The Lee-Carter quantile mortality model

Abstract

The Lee-Carter (LC) stochastic mortality model has been widely used for making future projections of mortality rates. In the framework of the LC model, the response function is non-linear in parameters. Here, we adapt this LC framework to compute conditional quantiles. The LC quantile model can be defined as quantile non-linear regression conditioned to age and the calendar year. Two strategies for estimating coefficients based on interior-point methods are described. We show that the LC quantile model provides additional information to that furnished by the traditional LC conditional mean. An application to Spanish mortality data is reported.

Should Selection of the Optimum Stochastic Mortality Model Be Based on the Original or the Logarithmic Scale of the Mortality Rate?

“…where α ∈ (0, 1). Santolino (2020) introduced the quantile Lee-Carter model equivalent to expression (1). Let us consider the following expression for the log mortality rate:…”

“…Here, by comparing the use of selection criteria measures based on mortality rates in either the original or log scales, we seek to determine if the preference for the Gaussian or Poisson assumption is conditional on the scale involved. While Santolino (2020) introduced the LC quantile stochastic model to estimate the quantiles of the log mortality rate, here, we focus our attention on the median LC model as a specific version of the LC quantile model that models the median log mortality rate (Santolino 2021). Recall that the mean is the value that minimizes the squared error while the median minimizes the absolute error.…”

Suitability of stochastic models for mortality projection in Korea: a follow-up discussion

“…In addition, although stochastic mortality models are usually applied to model overall mortality, Mubarik et al (2020) tested their suitability for modeling mortality due to breast cancer. A group of studies such as De Jong and Tickle (2006), Park et al (2013), Lee et al (2016), Santolino (2020), andDe Jong et al (2020) suggested methods for improving the Lee-Carter model in terms of parameter estimation, robustness, and interpretability.…”

Estimación de modelos de mortalidad estocástica para Chile

“…Lee y Carter (1992) propusieron un sencillo modelo para describir la evolución de la mortalidad. El modelo Lee-Carter ha sido utilizado para modelizar y pronosticar la mortalidad en diversos países como, por ejemplo, en Estados Unidos (Lee y Carter, 1992), Chile (Lee y Rofman, 1994), Bélgica (Brouhns, Denuit y Vermunt, 2002) y España (Betzuen, 2010;Debón, Martínez, Montes y Moshuk, 2015;Santolino, 2020), entre otros. Es un modelo bilineal en las variables edad (x) y año calendario (t) y se expresa de la siguiente manera:…”