Bivariate smoothing of mortality surfaces with cohort and period ridges

Mortality rates typically vary smoothly over age and time. Exceptions occur owing to events such as wars and epidemics, which create ridges in the age-period surface of mortality rates in a particular year or for cohorts born in a particular year. We propose a new practical method for modelling the age-period surface of mortality rates. Our approach uses L₁ regularization with bivariate smoothing and allows for age-varying period and cohort ridges in the otherwise smooth surface. Cross-validation on data from many countries and from simulations demonstrates that our approach is superior to existing approaches in estimating the “true” age-period mortality surface. It also provides greater insight into the underlying mortality dynamics, informing mortality modelling, analysis and forecasting. Although designed for the modelling of mortality rates, our method can also be applied to any bivariate data with occasional ridges and extends the statistical literature on quantile smoothing.