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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