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06/2011

FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

Working-life Expectancy in Finland:

Development in 2000–2009

and Forecast for 2010–2015

A Multistate Life Table Approach

Markku Nurminen

Finnish Centre for Pensions

eläketurvakeskus

Eläketurvakeskus

PENSIONSSK YDDSCENTRALEN

06/2011

FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

Markku Nurminen

Working-life Expectancy in Finland:

Development in 2000–2009

and Forecast for 2010–2015

A Multistate Life Table Approach

Finnish Centre for Pensions

FI-00065 ELÄKETURVAKESKUS, FINLAND

Telephone +358 10 7511

E-mail: ﬁrstname.surname@etk.ﬁ

Eläketurvakeskus

00065 ELÄKETURVAKESKUS

Puhelin: 010 7511

Sähköposti: etunimi.sukunimi@etk.ﬁ

Pensionsskyddscentralen

00065 PENSIONSSKYDDSCENTRALEN

Telefon: 010 7511

E-post: förnamn.efternamn@etk.ﬁ

Edita Prima Oy

Helsinki 2011

ISSN-L 1795-3103

ISSN 1795-3103 (printed)

ISSN 1797-3635 (online)

FOREWORD

During the past few years, policy makers have been preoccupied with increasing longevity.

Life expectancy has risen rapidly and this development has also affected the views on future

population development. The aging of society will have many consequences, but for pension

policies it raises the question about the division of time spent in work and in retirement.

Postponing retirement and extending time spent in working-life has become a top priority

in most industrialized countries. In Finland, the target is to raise the effective retirement

age by three years by year 2025. This target should be seen in the light of a more general

employment objective.

The Finnish Centre for Pensions is devoting more research energy to measuring how

working careers develop. This Working Paper is part of an on-going partnership project

between the Research Department of the Finnish Centre for Pensions and Markstat

Consultancy. The research objective is to measure the length of and evaluate the development

in working careers – and later and even more ambitiously – to assess the role of pension

policy and other contributing factors in the process. This rst working paper that springs

from the project is devoted to measurement issues and has been written by adjunct professor

Markku Nurminen, PhD (Stat.), DrPh (Epid.).

Mikko Kautto

Head of Research Department

Finnish Centre for Pensions

ABSTRACT

Working-life expectancy is the estimated future time that a person will spend in employment.

This paper is concerned with its estimation jointly with the time spent in the opposite state

of unemployment, and their sum, the expected duration of active working-life, that is, the

length of a person’s working career.

This paper employs a multistate method, which has previously been applied to Finnish

data from 1980 to 2001. The multistate life table approach rst estimates year- and age-

dependent probabilities of being in the working-life states by stochastic regression modeling.

Updated estimates of probabilities, and subsequently of expectancies, are given for the data

of Finnish men and women aged 15–64 years in the period 2000–2009. Further, model-

based extrapolations are calculated for the years 2010–2015.

According to results, a general development of longer working careers is evident. During

the past decade, the future employment time increased in all age groups and for both genders.

For a 15-year-old male in 2009 the tted estimate of the length of working career is 34.2

years, while for females, it tails at 33.8 years. During the ten-year period 2000–2009, there

was an increase of 10 percentage points or more in the expectancies of future working life

spent in the employed state for females starting from age 40 and for males from age 50 on.

The respective predicted working-career lengths for 2015 are longer: 36.0 years for

males and 35.5 years for females. The female expectancy for ages 40 years and above is

forecast to overtake the respective male gure by year 2010 and to continue to do so up to

2015.

Keywords:

• Working-life expectancy

• Stochastic inference

• Statistics in society

ABSTRAKTI

Työajanodote on luku, joka ilmaisee tietyn ikäisen henkilön jäljellä olevan ajan työelämässä.

Tämä tutkimus käsittelee työllisen ajan odotteen, työttömänä oloajan odotteen, sekä niiden

yhteenlasketun työvoimaan kuulumisajan odotteen estimointia eli henkilön koko tulevan

työuranpituuden mittaamista. Tutkimusmenetelmänä käytettiin tilastotieteellistä monitila-

mallia, jota on aiemmin sovellettu Työterveyslaitoksessa käyttäen hyväksi Tilastokeskuksen

työvoimatutkimuksen otannan tietoja henkilöiden lukumääristä työmarkkina-aseman mu-

kaan ja kuolleisuudesta Suomessa vuosina 1980–2001.

Eläketurvakeskuksen päivitetyssä arvioinnissa laskettiin ensin aineistoon sovitetun sto-

kastisen estimointimallin avulla ikä- ja kalenterivuosittaiset todennäköisyydet olla ansio-

työssä, työttömänä tai työvoiman ulkopuolella. Todennäköisyyksistä johdettiin integroimal-

la odotteet 15–64-vuotialle suomalaisille miehille ja naisille vuosina 2000–2009. Odotteiden

ennustemalliin perustuvat eskstrapolaatiot projisoitiin vuosille 2010–2015.

Tulosten mukaan yleinen positiivinen kehitys kohti pidempiä työuria on ilmeistä. Viime

vuosikymmenen kuluessa jäljellä oleva työssäoloaika kasvoi molemmilla sukupuolilla kai-

kissa ikäryhmissä. 15-vuotiaiden miesten työajanodote oli lamavuonna 2009 mallin antaman

arvion mukaan 34,2 vuotta, naisten odote oli hieman lyhyempi eli 33,8 vuotta. 10-vuoden

ajanjaksolla 2000–2009 työajanodotteen kasvu oli naisilla 10 %-pistettä tai enemmän alka-

en ikävuodesta 40, miehillä ikävuodesta 50 lähtien. Yli 40-vuotiaitten naisten odotteen en-

nustettiin ylittävän miesten vastaavan odotteen vuoteen 2010 mennessä. Ennusteet 15-vuoti-

aiden henkilöiden työurien kestoille vuonna 2015 ovat entistä pidempiä (olettaen kehityksen

jatkuvan samansuuntaisena): miehillä 36,0 vuotta, naisilla lähes yhtä pitkä eli 35,8 vuotta.

Avainsanat:

• Työajanodote

• Stokastinen päätäntä

• Tilastotiede yhteiskunnassa

ACKNOWLEDGMENTS

Dr. Brett A. Davis, Australian Government Department of Employment and Workplace

Relations, Canberra, ACT, gave invaluable expert advice in the application of stochastic

processes to life sciences.

Dr. Martin Tondel, Section of Occupational and Environmental Medicine, Department of

Public Health and Community Medicine, Institute of Medicine, University of Gothenburg,

Gothenburg, Sweden, contributed useful methodological points on the validity of the ofcial

data used for predicting the working-life expectancies.

Suvi Pohjoisaho, Publications Assistant at the Finnish Centre for Pensions, has taken

care of transforming the manuscript into a publication.

Statistics Finland provided the population employment data on labor force and mortality

rates.

CONTENTS

1 Introduction ...................................................................................................................... 9

2 Ofﬁcial Data ....................................................................................................................13

3 Outline of the Method ...............................................................................................16

4 Estimates of Model Parameters ............................................................................18

5 Estimates of State Probabilities ...........................................................................21

6 Estimates of Working-life Expectancies ...........................................................24

7 Forecasts of Working-life Expectancies ............................................................32

8 Discussion .......................................................................................................................36

8.1 Longer Working Lives Tackle Aging Societies..................................36

8.2 Prevalence versus Multistate Life Table Analysis ........................37

9 Methodological Recommendations ....................................................................40

Appendices............................................................................................................................41

Appendix A: Details of Modeling and Estimation Methods ..............41

Appendix B: Forecasting from the Regression Model..........................44

Appendix C: Approaches to Setting Prediction Intervals ...................45

References .............................................................................................................................47

The Working-life Expectancy in Finland 2000–2015 9

1 Introduction

Extending working-life has become a strategic objective in many industrialized countries

facing budgetary concerns in the foresight of the demographic aging. Population aging is

likely to lead to lower productivity both because the workforce grows older and because

a lower proportion of the population is working. Shorter working lives, coupled with

increased life expectancy, low fertility and the retirement of the large post-war generation,

have an ageing and shrinking effect on the economically active share of the population. This

will have major implications for work productivity and overall economic growth (Skirbekk,

2005).

The increase in life expectancy in Finland has been more rapid than projected, resulting

in a situation where pension expenditure will be higher than was predicted at the time

of planning the 2005 pension reform, unless working careers grow longer accordingly.

Measures aimed at lengthening working careers can be divided into two groups: measures

related to developing working life and measures aimed at developing pension systems

(Prime Minister’s Ofce, 2010).

The Finnish Government and the labor market organizations have agreed that the

expectancy for the effective retirement age for 25-year-olds should be raised from 59.4 (in

2008) by at least 3 years by year 2025.

The question of postponing retirement should be seen in the context of the entire working

career. The working group considering working careers from the perspective of the earnings-

related pension scheme held it essential that the length of the working career should not

be measured singularly based on the expected exit age to retirement. This measure should

be complemented with the expectation of active working life and employment rate (Prime

Minister’s Ofce, 2011.)

At present in Finland there are different statistical indicators in use that measure the

duration of various phases in life from the separate perspectives of the pension system

and the labor market (for a review, in Finnish, see Hytti, 2009). The Finnish Centre for

Pensions (Eläketurvakeskus, ETK) has computed the expected effective retirement age

indicator (Kannisto, 2006), and later complemented it by publishing the expected duration

of employment (or active working-life) indicator developed by Helka Hytti and Ilkka Nio

(2004). The former indicator is based on data on insured persons moving into earnings-

related pension, and it is computed from age-specic transition frequencies into retirement

and from mortality statistics.

The latter indicator is suitable in planning labor force policies and in assessing the

efciency of employment programs. However, this working-life expectancy is preferably

estimated from the total population probabilities of being in the three mutually exclusive

states of employed, unemployed, and outside the labor force (e.g. on disability pension),

rather than just in the two classes of active and inactive, as has been previously customary.

Recently, the EU Commission’s study has recommended using the duration of working-

life expectancy, which partitions the life expectancy into separate life stages, as a core labor

market indicator at European and Member State level (Vogler-Ludwig and Düll, 2008). The

expert consultants’ report suggests that the application of the expectancy would appear to be

10 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

useful for the description and analysis of long-term behavioral and institutional conditions

in national employment systems rather than for the monitoring of short-term changes.

For a worker of a given initial age, working-life expectancy (WLE) is the expected future

time a person spends in gainful employment earning wages and benets (or looking for

work) assuming that the prevailing patterns of mortality, morbidity and disability remain

unchanged (Nurminen, 2008). It is a period or cohort measure, depending on whether cross-

sectional or longitudinal data are available. Life expectancy at birth is naturally somewhat

different to that calculated for an actual cohort at the start of follow-up (Myrskylä, 2010).

Usually, in the case of WLE studies, only cross-sectional data from ofcial statistics

can be readily obtained (cf. Nurminen et al., 2004a). This situation is similar to the usual

circumstances in which life expectancy is calculated. Our interest in this Working Paper

is in WLE and similar expectations of times spent in states other than employment, such

as unemployment, or being temporally or permanently outside the labor force (e.g. in

rehabilitation or on disability pension). The estimation of expectations is conditional on

having reached a given age. For persons of working age these expectations are termed

partial life expectancies.

In our previous cohort follow-up study (Nurminen et al., 2004) of initially active Finnish

municipal workers, aged 45 to 58 years in 1981, we assumed that the earliest commencing

date in employment is in the middle of the initial age interval (45–46), and that the

retirement date is no later than the 63rd birthday. Thus the maximum duration of work

for the cohort members was 17.5 years. The effective expected retirement age was 59.8 or

approximately 60 years in Finland in 2009 (Finnish Centre for Pensions, 2011). We found

that men permanently leave the work force due to disability or death earlier than women

in all age groups, regardless of whether they commenced in better or worse work ability

(Nurminen et al., 2004b). Women tended to retire on old-age or similar pension before

men, especially those women with an initially fair or poor capacity for work. The cross-

sectional survey data suggested that the work ability of Finnish aging workers appears to

deteriorate prematurely and that individuals leave too frequently employment before the

statutory retirement age. Rather remarkably, the work-physiological effect of transition at

the age of 45 years from the initial state of ’poor’ to ’good or excellent’ work ability was

estimated to be, on average, four years of gained active work life for both genders. Such an

achieved improvement would mean that an advancement of the expectancy for the effective

retirement age can conceivably reach a higher target than that set for the year 2025, viz.

62.4 years, because 60 + 4 = 64; hence it could also exceed the current lower limit of the

statutory retirement age, i.e. 63 years.

The Working-life Expectancy in Finland 2000–2015 11

Figure 1.

WLE of male municipal workers by their work ability and age.

45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

Age, years

0

2

4

6

8

10

Expectancy, years

Working Life Expectancy by Work Ability Status

Good work ability

Fair work ability

Poor work ability

In Figure 1, the WLEs are plotted along the age axis with the subsequent values for fair

work ability and good work ability ’stacked’ on top of the previous ones. E.g., at 45 years,

an ’average’ male worker is expected to be employed 5.5 (= 11.5 – 6.0) years with ’good

or excellent’, 4.5 (= 6.0 – 1.5) years with ’fair’, and 1.5 years with ’poor’ work ability. The

WLEs add up to 5.5 + 4.5 + 1.5 = 11.5 years. Six years is spent outside work life before the

retirement at age of 62.5 (= 45 + 11.5 + 6.0) years. Note that the expectations add up to the

duration of maximum remaining work life at age 45, taken as 17.5 (= 63 – 45 – ½) years; ½

is subtracted since persons enter work on average in the middle of the age interval (45, 46).

The additive partition of the WLEs in relation to the specied levels of work ability is

an appealing methodological property of the WLE measure. The decomposition is helpful in

understanding at what stages changes in people’s health are occurring and in quantifying the

magnitude of those transitions conditionally on the initial work ability.

The present paper is concerned with the joint estimation by year and age of the

probabilities and expectancies of working-life states. We applied a modern regression

model to cross-sectional life table data from Finland for each of the years 2000 to 2009 with

projections to 2010–2015. Our estimates are for ages 15 to 64 inclusive, conditional only on

a person being alive at age 15. We used the multistate life table modeling approach (Davis

et al., 2001) to overcome certain limitations of the traditional prevalence life table technique

(Hytti and Nio, 2004). The stochastic modeling approach yields a wealth of information

about working-life behavior when applied to intrinsically dynamic life processes with

multiple decrements, like the labor force process. Thus, for instance, it is possible to test

statistically the effect (trend change) of the pension reform that was enforced in 2005 on the

WLEs.

Working-life and related expectancies are conceptually analogous to health expectancies,

both representing expected occupation times; the difference is that the former arise in the

context of labor force activity rather than health status. Consequently, given a suitable

12 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

formulation of the problem, similar methods of analysis can be used, and we employ the

large-sample, weighted least squares version of logistic regression modeling originally

developed for the Australian health surveys by Davis et al. (2001, 2002b). This statistical

framework is different to the frequency-based methods previously applied to health

expectancies (Sullivan, 1971). A bibliography can be found in the handbook of Réseau sur

l’Espérance de Vie en Santé, REVES (2002).

Given discrete-time data from multiple cross-sectional population surveys, a multistate

regression model can be used to estimate consistently marginal probabilities that a person

is in a given work-health state or transition probabilities between the states, and, thereby,

working-life expectancies (Nurminen and Nurminen, 2005). Expectancies conditional on

an initial state and based on transition probabilities can be estimated under the Markov

assumption from aggregate data that are produced by ofcial statistical agencies’ longitudinal

time series and were presented and applied in Davis et al. (2002a, 2000b, and 2007).

This paper is organized as follows: Section 1 briey reviews the background to the topic

and introduced the working-life expectancy for measuring the future career length. The

ofcial data used in the study are described in Section 2. Section 3 presents an outline

of the statistical methodology. Estimates of the model parameters are given in Section 4,

those of the state probabilities in Section 5, while Section 6 presents current estimates of

WLEs, followed by forecasts of the WLEs in Section 7. Finally, Section 8 discusses the

results obtained using modern regression and compares them to those obtained by actuarial

techniques. Section 9 proposes recommendations on the applicable methodology. Statistical

modeling, estimation, and prediction issues are detailed in the Appendices.

The Working-life Expectancy in Finland 2000–2015 13

2 Ofﬁcial Data

Estimates of the sizes of the Finnish populations for the years 2000–2009, by labor force

status, sex and single-year working-age groups, taken from 15 to 64, were provided by the

Information Services of Statistics Finland (SF, 2010) based on the Labour Force Survey

(LFS) data. In all, the data set consisted of a four-dimensional array of 4,000 frequencies

indexed by sex, age (15–64 years), calendar year (2000–2009), and labor force status.

Annual Gross Domestic Product (GDP) (as of July 1, 2011) was included as an explanatory

variate in the regression model.

The Finnish LFS collects statistical data on the participation in work, employment,

unemployment and activity of persons outside the labor force, among the population aged

between 15 and 74. The LFS data acquisition is based on a random sample drawn twice a

year from the population database. The monthly sample consists of some 12,000 persons and

the data are obtained by means of computer-assisted telephone interviews. The information

given by the respondents is used to produce a representative picture of the activities of the

entire working-age population.

The concepts and denitions used in the Survey comply with the recommendations of

ILO, the International Labour Organisation of the UN, and the regulations of the European

Union on ofcial statistics. The quality of the LFS is described in detail by SF (2011).

1

The numbers of annual deaths in the study years were extracted from the les kept by

Statistics Finland. The statistics on deaths cover persons permanently domiciled in Finland.

Data on the population and age and gender distribution of deaths are used to calculate annual

gures on life expectancy.

Figure 2 shows the actual observations which we used to estimate probabilities and

expectancies. The tted values were smoothed by Friedman’s local regression spline function.

Our interest focused on the three mutually exclusive states: ’employed’, ’unemployed’, and

’economically inactive’. This complementary ’inactive’ or ’other alive’ group represents

a mixed population and includes persons who are outside the labor force; that is, those

individuals who are not employed or unemployed during the survey week, on pensions due

to various causes of disability, as well as students, conscripts and civil servants. ’Deceased’

was taken as a reference state.

1 The Ministry of Employment and the Economy also publishes data on unemployed job seekers. The Ministry’s data derive from

register-based Employment Service Statistics, which describe the last working day of the month. The deﬁnition of unemployed applied

in the Employment Service Statistics is based on legislation and administrative orders which make the statistical data internationally

incomparable. In the Employment Service Statistics an unemployed person is not expected to seek work as actively as in the Labour

Force Survey. There are also differences in the acceptance of students as unemployed.

14 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

Figure 2.

Population rates (per 1,000 people) and probability surfaces ﬁtted by a Friedman’s smoothing

spline function for (1) males and (2) females:

(a) observed, employed (b) ﬁtted, employed

(c) observed, unemployed (d) ﬁtted, unemployed

(e) observed, inactive (f) ﬁtted, inactive

(g) observed, deceased (h) ﬁtted, deceased

Figure 2.1

Males

c) Population Unemployment Rates for Males d) Probability Surface of Unemployment for Males

a) Population Employment Rates for Males

b) Probability Surface of Employment for Males

e) Population Rates for Economically Inactive Males

f) Probability Surface for Economically Inactive Males

g) Population Death Rates for Males

h) Probability of Death for Males

The Working-life Expectancy in Finland 2000–2015 15

Figure 2.2

Females

a) Population Employment Rates for Females

b) Probability Surface of Employment for Females

e) Population Rates for Economically Inactive Females

f) Probability Surface for Economically Inactive Females

g) Population Death Rates for Females

h) Probability of Death for Females

c) Population Unemployment Rates for Females d) Probability Surface of Unemployment for Females

16 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

3 Outline of the Method

It is convenient to describe the method used in terms of a population cohort of n lives initially

aged 15 years. Of particular importance are the probabilities that an individual is in state j

at a subsequent age x, written p

j

(x). In the present application, j = 0 denotes ’alive’ and j =

1,2,3,4 indexes the exhaustive (non-overlapping) states (1) ’employed’, (2) ’unemployed’,

(3) ’economically inactive’, and (4) ’dead’. Here our interest is on estimating the marginal

probabilities and working-life expectancies that are not conditional on the initial state, but

only on the initial age. Aggregate data were available at ages x = 15, ..., 64.

Estimation of the unconditional probabilities p

j

(x) is done by a large-sample version

of logistic regression. We shall call p

1

(x) the working life survival curve. Advantage is

taken of the fact that ofcial statistics are almost always given in terms of large numbers,

which in the present case translates as large n, the number of individuals in the cohort. The

theoretical premises of the method are given in Davis et al. (2001, 2002b), and in some

detail in Appendix A.

With state 4 (dead) as the reference, we formed the log ratios

3 Outline of the Method

It is convenient to describe the method used in terms of a population cohort of n lives initially aged 15

years. Of particular importance are the probabilities that an individual is in state j at a subsequent age

x, written p

j

(x). In the present application, j = 0 denotes 'alive' and j = 1,2,3,4 indexes the exhaustive

(non-overlapping) states (1) 'employed', (2) 'unemployed', (3) 'economically inactive', and (4) 'dead'.

Here our interest is on estimating the marginal probabilities and working-life expectancies that are not

conditional on the initial state, but only on the initial age. Aggregate data were available at ages x =

15, ..., 64.

Estimation of the unconditional probabilities p

j

(x) is done by a large-sample version of logistic

regression. We shall call p

1

(x) the working life survival curve. Advantage is taken of the fact that

official statistics are almost always given in terms of large numbers, which in the present case

translates as large n, the number of individuals in the cohort. The theoretical results of the method are

given in Davis et al. (2001, 2002b), and in some detail in Appendix A.

With state 4 (dead) as the reference, we formed the log ratios

= log{p

j

(x)/p

4

(x)}, j = 1,2,3.

(Eq 1)

Exploratory analysis can be used to suggest a parametric form for the partial log ratios,

ξ

(x) ≡

ξ

(x;

β), and the estimation of β is done by weighted least squares. With the resulting estimate of β we

have the derived parameter estimates

(x) =

(x;

),

j

p

ˆ

(x) =

4

ˆ

p

(x) exp[

j

x

ˆ

(x)], j = 1,2,3, (Eq 2)

4

ˆ

p

(x) = {1 +

∑

exp

[

(x)]}

-1

.

Thence the estimated working life and related expectancies of interest (for a given age z) are

defined as a definite integral function

j

e

ˆ

(z) =

∫

64

)(

ˆ

z

j

dxxp . (Eq 3)

The expectation of main interest, e

1

, yields the working life expectancy (WLE). These quantities

are conditional only on the fact that an individual is alive at age 15, and they should be distinguished

(Eq 1)

Exploratory analysis can be used to suggest a parametric form for the partial log ratios,

(x) ≡ (x; β), and the estimation of β is done by weighted least squares. With the resulting

estimate of β we have the derived parameter estimates

(Eq 2)

(x) =

(x;

),

j

p

ˆ

(x) =

4

ˆ

p

(x) exp[

j

x

ˆ

(x)], j

= 1,2,3, (Eq 2)

3 Outline of the Method

It is convenient to describe the method used in terms of a population cohort of n lives initially aged 15

years. Of particular importance are the probabilities that an individual is in state j at a subsequent age

x, written p

j

(x). In the present application, j = 0 denotes 'alive' and j = 1,2,3,4 indexes the exhaustive

(non-overlapping) states (1) 'employed', (2) 'unemployed', (3) 'economically inactive', and (4) 'dead'.

Here our interest is on estimating the marginal probabilities and working-life expectancies that are not

conditional on the initial state, but only on the initial age. Aggregate data were available at ages x =

15, ..., 64.

Estimation of the unconditional probabilities p

j

(x) is done by a large-sample version of logistic

regression. We shall call p

1

(x) the working life survival curve. Advantage is taken of the fact that

official statistics are almost always given in terms of large numbers, which in the present case

translates as large n, the number of individuals in the cohort. The theoretical results of the method are

given in Davis et al. (2001, 2002b), and in some detail in Appendix A.

With state 4 (dead) as the reference, we formed the log ratios

= log{p

j

(x)/p

4

(x)}, j = 1,2,3. (Eq 1)

Exploratory analysis can be used to suggest a parametric form for the partial log ratios,

ξ

(x) ≡

ξ

(x;

β), and the estimation of β is done by weighted least squares. With the resulting estimate of β we

have the derived parameter estimates

(x) =

(x;

),

j

p

ˆ

(x) =

4

ˆ

p

(x) exp[

j

x

ˆ

(x)], j = 1,2,3, (Eq 2)

4

ˆ

p

(x) = {1 +

∑

exp

[

(x)]}

-1

.

Thence the estimated working life and related expectancies of interest (for a given age z) are

defined as a definite integral function

j

e

ˆ

(z) =

∫

64

)(

ˆ

z

j

dxxp . (Eq 3)

The expectation of main interest, e

1

, yields the working life expectancy (WLE). These quantities

are conditional only on the fact that an individual is alive at age 15, and they should be distinguished

Thence the estimated working life and related expectancies of interest (for a given age z)

are dened as a denite integral function

3 Outline of the Method

It is convenient to describe the method used in terms of a population cohort of n lives initially aged 15

years. Of particular importance are the probabilities that an individual is in state j at a subsequent age

x, written p

j

(x). In the present application, j = 0 denotes 'alive' and j = 1,2,3,4 indexes the exhaustive

(non-overlapping) states (1) 'employed', (2) 'unemployed', (3) 'economically inactive', and (4) 'dead'.

Here our interest is on estimating the marginal probabilities and working-life expectancies that are not

conditional on the initial state, but only on the initial age. Aggregate data were available at ages x =

15, ..., 64.

Estimation of the unconditional probabilities p

j

(x) is done by a large-sample version of logistic

regression. We shall call p

1

(x) the working life survival curve. Advantage is taken of the fact that

official statistics are almost always given in terms of large numbers, which in the present case

translates as large n, the number of individuals in the cohort. The theoretical results of the method are

given in Davis et al. (2001, 2002b), and in some detail in Appendix A.

With state 4 (dead) as the reference, we formed the log ratios

= log{p

j

(x)/p

4

(x)}, j = 1,2,3. (Eq 1)

Exploratory analysis can be used to suggest a parametric form for the partial log ratios,

ξ

(x) ≡

ξ

(x;

β), and the estimation of β is done by weighted least squares. With the resulting estimate of β we

have the derived parameter estimates

(x) =

(x;

),

j

p

ˆ

(x) =

4

ˆ

p

(x) exp[

j

x

ˆ

(x)], j = 1,2,3, (Eq 2)

4

ˆ

p

(x) = {1 +

∑

exp

[

(x)]}

-1

.

Thence the estimated working life and related expectancies of interest (for a given age z) are

defined as a definite integral function

j

e

ˆ

(z) =

∫

64

)(

ˆ

z

j

dxxp

. (Eq 3)

The expectation of main interest, e

1

, yields the working life expectancy (WLE). These quantities

are conditional only on the fact that an individual is alive at age 15, and they should be distinguished

(Eq 3)

The expectation of main interest, e

1

, yields the working life expectancy (WLE). These

quantities are conditional only on the fact that an individual is alive at age 15, and they

should be distinguished from working life expectancies conditional on knowledge of the

initial work-life or health state. Observe that the expectation e

0

= Σ

3

j=1

e

j

is the partial life

expectancy to age 65 for an individual known to have been alive at 15, and that Σ

4

j=1

e

j

= 50.

The large-sample arguments apply to estimating current survival curves and expectancies

as functions of age for a given year. However, we had data available for the decade 2000 to

2009 and clearly variation with year is also of interest. It is therefore natural to model the

The Working-life Expectancy in Finland 2000–2015 17

vector of log ratios as a function of both year t and age x, (t,x), bearing in mind that only

cross-sectional data are available.

We also used the S-PLUS program function predict on a generalized linear model object

to compute preliminary predicted values for working-life expectancies in a new data frame

containing the values at future time points as well as their associated prediction intervals

(see Appendix C).

18 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

4 Estimates of Model Parameters

A variety of plausible models can be used to describe the same data. Our selection of a

multistate model for the four states required the estimation of 33 separate sets of parameters

for both genders. The choice of the model covariates was based on signicance testing

using the original standard errors (uncorrected for population heterogeneity). To motivate

the argument, the observed rates for 2009 plotted in Figure 2 were considered. Upon

examination of the contours of the surfaces, a cubic function at age x for the log ratios was

estimated from the numbers. Similar results were obtained for other years.

Recession effects, episodes of unemployment, effects of the Finnish new pension law

(which was put in force in 2005) and interaction effects enter into the formulation of models

incorporating change both with year as well as age. The left hand columns of Figures 2.1

and 2.2 give the observed frequency rates. Some experimentation led to the tted model

parameters listed in Tables 1 and 2 (9 + 12 + 12 = 33 parameters for the male odds ratios and

10 + 11 + 12 = 33 for the female log ratios) together with their standard errors. Specically,

to describe the particular behavior of the estimates at the youngest and oldest ages, we

included indicators for the age groups 15–17 and 60+. Also an indicator was entered in the

model for the years following 2005, when the new pension law was enacted in Finland. For

men, the effect was signicant for the states of ’unemployed’ and economically ’inactive’

(Table 1) and for women for the state of ’inactive’ (Table 2). The nal model form is

specied in Appendix A.

Substitution in Equation 1 gives the tted probability surfaces (interpolating through

data points by means of a cubic spline) shown in the right hand column of Figures 2.1 and

2.2. Numerical values of the estimated model parameters with their standard errors are given

in Table 1 for males and in Table 2 for females.

The Working-life Expectancy in Finland 2000–2015 19

Table 1.

Regression model parameter estimates and standard errors of the three working-life states for

males.

Regression term

Results for state employed Results for state unemployed Results for state inactive

Parameter Estimate

Standard

error

Parameter Estimate

Standard

error

Parameter Estimate

Standard

error

Intercept (mean)

β

1

6.06e+0 1.86e-1 β

10

3.27e+0 1.96e-1 β

22

3.32e+0 1.91e-1

Age (centered at

39.5 years), x

β

2

-7.35e-2

§

2.00e-2 β

11

-6.95e-2 2.05e-2 β

23

-4.68e-2 2.01e-2

Squared term, x

2

β

3

-2.67e-3 8.13e-4 β

12

8.13e-5 8.32e-4 β

24

4.01e-3 8.18e-4

Cubic term, x

3

β

4

4.41e-5 5.99e-5 β

13

-3.50e-5 6.17e-4 β

25

5.55e-5 6.01e-5

Teen age indicator,

I(15 ≤ x ≤ 17)

* β

14

-1.68e-1 1.48e-1 β

26

2.18e-1 9.61e-2

Senior age

indicator, I(x ≥ 60)

β

5

-3.38e-1 3.92e-1 β

15

-9.30e-1 4.32e-1 β

27

1.85e-1 3.94e-1

Calendar year

(ordinally scaled), t

β

6

1.86e-2 6.04e-2 β

16

-2.86e-2 6.56e-2 β

28

2.13e-2 6.38e-2

Interaction effect

product term, tx

β

7

9.64e-4 2.61e-3 β

17

-1.66e-3 6.18e-3 β

29

-7.75e-4 6.07e-3

Squared term, tx

2

β

8

1.84e-5 1.60e-4 β

18

8.12e-5 2.65e-4 β

30

-4.27e-5 2.61e-4

Cubic term, tx

3

β

9

4.41e-6 7.14e-5 β

19

4.67e-6 1.64e-5 β

31

8.39e-8 1.60e-5

Pension year

indicator

I(2005 ≤ t ≤ 2010)

* β

20

-8.77e-2 9.71e-2 β

32

-5.22e-2 6.58e-2

Gross domestic

product, GDP

* β

21

-2.60e-2 7.69e-3 β

33

4.57e-3 5.11e-3

§

Exponential notation, e.g., −7.35e − 2 = −7.35 x 10–2 = −0.0735

* Insigniﬁcant main effect is not represented as a statistical term in the model.

20 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

Table 2.

Regression model parameter estimates and standard errors of the three working-life states for

females.

Regression term

Results for state employed Results for state unemployed Results for state inactive

Parameter Estimate

Standard

error

Parameter Estimate

Standard

error

Parameter Estimate

Standard

error

Intercept (mean)

β

1

6.81e+0 3.09e-1 β

11

4.09e+0 3.12e-1 β

22

4.82e+0 3.12e-1

Age (centered at

39.5 years), x

β

2

-6.39e-2

§

3.26e-2 β

12

-8.07e-2 3.29e-2 β

23

-1.10e-1 3.27e-2

Squared term, x

2

β

3

-1.88e-3 1.54e-3 β

13

5.97e-5 1.55e-3 β

24

2.38e-3 1.54e-3

Cubic term, x

3

β

4

-1.27e-5 1.05e-4 β

14

-2.96e-5 1.06e-4 β

25

8.84e-5 1.05e-4

Teen age indicator,

I(15 ≤ x ≤ 17)

β

5

-8.84e-1 2.06e-0 β

15

-5.15e-1 2.06e-0 β

26

5.27e-1 2.06e-0

Senior age

indicator, I(x ≥ 60)

β

6

-3.99e-1 5.96e-1 β

16

-1.04e+0 6.26e-1 β

27

1.89e-1 5.97e-1

Calendar year

(ordinally scaled), t

β

7

3.04e-2 9.95e-2 β

17

-2.24e-2 1.00e-1 β

28

3.33e-2 1.00e-1

Interaction effect

product term, tx

β

8

-3.37e-3 9.66e-3 β

18

-2.49e-3 9.75e-3 β

29

-3.06e-3 9.68e-3

Squared term, tx

2

β

9

1.31e-5 4.17e-4 β

19

1.59e-5 4.20e-4 β

30

-1.05e-4 4.17e-4

Cubic term, tx

3

β

10

1.13e-5 2.49e-5 β

20

7.73e-6 2.52e-5 β

31

6.39e-6 2.49e-5

Pension year

indicator

I(2005 ≤ t ≤ 2010)

* * β

32

-5.10e-2 6.02e-2

Gross domestic

product, GDP

* β

21

-6.05e-3 7.45e-3 β

33

9.91e-4 4.76e-3

§

Exponential notation, e.g., −6.39e − 2 = −6.39 x 10 – 2 = −0.0639

* Insigniﬁcant main effect not represented as a statistical term in the model.

The Working-life Expectancy in Finland 2000–2015 21

5 Estimates of State Probabilities

Numerical values for the estimated probabilities of the four occupancy states are given in

Table 3 separately for (a) males and (b) females.

After the economic downturn in 2001–2003, the estimated probabilities of being

employed increased rather consistently between the years 2000–2008 in all age groups and

for both genders, whereas the probabilities of unemployment diminished.

The severe economic recession that started in the late 2008 led to an exceptionally sharp

drop in GDP (-8 %), followed by a fairly rapid rebound in the probability of employment

in around 2009. Conversely, the probabilities of unemployment were markedly greater than

the estimates for the years neighboring 2009. The recession effect was more signicant for

men than for women. This effect bears some consequences to 2010 and to the following

years.

In Table 3a and Table 3b the one-year-ahead forecasts of the work life state probabilities

for the year 2010 were determined by estimating parameters from all the data in the interval

from 2000 up to 2009. The entries for the estimated probabilities in the columns for 2010

were obtained by rst extrapolating the regression ts to the log ratios within the sample and

using these to give projected probabilities and thereby expectancies.

These projections are thus essentially those given by standard regression methods. No

attempt was made to forecast by altering regression coefcients to reect possible future

case scenarios. The standard errors for the probabilities in Table 3a and Table 3b are not

exhibited to conserve space.

Large-sample signicance tests can easily be constructed. To take a particular case,

consider the difference between males and females in the probability of employment in the

economic recession year 2009. The gender difference for an ”average” (or randomly chosen)

25-year-old male worker was greater than that for women (Table 3a and Table 3b):

5 Estimates of State Probabilities

Numerical values for the estimated probabilities of the 4 occupancy states are given Table 3

separately for (a) males and (b) females.

After the economic downturn in 2001-2003, the estimated probabilities of being employed

increased rather consistently between the years 2000-2008 year in all age groups and for both

genders, whereas the probabilities of unemployment diminished.

The severe economic recession that started in the late 2008 led to an exceptionally sharp drop

(GDP = -8%) and then a fairly rapid rebound in the probability of employment occurred in around

2009. Conversely, the probabilities of unemployment were markedly greater than the estimates for the

years neighbouring 2009. The bulge was more significant for men than for women. This effect carries

a weakening aftermath to 2010 and to the following years.

In Table 3 a and Table 3 b the one-year-ahead forecasts of the worklife state probabilities for the

year 2010 were determined by estimating parameters from all the data in the interval from 2000 up to

2009. The entries for the estimated probabilities in the columns for 2010 were obtained by first

extrapolating the regression fits to the log ratios within the sample and using these to give projected

probabilities and thereby expectancies.

These projections are thus essentially those given by standard regression methods. No attempt

was made to forecast by altering regression coefficients to reflect possible future case scenarios. The

standard errors for the probabilities in Table 3 a and Table 3 b are not exhibited to conserve space.

Large-sample significance tests can easily be constructed. To take a particular case, consider the

difference between males and females in the probability of employment in the economic recession

year 2009. The gender difference for an "average" (or randomly chosen) 25-year old male worker was

greater than that for women (Table 3 a and Table 3 b):

̂

2009,

1

M

(25) -

̂

2009,

1

F

(25) = 0.7275 – 0.6466 = 0.0809

The standard error of the difference was estimated by computing the variance-

covariance matrix for the fitted probabilities (using the Liang-Zeger delta method modified

for the heterogeneous aggregate data):

SE{̂

2009,

1

M

(25) - ̂

2009,

1

F

(25)} = {SE[̂

2009,

1

M

(25)]

2

+ SE[̂

2009,

1

F

(25)]

2

}

½

= (0.01082

2

+ 0.01142

2

)

½

= 0.0157

The standard error of the difference was estimated by computing the variance-covariance

matrix for the tted probabilities (using the Liang-Zeger delta method modied for the

heterogeneous aggregate data):

5 Estimates of State Probabilities

Numerical values for the estimated probabilities of the 4 occupancy states are given Table 3

separately for (a) males and (b) females.

After the economic downturn in 2001-2003, the estimated probabilities of being employed

increased rather consistently between the years 2000-2008 year in all age groups and for both

genders, whereas the probabilities of unemployment diminished.

The severe economic recession that started in the late 2008 led to an exceptionally sharp drop

(GDP = -8%) and then a fairly rapid rebound in the probability of employment occurred in around

2009. Conversely, the probabilities of unemployment were markedly greater than the estimates for the

years neighbouring 2009. The bulge was more significant for men than for women. This effect carries

a weakening aftermath to 2010 and to the following years.

In Table 3 a and Table 3 b the one-year-ahead forecasts of the worklife state probabilities for the

year 2010 were determined by estimating parameters from all the data in the interval from 2000 up to

2009. The entries for the estimated probabilities in the columns for 2010 were obtained by first

extrapolating the regression fits to the log ratios within the sample and using these to give projected

probabilities and thereby expectancies.

These projections are thus essentially those given by standard regression methods. No attempt

was made to forecast by altering regression coefficients to reflect possible future case scenarios. The

standard errors for the probabilities in Table 3 a and Table 3 b are not exhibited to conserve space.

Large-sample significance tests can easily be constructed. To take a particular case, consider the

difference between males and females in the probability of employment in the economic recession

year 2009. The gender difference for an "average" (or randomly chosen) 25-year old male worker was

greater than that for women (Table 3 a and Table 3 b):

̂

2009,

1

M

(25) - ̂

2009,

1

F

(25) = 0.7275 – 0.6466 = 0.0809

The standard error of the difference was estimated by computing the variance-

covariance matrix for the fitted probabilities (using the Liang-Zeger delta method modified

for the heterogeneous aggregate data):

SE{

̂

2009,

1

M

(25) -

̂

2009,

1

F

(25)} = {SE[

̂

2009,

1

M

(25)]

2

+ SE[

̂

2009,

1

F

(25)]

2

}

½

= (0.01082

2

+ 0.01142

2

)

½

= 0.0157

The difference in the probabilities is multiple times as large as the normal (Gaussian)

standard deviation. This test realization corresponds to the two-tailed P-value < 0.001. So

the gender gap in employment probabilities was still statistically highly signicant, although

men typically suffer more from jobs lost in recession. On the other hand, while the estimated

probability of employment for 25-year-old men was predicted to rebound from 0.7275 in

2009 to 0.7539 in 2010, no such ascent was foreseen for women (0.6466 in 2009 vs. 0.6480

in 2010).

22 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

Table 3a.

Fitted probabilities for men of the four states 1 = ’employed’, 2 = ’unemployed’, 3 = ’economically

inactive’, and 4 = ’dead’, expressed as percentages, with projections for 2010, for selected years

and ages.

Age

x

State

j

Men

2001 2003 2005 2007 2009 2010

15 1

9.35 8.95 9.06 8.79 7.82 8.15

2

6.80 6.61 6.03 5.53 7.01 5.47

3

83.81 84.41 84.88 85.64 85.14 86.35

4

0.03 0.03 0.03 0.03 0.03 0.03

20 1

44.07 43.83 45.33 45.66 42.51 44.91

2

12.61 12.35 11.16 10.31 13.25 10.34

3

43.22 43.72 43.41 43.93 44.15 44.66

4

0.10 0.10 0.10 0.10 0.09 0.09

25 1

72.56 72.84 74.60 75.41 72.75 75.39

2

9.90 9.53 8.31 7.51 9.74 7.36

3

17.42 17.51 16.97 16.97 17.41 17.14

4

0.13 0.12 0.12 0.12 0.11 0.11

30 1

84.12 88.21 85.92 86.65 84.84 86.84

2

7.38 5.84 5.90 5.21 6.72 4.96

3

8.36 5.79 8.05 8.01 8.32 8.09

4

0.14 0.16 0.13 0.13 0.12 0.12

35 1

87.80 88.39 89.42 90.08 88.65

90.30

2

6.29 5.66 4.86 4.22 5.39 3.93

3

5.74 5.72 5.56 5.55 5.81 5.63

4

0.17 0.22 0.16 0.15 0.14 0.14

40 1

87.96 85.95 89.60 90.24 88.90 90.47

2

6.15 6.04 4.67 4.02 5.09 3.69

3

5.66 7.67 5.52 5.52 5.82 5.64

4

0.23 0.33 0.22 0.21 0.20 0.20

45 1

85.48 80.04 87.31 88.02 86.58 88.29

2

6.58 6.59 4.98 4.27 5.38 3.91

3

7.60 12.84 7.38 7.38 7.73 7.50

4

0.34 0.53 0.33 0.32 0.31 0.31

50 1

79.42 80.04 81.77 82.69 81.14 83.16

2

7.13 6.59 5.48 4.74 5.98 4.37

3

12.90 12.84 12.22 12.05 12.39 11.98

4

0.54 0.53 0.53 0.52 0.49 0.50

55 1

67.29 68.48 71.07 72.63 71.43 73.95

2

7.04 6.64 5.67 5.01 6.40 4.75

3

24.79 24.03 22.42 21.54 21.41 20.53

4

0.87 0.85

0.84 0.81 0.76 0.77

60 1

36.41 38.97 43.02 46.06 47.01 49.91

2

2.31 2.34 2.16 2.04 2.75 2.11

3

59.92 57.37 53.48 50.60 49.02 46.74

4

1.35 1.32 1.33 1.31 1.22 1.24

The Working-life Expectancy in Finland 2000–2015 23

Table 3b.

Fitted probabilities for women of the four states 1 = ’employed’, 2 = ’unemployed’, 3 =

’economically inactive’, and 4 = ’dead’, expressed as percentages, with projections for 2010, for

selected years and ages.

Age

x

State

j

Women

2001 2003 2005 2007 2009 2010

15 1

14.67 14.80 15.51 15.63 15.81 16.40

2

9.26 8.99 9.00 8.59 9.04 8.24

3

76.05 76.19 75.46 75.75 75.12 75.33

4

0.02 0.02 0.02 0.02 0.03 0.03

20 1

47.62 48.53 50.46 51.39 52.13 52.71

2

12.03 11.29 10.72 9.89 9.99 9.04

3

40.32 40.15 38.79 38.69 37.85 38.22

4

0.03 0.03 0.03 0.03 0.03 0.03

25 1

59.93 60.96 60.96 63.87 64.66 64.80

2

9.74 8.91 8.91 7.37 7.26 6.56

3

30.29 30.10 30.10 28.72 28.05 28.61

4

0.05 0.04 0.04 0.04 0.03 0.03

30 1

70.80 71.74 73.29 74.06 74.60 74.60

2

8.21 7.41 6.71 5.95 5.79 5.79

3

20.83 20.80 19.95 19.95 19.57 19.57

4

0.06 0.06 0.05 0.05 0.04 0.04

35 1

78.47 79.08 80.24 80.78 81.08

81.25

2

7.15 6.45 5.82 5.16 5.01 4.49

3

14.30 14.39 13.88 13.99 13.85 14.20

4

0.08 0.07 0.07 0.06 0.06 0.06

40 1

82.47 82.96 83.88 84.31 84.48 84.82

2

6.54 5.93 5.37 4.80 4.69 4.17

3

10.88 11.01 10.65 10.80 10.75 10.93

4

0.11 0.10 0.10 0.09 0.09 0.08

45 1

83.35 83.83 84.73 85.18 85.35 85.87

2

6.32 5.78 5.28 4.75 4.68 4.13

3

10.19 10.25 9.86 9.94 9.83 9.86

4

0.15 0.14 0.14 0.14 0.13 0.13

50 1

80.58 81.31 82.52 83.21 83.64 84.38

2

6.43 5.91 5.43 4.91 4.87 4.29

3

12.76 12.56 11.82 11.66 11.28 11.13

4

0.22 0.22 0.22 0.22 0.22 0.21

55 1

70.82 72.50 74.87 76.42 77.75 78.83

2

6.52 6.03 5.59 5.07 5.04 4.46

3

22.28 21.10 19.17 18.15 18.86 16.37

4

0.38 0.37

0.37 0.36 0.38 0.34

60 1

33.71 37.46 42.53 46.52 50.83 62.21

2

2.05 2.01 1.99 1.89 1.97 1.43

3

63.59 59.89 54.84 50.98 46.61 35.90

4

0.65 0.64 0.64 0.61 0.59 0.46

24 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

6 Estimates of Working-life Expectancies

A general development is that during the decade 2000–2009 the future employment time

increased in all age groups for both genders (Figure 3). An exception is the year 2009 for

which the expectancies are markedly smaller than the neighboring estimates for males. This

is an aftermath of the recession in Finland between 2008 and 2010 which affected especially

men’s employment in private enterprises, whereas women were employed more prevalently

in the public sector which was less insecure to discontinuation of the employment contract.

Parallel observations are from the recession in the early 1990s (Salonen, 2009).

Figure 3.

Density plots of the working-life expectancies for Finnish males and females at ages x = 15, 25,

and 50 years from year 2000 to 2010. The lines are nonparametric estimates of the probability

density of the data points, eˆ

1

(x), with a bandwidth speciﬁed as a multiple of the standard deviation

of the normal kernel function.

2000 2002 2004 2006 2008 2010

Year

0

10

20

30

40

Working-life Expectancies for Finnish Males and Females

Expectancy, years

Males 15 yr

Females 15 yr

Males 25 yr

Females 25 yr

Males 50 yr

Females 50 yr

Table 4a and Table 4b give estimates (as of 2011) of the expectancies of states 1, 2 and 3

for selected ages for both genders. The estimates obtained for 2009 were the following:

For a 15-year-old male, the WLE up to age 64 years is 34.2 years, while for females, it is

33.8 years; the gender difference being only 0.4 years in favor of men. The corresponding

projections for 2010 are 35.2 and 34.6 years.

An interesting feature of the development is that for 2000–2010 the estimated WLE for

males, eˆ

1

(x), is for ages 30 and under uniformly greater than the corresponding estimate for

females. As anticipated in our previous paper (Nurminen et al., 2005), the trend of females

having an equally long or greater duration of employment than that for males started already

in 2004 at ages 50 to 55 and widened to the age range 35 to 60 by year 2009 (boldface cells

in Table 5).

The Working-life Expectancy in Finland 2000–2015 25

In numerical terms, the expectations for a randomly chosen 50-year-old employed male

worker were: eˆ

1

M,2004

(50) = 8.5 yrs; eˆ

1

M,2009

(50) = 9.1 yrs, i.e. +7.1 %; and for a female they

were eˆ

1

F,2004

(50) = 8.6 yrs, eˆ

1

F,2009

(50) = 9.6 yrs, i.e. +1.6 %. Projected WLEs for 2010 conrm

the consistent pattern, with a maximum difference of eˆ

1

F,2010

(50) - eˆ

1

M,2010

(50) = 0.7 yrs, in

favor of women.

The standard errors of the expectancies were estimated directly by summing the

covariance matrix for the tted probabilities over age from present age to retirement

age. Assuming that the male and female models are stochastically independent, the SEs

(unpublished) can be used to make precise comparisons. To take a particular case, consider

the male and female expectancies of state 2 (unemployed) for 20-year-olds in 2009. Their

difference is 2.87 – 2.32 = 0.55, with a standard error (modied for the aggregate sampling)

of (0.171

2

+0.155

2

)

½

= 0.23, and one may infer that males of that age and in that year expect

to spend statistically signicantly (P = 0.017) more future time (in this case 6 months) in the

unemployed state than females.

26 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

Table 4a.

Partial life expectancies for Finnish males, expressed in years, of the three states 1 = ’employed’,

2 = ’unemployed’, and 3 = ’economically inactive’, for the quinquennial ages 15–60, and for the

decennial years 2000–2009, with projections for 2010. Women having an equally long or greater

expected duration of employment than that for males are shown in Table 4b in boldface ﬁgures.

Age State 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

15 1

33.2 33.1 33.3 33.5 33.8 34.4 34.7 34.9 34.7 34.2 35.2

2

3.4 3.6 3.5 3.4 3.2 2.9 2.8 2.6 2.8 3.4 2.5

3

12.7 12.6 12.5 12.5 12.4 12.0 11.9 11.8 11.8 11.8 11.6

20 1

32.1 32.1 32.2 32.4 32.8 33.3 33.6 33.9 33.7 33.3 34.2

2

3.0 3.1 3.0 2.9 2.7 2.5 2.4 2.2 2.4 2.9 2.1

3

9.2 9.2 9.1 9.0 8.8 8.5 8.4 8.3 8.2 8.2 8.0

25 1

29.3 29.2 29.4 29.6 29.9 30.4 30.7 30.9 30.8 30.4 31.3

2

2.4 2.5 2.5 2.4 2.2 2.0 1.9 1.8 1.9 2.3 1.7

3

7.7 7.6 7.5 7.4 7.3 7.0 6.8 6.7 6.7 6.7 6.4

30 1

25.3 25.3 25.5 25.7 26.0 26.4 26.6 26.8

26.8 26.6 27.2

2

2.0 2.1 2.0 2.0 1.8 1.6 1.5 1.4 1.5 1.8 1.4

3

7.0 7.0 6.9 6.8 6.6 6.3 6.2 6.1 6.0 6.0 5.8

35 1

21.0 21.0 21.2 21.3 21.6 22.0 22.2 22.4 22.4 22.2 22.8

2

1.7 1.7 1.7 1.6 1.5 1.4 1.3 1.2 1.3 1.5 1.1

3

6.7 6.6 6.5 6.4 6.3 6.0 5.9 5.7 5.7 5.7 4.4

40 1

16.6 16.6 16.8 16.9 17.2 17.5 17.7 17.9 17.9 17.7 18.3

2

1.4 1.4 1.4 1.3 1.2 1.1 1.1 1.0 1.1 1.3 1.0

3

6.4 6.3 6.2 6.1 6.0 6.0 5.6 5.5 5.4 5.4 5.2

45 1

12.2 12.3 12.4 12.5 12.8 13.1 13.3 13.4 13.4 13.3 13.8

2

1.1 1.1 1.1 1.0 1.0 0.9 0.8 0.8 0.9 1.0 0.8

3

6.1 6.0 5.9 5.8 5.7 5.4 5.3

5.2 5.1 5.1 4.9

50 1

8.0 8.1 8.2 8.4 8.5 8.8 9.0 9.1 9.2 9.1 9.5

2

0.7 0.8 0.8 0.7 0.7 0.6 0.6 0.6 0.6 0.7 0.6

3

5.7 5.6 5.5 5.4 5.2 5.0 4.9 4.7 4.7 4.6 4.4

55 1

4.3 4.4 4.5 4.6 4.7 4.9 5.1 5.2 5.2 5.2 5.5

2

0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.4 0.4 0.3

3

4.8 4.7 4.6 4.5 4.4 4.2 4.1 3.9 3.9 3.8 3.6

60 1

1.3 1.3 1.4 1.4 1.5 1.6 1.7 1.8 1.9 1.9 2.0

2

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

3

3.2 3.1 3.0 3.0 2.9 2.8 2.7 2.6 2.6 2.5 2.4

The Working-life Expectancy in Finland 2000–2015 27

Table 4b.

Partial life expectancies for Finnish females, expressed in years, of the three states 1 = ’employed,

2 = ’unemployed’, and 3 = ’economically inactive’, for ages 15–60 at quinquennial intervals, and

for the decennial years 2000–2009, with projections for 2010. Women having an equally long or

greater expected duration of employment than that for males are shown in boldface ﬁgures.

Age State 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

15 1

31.0 31.2 31.5 31.8 32.1 32.7 33.0 33.3 33.6 33.8 34.6

2

3.7 3.6 3.5 3.3 3.2 3.1 2.9 2.8 2.8 2.8 2.5

3

14.8 14.6 14.5 14.3 14.2 13.6 13.5 13.3 13.1 12.8 12.4

20 1

29.7 29.9 30.2 30.5 30.8 31.4 31.6 31.9 32.2 32.3 33.1

2

3.2 3.1 3.0 2.8 2.7 2.6 2.5 2.4 2.3 2.3 2.1

3

11.6 11.4 11.3 11.1 11.0 10.5 10.3 10.2 10.0 9.7 9.3

25 1

27.1 27.3 27.5 27.8 28.1 28.6 28.8 29.1 29.3 29.5 30.2

2

2.7 2.5 2.4 2.3 2.2 2.1 2.0 1.9 1.9 1.9 1.7

3

9.8 9.6 9.5 9.3 9.2 8.7 8.6 8.4 8.2 8.0 7.5

30 1

23.9 24.1 24.3 24.5 24.8 25.2 25.4 25.7

25.9 26.1 26.8

2

2.2 2.1 2.0 1.9 1.8 1.8 1.7 1.6 1.5 1.6 1.4

3

8.5 8.3 8.2 8.0 7.9 7.5 7.3 7.2 7.0 6.8 6.3

35 1

20.2 20.4 20.6 20.8 21.0 21.4 21.6 21.8 22.0

22.2 22.9

2

1.8 1.7 1.6 1.6 1.5 1.4 1.4 1.3 1.3 1.3 1.1

3

7.6 7.4 7.3 7.1 7.0 6.6 6.5 6.3 6.1 5.9 5.4

40 1

16.2 16.3 16.5 16.7 16.9 17.3 17.5 17.7

17.9 18.1 18.8

2

1.4 1.4 1.3 1.2 1.2 1.2 1.1 1.1 1.0 1.0 0.9

3

6.9 6.8 6.6 6.5 6.3 6.0 5.9 5.7 5.5 5.3 4.8

45 1

12.0 12.2 12.4 12.6 12.7

13.1 13.3 13.5 13.7 13.8 14.5

2

1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.8 0.8 0.8 0.7

3

6.4 6.2 6.1 6.0 5.8 5.5 5.3

5.2 5.0 4.8 4.3

50 1

7.9 8.1 8.2 8.4

8.6 8.9 9.1 9.2 9.4 9.6 10.2

2

0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.5

3

5.9 5.7 5.6 5.4 5.3 5.0 4.8 4.7 4.5 4.3 3.8

55 1

4.1 4.2 4.4 4.5

4.7 4.9 5.1 5.2 5.4 5.6 6.1

2

0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3

3

5.0 4.9 4.7 4.6 4.5 4.2 4.1 3.9 3.8 3.6 3.1

60 1

1.0 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

1.9 2.4

2

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

3

3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.1

28 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

Table 5 lists WLEs as percentages of the future years in working life up to age 64. For

example, the entry for 15-year-old males in 2010 is calculated from Table 4a as follows:

100 × e

1

(15)/e

0

(15) = 100 × 35.2/(35.2+2.5+11.6) = 71 %. The percentages increased fairly

steadily over the 10 years from 2000 to 2009 for both genders, with a slower movement at

younger ages compared to ages 35 and above. During this decade, there was an increase

of 10 percentage points or more in the future proportion of life spent in employment for

females starting from age 40 years and for males from age 50 years. The female percentage

for ages 40 years and above is forecast to overtake the male gure by year 2010.

Figure 4 depicts these percentages as a smooth probability surface for either gender. The

upslope trajectories or contour lines from end-points of the age-year area to higher points

reach their local maxima for men and women at the age of 25 years in 2007. In the post-

recession year of 2010, even more elevated percentages of the future share of time being

spent in employment were attained. Therefore, the model can be employed for representing

visually in the three-dimensional graph working life processes in the eld of demography.

To put these ndings into a more general perspective, the bar graph in Figure 5 presents

partial life and working-life expectancies for Finnish men and women in 2000–2010. The

height of the bar stands for life expectancy divided into four consecutive phases. The tacit

assumption – made for the sake of simplifying the graphical presentation – is that there were

no intermittent periods of unemployment, leave, disability, or retirement.

The proportion of time in employment between ages 15 up to 64 years increased in

the 11-year period from 2000 to 2010 for both genders. Although there was only a slight

increase in the male life expectancy (+2.6 yrs) compared to the female gure (+2.4 yrs), the

future proportion of working-life at age 15 grew markedly less for men (+2.0 yrs) than for

women (+3.6 yrs).

These trends run counter to the negative development in the preceding two decades

from 1981 up to 2001: While the life expectancy at birth grew more for men (+5.1 yrs)

than for women (+3.7 yrs), the working-life expectancy at the age of 25 years decreased for

both genders, although slightly more for males (-4 %-points) than for females (-3 %-points)

(Nurminen, 2008, Figure 6).

The Working-life Expectancy in Finland 2000–2015 29

Table 5.

Expectancies as percentages of future working life, of the three states 1 = ’employed’ 2 =

’unemployed’, and 3 = ’economically inactive’, for selected ages and years, separately for males

and females. For example, the expected percentage for a 15-year-old male in 2010 is calculated

from the ﬁgures in Table 4a as follows: 100 x (35.2/(35.2 + 2.5+11.6)) = 71 %.

Expectancies (%) for males Expectancies (%) for females

Age State 2001 2003 2005 2007 2009 2010 2001 2003 2005 2007 2009 2010

15 1

67 68 70 71 69 71 64 63 67 68 70 70

2

7 7 6 5 7 5 7 7 6 6 6 5

3

26 25 24 24 24 24 30 29 28 27 26 25

20 1

72 73 75 76 75 77 67 69 71 72 73 74

2

7 7 6 5 7 5 7 6 6 5 5 5

3

21 20 19 19 19 18 26 25 24 23 22 21

25 1

74 75 77 78 77 79 69 71 73 74 75 77

2

16 15 13 12 15 11 6 6 5 5 5 4

3

19 19 17 17 17 16 24 24 22 21

20 19

30 1

74 75 77 78 77 79 70 71 73 74 76 78

2

6 6 5 4 5 4 6 6 5 5 5 4

3

20 20 18 18 17 17 24 23 22 21 20 18

35 1

72 73 75 77 76 81 69 71 73 74 76 78

2

6 6 5 4 5 4 6 5 5 4 4 4

3

23 22 20 20 19 16 25 24 22 21 20 18

40 1

68 70 71 73 73 75 67 68 70 72 74 77

2

6 5 5 4 5 4 6 5 5 4 4 4

3

26 25 24 23 22 21 28 27 24 23 22 20

45 1

63 65 68 69 69 71 63 64 67 69

71 74

2

6 5 5 4 5 4 5 5 5 4 4 4

3

31 30 28 27 26 25 32 31 28 27 25 22

50 1

56 58 61 63 63 66 56 58 61 63 66 70

2

6 5 4 4 4.9 4 5 5 4 4 4 3

3

39 37 36 33 32 30 39 37 34 32 30 26

55 1

46 48 52 55 55 59 44 47 52 55 59 64

2

4 4 4 3 4 3 4 4 4 3 3 3

3

50 47 44 42 40 38 52 48 44 42 38 33

60 1

29 31 36 40 42 44 22 27 31 36 41 52

2

2 2 2 2 2 2 2 2 2 2 2

2

3

69 67 62 58 56 53 76 71 67 62 57 46

30 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

Figure 4.

Model ﬁtted probability surface (with color draping) of the proportion of future time in working-

life by age and year, separately for males and females.

Percentage of Male Future Time in Working Life

Percentage of Female Future Time in Working Life

The Working-life Expectancy in Finland 2000–2015 31

Figure 5.

Partial life expectancies and WLEs for the Finnish male and female populations in 2000–2009,

and forecast for 2010.

Partial Life Expectancies, Finnish Males 2000–2010

Expectancy, years

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Year

80

60

40

20

0

15.0

33.2

3.4

12.7

9.8

74.1

15.0

35.2

2.5

11.6

12.4

76.7

Under 15 yrs

Employed

Unemployed

Inactive

Over 65 yrs

Partial Life Expectancies, Finnish Females 2000–2010

Expectancy, years

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Year

80

60

40

20

0

15.0

31.0

3.7

14.8

16.5

81.0

15.0

34.6

2.5

12.4

18.9

83.4

Under 15 yrs

Employed

Unemployed

Inactive

Over 65 yrs

32 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

7 Forecasts of Working-life Expectancies

We can make predictions for the future years 2010–2015 from the estimates eˆ

i

(x)

2000

,...,

eˆ

i

(x)

2009

by tting a generalized linear model using the predict function of S-PLUS. The

predictions and their 90 % simultaneous intervals are presented numerically for the

quinquennial ages 15 through 60 in Table 6a and Table 6b and graphically for ages 15 and

50 in Figure 6.

An interesting result is that women's WLEs for ages 40 years and above are forecast

to continue to overtake the respective male gures in the years 2010–2015 (boldface

cells in Table 6b). Note that the predictions for year 2010 in Table 4 and Table 6 differ

slightly from each other. This discrepancy is due to the different regression models tted

(multistate regression model vs. generalized linear model) and the prediction ranges targeted

(extrapolation for a single year vs. simultaneous prediction for six years).

The age- and gender-specic development is clear in Figure 6. While the male WLE at

age 15 stayed consistently at a higher level than that of females, the rate of increase from

2010 to 2015 was predicted to be faster among women. When people reach the middle age

of 50 years, the predicted female expectancy has superseded that of males throughout the

prediction period.

An interesting nding is that for men aged 15 in 2015, the predicted future duration

of employment is estimated to be 36.0 (35.7–36.4) years. This estimate agrees with the

expected value of 36.3 years (computed at ETK) that would be needed in the development of

the length of working careers, if the ratio of the time spent on pension to that at work would

remain constant with the elongation of general male life expectancy (Laesvuori, 2011).

The Working-life Expectancy in Finland 2000–2015 33

Table 6a.

Predicted male future years of employment, with 90 % prediction intervals

2

, given for the years

2010–2015, for selected ages. Women having an equally long or greater predicted duration of

employment than that for males are shown in Table 6b in boldface numbers.

Age Estimate

Predictions for males

2010 2011 2012 2013 2014 2015

15 Mean

35.3 35.5 35.6 35.7 35.9 36.0

Lower

35.1 35.2 35.3 35.4 35.6 35.7

Upper

35.5 35.7 35.8 36.0 36.2 36.4

20 Mean

34.3 34.5 34.6 34.8 34.9 35.1

Lower

34.0 34.1 34.2 34.3 34.5 34.6

Upper

34.6 34.8 35.0 35.2 35.4 35.6

25 Mean

31.3 31.5 31.6 31.8 32.0 32.1

Lower

31.2 31.3 31.4 31.6 31.7 31.8

Upper

31.5 31.7 31.8 32.0 32.2 32.4

30 Mean

27.3 27.5 27.6 27.8 28.0 28.1

Lower

27.1 27.3 27.4 27.6 27.7 27.9

Upper

27.4 27.7 27.8 28.0 28.2 28.4

35 Mean

22.8 23.0 23.1 23.3 23.4 23.6

Lower

22.7 22.8 23.0 23.1 23.2 23.3

Upper

22.9 23.1 23.3 23.4 23.6 23.8

40 Mean

18.3 18.5 18.6 18.8 18.9 19.1

Lower

18.2 18.3 18.5 18.6 18.7 18.8

Upper

18.4 18.6 18.8 18.9 19.1 19.3

45 Mean

13.8 13.9 14.0 14.2 14.3 14.4

Lower

13.6 13.7 13.8 13.9 14.1 14.1

Upper

14.0 14.2 14.3 14.5 14.6 14.8

50 Mean

9.5 9.6 9.7 9.9 10.0 10.1

Lower

9.3 9.4 9.5 9.6 9.7 9.8

Upper

9.7 9.8 10.0 10.1 10.3 10.4

55 Mean

5.5 5.6 5.7 5.8 5.9 6.0

Lower

5.3 5.4 5.5 5.5 5.6 5.7

Upper

5.6 5.7 5.9 6.0 6.1 6.3

60 Mean

2.0 2.1 2.1 2.2 2.3 2.3

Lower

1.7 1.8 1.8 1.9 1.9 1.9

Upper

2.2 2.3 2.4 2.5 2.6 2.7

2 The simultaneous prediction intervals (given by lower and upper limits) adjust for the fact that we are estimating from the whole data

of 10 years 2000–2009, and hence are wider than the pointwise intervals.

34 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

Table 6b.

Predicted female future years of employment, with 90 % prediction intervals, given for the years

2010–2015, for selected ages. Women having an equally long or greater predicted duration of

employment than that for males are shown in boldface numbers.

Age Estimate

Predictions for females

2010 2011 2012 2013 2014 2015

15 Mean

34.1 34.4 34.7 35.0 35.2 35.5

Lower

33.9 34.1 34.4 34.6 34.9 35.1

Upper

34.3 34.7 35.0 35.3 35.6 35.9

20 Mean

32.7 33.0 33.3 33.6 33.8 34.1

Lower

32.5 32.8 33.0 33.3 33.5 33.8

Upper

33.0 33.3 33.6 33.9 34.2 34.5

25 Mean

29.8 30.1 30.3 30.6 30.8 31.1

Lower

29.7 29.9 30.1 30.4 30.6 30.8

Upper

30.0 30.3 30.5 30.8 31.1 31.4

30 Mean

26.4 26.6 26.8 27.1 27.3 27.5

Lower

26.2 26.4 26.6 26.8 27.0 27.2

Upper

26.5 26.8 27.0 27.3 27.5 27.8

35 Mean

22.4 22.6 22.8 23.0 23.2 23.4

Lower

3

22.4 22.6 22.8 23.0 23.2 23.4

Upper

3

22.4 22.6 22.8 23.0 23.2 23.4

40 Mean

18.3 18.5

18.6 18.8 19.0 19.2

Lower

18.1 18.3 18.4 18.6

18.8 18.9

Upper

18.4 18.6 18.9 19.1 19.3 19.5

45 Mean 14.0 14.2 14.4 14.6 14.8 15.0

Lower

13.9 14.0 14.2 14.3 14.5 14.7

Upper

14.2 14.4 14.6 14.8 15.1 15.3

50 Mean 9.7 9.90 10.1 10.2 10.4 10.6

Lower

9.6 9.72 9.9 10.0 10.2 10.3

Upper

9.9 10.1 10.3 10.5 10.7 10.8

55 Mean 5.7 5.8 6.0 6.2 6.3 6.5

Lower

5.5 5.7 5.8 5.9 6.1 6.2

Upper

5.9 6.0 6.2 6.4 6.6 6.8

60 Mean

1.9 2.0 2.1

2.1

2.2

2.3

Lower

1.7 1.7 1.8 1.8 1.9 2.0

Upper

2.1 2.2 2.3 2.4 2.6 2.7

3 The residual deviance of the model ﬁt is negligible for females aged 35 years, because of the straight regression line on either side of

year 2005. Hence the widths of the associated prediction intervals are zero.

The Working-life Expectancy in Finland 2000–2015 35

Figure 6.

Predicted mean future years of employment shown by boldface solid line, with simultaneous

90 % prediction intervals (lower and upper limits) shown by thinner lines, for 15- and 50-year-

old men and women are given for the years 2010–2015.

2010 2011 2012 2013 2014 2015

Calendar year

33.5

34.0

34.5

35.0

35.5

36.0

36.5

Females 15 yrs Mean

Females 15 yrs Upper

Females 15 yrs Lower

Males 15 yrs Mean

Males 15 yrs Upper

Males 15 yrs Lower

Predicted Future Career Length at Age 15 Years

With Lower and Upper Limits of 90 % Prediction Interval

Years of

work life

2010 2011 2012 2013 2014 2015

Calendar year

9.0

9.5

10.0

10.5

11.0

Predicted Future Career Length at Age 50 Years

With Lower and Upper Limits of 90 % Prediction Interval

Years of

work life

Females 50 yrs Mean

Females 50 yrs Upper

Females 50 yrs Lower

Males 50 yrs Mean

Males 50 yrs Upper

Males 50 yrs Lower

36 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

8 Discussion

8.1 Longer Working Lives Tackle Aging Societies

Population aging is not looming in the future, it faces us already. Economic challenges come

about when the increasing number of people in an advanced age and the younger generation

supporting them cause the growth in society's consumption needs to outpace growth in its

productive capacity. Maestas and Zissimopoulos (2010), Professors of Economics at Pardee

RAND Graduate School, CA, argue that encouraging work at older ages serves a variety of

social goals, including counteracting the slowdown of labor force increase and supporting

the nances of social security and medical care. As men and women extend their working

lives, they can enhance their own retirement income security and may ease the strain of an

aging population on economic growth. Prolonging working life is similarly an essential

element of a successful policy to meet the concerns confronting Finland. Thus it is important

to use accurate statistics to quantify the WLE’s.

In the present paper, stochastic process analysis was applied for estimating the future

time that an individual of a given initial age in the Finnish working-age population belongs

to one of the following three sub-groups:

• gainfully employed

• currently unemployed, but has actively sought employment and would be available

for work

• economically inactive, i.e., persons outside the labor force prior to permanent

departure from work life by retirement or death.

These projected estimates were obtained (in 2011) for 2010: For a 15-year-old male the

WLE up to age 64 years is 35.3 years, while for females it is 34.1 years. The corresponding

forecasts for 2015 are 36.0 and 35.5 years.

The comparable expected employment durations computed at the ETK (Lampi, personal

communication, August 3, 2011) for 2009 were [our gures in brackets]: 33.5 [34.2] years

for males and 33.7 [33.8] years for females. In the European Union, the difference between

men and women was smallest in Finland (1.3 yrs), followed by Sweden (2.5 yrs) and

Denmark (3.7 yrs) (Laesvuori, 2010). The expected employment participation years of the

15- to-74-year-old population computed by the Social Insurance Institution of Finland (Hytti

and Valaste, 2009) for 2005 were [our gures in brackets]: 33.4 [33.4] years for men and

32.2 [32.7] years for females. These estimates are quite comparable taking into consideration

the differences in the estimation approaches: viz. prevalence-based vs. regression modeling;

Finnish vs. European LFS; age bracket 15–64 vs. 15–74 years.

The four major demographic determinants that shorten working careers in the Finnish

workforce are: delayed start of employment due to prolonged duration of education;

unemployment (268,200 persons, June 29, 2011); disability (267,200 pensioners, in 2010);

and early retirement. Lengthening the working careers has become to be regarded as a

possible solution to the economic problems of the public sector due to the rapid population

aging in Finland (Kiander, 2010). It is argued that if people continued working longer,

The Working-life Expectancy in Finland 2000–2015 37

revenue from taxation would increase, and there would be less need for austerity measures.

Basically, the extension of working careers determines the rise in employment rate. Roughly,

it can be estimated that extending the working life from 35 to 40 years would mean a rise in

the employment rate from 68

% to 77 % (i.e., 200 000 new workplaces). An assertion is that

work careers can only grow longer if a sufcient number of new workplaces will spring up

in the enterprises (as against in the public sector).

The efcacy of national measures adopted in Finland (up to 2005) aimed at extending

working life has been analyzed as successful comprehensive reforms because they are

simultaneously punitive and long term and stress incentives (Sigg and De-Luigi, 2007).

These measures appear to have made prolonging labor force participation an attractive

option. During the last decade, social policy has been adjusted in many ways to take better

account of the challenges created by population aging and substantial progress has been

made in many sectors. Yet the success of Finnish pension reforms and employment policies

aimed at strengthening the sustainability of public nances has been assessed still to be

insufcient in a report issued by the Prime Minister’s Ofce (2009; Vihriälä, 2009).

8.2 Prevalence versus Multistate Life Table Analysis

The methodological interest in this working paper has been in the application of inferential

tools for discrete time stochastic processes for application to register data which are readily

available. It is contended that this modern approach has multiple advantages over the cur-

rently used practices.

Earlier applications of population health measures (Nurminen, 2004) such as active life

expectancy have been numerous, especially in the US (Katz et al. 1983). These measures

have also been recently applied in Finland for working life (Hytti and Nio, 2004) and for

retirement (Kannisto, 2006). Active life expectancy answers the question: Of the remaining

years of life for a cohort of persons, what proportion is expected to be spent disability free?

The correct answer has implications for individuals, families and societies. The specic term

of labor market activity rate is the percentage of the population that reports, e.g., in a labor

survey that they have been working during the month of the interview. This measure might

overstate the labor market activity of persons with disability (or defect or disease), because

some people may have experienced the onset of disability, for instance, in the middle of the

survey period and did not work after that.

Our approach to estimating working-life expectancy differs from the traditional actuarial

method in many fundamental facets. First, although we also use data from the life tables and

the LFSs of Statistics Finland, we estimate the WLEs jointly for multiple years throughout

the study period. The alternative approach to the analysis is to carry out separate estimations

for a series of survey or census years and then t a curve to describe trends, as was done in

Hytti and Nio (2004) in their monitoring of cross-sectional employment activity data over

a number of years. Since these data span 10 years and a large number of individuals, the

results may not be as sensitive to economic conditions as a survey that would rely on only

one year of data, unless period-specic effects are explicitly modeled.

Second, we base our analysis of panel or cohort data on a large-sample regression

model tted to a multistate life table, instead of a simple relative frequency calculation

38 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

using the average demographic experiences of the synthetic cohorts at each given age. This

stochastic inferential approach allows us to draw probabilistic inferences on markedly more

information about work life characteristics and also permits much more detailed working-

life tables to be estimated, for example stratifying by socioeconomic factors. We explicitly

modeled the state probabilities as a function of age, year, GDP, etc. The set of variates

describing demographic and economic conditions faced by persons can be expanded, but

not at will. This modeling approach enables one to circumvent the problem of small cell

sizes encountered in modest disaggregation of data.

Third, the traditional prevalence life table (PLT) technique is limited when applied to

intrinsically dynamic processes with multiple decrements, like the labor force process. In a

similar manner, the life table calculated from prevalence rates cannot provide the occurrence/

exposure rates in a continuous time frame. If labor force participation rates change over time,

these trends are incorporated more accurately in the multistate life table (MSLT) method

than in the PLT technique. However, the former method is very sensitive to particular

uctuations in labor force activities. Calculations could therefore overstate the labor force

involvement in times of expansion and understate in a recessionary period (Richards, 2000).

In reviewing the alternative employment activity measures, Hytti (2009) discussed the

relative advantages and limitations of the retirement exit age versus active-life expectancy.

She pointed out that exit age acts rapidly and to the correct direction of the changes in the

transitions to retirement. However, the exit age measure does this ignoring the cumulative

experience up to the present time. By comparison, the expectancy was said to react slowly

to the changes in the usage of pension scheme and in the participation of labor market. But

the expectancy measure – which can be regarded as a far-sighted feature – is inuenced

by the behavior of the studied population in the preceding years. Another advantage is

that expectancy shows whether or not the development tends towards the targets set in the

ofcial employment and pension policies.

Evidently, the above criticism of the insensitiveness property is unfounded, and derives

as a defense against the fact that the retirement age indicator is an inferior measure of the

total career length (see Nurminen [2008] for the comparative advantages and limitations

pertaining to the actuarial-type and regression-type expectancy measures). By denition,

the Sullivan method cannot supply estimates of cohort health expectancies which are of

importance to persons now living and to planners of future health services, except in so far

that a period measure is a surrogate for the analogues cohort quantity (Myrskylä, 2010). We

argue that the fundamentally different Davis et al. approach may be helpful in this regard.

In fact, the regression function can be estimated based either on a long time span (e.g. a

decade) or on a shorter time period (e.g. a year).

Then again, the working-life expectancy has been characterized as being sensitive to

volatile labor market variations by the report of the Government’s working group (Prime

Minister’s Ofce, 2011), who gave an example: In 2008 the Finnish WLE at age 15 was

34.6 years but it reduced due to the rapid decline in employment in the recession year 2009

by one whole year (1.7 years for men). Actually, the expectancy was computed using the

traditional actuarial (Sullivan) PLT technique on a year-by-year basis. The MSLT regression

(Davis) approach to expectancy, which is based on tting a smooth model over the studied

interval, say 2000–2009, does not overestimate the effect of such changes on the total length

The Working-life Expectancy in Finland 2000–2015 39

of working career. In order to react to the short-term uctuations, the model can be specied

to include terms to describe the recession period (2008–2010). Entering a single indicator

for the particular year 2009, the developed model yielded the following estimates of male

WLEs for the years 2008, 2009, 2010: 34.7, 34.2, 35.2 (Table 4). The drop from 2008 to

2009 was only half a year, but the counteractive rise from 2009 to 2010 was one year.

Fourth, the MSLT methods were developed to overcome the limitations of the traditional

PLT techniques. The states are dened to be multiple, some of which are transient (or

recurrent) while others are assumed non-transient. We enhanced the customary life table

by explicitly dening a three-state employment state space: (1) employed (permanently

employed, employed for xed-term, and self-employed); (2) unemployed; (3) persons

outside the labor force (students, conscripts, disability and old-age pensioners, etc.). This

denition is different to the two-state system which estimates the duration of ’active

working life’ by classifying persons as ’active’ (in the labor force) or ’inactive’ (out of

the labor force) (Hytti and Nio, 2004). The tabular analysis of further disaggregated data

(e.g. allowing various modes of exit from the labor force) would necessarily turn out to be

cumbersome or impossible without resorting to modeling. The regression analysis of panel

or cohort data is applicable when the numbers are reasonably large; frequencies of 10 or

more in the non-absorbing cells of the multistate life tables – say at 10 tables – should be

sufcient (Prof. C.R. Heathcote, ANU, personal communication, December 3, 2001).

Finally, because working-life tables are generated from survey data, sampling variation

may be important (e.g., due to population dynamics, economic uctuations, interview

methods), especially in small samples. Although the Finnish ofcial research institutes

acknowledge this fact, they do not provide standard error estimates for their active working

life expectancies (Appendix Table 4, Kannisto 2006). Under stationary conditions (i.e.

independence of an initial health state), a new ’equilibrium’ estimate of the prevalence rate

and its approximate variance has been developed by Diehr et al. (2007). In the Davis et al.

(2001) approach, standard errors (and covariance) can be found by using the delta method

based on the maximum likelihood function or, alternatively, by the Monte Carlo sampling

from the estimated asymptotic normal distribution of the estimated regression coefcients.

40 FINNISH CENTRE FOR PENSIONS, WORKING PAPERS

9 Methodological Recommendations

A study for the EU Commission sought to investigate the working life expectancy (WLE)

indicator which should complement the monitoring instruments of the European Employment

Strategy by focusing on the entire life cycle of active persons and persons in employment

(Vogler-Ludvig, 2009). The study suggested three indicators for the measurement of WLE:

• duration of active working life indicator based on average annual activity rates

• duration of employment indicator based on average employment rates

• duration of working time indicator based on annual working hours

All three indicators have their counterparts in the form of duration of inactive working-life,

duration of unemployment, and duration of non-working time.

The WLE indicators were assessed to provide sufciently accurate and easily

understandable results, in that they:

–

are highly stable over time, even for single ages

– show great continuity over the lifespan

– react directly to changes of activity rates and working hours

– reveal expected differences between gender, ages, and countries

A limitation of these actuarial indicators appear (sic) to be that they are descriptions of the

whole life cycle rather than specic periods of working life. Moreover, they describe the

present state of working life participation over all ages, rather than providing forecast of

future working life. However, these limitations pertain only to the traditional PLT (Sullivan)

method, not to the modern MSLT (Davis) regression modeling approach.

Based on the positive assessment of the considered indicators, the study recommended

using the WLE indicator as one of the core labor market indicators at European and

national level (Dr. Kurt Vogler-Ludvig, personal communication, November 9, 2009). Out

of the considered indicators, the duration of active working life received a dominating

position. The PLT indictor has been discussed in the Employment Committee Indicators

Group (Guido Vanderseypen, Directorate-General Employment, personal communication,

November 4, 2010), and there has been a rather broad approval for the proposed formula

(Eric Meyermans, European Parliament, Committee on Employment and Social Affairs

(EMPL), personal communication, April 22, 2011).

Considering the comparative advantages and limitations of the actuarial life table

method (Hytti and Nio) and the multistate life table regression approach (Davis et al.), our

stand is that, while the former prevalence-type indicator is suitable and easy for the purpose

of routine statistics, the modern regression model-based expectancy is appropriate for more

demanding research objectives. This conclusion is reached because the latter statistical

measure is theoretically founded on large-sample, weighted least squares theory, and

therefore allows reliable data analyses and stochastic inferences (inter alia, with respect to

signicance tests, interval estimates, interaction effects, time tends, and projections).

The Working-life Expectancy in Finland 2000–2015 41

APPENDICES

Appendix A: Details of Modeling and Estimation Methods

The details are extracted from the method description in Nurminen et al. (2005). For full

explication of the stochastic modeling, see Davis (2003).

The major difference and the novelty of the method of, for example, Davis et al. (2001),

compared to the method of Millimet at al. (2003), is that it rst proves the asymptotic

normality of