Deterministic and stochastic trends in the Lee-Carter mortality model

TY - UNPB

T1 - Deterministic and stochastic trends in the Lee-Carter mortality model

AU - Callot, Laurent

AU - Haldrup, Niels

AU - Kallestrup-Lamb, Malene

PY - 2014/11/20

Y1 - 2014/11/20

N2 - The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics loads with identical weights when describing the development of age specific mortality rates. Effectively this means that the main characteristics of the model simplifies 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 a too strong 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 over estimate the reduction of mortality for the younger age groups and will under estimate 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.

AB - The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics loads with identical weights when describing the development of age specific mortality rates. Effectively this means that the main characteristics of the model simplifies 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 a too strong 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 over estimate the reduction of mortality for the younger age groups and will under estimate 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.

KW - Mortality modelling, factor models, principal components, stochastic and deterministic trends

KW - Mortality modelling

KW - Factor models

KW - Principal components

KW - Stochastic and deterministic trends

M3 - Working paper

T3 - CREATES Research Paper

BT - Deterministic and stochastic trends in the Lee-Carter mortality model

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -