The Beckerian theory of fertility decisions in the family is based on the rationality and self-control of the involved parties, which is in stark contrast of the Malthusian theory of population growth, which relies on people breeding without control. As so often, the truth lies somewhere in between, as it is clear people guide their fertility outcomes but their is a substantial stochastic element to it.
Bertrand Wigniolle reinterprets Becker's theory by adding lack of self-control in the for of hyperbolic discounting, that is, discounted values fall rapidly in the near future and more slowly for the distant future. Wigniolle uses a three period model with parents valuing number and quality of children. In period 1, they choose the number of children and pay time costs for rearing them. In period 2, they choose their education, and support the associated costs. In period 3, they only enjoy their children. Hyperbolic discounting implies that every period they regret some of their past choices. The model yields very different results depending on parameter values. If parents have grounds to invest in the education of their children, then fertility is lower due to the lack of self-control. Call this a developed economy. If parents have no reason to invest in education (say because its return is low), then fertility gets higher with hyperbolic discounting. Call this a developing economy. And this is very sensitive to parameter values. A further reason to push for more schools and opportunities to use human capital in developing economies.