The magnitude of error due to different vital processes in population forecasts

The propagation of error in stochastic cohort-component forecasts of population is discussed. The uncertainty of the forecasts is due to uncertain estimates of the jump-off population, and to errors in the forecasts of the vital rates: fertility, mortality, and migration. Empirically based (ex post) estimates of each source are presented and propagated first through a simplified analytical model of population growth. Being analytic, the model readily permits the assessment of the role of each component in the total error. Then, the paper considers numerical estimates based on the (ex ante) errors of an actual vector ARIMA forecast of the vital rates and propagates them through a forecast of the U.S. female population. The results agree in broad outline with those of the analytical model. In particular, the uncertainty in the forecasts of fertility is shown to be so much higher than that in the other sources that the latter can be ignored in the propagation of error calculations for those cohorts that are born after the jump-off year of the forecast. This simplifies the propagation of error calculations considerably. However, both the uncertainty of the jump-off population, migration, and mortality needs to be considered in the propagation of error for those alive at the jump-off time of the forecast.