A Piecewise Linear Cohort Extension to the Cairns-Blake-Dowd Model

Age-Period-Cohort (“APC”) models have been criticised on a number of grounds. One area of concern is in relation to projecting future cohorts. However, we would argue that such projection is unnecessary in some key cases, such as for closed defined benefit pension schemes.

More fundamental issues relate to the fit itself. APC models typically use at least one parameter for each cohort, in addition to those used for parameters age and period. This leads to a large number of parameters which are not necessarily independent.

However, the model we propose here uses a potentially far smaller number of parameters that essentially describe times where a new type of cohort emerges. This is similar to the trend-change models of mortality improvement discussed by as described by Sweeting (2011), Coelho and Nunes (2011), and van Berkum et al (2014). Because this cohort approach identifies a small number of changes in cohort rather than imposing a new cohort parameter for each year of birth, this reduces the risk of interdependence.