Forecasting Mortality Rates with a Two-Step LASSO Based Vector Autoregressive Model

Abstract

This paper proposes a two-step LASSO based vector autoregressive (2-LVAR) model to forecast mortality rates. Within the VAR framework, recent studies have developed a spatial–temporal autoregressive (STAR) model, in which age-specific mortality rates are related to their own historical values (temporality) and the rates of the neighboring cohorts (spatiality). Despite its desirable age coherence property and the improved forecasting accuracy over the widely used Lee–Carter (LC) model, STAR employs a rather restrictive structure that only allows for non-zero cohort effects of the same cohorts and the neighboring cohorts. To address this limitation, the proposed 2-LVAR model adopts a data-driven principle, as in a sparse VAR (SVAR) model, to offer more flexibility in the parametric structure. A two-step estimation strategy is developed accordingly to resolve the challenging objective function of 2-LVAR, which consists of non-standard L2 and LASSO-type penalties with constraints. Using empirical data from Australia, the United Kingdom, France, and Switzerland, we show that the 2-LVAR model outperforms the LC, STAR, and SVAR models in most of our forecasting results. Further simulation studies confirm this outperformance, and analyses based on life expectancy at birth empirically support the existence of age coherence. The results of this paper will help researchers understand the mortality projections in the long run and improve the reserving/ratemaking accuracy for life insurers.

Keywords

• mortality forecasting
• LASSO
• adaptive weights
• cohort effects
• age-coherence
• Lee–Carter model