 3 describes the data, and Section 4 discusses the results of both the initial calibration and the subsequent optimized estimation of the model with the implied multiple steady states. Section 4 also includes a test of the hypothesis of a rising elasticity of substitution and the time paths of generalized costs, which we compare with the model predictions. Finally, in Section 5, we simulate auxiliary regression estimates of contributions to the generalized costs to establish their relative importance in the English fertility transition.

Item Type: Article
Date Type: Published Online
Status: In Press
Schools: Business (Including Economics)
Publisher: Springer Verlag (Germany)
ISSN: 0933-1433
Date of First Compliant Deposit: 9 November 2020
Date of Acceptance: 30 November 2020
Last Modified: 13 Jan 2021 09:32

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