TOPALS: A Tool for Projecting Age Patterns using Linear Splines

Joop De Beer, Netherlands Interdisciplinary Demographic Institute (NIDI)
Nicole Van der Gaag, Netherlands Interdisciplinary Demographic Institute (NIDI)

This paper proposes a simple but flexible method that is capable of describing all kinds of age curves using a limited number of parameters that can be interpreted easily. This method is called TOPALS: a TOol for Projecting Age patterns using Linear Splines. The basic idea is to choose a standard age schedule that captures the general pattern of the demographic process and to model deviations from this curve by a linear spline function. The standard pattern can be the age curve of another country, the average age pattern of several countries, the age curve of another year, or a model age schedule, such as the Hadwiger function for fertility, the Heligman-Pollard model for mortality or the double exponential function for migration. The idea of modeling deviations from a standard age schedule was developed by Brass (1974). TOPALS is more simple and flexible than the Brass method and provides a better fit. Using TOPALS for projections implies that the forecaster specifies to what extent future rates for different age categories will differ from the standard age schedule. For example, in specifying assumptions on future mortality rates, the forecaster can indicate that mortality at young ages will differ x percent from the standard age schedule, mortality at middle ages y percent, and mortality at old ages z percent. TOPALS can be used to take the effects of covariates into account as well. Based on estimates of relative risks, the forecaster can for instance assume that mortality rates of highly educated persons are p percent lower than those of people with a low level of educational attainment. The method will be illustrated using data for the Netherlands and Italy. Examples will be shown for mortality, fertility and migration. TOPALS is developed within the MicMac project: Bridging the micro-macro gap in population forecasting.