Lee Carter Mortality Projection: Application to British Population

The assignment delves into the Lee-Carter mortality forecasting technique, examining its application to the British population through various research studies. It critiques the method's effectiveness in predicting future mortality rates, highlighting successes and challenges associated with the model.

Lee Carter Mortality projection:
Application to The British Population

TABLE OF CONTENTS
DISSERTATION CHAPTER: LITERATURE REVIEW..............................................................1
REFERENCES................................................................................................................................4

DISSERTATION CHAPTER: LITERATURE REVIEW
This chapter of the study emphasizes on studying the views of different authors so as to
create a conceptual framework. This section uses only secondary information sources to study
Lee carter model from the earlier scholarly research studies and articles. Critical understanding
of the concept will helps to find out its strength as well as difficulties in the practical application
of the model to forecast the mortality rate.
Lee-Carter mortality projection is one of the most tools that run on numerical algorithm
to forecast mortality and future life expectancy. The model uses age specific mortality rates
matrix by time, in which, ages are arranged in columns whereas years are arranged in rows. It is
based on Singular Value Decomposition (SVD) to determine a univariate time series that alone
captures about 80%-90% of mortality trend.
As per the views of Spedicato mortality rate across distinctive age group shows
continuous falling trend across different countries all over the world. Higher the life expectancy
among people drives concerns towards public spending to support old age people. Therefore, in
order to determine cost of life insurance as well as pension annuities, it is necessary to project
mortality rates. The study was carried upon Italian population that used mortality database via
demographic factors and lifecontigencies package so as to forecast the cost of pension annuity.
In this, mechanical approach had been used because the main concern of the researchers was to
show its procedure instead of deriving justifiable and sensible output. The model was applied on
three categorized data sets including male, female and total population.
Haberman and Russolillo (2005) investigated the feasibility of Lee-Carter model to
project mortality rate, particularly for life expectancy. There were two reasons why researchers
1

had used the model that is it was highly influential development during that period and helpful to
identify a precise value of time index which helps to develop a series of death probability to
construct life table. At the same time, the study states that the methodology allows adjustments
for uncertainty, known as longevity risk.
Similarly, to Spedicato, this study also used gender-categorized database of Human
Mortality and consider age interval and time to construct 5*1 matrices of Number of Death and
Exposure to Risk. As per the study, ordinary regression seems not useful for LC model because
of no regressors therefore, close approximation is used as suggested under SVD method of LC
methodology. In the study, initially, estimation were based on log of death rate, therefore, it
recognized significant discrepancies in predicted and original death rates. Hence, in order to
correct it, the value had been re-estimated taking into account first step results.
The applied approach predicted different results to that of SVD estimate. It is because
youth accounted for lower death rates and contributes very less to the total amount of death.
However, when they are fitted into log-transformed data, they are assigned with the equal weight
to that of high death rates among older age people. Another interesting fact is differences in the
age group size of the population also provide distinctive weights at the second stage for
estimating the mortality.
On the other side, Wang (2007) used the Lee Carter methodologies to forecast mortality
rates for Sweden considering long-term perspective. The study had used SVD method to forecast
the model parameters. In this, four time series 1860-2004, 1900-2004, 1950-2004 and 1980-2004
had been used to assess the common trend in the change of mortality rates. The research findings
of the projected mortality rate for he period of 1901-2004 and 1951-2004 considering 7
distinctive estimated periods and its comparison with the results applying extended model with
2

fixed bx found that in order to project justifiable and realistic mortality rates, it is the most
important requirement to select an appropriate estimation period.
Lee & Carter (1992) used time-series analysis to make projection for long-run period. In
this, age-specific mortality from 1990 to 2065 was used and death rates are linearly modelled
considering age parameters. The method was performed on within-sample forecasts which found
insensitive that reduced base period length from 90 to 30 years mainly due to the base period of
10 or 20 years. The application of the method found an increase in the life expectancy of 10.5
years when both the sexes were combined at confidence interval of +3.9 or -5.6 due to
uncertainty about future. The forecasting about life expectancy identified that 46% survive to 80,
46% to 90 years and 74% to 65 years which was substantially below the time-series projection
but significantly greater that Social Security Administration forecasts. While applying the model,
it is discovered that least square estimates of K(t), bx and ax do not seems fitted on the life table
which reflect exact death rates for the actual population age distribution. To correct such
discrepancy, it requires a revise calculation of K(t) taking into account expected ax and bx. In
US, as the publication of data set takes time, thus, last year’s death rates must be used as a base
year to project future. If the model is applied for specific age group independently then it will
raise complexity because it will provide different covariance of errors.
Renshaw, Arthur and Steven Haberman (2003) reinterpreted the model using LC
methodology for mortality projection. Parallel methodology considering linear modelling had
been used. Moreover, residual plots were created to assess goodness of fitness. Both the model
results were compared and analysed taking into account age and gender-specific mortality
projections for England and Wales for the period of 1950-1998. The method found that Coale-
Guo method is highly effective to extrapolate rates of mortality among older age.
3

REFERENCES
Books and Journals
Haberman, S., and M Russolillo, ”Lee-Carter Mortality Forecasting Application to the Italian
Population. Actuarial Research Paper No. 167.”, City University(2005).
Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting US mortality. Journal of the
American statistical association. 87(419). 659-671.
Renshaw, Arthur, and Steven Haberman ”LeeCarter mortality forecasting: A parallel generalized
linear modelling approach for England and Wales mor- tality projections.”, Journal of the
Royal Statistical Society: Series C (Ap- plied Statistics) 52.1 (2003): 119-137
Spedicato, G. A. Mortality projection with demography and lifecontingencies packages.
Wang, J.Z., 2010. Fitting and Forecasting Mortality for Sweden: Applying the Lee-Carter Model,
Mathematical Statistics, Stockholm University, 2007.
4