Abstract
Age–sex-specific population forecasts are derived through stochastic population renewal using forecasts of mortality, fertility and net migration. Functional data models with time series coefficients are used to model age-specific mortality and fertility rates. As detailed migration data are lacking, net migration by age and sex is estimated as the difference between historic annual population data and successive populations one year ahead derived from a projection using fertility and mortality data. This estimate, which includes error, is also modeled using a functional data model. The three models involve different strengths of the general Box–Cox transformation chosen to minimise out-of-sample forecast error. Uncertainty is estimated from the model, with an adjustment to ensure that the one-step-forecast variances are equal to those obtained with historical data. The three models are then used in a Monte Carlo simulation of future fertility, mortality and net migration, which are combined using the cohort-component method to obtain age-specific forecasts of the population by sex. The distribution of the forecasts provides probabilistic prediction intervals. The method is demonstrated by making 20-year forecasts using Australian data for the period 1921–2004. The advantages of our method are: (1) it is a coherent stochastic model of the three demographic components; (2) it is estimated entirely from historical data with no subjective inputs required; and (3) it provides probabilistic prediction intervals for any demographic variable that is derived from population numbers and vital events, including life expectancies, total fertility rates and dependency ratios.
Highlights
Stochastic methods of population forecasting are rapidly gaining recognition
We use the standard life table approach used in population projection: cohort deaths are estimated as the product of the population at time t, or births in year t, and the complement of the relevant survivorship ratio from the life table calculated using mt (x )
The dynamics of the process are controlled by the time series coefficients {βt,k} which are assumed to behave independently of each other
Summary
Stochastic methods of population forecasting are rapidly gaining recognition. Stochastic population forecasts have been produced for the US, Australia and several European and other countries, as well as for the world and world regions. This is generally the case for developed countries: vital registration provide lengthy series of data with the necessary detail. A solution to this lack of data is to estimate net migration as the difference between the increment in population size and natural increase using the demographic growth-balance equation. Stochastic population forecasts using functional data models for mortality, fertility and migration data are not collected. This paper applies functional data models in forecasting mortality, fertility and net international migration for use in national population forecasting. These forecast components are combined using the cohort-component method to produce probabilistic population forecasts by age and sex. As complete and reliable data on international migration are lacking, annual net migration for 1972–2003 is estimated using the growth-balance equation
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