Complements versus Substitutes and Trends in Fertility Choice in Dynastic Models

Abstract

The Barro-Becker model is a simple intuitive model of fertility choice. In its original formulation, however, it has not been very successful at reproducing the changes in fertility choice in response to decreased mortality and increased income growth that demographers have emphasized in explaining the demographic transition. In this paper we show that this is due to an implicit assumption that number and utility of children are complements, which is a byproduct of the high intertemporal elasticity of substitution (IES) typically assumed in the fertility literature. We show that, not only is this assumption not necessary, but both the qualitative and quantitative properties of the model in terms of fertility choice change dramatically when substitutability and high curvature are assumed. To do so, we first derive analytical comparative statics and perform quantitative experiments. We find that if IES is less than one, model predictions of changes in fertility amount to about two-thirds of those observed in U.S. data since 1800. There are two major sources to these predicted changes, the increase in the growth rate of productivity which accounts for about 90 percent of the predicted fall in fertility before 1880, and changes in mortality which account for 90 percent of the predicted change from 1880 to 1950.

Fertility Theories: Can They Explain the Negative Fertility-Income Relationship?

“…8. See Greenwood, Seshadri, and Vandenbroucke (2005); Doepke, Hazan, and Maoz (2007); and Jones and Schoonbroodt (2007). security.…”

Explaining intergenerational mobility: The role of fertility and family transfers

“…The fact that the utility function u is positive is necessary to model altruism in a model with endogenous fertility. As shown byJones and Schoonbroodt (2010), the implicit assumption that parents enjoy having children requires that the utility function must be always positive or always negative. If we choose the negative case, we need an extra assumption for the value of having zero children.…”

Complements Versus Substitutes and Trends in Fertility Choice in Dynastic Models*

“…Further, the same representation for the choice problem of the individual parent will hold (approximately) if the fraction of potential children that can feasibly be born is small. See the additional appendix, Jones and Schoonbroodt (2009), for more details on this point.…”

“…15 15 Note that using the definition of and normalizing leads to as the utility for a household of generation t , where . A detailed derivation is available in the additional appendix, Jones and Schoonbroodt (2009). For , this boils down to the utility function used in Lucas (2002) and Bar and Leukhina (2010) and is also a special case of the one used in Razin and Ben‐Zion (1975). …”

“…24 24 Details can be found in the additional appendix, Jones and Schoonbroodt (2009), available online. …”