Mortality effects of temperature changes in the United Kingdom

• DOI: http://doi.org/10.1002/for.2473
• Date: 01 November 2017
• Published date: 01 November 2017

Received: 13 December 2016 Revised: 2 March 2017 Accepted: 13 March 2017

DOI: 10.1002/for.2473

RESEARCH ARTICLE

Mortality effects of temperature changes in the United Kingdom

Malgorzata Seklecka1Athanasios A. Pantelous1Colin O’Hare2

1Department of Mathematical Sciences,

University of Liverpool, UK

2Department of Econometrics and Business

Statistics, Monash University,Melbour ne,

Australia

Correspondence

Athanasios A. Pantelous, Department of

Mathematical Sciences, University of

Liverpool, Peach Street, Liverpool L69 7ZL,

UK.

Email: a.pantelous@liverpool.ac.uk

Funding information

EPSRC and ESRC Centre for Doctoral

Training on Quantification and Management

of Risk & Uncertainty in Complex Systems

& Environments, Grant/AwardNumber:

EP/L015927/1

Abstract

Temperature changes are knownto affect the social and environmental determinants

of health in various ways. Consequently, excess deaths as a result of extreme weather

conditions may increase over the coming decades because of climate change. In this

paper, the relationship between trends in mortality and trends in temperature change

(as a proxy) is investigatedusing annual data and for specified (warm and cold) peri-

ods during the year in the UK. A thoughtful statistical analysis is implemented and

a new stochastic, central mortality rate model is proposed. The new model encom-

passes the good features of the Lee and Carter (Journal of the American Statistical

Association, 1992, 87: 659–671) model and its recent extensions, and for the very

first time includes an exogenous factor which is a temperature-related factor. The

new model is shown to provide a significantly better-fitting performance and more

interpretable forecasts. An illustrative example of pricing a life insurance product is

provided and discussed.

KEYWORDS

climate change (temperature), forecasting, Lee–Carter model, longevity, pricing life annuity, United

Kingdom population

1INTRODUCTION

It is a remarkable achievement that, owing to the recent

advances in science and technology, humans are living

on average longer than ever before. Comparing the life

expectancy at the beginning of the 21st century with that at the

middle of the 18th century, it can be seen that life expectancy

has increased by over 30 years in a period of less than 200

years. This is an impressive achievement if someone also

considers that lifespan increased by 25 years over the previ-

ous 10,000 years (Niu & Melenberg, 2014; Pitacco, Denuit,

Haberman, & Olivieri, 2009). Obviously, as a direct conse-

quence, longevity risk is and will be a key issue for the future

of individuals, governments, and financial institutions. Thus

appropriate mortality modeling and accurate forecasting are

becoming increasingly important.

The climate, which is always a key parameter in the com-

plexity of the Earth’s system, and changesin average tempera-

ture may impact on life expectancyin various ways. Scientific

consensus indicates that climate change is likely to cause a

range of direct and indirect effects on human health in devel-

oped and developing countries (Easterling et al., 2000; Field

et al., 2014). The World Health Organization suggests that

between 2030 and 2050 climate change is expected to cause

approximately 250,000 additional deaths per year, because of

malnutrition, malaria, diarrhea, and heat stress (WHO, 2014).

Researchers across the world haveinvestigated links between

mortality and temperature changes. Results from these stud-

ies show that the magnitude of temperature that is related

to deaths varies between countries (Analitis et al., 2008;

Gasparrini et al., 2015; Meehl & Tebaldi, 2004) and popula-

tion groups. According to Hajat, Vardoulakis, Heaviside, and

Eggen’s (2014) findings, the most vulnerable age group is

elderly people. In addition, Christidis, Donaldson, and Stott

(2010) suggested that the ability of individuals or cohorts

to adapt is a major influence on changing mortality rates.

At the same time, absence of adaptation can result in cli-

mate being a main contributor to increases in heat- and

824 Copyright © 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/for Journal of Forecasting.2017;36:824–841.

SEKLECKA ET AL.825

cold-related mortality in comparison to an intermediate

“comfortable” temperature range (Patz, Campbell-Lendrum,

Holloway, & Foley, 2005; McMichael, Woodruff, & Hales,

2006).

One of the main goals of this paper is to examine for the

very first time (according to the authors’ knowledge), the

relationship between trends in mortality and trends in tem-

perature change (as a proxy for climate change) that can

be observed for annual data and for more specified (warm

and cold) periods during the year in the UK over the period

1974–2011. Consequently, we propose and explore the rela-

tionship between the time-dependent factor of the Lee and

Carter (1992) model (hereafter referred to as the LC model)

k1

t, and the logarithm of the average temperature for males

and females at ages between 20 and 85+. What is more,

we investigate the long-run relationship among time series

data using the Johansen (1988) cointegration test. Addition-

ally, we check correlation between those factors according to

various tests. We also use Pearson’s correlation coefficient

to analyze behavior between age-specific mortality rates and

averagetemperatures. Results of our investigation suggest that

there is a long-run relationship between the mortality index

and average temperature changes as we observe strong nega-

tive correlation coefficients. Additionally, similar results are

obtained from the analysis of mortality rates (by ages) and

average temperature fluctuations. The analysis of the statis-

tical results gives us a strong foundation and motivation to

investigate further this relationship. Thus we introduce a new

stochastic central mortality rates model by extending Plat’s

(2009) and O’Hare and Li’s (2012) approaches and imple-

menting an additional temperature-related factor to capture

temperature fluctuations. Furthermore, by using the mortality

rates produced by the proposed new model, as an illustrative

example, the present actuarial value of a lifeinsurance product

(more precisely, for nyears’ annuity) is calculated and com-

pared with results derived from existing, standard mortality

models. Additionally, the forecastingoutcomes from the pro-

posed model using autoregressive integrated moving average

(ARIMA) and exponential smoothing methods are reported.

Obviously, the stepping stone for our research is the cele-

brated mortality model introduced by Lee and Carter (1992).

Additionally, since we want to include advantageous features

of other existing extensions of the LC model, we also con-

sider the ideas of Plat’s (2009) and O’Hare and Li’s (2012)

models (hereafter referred to as the P and OL model, respec-

tively). The proposed new model takes into account all the

advantageous aspects of previous models and also includes

the temperature-related factor. It performs better when it is

compared with the above mortality models and gives very

good forecasting results. Mortality rates produced by the new

model also improve the valuation and pricing accuracy of

actuarial products.

The organization of the paper is as follows. In Section 2,

we briefly review the main models considered in this study,

and the relationship between climate (temperature) changes

and mortality rates is investigated. Additionally, Section 3

focuses on the statistical analysisof t he data from the National

Offices for Statistics, and the Met Office for the UK popula-

tion. Results on the long-run relationship among time series

data using the Johansen (1988) cointegration test, and corre-

lation according to various tests can be found. In Section 4

the new temperature-related model is introduced, and the fit-

ting estimation is discussed. Forecasting performance using

the ARIMA process and exponential smoothing is consid-

ered in Section 5. Results regarding the financial impact

are presented in Section 6. Finally, Section 7 concludes the

discussion in this paper.

2LITERATURE REVIEW

Mortality modeling and, in particular, the accurate forecast-

ing of mortality rates has a very long history. Probably the

first person who considered a scientific approach to mortality

data was Edmund Halley in 1693. Early mortality tables were

deterministic and static in nature and did not take account of

potential future improvements in mortality rates over time.

We can observe two main approaches in modeling mortal-

ity rates over time: extrapolative and explanatory.However,

in the corresponding literature we find that the vast major-

ity of mortality forecasting methods are extrapolative. They

make use of the observable patterns and trends over time

and forecast these into the future. The second approach (i.e.,

explanation) takes into account relationships between mortal-

ity and medical diseases or risk factors. It relies on medical

knowledge, information on behavioral or environmental fac-

tors (e.g., the dependence of lung cancer on tobacco smok-

ing), and the use of structural or epidemiological models of

mortality from certain causes of death where the key exoge-

nous variables are known and can be measured. We can also

find one more forecasting method in the literature based on

subjective expectation (Booth & Tickle, 2008). This approach

is one adopted by experts in the field, for example, actuaries.

Obviously, each of those methods has advantages and dis-

advantages and it is difficult to say which one is better. In

addition, comparison of outcomes from different approaches

is hampered by differences in the explicit assumptions—for

example, the choice of length of the historical period. In this

paper, we combine extrapolation and explanation by consid-

ering well-known models and improving them by adding the

new temperature-related factor.

2.1 Extrapolative mortality modeling

The initial step in developing a mortality model came from

the early mortality laws originated by fitting a mathematical