2017 Reports

Parameter Shrinkage for Joint Age-Period-Cohort Modeling of Related Datasets

Venter, Gary

Actuaries use age-period-cohort (APC) models for mortality modeling and general insurance loss reserving. Several recent papers have addressed simultaneously modeling related datasets, such as loss triangles for subsets of a class of business or mortality data across regions. This paper does joint modeling by shrinking the differences among the same parameters for different datasets. This could loosely be described as credibility weighting for triangles, but it comes more directly from statistical approaches such as ridge regression and lasso. Like credibility, these seek to reduce estimation and prediction error by various forms of shrinkage.
The models discussed here already incorporate parameter reduction by smoothing linear spline slope changes. This is extended to also shrink the differences between the same slope changes for different datasets. Doing so can reduce prediction error, measured using penalized log-likelihood, by increasing model parsimony. Bayesian Markov Chain Monte Carlo (MCMC) estimation is used in an example to illustrate the method. A related classical approach based on random effects is introduced as an alternative. The example is a joint model of historical female mortality data for Spain and Japan – two of the world's longest lived populations.