Page 129 - Contributed Paper Session (CPS) - Volume 3

CPS1970 Nurul Aityqah Y. et al.

The Lee-Carter Model: Extensions and
applications to Malaysian mortality data
1
1,2
1
Nurul Aityqah Yaacob , Dharini Pathmanathan , Ibrahim Mohamed , Siti
3
Haslinda Mohd Din
1 Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur
2 Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Cawangan
Negeri Sembilan, 72000 Kuala Pilah, Negeri Sembilan
3 Department of Statistics Malaysia, Federal Government Administrative Centre, Putrajaya

Abstract
This study examines the application of Lee-Carter (LC) model and some of its
extensions to Malaysia mortality data. The parameters were estimated by
using the singular value decomposition (SVD) method while ARIMA (p,d,q) was
used to forecast the mortality index. We find that, the log mortality rates for
all populations decreased and the female population in Malaysia is expected
to have longer life compared to the male population.

Keywords
Lee-Carter model; ARIMA; mortality; age-specific death rates; forecast

1. Introduction
Mortality forecasts have a long history in demography for population
projections and actuarial science. Actuaries applied mortality forecasts for cash
flow projections and assessment of premium and reserves in life insurance and
pension. Various models have been proposed since Gompertz published the
law of mortality in 1825. Commonly used methods in demographic forecasting
such as extrapolation, explanation and expectation. Extrapolation is the most
popular approach in demographic forecasting. The LC model which has been
widely applied in mortality forecasting uses the extrapolation approach. The
model is developed by Lee & Carter in 1992 to forecast mortality rates in the
United States from 1990 to 2065 (Lee & Carter, 1992).
Lee & Miller (2001) found that the LC model did not perform well for
United States when using the fitting period 1900-1989 to forecast the period
1990-1997. The pattern of change in mortality was not fixed over time. Due to
the different age patterns of change for 1900-1950 and 1950-1995, the fitting
period is reduced to commence in 1950 for the Lee-Miller (LM) variant (Booth
et al., 2005).
The Booth-Maindonald-Smith (BMS) variant was used to fit Australian data
from 1907 to 1999 and addressed two main issues in the original LC model;
linearity in estimated parameter and invariance in (Booth et al., 2002).

Thus, the optimal fitting period was applied, so the assumption of invariant

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