A contribution to the economic theory of fertility

The evidence strongly suggests a robust negative relationship between income and fertility, and a positive relationship between income and longevity. This is puzzling for standard dynamic models. For instance, altruistic models that use the most standard preferences in macro --time separable CRRA with low elasticity of intertemporal substitution (EIS)-- correctly predict a positive longevity-income relationship for rich individuals, but also predict a positive fertility-income relationship, contrary to the data. We show that a non-separable formulation of preferences that allows for a low EIS but a high "elasticity of intergenerational substitution" (EGS) can simultaneously account for the evidence of declining demand for children and increasing demand for longevity as income increases. The model with a single elasticity cannot account for both. Our results suggests a major role for a new parameter in macro, the EGS. While the EIS mostly influences short-term economic decisions, the EGS influences mostly long-term economic choices.