Demographic uncertainty and the stable equivalent population

That age distribution matters in understanding population dynamics is fundamental to demographic thinking, so we expect that the initial composition of a population will influence its subsequent evolution. This paper studies this influence in the context of stochastic population renewal models and stochastic forecasts. The effect of initial population age distribution is described in terms of reproductive value and the stable equivalent population (SEP), both of which are randomly distributed in stochastic projection models. We use analytical methods supported by simulation results to describe the properties of these random quantities. We find that random variation in vital rates can produce substantial uncertainty in both these quantities, when we deal with fertility variations of the sort that have characterized the United States in recent decades. We argue that stochastic projections should estimate and incorporate the uncertainty in the SER if they are to provide a good estimate of overall uncertainty.