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PARSIMONIOUS PARAMETERIZATION OF AGE-PERIOD-COHORT MODELS BY BAYESIAN SHRINKAGE

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Insurance, Mortality, Demography, Risk Management Statistical Distribution Estimation and Applications Statistical Methods and Bayesian Inference

Abstract

Abstract Age-period-cohort models used in life and general insurance can be over-parameterized, and actuaries have used several methods to avoid this, such as cubic splines. Regularization is a statistical approach for avoiding over-parameterization, and it can reduce estimation and predictive variances compared to MLE. In Markov Chain Monte Carlo (MCMC) estimation, regularization is accomplished by the use of mean-zero priors, and the degree of parsimony can be optimized by numerically efficient out-of-sample cross-validation. This provides a consistent framework for comparing a variety of regularized MCMC models, such as those built with cubic splines, linear splines (as ours is), and the limiting case of non-regularized estimation. We apply this to the multiple-trend model of Hunt and Blake (2014).

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References

1992Modeling and Forecasting U. S. Mortality 1965The Cohort as a Concept in the Study of Social Change 1985The Cohort as a Concept in the Study of Social Change 1999Loss Models: From Data to Decisions 2006A cohort-based extension to the Lee–Carter model for mortality reduction factors 2009A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States 1984Some Generalized Functions for the Size Distribution of Income 2008Some Generalized Functions for the Size Distribution of Income

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2019Loss Reserving Models: Granular and Machine Learning Forms 2021A GROUP REGULARISATION APPROACH FOR CONSTRUCTING GENERALISED AGE-PERIOD-COHORT MORTALITY PROJECTION MODELS

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