Chapter 11 longevity risk and private pensions

11.2.1 Th e Link between Mortality and Life Expectancy: 11.2.3 Approaches to Forecast Mortality and Life Expectancy 248 11.2.4 Measuring Uncertainty Surrounding Mortality 11.3 Th e Impa

11.2.1 Th e Link between Mortality and Life Expectancy:

11.2.3 Approaches to Forecast Mortality and Life Expectancy 248 11.2.4 Measuring Uncertainty Surrounding Mortality

11.3 Th e Impact of Longevity Risk on Defi ned-Benefi t Private

11.3.1 How Does Longevity Risk Aff ect DB Private

11.3.2 How Do Private Pension Funds Account for Future

Improvements in Mortality and/or Life Expectancy? 258 11.3.3 Th e Impact of Longevity Risk on Net Pension

This ch a pter e xa mines how uncertainty regarding future mortality

and life expectancy outcomes, i.e., longevity risk, aff ects

employer-provided defi ned benefi t (DB) private pension plan liabilities Th e ter a rgues t hat t o a ssess u ncertainty a nd a ssociated r isks adeq uately,

chap-a stochchap-astic chap-approchap-ach to model mortchap-ality chap-a nd l ife ex pectchap-ancy is able bec ause i t per mits t o a ttach p robabilities t o d iff erent f orecasts I n this regard, the chapter provides the results of estimating the Lee–Carter model for se veral OECD countries Furthermore, it conveys t he u ncer-tainty su rrounding f uture m ortality a nd l ife ex pectancy o utcomes b y means of Monte-Carlo simulations of the Lee–Carter model

prefer-In order to assess the impact of longevity risk on employer-provided

DB pension plans, t he chapter examines t he d iff erent approaches t hat private pension plans follow i n practice when i ncorporating longevity risk in their actuarial calculations Unfortunately, most pension funds do not fully account for future improvements in mortality and life expect-ancy Th e chapter then presents estimations of the range of increase in the net present value of annuity payments for a theoretical DB pension fund Finally, the chapter discusses several policy issues on how to deal with longevity risk emphasizing the need for a common approach

Keywords: Demographic forecast; mortality and life expectancy;

life t ables; l ongevity r isk, r etirement; p rivate pens ions; defi benefi t pension plans; Lee–Carter models; Monte-Carlo methods, histograms

ned-JEL classifi cations: J11, J26, J32, G23, C15, C32

11.1 INTRODUCTION

Th e length of time people are expected to live in most OECD countries has increased by 25–30 years during the last century Th ese gains in life expectancy are good news However, policy makers, insurance companies, and private pension ma nagers worry about t he i mpact t hat t hese gains may have on retirement fi nances As long as gains in life expectancy are foreseeable a nd t hey a re t aken i nto account when planning retirement, they would have a negligible eff ect on retirement fi nances Unfortunately, improvements i n m ortality a nd l ife ex pectancy a re u ncertain I n t his regard, the longevity risk is associated with the risk that the future mor-tality and the life expectancy outcomes turn out diff erent than expected

As a r esult o f t his u ncertainty su rrounding f uture de velopments i n mortality and life expectancy, individuals run the risk of outliving their resources and being forced to reduce their standard of living at old ages Pension funds and life annuity providers (e.g., insurance companies), on the other hand, run the risk that the net present va lue of their annuity

payments will turn out higher than expected, as they will have to pay out

a periodic sum of income that will last for an uncertain life span In this context, individuals bear the full extent of the longevity risk when this risk

is “uncovered.” However, private pension funds and national governments providing defi ned retirement benefi ts, as well as fi nancial institutions pro-viding lifetime annuity payments face this longevity risk

Th e ma in purpose of t his chapter i s t o d isentangle how u ncertainty regarding f uture m ortality a nd l ife ex pectancy o utcomes w ould a ff ect employer-provided defi ned benefi t (DB) private pension plans liabilities

In this regard, this chapter fi rst focuses on assessing the uncertainty rounding f uture developments in mortality and life expectancy, t hat is, longevity risk.* Second, it examines the impact that longevity risk could have on employer-provided DB pension plans

sur-In order to assess the uncertainty surrounding future mortality and life expectancy outcomes, Section 11.2 fi rst examines the link between mortality and life expectancy, explaining how life tables are constructed from mortality data Second, it provides an overview of the developments

in mortality and life expectancy over the past century Th e improvements seen in mortality and life expectancy were unanticipated as the consis-tent underestimation of actual outcomes illustrates Th ird, it focuses on the main problem facing pension f unds, t hat is, to forecast t he f uture path of mortality and life expectancy to ascertain their future liabilities

In this context, aft er discussing the main arguments behind two gent views as regards the outlook for human longevity, this chapter dis-cusses diff erent approaches available to forecast or project mortality and life expectancy It then argues that a stochastic approach to model mor-tality and life expectancy is preferable because it permits to attach prob-abilities to diff erent forecasts and, as a result, uncertainty and risks can

diver-be gauged adequately Consequently, this chapter presents a st ochastic approach to model u ncertainty su rrounding mortality a nd l ife ex pec-tancy In this regard, it provides the results of estimating the Lee–Carter model for several OECD countries However, as the goal is far from pro-viding j ust a nother se t o f f orecasts b ut t o a ssess t he u ncertainty su r-rounding diff erent mortality and life expectancy outcomes, Section 11.2 concludes with the Monte-Carlo simulations of the Lee–Carter model

* Th roughout this chapter, point forecasts on mortality and life expectancy are not discussed because the aim of t his chapter is to prov ide ways of e xploring and assessing uncertainty instead of providing another set of projections.

Th ese randomly generated simulations facilitate the task of assessing the uncertainty surrounding those forecasts.

Th e second part of this chapter focuses on the impact that the ity risk may have on employer-provided DB pension plans Th e longevity risk a ff ects t he n et l iabilities o f D B pens ion p lans t hrough t heir l ife-time annuity payments as unexpected improvements in mortality and life expectancy increase the length of the payment period Section 11.3

longev-fi rst examines t he d iff erent approaches t hat private pension plans low in practice when incorporating future improvements in mortality and life expectancy in their actuarial calculations While some pension funds account for future improvements in mortality and life expectancy, but only pa rtially, others u se only t he latest available l ife t ables when evaluating t heir l iabilities S econd, i t a ssesses t he i mportance o f t he impact of longevity risk on the liabilities of private pension plans For this task, t his chapter presents estimations of t he range of increase in the net present value of annuity payments for a theoretical DB pension fund Th e results suggest that the younger the membership structure of

fol-a pension f und, t he more ex posed to longevity risk t he pension f und However, older pension funds have less room for maneuver to deal with the costs associated with the materialization of longevity risk

Finally, Section 11.4 discusses several policy issues on how to deal with longevity risk, w ith a pa rticular emphasis on indexing pension benefi ts

to l ife ex pectancy Th e fi rst t ask w ould be t o a gree o n a co mmon st chastic methodology to assess future mortality and longevity outcomes Governmental agencies are the best-placed institutions to produce these forecasts However, as the membership structure diff ers among pension funds, making assumptions regarding the overall population renders those forecasts less useful for particular pension funds In this regard, pension funds are inclined to use diff erent mortality tables according to socioeco-nomic status However, this remains controversial Finally, changes in the regulatory framework requiring pension plans to fully account for future improvements in mortality and life expectancy may be required

o-11.2 UNCERTAINTY SURROUNDING

MORTALITY AND LIFE EXPECTANCY

11.2.1 The Link between Mortality and Life Expectancy: Life TablesLife tables provide a summary description of mortality, survivorship, and life expectancy for a specifi ed population Th ey can contain data for every

single year of age (complete life tables) or by 5 or 10 year intervals (abridged life tables) In its simplest form, a life table can be generated from a set of age-specifi c death rates (ASDRs) ASDRs are calculated as the ratio of the number of deaths during a year (from vital statistics) to the correspond-ing population size (from censuses and annual population size estimates)

Th ey are commonly expressed as per 1000 habitants Mortality rates, on the other hand, are the probability that an individual of a given exact age will die during the period in question (i.e., the probability of dying) In the case of annual probabilities, the denominator is the size of the generation

who reach age n during t he year in question, a nd t he numerator is t he number of individuals from this generation who die between age n and age n + 1.* Th e annual probability of dying by age diff ers from the annual

death rate because the latter is the proportion of people of that age who die during the year, while the probability of dying is the proportion of people

at that age dying during the age interval.†

Th erefore, life tables provide a l ink between mortality and life tancy Th e fi nal outcome of a life table is the mean number of years still to

expec-be lived by a person who has reached that exact age (i.e., the age-specifi c life expectancies), if subjected throughout the rest of his or her life to the current age-specifi c probabilities of dying Table 11.1 is an example of a life table for males in France in 2003 It is constructed from the ASDRs, expressed in death rates per 1000 Th e fi rst column reports diff erent ages

x I n t he seco nd co lumn, m x i s t he o bserved per iod A SDRs per c apita (i.e., dividing ASDRs by 1000) Th e next column contains the age-specifi c

probabilities of dying, q x , computed as (2 ⋅ m ⋅ n)/(2 + m ⋅ n), where n is the

width of the age interval In the case of the open-ended age interval 110+, the probability of dying is 1 Th e fourth column shows the mean number

of person-years lived in t he interval by t hose dy ing in t he interval, a x.‡

People are assumed to die in the middle of the age-interval, however, at birth people are assumed to die at the beginning of the interval, while at ages 110+ people are assumed to die late in the interval

* Some deaths occur during the year in question, while other deaths occur the following year.

† For example, a person reaching age 65 in 2000 who dies at age 65 but in 2001 will be counted when calculating t he probability of d ying at 65 i n 2000, but it w ill not b e counted when calculating the death rate at age 65 in 2000.

‡ Th is is a k ey variable When using 1-year age groups, it i s assumed that people die in the middle of the age-interval (i.e., a value of 1/2), when using a 5-year age intervals you can also assume the middle of the interval (1/2) or, if data is available, use the single-year age data to build the mean.

Th e next columns compute the number of survivors at each age x of a hypothetical cohort of 100,000 individuals, l x; the number of deaths in the

cohort between two consecutive ages, d x; the number of person-years lived

by the cohort, L x ; and the total person-years remaining at each age, T x.*

Life expectancies at age x, e x , are computed by dividing T x by l x

Th erefore, given age-specifi c mortality rates (ASMRs), a life table vides the associated age-specifi c life expectancies (Table 11.1) Having

pro-a link between mortpro-ality pro-and life expectpro-ancy, Section 11.2.2 focuses on

* Th e number of deaths, d x, is computed by multiplying the number of survivors of the cohort

by the probability of dying Th e number of survivors, l x , at age x + 1 is the diff erence between those surviving at x minus those dying at x Computing the number of person-years lived,

L x, is a bit more t ricky because we do not k now when people dying in the age interval died,

at t he beginning, m iddle, or t he end It i s generally a ssumed i n t he m iddle W hen u sing 1-year intervals this assumption is alright, but when using 5 year intervals it may not be fully

accurate Th e formula is (n (l-(d a) ) Finally, T x is obtained by accumulating the L column

Source: Human Mortality Database (http://www.mortality.org/index.html ).

Notes: Selected ages from table period 1 × 1 (ag e by year), m x is t he per capita annual

person-years lived in the interval by those dying in the interval It indicates when

life expectancy at age x.

reviewing developments in both variables over the last 100 years in eral OECD countries.

sev-11.2.2 Uncertainty Surrounding Mortality Outcomes

Mortality r ates have decl ined ste adily over t he pa st century, wh ich ha s translated into large increases in life expectancy at both birth and age 65

reduc-tions in mortality rates at younger ages and, to some extent, improvements

at old-ages During the fi rst part of the twentieth century, the decline in mortality was mainly due to a r eduction of infectious diseases aff ecting mainly young ages During the last decades of the twentieth century, the decline in mortality was due to reductions in deaths due to chronic dis-eases aff ecting primarily older ages.* Th is is confi rmed when looking at the increases in life expectancy at birth and at age 65 during the twentieth century (Table 11.2) Life expectancy at birth increased faster during the

fi rst half of the twentieth century while life expectancy at age 65 increased faster during t he second ha lf, as comparing t he top a nd bottom pa nels

in Table 11.2 confi rms Employer-provided DB pension plans are mostly aff ected by changes in mortality and life expectancy at older ages In this regard, it is important to highlight that for most OECD countries, more than half of the improvement in life expectancy since the 1960s is due to increases in life expectancy at age 65

Past projections have consistently underestimated actual improvements

in mortality rates and life expectancy Improvements in mortality rates and life expectancy have increased the number of years that people spend in retirement, bringing in fi nancial troubles for DB pension funds, individu-als, and social security systems During the past decades governmental agencies, actuaries and academics have tried to project and forecast mor-tality rates and life expectancy to assess future liabilities However, past projections ha ve co nsistently u nderestimated i mprovements Table 11.3

shows h ow l ife ex pectancy p rojections b y i nternational o rganizations (e.g., the UN and Eurostat) and actuaries have failed to account for actual improvements A pos itive sign indicates t hat life expectancy at birth in

2003 has already bypassed the UN projected life expectancy for the age of t he period 2000–2005 (fi rst column) and the Eurostat projection

aver-* Th is reduction was mainly due to reduced illnesses from cardiovascular diseases.

FIGURE 11.1 Life expectancy and mortality rates in selected OECD countries, 1950–2003.

for 2005.* In the same context, Figure 11.2 shows the U.S Social Security Administration (SSA) p rojections o f l ife ex pectancy co nsistently bel ow actual outcomes.†

Moreover, projections for the next 50 years incorporate a slower ment in mortality and life expectancy than in the recent past Future pro-jections by international organizations a nd national statistical institutes assume t hat t he projected gains i n l ife ex pectancy at birth for t he next

improve-* UN projections were produced i n 1999 using d ata up to 1 995, while Eu rostat projections were produced in 2000 using data up to 1999.

† Siegel (2005) also reports that the projection by the United States Actuary’s offi ce have been consistently below actual values for most projection years (see Table 10 in his report).

At Birth At 65 Twentieth Century

Actual, SSA data

2000 Predicted, Social Security (1992)

(From L ee a nd M iller 2 001; L ee, R a nd Tuljapurkar, S , P opulation f orecasting for fi scal p lanning: Is sues a nd i nnovations, i n A uerbach, A a nd L ee, R ( Eds.),

Demographic C hange an d F iscal P olicy, C hapter 2 , C ambridge U niversity P ress,

Cambridge, U.K., 2001.)

in Life Expectancy at Birth with Past

in 2003 has already by passed projected life expectancy for the average 2000–2005 (UN) and 2005 (Eurostat).

50 years will slow down by almost half from the gains experienced in the second half of the last century (Table 11.4) Unfortunately, it is impossible

to a ssess t he l ikelihood su rrounding t hese projections bec ause t hey a re deterministic, and as such they do not incorporate a distribution function

or probabilities to assess the likelihood of the range of possible outcomes.Future increases in life expectancy will have to come mainly from fur-ther decl ines i n mortality r ates at old a ges Th ere is a c ertain deg ree of uncertainty about t he ex tent of f uture i mprovements i n mortality r ates and life expectancy Nevertheless, as mortality rates at young and middle ages have reached very low levels, improvements would have to come from declines in mortality at old ages, that is, from increases in life expectancy at age 65 or more, and, in particular, at very old ages (85+) However, there are diff erent views as regard the outlook for human longevity (Siegel, 2005)

Th ere is a g reat debate on t he ex tent of t hose increases in longevity Essentially, there are two groups, those who argue that there are no lim-its to life expectancy (e.g., Oeppen and Vaupel, 2002) and those who are more conservative (e.g., Olshansky et al., 2005) Th e fi rst group concludes from historical trends and age trajectories that no limits can be set to

Gains in Life Expectancy at Birth

(A) Average Gains 1960–2000

(B) Projected Gains

Source: OECD/DELSA Population database, OECD Health

Data and Eurostat EUROPOP2004.

Note: In number of years per decade.

already higher than the projected life expectancy for the

average f rom 2000 t o 2005 (UN co lumn) a nd f or 2005

(Eurostat column).

life expectancy Th ey argue that mortality is likely to level off aft er some (unspecifi ed) threshold, and, as a result, longevity would be uncapped and would keep increasing in the next decades However, this view remains controversial Th e more conservative group argues that the epidemiologi-cal transition,* as well as the massive reductions in mortality rates required

to produce even small increases in life expectancy, suggest that increases

in life expectancy will slow down if not to stop (Olshansky et al., 2005)

Th ey believe that human life might have natural limits Furthermore, the empirical evidence showing that survival probability curves have become increasingly re ctangular or c ompressed (K annisto, 2 000) s uggests t hat there a re l imits t o l ife ex pectancy U nfortunately, t he co mpression o f mortality or “rectangularization” theory is not conclusive (Siegel, 2005)

Th erefore, t here i s a la rge deg ree o f u ncertainty su rrounding f uture improvements in mortality and life expectancy, in particular at old ages

Th is uncertainty requires a d iff erent approach to model future ments a nd, i n pa rticular, t o a ssess t he u ncertainty su rrounding t hese improvements In this context, Section 11.2.3 argues for using a stochastic instead of a de terministic approach to forecast those improvements as it allows attaching probabilities to a full range of diff erent forecasts and thus

improve-it allows assessing uncertainty and risks adequately

11.2.3 Approaches to Forecast Mortality and Life Expectancy

Th ere are several approaches available in the literature to project mortality rates (CMI, 2004, 2005; Wong-Fupuy and Haberman, 2004) Public pension systems or private pension funds providing defi ned pension benefi ts need population projections to assess the number of people who will potentially

be entitled to a pension Th e main inputs necessary to produce population projections are assumptions regarding fertility, mortality, and net migra-tion fl ows As this chapter focuses on the longevity risk and its impact on

DB pension plans, t he focus i s on mortality a nd l ife ex pectancy tions In this regard, there are several approaches to model mortality and life expectancy Th ere a re process-based methods t hat u se models ba sed

projec-on the underlying biomedical processes; there are also explanatory-based

* Gains in longevity during the last century were mainly at you ng ages and were based on successes dealing w ith infectious a nd parasitic diseases Th ese a re externally caused a nd relatively easy to treat with vaccines and immunization However, future gains should focus

on old a ges w here t here i s a pre dominance of d egenerative d iseases of l ater l ife, such a s cancer, cardiovascular diseases, and diabetes Th ese are chronic and progressive, and more diffi cult to treat.

approaches that employ a causal forecasting approach involving ric relationships; and there are extrapolative methods that are based on pro-jecting historical trends in mortality forward.

economet-Extrapolative models are the type of models most used by actuaries and offi cial agencies Th ese models express age-specifi c mortality as a function

of calendar time using past data and as such, they can be deterministic or stochastic Deterministic models forecast by directly extending past trends and, as a result, they do not come with standard errors or forecast prob-abilities Stochastic models, on the other hand, forecast using probability distributions Th ey fi t a st atistical model to the historical data and then project i nto t he f uture A s a n outcome of t he forecast process, forecast values have probabilities attached that allow assessing the likelihood that

an outcome will occur Among the extrapolative stochastic methods, the literature distinguishes between (1) models based on the interdependent projection of age-specifi c mortality or hazard rates (including graduation models, CM I);* ( 2) m odels u sing st andard t ime ser ies p rocedures l ike the Lee–Carter method (Lee and Carter, 1992) where a l og linear trend for A SMRs i s o ft en a ssumed f or t he t ime-dependent co mponent; a nd (3) models using econometric modeling (e.g., Spline models)

However, governmental agencies tend to extrapolate historical trends in

a deterministic manner, while actuaries use several smoothing approaches, generally parametric approaches (e.g., Gompertz model) Governmental agencies project mortality rates by using past trends and expert opinion Parametric smoothing models are the most familiar to actuaries since they have been u sed for mortality g raduations.† Neither of t hese approaches provides t herefore f orecast p robabilities B oth E urostat a nd t he U S Census Bureau population projections use a deterministic approach.‡ Th ey use historical trends in ASMRs, generally the last 15 years, and assume that they will continue in the future, however, weighted by some expert assessment of the causes of death (European Commission, Eurostat, 2005; Hollman et al., 2000) Th ey estimate the values of the ASMRs in an inter-mediate year (e.g., 2018) and at the end target year (e.g., 2050) Th is is done

* Among these are parametric models which fi t a specifi c distribution (e.g., logistic, Gompertz)

to the historical data and forecast given the statistical characteristics of the parametric tribution Some commentators consider them neither deterministic nor stochastic.

dis-† Examples are the Gompertz model and its many generalizations (e.g., Gompertz-Makeham family) which have been used for recent CMIB graduations.

‡ Th e United States SSA projects mortality using causes of d eath (Siegel, 2005) Th is is also

a deterministic approach and it incorporates expert opinion.

by applying the improvement rate to the average mortality rate in the last

3 to 5 available years.* Finally, ASMRs for each intermediate year are culated by an interpolation method based on fi tting third-degree curves

cal-Th ey extrapolate the intermediate years by assuming a pa rametric tion such as the logistic or the Gompertz function

func-Additionally, governmental agencies and actuaries use diff erent ulations when projecting mortality and life expectancy Governmental agencies produce mortality tables and project life expectancy for the pop-ulation of their respective countries as a whole However, private pension plans use t heir own actuarial mortality tables, because mortality rates

pop-of pension funds’ participants can diff er substantially from those pop-of the overall population It is a well-known fact that mortality rates are lower, and life expectancy higher, for women, highly educated and high-income people (Drever et al., 1996; Goldman, 2001) However, using life tables diff erentiating by socioeconomic groups could give rise to a diff erent set

of problems (see Section 11.4) In addition, in some countries, private pension funds use mortality tables from other countries (e.g., from the United Kingdom) as their data records do not go far back enough.Finally, due to the lack of enough data, estimating and forecasting mor-tality rates and life expectancy for the very old (those aged 85 or more) is challenging Data at very old ages are not very accurate because of small sample problems Only a few countries have offi cial population statistics that are suffi ciently accurate to produce reliable estimates of death rates at higher ages It is commonly accepted that between ages 30 and 85, ASDRs tend to rise roughly at a fi xed rate of increase.† Th is rate of increase tends

to fall for ages above 85, and even possibly, at the more extreme ages, to become z ero o r n egative, a lthough o ne c annot be c ertain o f t he la tter because of the sparseness of the data above age 100 (Robine and Vaupel, 2002; Wilmoth, 1998) Th is chapter uses data from the human mortality database (www.mortality.org) and takes at face value the ASDRs at very old age provided.‡

* Always distinguishing by age and gender.

† Roughly in accordance with the Gompertz curve.

‡ Th e human mortality database (HMD) was created to provide detailed mortality and lation data to researchers, students, journalists, policy analysts, and others interested in the history of h uman lon gevity Th e project b egan a s a n out growth of e arlier projects i n t he Department of D emography at t he University of C alifornia, B erkeley, United St ates, a nd

popu-at the Max Planck Institute for Demographic Research in Rostock, Germany Th e dpopu-atabase contains detailed data for a collection of 26 countries.

11.2.4 Measuring Uncertainty Surrounding Mortality

and Longevity Outcomes

The u ncertainty su rrounding f uture m ortality a nd l ife ex pectancy outcomes can be g auged using a st ochastic approach because it attaches probabilities to diff erent outcomes, permitting therefore to a ssess uncer-tainty and risks adequately Future developments in mortality rates and life expectancy are uncertain, but some paths or trajectories are more likely than o thers H ence, a ttempts t o f orecast m ortality a nd l ife ex pectancy should include a range of possible outcomes, and probabilities attached to that range Together, these elements constitute the “prediction interval” for the mortality and life expectancy variables concerned Th ere is a clear trade-off be tween g reater c ertainty ( higher odd s) a nd be tter p recision (narrower i ntervals) Th is sec tion presents t he results of ex amining t he uncertainty surrounding forecasts of mortality and life expectancy using the Lee–Carter stochastic methodology (Lee and Carter, 1992) by means

of the level of mortality that describes the change in overall mortality over

time Th at is, as k(t) falls mortality falls and vice versa Moreover, if k(t) decreases linearly, then the cause of mortality or mortality rate, m(x, t),

* Th e Lee–Carter model and the P-Spline model (Currier et al., 2004) are the two approaches recommended by the Mortality Committee of the English actuarial profession (CMI, 2005, 2006) Stata programs to estimate mortality using the Lee–Carter have been developed in- house, while Stata programs to estimate mortality using S-splines are being considered.

† Monte-Carlo simulations are the result of repeating the estimated Lee–Carter model several thousand times using random number generators for the error terms.

‡ Th ese include France, the Netherlands, Spain, Sweden, the United Kingdom, and the United States Results are available upon request.