Internal and External Consistency in Multidimensional Population Projection Models

In this paper the impact of consistency requirements upon the formulation of multidimensional population projection models is dealt with. The problem of internal consistency arises when certain output variables of the model have to be consistent with one another, as in models containing marital status (two-sex problem). External consistency problems arise when certain output variables have to satisfy externally specified restrictions. For instance, regional population projections may have to add up to national projections. The paper gives internal and external consistency algorithms, which control both for stock and for flow variables. Two approaches are discussed: a simple proportional adjustment for each relevant demographic component and an approach that minimises deviations in age-specific patterns of the input rates. Both algorithms are illustrated using data from the Netherlands. In the first illustration the internal consistency algorithm is applied to the age, sex, and marital-status-specific model of the official 1980 national population forecasts. In the second, external consistency is considered within the context of the multiregional projection model which was constructed for the regional population forecasts for the Netherlands.