Fertility Choice and Semi-Endogenous Growth: Where Becker Meets Jones
Introducing fertility choice into an R&D-based semi-endogenous growth model makes it possible for the economy's long-run growth rate to be again fully endogenously determined. A positive growth rate along the balanced growth path requires a certain knife-edge assumption, though. In the usual framework, it would be the assumption that the intertemporal elasticity of substitution in consumption be exactly unity (IES=1). We argue that such an assumption constitutes the ultimate source of long-run growth in these models; thus, we analyze the alternatives. If one relaxes the IES=1 assumption, and introduces a minimum "subsistence" fertility level to the model, there may (but may not) emerge an asymptotic balanced growth path with positive growth rates, to which the economy eventually converges as levels of variables diverge to infinity. This balanced growth path is either saddle-path stable or completely stable. We also address the issue of the economy's invariance towards fertility-promoting policy within the semi-endogenous growth framework. We conclude, that such policy can bring long-run effects only in the knife-edge case of IES=1 type, so that Jones' policy invariance result is typically consistent with endogenous fertility.
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