Abstract: Population forecasts for small areas within a country are an important planning tool. Standard methods for forecasting demographic rates do not, however, perform well with the noisy data that are typical of small areas. We develop a Bayesian model that combines ideas from the demographic, time series, and small area estimation literatures. We apply the model to the problem of forecasting emigration rates, disaggregated by age and sex, for 73 regions within New Zealand for the period of 2014-2038. We also deal with missing regional information and a change of geographic boundary. We test the calibration of the model using held-out data, and present extensions to accommodate age profiles and regional shares that vary over time. A key advantage of our approach is to provide meaningful uncertainty measures about forecasting. The prediction intervals for long-term forecasting are necessarily wide, engaging users to confront the substantial uncertainty about long-term trends.

Key words and phrases: Bayesian hierarchical model, multiple imputation, small area estimation, time series.