The Dynamics of the Age Structure , Dependency , and Consumption ∗

We examine the dynamic interaction of the population age structure, economic dependency, and fertility, paying particular attention to the role of intergenerational transfers. In the short run, a reduction in fertility produces a “demographic dividend” that allows for higher consumption. In the long run, however, higher old-age dependency can more than offset this effect. To analyze these dynamics we develop a highly tractable continuous-time overlapping generations model in which population is divided into three groups (young, working age, and old) and transitions between groups take place in a probabilistic fashion. We show that most highly developed countries have fertility below the rate that maximizes steady state consumption. Further, the dependency-minimizing response to increased longevity is to raise fertility. In the face of the high taxes required to support transfers to a growing aged population, we demonstrate that the actual response of fertility will likely be exactly the opposite, leading to increased population aging. JEL Classification Numbers: E10, E21, H55, J11, J13