Growth vs level effect of population change on economic development: An inspection into human-capital-related mechanisms

We study the impact of demographic change on economic short and long-term dynamics in an enlarged Lucas-Uzawa model with intratemporal altruism. Demographics are summarized by population growth rate and initial size. In contrast to the existing literature, the long-run level effects of demographic changes, i.e. their impact on the levels of variables along the balanced growth paths, are deeply characterized in addition to the more standard growth effects. It is shown that the level effect of population growth is a priori ambiguous due to the interaction of three causation mechanisms, a standard one (dilution) and two non-standard, featuring in particular the transmission of demographic shocks into human capital accumulation. Overall, the sign of the level effect of population growth depends on preference and technology parameters, and on the initial conditions as well. In contrast, we prove that the long-run level effect of population size on per capita income is negative while its growth effect is zero. Finally, we show that the model is able to replicate complicated time relationships between economic and demographic changes. In particular, it entails a negative effect of population growth on per capita income, which dominates in the initial periods, and a positive effect which restores a positive correlation between population growth and economic performance in the long-run.