Endogenous education and the reversal in the relationship between fertility and economic growth

To reconcile the predictions of research and development (R&D)-based growth theory regarding the impact of population growth on productivity growth with the available empirical evidence, we propose a tractable, continuous-time, multisector, R&D-based growth model with endogenous education and endogenous fertility. As long as the human capital dilution effect is sufficiently weak, faster population growth may lead to faster aggregate human capital accumulation, to faster technological progress, and, thus, to a higher growth rate of productivity. By contrast, when the human capital dilution effect becomes sufficiently strong, faster population growth slows down aggregate human capital accumulation, dampens the rate of technical change, and, thus, reduces productivity growth. Therefore, the model can account for the possibly negative correlation between population growth and productivity growth in R&D-based growth models depending on the strength of the human capital dilution effect.