We thank Todd Schoellman, John Knowles, and the participants at the NBER pre-conference in Boston, the Stanford Junior Faculty Bag Lunch, and the Economics and Demography conference in Napa California for helpful suggestions. We thank Amalia Miller in particular for a thoughtful discussion.

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.

Is there an economic rationale for pronatalist policies? We propose and analyze a particular market failure that leads to inefficiently low fertility in equilibrium. The friction is caused by the lack of ownership of children: if parents have no claim on their children's income, the private benefit from producing a child can be smaller than the social benefit. We analyze an overlapping-generations model with fertility choice and parental altruism. Ownership is modeled as a minimum constraint on transfers from parents to children. Using the efficiency concepts proposed in Golosov, Jones, and Tertilt (2007), we find that whenever the transfer floor is binding, fertility choices are inefficient. Second, we show that the usual conditions for efficiency are not sufficient in this context. Third, in contrast to settings with exogenous fertility, a PAYG social security system cannot be used to implement efficient allocations. To achieve an efficient outcome, government transfers need to be tied to fertility choice. JEL Classification: D6, E1, H55, J13

Demographers emphasize decreased mortality and "economic development" as the main contributors generating the demographic transition. Contrary to previous findings, we show that simple dynastic modelsà la Barro-Becker can reproduce observed changes in fertility in response to decreased mortality and increased productivity growth if the intertemporal elasticity of substitution is low enough. We show that this is largely due to number and welfare of children being substitutes in the utility of parents in this case. We find that with an IES of one-third, model predictions of changes in fertility amount to two-thirds of those observed in U.S. data since 1800.