Modelling and Forecasting Interregional Migration for Multiregional Population Projections

In this paper we focus on modelling and forecasting gross interregional migration in a way that can be embedded within multiregional population projections. We revisit, and apply, a family of spatial interaction models first formulated during the 1970s. The classic gravity model-in which migration is positively related to the populations of sending and receiving areas, but inversely related to various types of spatial friction associated with migrating between them-is a special case that is nested within this family of models. We investigate which member of the family of models gives the best fit when modelling five-year migration flows between the 66 Territorial Authorities (TAs) of Aotearoa New Zealand, using 2013 and 2018 census data. We find that predicting migration between two TAs can be improved by taking into account, firstly, an index of the 'draw' from all other TAs when modelling out-migration of any TA and, secondly, an index of the 'competitiveness' of a TA vis-& agrave;-vis all other TAs when modelling in-migration of any TA. We highlight the properties of the statistically-preferred model by simulating the impact on internal migration of an exogenous increase in Auckland's population. In this model, such a population change affects not only migration flows from and to Auckland, but also migration between other TAs. The usefulness of this approach for population projections is assessed by forecasting the 2013-18 migration matrix by means of 2013 census data only. In this specific case, the model outperforms the classic gravity model in terms of forecasting gross migration, but not net migration.