Deterministic and stochastic trends in the Lee–Carter mortality model

ABSTRACT

The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics load with identical weights when describing the development of age-specific mortality rates. Effectively this means that the main characteristics of the model simplify to a random walk model with age-specific drift components. But restricting the adjustment mechanism of the stochastic and linear trend components to be identical may be too strong a simplification. In fact, the presence of a stochastic trend component may itself result from a bias induced by properly fitting the linear trend that characterizes mortality data. We find empirical evidence that this feature of the Lee–Carter model overly restricts the system dynamics and we suggest to separate the deterministic and stochastic time series components at the benefit of improved fit and forecasting performance. In fact, we find that the classical Lee–Carter model will otherwise overestimate the reduction of mortality for the younger age groups and will underestimate the reduction of mortality for the older age groups. In practice, our recommendation means that the Lee–Carter model instead of a one-factor model should be formulated as a two- (or several) factor model where one factor is deterministic and the other factors are stochastic. This feature generalizes to the range of models that extend the Lee–Carter model in various directions.

KEYWORDS:

• Mortality modelling
• factor models
• principal components
• stochastic and deterministic trends

JEL CLASSIFICATION:

• C23
• J11

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Human Mortality Database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org or www.humanmortality.de (data downloaded 9 September 2014).

Additional information

Funding

This research was supported by CREATES – Center for Research in Econometric Analysis of Time Series (DNRF78), funded by the Danish National Research Foundation.