Three Equations Generating an Industrial Revolution?

In this paper we evaluate quantitatively the relationship between economic and demographic growth. We use simple models of endogenous growth, featuring human capital investment at the individual level in conjunction with either of two models of fertility choice, the B&B dynastic motive, and the B&J lateage-security motive. We find that exogenous improvements in agespecific survival probabilities, lead to increases in the rate of return to human capital investment. This, in turn, engenders an increase in the growth rate of output per capita much like what is typically seen when countries go through industrialization. In the models implemented so far, we also find that this is accompanied either by a permanent increase in the growth rate of population (for the B&B), or by too much late age consumption and a rate of return on capital that is too high relative to available data (for the B&J). Historical records show that the increase in the growth rate of population during the takeoff was temporary, and that the transition eventually lead to a stationary population; it is unclear if a different version of the B&B model can be built that generates this crucial stylized facts. On the other hand, preliminary work shows that more realistic variations of the B&J model should eliminate the unrealistic predictions about old age consumption and rate of return on capital while maintaining the ability of the model to generate an IR and a DT.