Les retraites individuelles à long terme : une projection par microsimulation (version anglaise)
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Les retraites individuelles à long terme : une projection par microsimulation (version anglaise)


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L'avenir des retraites est généralement envisagé en termes globaux : projection des grandes masses, des niveaux de prestations ou des taux de cotisations moyens. Ceci peut se faire à l'aide de modèles relativement agrégés. Mais l'évolution des retraites présente aussi des enjeux individuels : qui seront les individus les plus touchés par tel ou tel type de réforme, comment les modifications de droits interagiront-elles avec d'autres évolutions, telles que l'évolution des carrières individuelles, des structures familiales ? Un modèle de microsimulation dynamique est l'outil le plus adapté pour répondre à de telles questions. A partir d'un échantillon de données individuelles, représentatif de la population totale, il consiste à simuler le vieillissement des individus, tant du point de vue démographique qu'économique, ainsi que de leur droits sociaux. La construction d'un tel modèle est nécessairement progressive. Quelques résultats préliminaires illustrent la variété de ses utilisations potentielles, mais aussi l'importance des hypothèses qui les sous-tendent.



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Individual Retirement Pensions
in the Long Run: a Projection
by Microsimulation*
The future of retirement pensions is usually considered in overall terms, with
projections of the main figures involved, average benefit levels and contribution
rates. These projections can be made using relatively aggregated models.
Yet the future of retirement pensions also raises personal issues: which individuals
Jean Marie
will be most affected by a given reform? How will changes in entitlements interact
with other developments in individual career paths and family structures?
A dynamic microsimulation model is the most appropriate tool for providing
answers to these questions. Using a sample of individual data that are
representative of the total population, it simulates the ageing of individuals,
both in demographic and economic terms, and their social entitlements.* Originally published as
"Les retraites individuelles
à long terme : une projec The construction of such a model has to be undertaken gradually. Some
tion par simulation," preliminary findings show the variety of potential uses for the model, as well as
Économie et Statistique,
no. 315, 1998 5. the importance of its underlying assumptions.
** Didier Blanchet was in
charge of the "Redistribu
tion and Social Policy" he dynamic microsimulation model For example, the impact of more restrictive
division of INSEE at the T presented here is mainly intended to conditions for entitlement to full pensionstime this article was writ
ten and Jean Marie project pensions, but we shall see that it cacalled for in the reform instituted n in the summer
Chanut works in the same also be used for broader purposes such as of 1993 will vary depending on individual
division. The current ver
projections of labour force participation career histories. New length of servicesion of the model is a test
version and the results are rates, family structures, etc. The reasons forrequirements (160 quarters) and new
given as an illustration undertaking this exercise are easy to under-entitlement calculations (with the switch to the
only. Since this article was
stand. Most of the thinking about the long 25 best years as the calculation basis) raise thewritten, work on the model
has continued under the term future of retirement pensions does notquestion as to whether the dispersion of
direction of Pierre Ralle. take on board the in house research work pensions will be wider or narrower, and by how
done by specific retirement funds and is much. Furthermore, even the average impact ofThe authors would like to
thank Anne Lafférère, based instead on macro demographic and the reform will depend on the dispersion in
Françoise Dumontier and macro economic tools. These tools can be individual situations, insofar as the schedules
Jérôme Accardo for sup
used to assess changes in average pensionsfor calculating pension entitlements are notplying the 1991 survey on
financial assets, and and the adjustments that may be required to straightforward linear scales.
Pierre Ralle for rereading prevent average pensions from falling too
this article.
far. But this type of result obscures the vaIsnt the same vein, we could look at how higher
Names and dates in variety of individual retirement situations, female labour force participation rates, longer
parentheses refer to the which more finely detailed analysis must life expectancy for men and women and
bibliography at the end of
take into account. changes in family structures will affectthe article.
INSEE Studies no. 37, August 1999 1women’s direct and derivative entitlements model itself in order to improve and diversify
and pensioners’ living standards. This wouldthe types of projections that can be produced.
require detailed analysis that takes into
account both past earnings and household
sizes. Detailed analysis is also required to The individual is the basic unit
study the redistributive impact of pension
systems within generations, and to assess theOut of the many surveys that could be used as a
effectiveness of measures to make systems starting point for microsimulation, we chose
more redistributive. the 1991 financial assets survey, which was
conducted between mid November 1991 and
When dealing with such issues, we soon early April 1992. This survey provides basic
encounter the limitations of conventional demographic data as well as information about
projection methods. These methods would careers (individual educational attainment,
require us to assume that the population can be years of service, earnings). It also provides
described by state vectors and large scale wealth and investment data, which have not
transition matrices that soon become too been used at this stage in the construction of the
complex to handle (see box). This is why model, but which could be added later to the
microsimulation appears to be the best choice.description of pensioners’ economic
It starts directly with a sample of individual circumstances, by providing the rate of home
data. Ageing and individual life paths are ownership for example. With a few
simulated by controlled random sampling adjustments, this survey provides an initial base
series and the renewal of the population by the of some 15,000 households containing some
arrival of new members is also simulated. Thi37,000 indis viduals.
method enables us to construct and maintain a
sample that we can then use to reproduce the Once the database has been chosen, there are
calculations carried out on the initial sample attwo possible ways to organise it. The choice
1 1Many examples of any future date. As long as the simulation between the two then determines how the
such models have been assumptions are valid and the sample is largsimulation program opee rates. The first
produced in other coun
enough to minimise the problem of stochasticpossibility is to make the household the unit oftries. See the surveys by
Harding (1990), Mot drift, we can envisage, for example, observation. Transitions in households are then
(1991) and Pennec distributions according to pensioners’ years ofsimulated by drawing samples for departing
service, cross tabulated with their earnings andmembers and the arrival of new members. This
their marital status. These elements can then be approach makes it easier to calculate standard
used to establish a wide variety of data on of living directly for each household. On the
pensioners’ living standards. other hand, it requires computer processing of
rapidly changing structural records to simulate
There are three main steps in the development the dissolution and formation of households. It
of such a model. The first step is to set up the also requires embedded subprocesses. For
initial database, which is a file of personal example, simulating deaths and ageing requires
records providing information about how a subprocess for the population of households
individuals are connected to others by variousand a subprocess for each member of each
links of kinship and cohabitation. Such data are household. Moreover, the household based
important for analysing households’ living approach does not save us from having to deal
standards and for many other purposes. The with kinship connections between individuals
second step is to construct the simulation who do not live or who no longer live in the
program per se, which will enable us to same household. For example, we still have to
maintain the sample by introducing such lifetake account of adults’ connections to their
changes as marriages, births and deaths and aged parents and to their own children who are
social and economic changes such as leavingno longer living at home.
school, and entering and leaving the labour
force. The third step is to use the results toThe other possible way of organising the
analyse the individual data produced by database is to have a record for each individual.
simulation for each future period and to sumThe connections between them are then
them in indicators of averages, distributions, managed by a cross tabulation system. Each
etc. Of course, these steps are not fully record is flagged by an identifier and includes a
sequential. The first use of data from a set of variables that identify the other
primitive version of the model may be followed individuals connected to the individual through
up by further work on the initial data and on cohabitation or kinship (spouse, children andthe
2 INSEE Studies no. 37, August 1999 Box
1 Conventional projections (matrix methods)
Deterministic projection methods start with a description of the population in the form of an initial state
vector. This vector is in the Pt column showing the distribution of the population into a certain number of
classes. We assume that the transition from this state at time t to the state at time t + 1 can be simulated
by applying a transition matrix A to Pt, where the element aij is generally equivalent to the probability that
an individual in category j will end up in category i at time t + 1. This gives:
P = A P et P = A A ... A P .
t + 1 t t t + n t + n 1 t + n 2 t t
A projection of this type is therefore programmed as a matrix multiplication chain.
A typical case is a long term projection of population structure by sex and age. For example, if we limit
ourselves to the case of the female sex, we can use pa,t to denote the number of individuals of age a at
the time t, qa,t to denote the mortality rate at age a and fa,t to denote the probability of giving birth to a
girl at age a (this probability is assumed to be nil under 15 years and over 45 years). We then see that
the population at time t + 1, arrayed in a column vector can be written:
p p 0 0 f ... f 0 0 , t + 1 0 , t 15 , t 45 , t
. .
. 0 . 1 q 0 0 0 0 0
o , t
. .
p . 0 0 0 p 0 0 0 15 , t + 1 15 , t
. .
. P = . = 0 0 . 0 0 0 . = A P
t + 1 t
. .
p 0 0 . 0 0 0 p 0 45 , t + 1 45 , t
. .
0 0 0 0 0 . 0 . .
. .
0 0 0 0 1 q 0 p 0 p 99 , t 99 , t + 1 99 , t
If the population is divided up according to more criteria than just sex and age, ve Pctor increases in size
and matrix A consequently becomes much more complicated.
This method quickly runs up against several limits.
– The division into classes is only valid for discrete variables. If we want to project population according
to income levels, we would have to group the population into income brackets. This would lead to a loss
of information and would require us to model the probabilities of transition from one income bracket to an
other, which is more difficult than simulating continuous modifications in income.
– The size of the matrices that have to be managed increases exponentially with the number of variables
– The model will only project indicators that can be calculated from vector P. The division into classes set
out at the start therefore determines all of the results produced. We would have to use a more finely de
tailed division to obtain further results, which would mean increasing the size of vector P. This in turn would
usually require substantial rewriting of the projection programme since it invalidates the indicator systems of
vector P and matrix A.
2 Dynamic microsimulation
Instead of describing the population with a matrix that shows the distribution in a given number of classes,
this methods is based directly on the base of raw data on individuals in the population or in a repre-
sentative sample. The data in the base are then aged for each date t. In the case of data where change
is determined totally by the passage of time, such as age, ageing, or simulation, is very straightforward.
When variables change randomly, simulation is conducted by pseudo random sampling. For example, sup
pose that the variable under consideration is labour force par icipation descrt ibed by variable a (ai =1 if
individual i is in the labour force and 0 otherwise) and let p(x1,...,xn) be the probability of leaving the labour
force as determined by the values of a certain number of other variablexs 1 ,..., xn (which can be age,
INSEE Studies no. 37, August 1999 3
ŒŒœŒŒŒŒøœŒœŒŒŒŒŒœœœœŒœœœßœ-œŒœŒœœßœœœœ-œŒØœŒœºœŒœŒøŒŒŒŒŒŒŒŒŒŒŒŒŒ-ŒœŒœŒœŒœŒœœ-œØœºßŒœŒøœœœœœœœœœØœŒœºœŒŒŒŒŒparents). We chose this approach in the end This involves reassigning sample members
because of the advantages it offers. It enables us plausible kinship connections within the
to record transitions in personal status withoutsample itself. Thus, the sample operates like a
having to alter household records, when such small closed community. Its structure may be
transitions are not important to the household unrealistic in terms of in breeding (which is not
per se. The resulting database is perfectly the topic of our study), but it nevertheless
regular in structure and easier to manage. It enables us to come up with an automated
enables us to reconstitute family circles simulation of kinship networks of appropriate
concentrically from the couple outwards to size and composition.
include siblings living elsewhere, etc.
Kinship connections outside of the household
However, this comprehensive approach to are reconstituted from parents down to children
kinship connections raises another problem. rather from children up to parents due to the
Kinship connections outside of the household nature of the survey data. The survey indicates
are not revealed in the initial survey data, nor the number of direct descendants of all ages
could they be since it would only be by pure that each adult has living outside of their own
coincidence that the head of a household’s household, indicating their sex, year of birth
parents and siblings end up in the same surveand educational attainmey nt. The survey data
sample. show that we have to come up with about
16,000 children living away from home for the
adults in the sample. Our method is to assign
A scale model of the aggregate population them from the 25,000 individuals in the survey
sample who are not living in their parents’
The approach used to overcome this problem is households.
to reconstitute artificial kinship connections
outside of the household so that connections are The matching of parents to children is done
with individuals in the same sample population. through successive iterations. In the first step,
Box (continued)
sex, education, etc.) In this case, for all of the individuals in the base af=o1r , wwhom e take a pseudo ran i
dom sampling R with uniform distribution on [0, 1], and we switch the value of a from 1 to 0 for alli
individuals for whom R < p(x ,..., x ).i 1i ni
This method has to be adapted when new individuals are added to the database. New records are cre
ated for them where characteristics are also attributed by random distributions.
This method has several advantages.
– The sampling of events can be determined by any combination of variables x ,..., x in the database at1 n
minimum programming cost. The only problem is being able to come up with the values for the determining
– Adding a variable to the base of individual data leads to a linear increase in the size of the file to be
managed and not an exponential increase. Once it has been added, a new variable can easily be used in
simulation and it can even be changed by simulation if the rules governing its change over time are known.
– Whereas conventional methods can only use indicators that can be calculated from vePctor , microsimu
lation enables us to reconstitute all of the indicators that can be calculated from the individual data ex post,
without the need to programme the projection of these indicators beforehand.
The main drawback of the method is the stochastic nature of results, which stems from the random samp
ling used to simulate individual changes. Nevertheless, the stochastic nature of results is a more or less
of a problem depending on the type of results under consideration. The stochastic nature of microsimula
tion results will not have much impact on highly aggregated level indicators, even if the database used is
not very large. On the other hand, it will create much greater instability in changes in flow variables or vari-
ables relating to small subpopulations. In this case, there are two solutions. The first is to repeat the
simulations using separate samplings and to average the results, but this does not eliminate sampling ef
fects stemming from the composition of the initial sample. The second solution is to work on a broader base
of individual data. The running time of programs will be extended accordingly in both cases.
4 INSEE Studies no. 37, August 1999 80% of the kinship connections needed can be How a simulation is run
constituted with fulfilment of the age, sex and
educational attainment criteria. After that, theSimulating a year’s changes in the sample
criteria are relaxed progressively until 94% ofrequires several steps (see flow chart).
the matches required have been made. This
covers some 15,000 people, leaving another The process starts with "simple" life events:
10,000 with no connection to parents within the deaths, births, dissolution of households and
sample population. These individuals, who children moving away from home. We call
make up 27% of the total sample, corresponded these simple events because they are random
to individuals with no surviving parents. binary drawings from the sample where
probability is determined by demographic
Once this reconstitution has been completed,variables such as age, sex and waiting time
we have a core of demographic data for eachsince the previous event. The model then
individual: identification of parents, spouse simulates marriage or the formation of
and children living at home and children livingcouples, which is a more "complex" life
outside the household, along with the two usual event. The complexity comes up because this
demographic variables of age and sex. simulation calls for matching individuals.
After that, we simulate transitions in
This core of data is supplemented by employment status and, finally, we calculate
conventional socio economic variables takenoccupational income and retirement
from the information provided by the financialpensions.
assets survey, which are the school leaving age
(we preferred this variable to educational In addition, prior to making the yearly
attainment, which is harder to compare updates, or simulations, of these events, we
between generations), status within the calculate and store some overall data
household (head of household, spouse or corresponding to the standard output of the
child), employment status (labour force
participant with no distinction between
employed and unemployed at this stage ,
Simulation flow chartworking age but not in the labour force and
retired). We also include a variable for the
General parameters are calculated or readduration of employment.
Base of initial individual data is readA third block of data is made up of earnings or
occupational income. Current occupational
Period simulation loop
income comes directly from the survey data.
Output of statistics on the current state of the data But we also need data about past earnings in
base and possibly storage of database in its current
order to calculate future pension entitlements. state for later use
These data are reconstituted in a two step
process. First, each individual’s theoretical Projection parameters specific to the current year are
readearnings profile is derived from an earnings
equation in which sex, school leaving age and Individual simulation loop
duration of employment are the main predictor
Simulation of simple life events (deaths, divorces,variables. A fixed individual effect term is
births). A birth adds a new record to the database. Two
added to the theoretical profile so that the curvelists are drawn up of male and female marriage candi
datesmatches actual occupational income observed
in the survey. These backcasted curves were
Simulation of economic events: joining and leaving the
then adjusted to produce earnings profiles that labour force, wage increases, retirement and calcula
tion of pensionwere consistent with the actual earnings
profiles observed at the same dates (taken from
Formation of new couples from the lists of male and fe-Bayet, 1996). It should be mentioned in passing
male candidates previously drawn up
that the reconstituted earnings are not adjusted
Individual simulation loop for inflation. These data can then be used
directly to calculate pension entitlements using
Incremental increases in individual counters for age
the rates in force or estimated rates with and duration of employment
adjustment coefficients for past earnings.
These coefficients are not necessarily in line
with inflation trends.
INSEE Studies no. 37, August 1999 5model and sometimes we may even store thconcentration of medium sized fe amilies in
complete current state of the database, whichparticular.
enables us to make later use of detailed data for
any of the dates on which they were saved. An individual’s simulated birth adds a new
Illustrations of this are provided at the end of record to the database, which naturally
the article. At the end of the simulation loop donescribes the kinship connection between the
a given date, we update the individual counters new born child and its parents. At this step, we
for age and duration of the current employment also decide the new arrival’s school leaving
status. age. This variable depends on the ages at which
the parents’ schooling ended in order to
approximate the inherited element of
Individual and household demographics educational attainment. The school leaving age
is used later on to simulate access to the labour
Simple life events are all simulated by drawing market and occupational income.
random sequential samples while running a
simulation loop on the total sample population.Simulating marriages is a two step process.
The simulated year’s events are sequential andFirst, lists of male and female candidates for
take place in the order set by the program. Wmearriage are drawn up from the sample
assume that the actual order of events will not population. The lists are made in the same way
have much impact on the results of as for any other simple life event, using
year by year updating of simulated events. binomial drawings according to the
Simulating death does not raise any special age and sex specific probabilities of marriage.
technical problems. For individual i, death is Once the lists are complete, we pair the
simulated after a pseudo random drawing individuals on them using a procedure that aims
according to the sex and age-specific to reproduce a realistic distribution of age
probability of dying shown in the mortality differences between spouses. We also compare
table assumed to be applicable for da t. Thete school leaving ages so that matches reflect
tables are those used for INSEE’s forecasts social homogamy.
(Dihn, 1994). Death does not remove an
individual’s record from the database. All Simple sampling is used to simulate the
records are maintained until the end of the dissolution of households caused by the
simulation. Dead individuals’ records are break-up of couples or by children leaving
needed to maintain the kinship connections that home. The probabilities of a child moving out
may pass through a them, as in the case of of the parental home are taken from Bozon and
connections between siblings, for example. Villeneuve Gokalp (1994). The probabilities of
a couple breaking up match current divorce
At a later date, the way the program is set up rates and depend on the duration of the
should make it possible to complete marriage. The dissolution of a household
simulation of death with a simulation of changes the status of the person who was not
inheritance. This is another reason for the head of dissolved household and leads to the
choosing a database structure that simulatescreation of a new household. If divorced
kinship connections between parents and spouses meet the age criteria, they may start
their adult children living outside of the forming new couples the following year under
parental household. the same assumptions applied to other single
Births are simulated according to the
probability of women having a first child or
additional children. The probability of givingEmployment and earnings
birth in the year depends on the number of
preceding births and the time elapsed sinceIn principle, individuals’ moves to join or
the most recent birth. This simulation doeswithdraw from the labour force could be
not match the findings of conventional simulated just as easily as simple life events, as
demography forecasts exactly, since the latterlong as we can establish the probabilities of
are based on simple age specific fertility such moves according to such variables as sex,
rates with no distinction of birth order. age and education. This approach is being
Nevertheless, we chose this method becausedeveloped for the new version of the model
it enables us to simulate the final distribution (Bonnet, 1997), but it is not the one used in the
of families by size more faithfully, and thefirst version of the model discussed here.
6 INSEE Studies no. 37, August 1999 Instead, our procedure fits in directly with theResults with regard to the overall
assumptions that "official" labour force ecastsfor demographic structure
generally make about statistical trends. We start
by defining the target labour force participation In line with usual practice, the projection was made
rates for the period being simulated. For men, out into the very long term future, up to the 050. year 2
this is merely the age specific rate, but for This is not because there is any special focus on such
women the rates are specific for age and the a distant future or because we attribute a specific
number of children at home. We use the rates predictive value to model in the very long run.
observed in 1990 and assume that they will Instead it is done to test the behaviour of the model
prevail throughout the forecast period. and the type of steady state on which it converges.
However, we could easily have come up with This is actually a way of validating the model.
variants by referring, for example, to the latest
forecasts published by INSEE and DARES If we start by looking at the change in aggregate
(Brondel et al., 1996). population count, we see that the stochastic nature
of the simulation does indeed affect its components
Then, at date t, we measure the ex ante (see Chart I). But we still see a very clear trend
participation rate of a given age group, towards more deaths and slightly fewer births each
prior to any moves to join or withdraw from year, which leads to a falling trend in net natural
the labour force. Roughly speaking, this is change in the aggregate population. The curve of
just the participation rate of the same groupthe trend falls between those predicted by
one year earlier, when it was one year conventional methods using two fertility
younger, adjusted for deaths and, in the case assumptions of 1.8 and 2.1 children per woman
of women, for changes in the number of (Dinh, 1994). In the same way, microslationimu
children since the previous year. We then produces an aggregate population count that
simulate just enough random moves into or falls between the two previous scenarios (see
out of the labour force to arrive at the targChart II). This time, the fet act that we are looking
rates from the ex ante rates. When
interpreting the findings, it must obviouslyChart I
be remembered that this procedure does not Projected population change
account for intra period changes and onlyThousands
reflects net change from year to year, which
means that total mobility is bound to be
The procedure for forecasting earnings is an
extension of the procedure described earlier
for the backward projection of past earnings.
The same earnings equations with fixed
individual effect terms are used to simulate
changes in earnings with age. This means that
individual career paths are perfectly parallel
with each other for people of a given
generation and educational attainment,
Chart II
except for deviations caused by withdrawals
Total population change
from the labour force. The new version of the
model now being developed corrects this
assumption by allowing for random changes
in earnings paths (Colin, 1997).
In addition to the predicted values of these
equations at future dates, there is an overall
productivity growth trend (variants with
different values for this trend are presented in
the scenarios discussed below) and an
inflation term, since the earnings data used to
calculate pension entitlements are not
adjusted for inflation, as is also the case for
backwards projections of past earnings.
INSEE Studies no. 37, August 1999 7Chart III at level data and not flow data practically
Population structures by (annual) age eliminates the stochastic nature of the
between 1991 and 2020 projection.
A – In 1991 However, some instability arises when we look
at the breakdown of aggregate population by
age (see Charts III A and III B). Nevertheless,
this instability still does not prevent us from
seeing the usual movement towards a more
top heavy age pyramid as the large generations
aged up to 45 years in 1991 move up the
pyramid over the thirty years to 2020 and are
replaced in the lower part of the pyramid by
slightly smaller generations.
Microsimulation also provides more detailed
projections of households. The usual method
for making these projections is called derived
forecasting. Projections are based on the fact
that there are exactly the same number of heads
of households as there are households. The
B – In 2020
probability of being a head of household is
assumed to depend on age and sex. ThisThousands
produces rates that merely have to be applied to
the predicted age and sex structures of the
population in order to come up with the number
of households and average household size.
The dynamic microsimulation proposed in this
paper enables us to make the same projection of
the number of households (see Chart IV). The
results are closely in line with those of the latest
projections made using the derived forecasting
method (Louvot, 1993). Yet microsimulation
also produces a very detailed prediction of
household composition. For example, we
predict household composition according to
size (see Chart V), which shows the expectedSource: microsimulation
Chart V
Chart IV Projection of distribution of households
by sizeProjection of number of households
% of householdby sexe of head of household
Source: microsimulation
8 INSEE Studies no. 37, August 1999 rise in single person households. Microsimulation the age of 65 is still 37.5 years. In the second
also enables us to decompose the factors variant, there is a gradual shift to calculating
contributing to this change. For example, we can entitlement on the basis of the 25 best years and
produce an a posteriori decomposition of the requiring 40 years of service. We assume that
effects of changes in widowhood, which comesthe effects of the reforms will not change
later and lasts longer, and the effects of changing current behaviour patterns regarding taking
marriage and divorce rates. retirement. However, it would be interesting to
introduce variations on this assumption in
future scenarios and an experiment along these
Application for pension forecasting lines has been proposed (Pelé, 1997).
The conventional indicator for measuring theWe assume that pensions paid by the fund will
distortion of the age pyramid mentioned abovekeep pace with inflation in both scenarios, since
is change in the ratio of population aged 60 and this was the practice before the 1993 reforms.
over to the population aged between 20 and 60 Index linking also applies to all the other
years (see Chart VI). The fact that the ratio is parameters for calculating entitlements under
highly aggregated practically eliminates the the general pension plan, such as revaluation
stochastic nature of the simulation. This ratiocoefficients for past earnings and the social
virtually doubles in about fifty years. This security earnings ceiling. The model also
doubling is mainly attributable to the increasesimulates survivor entitlements under the rules
in the ranks of the over-sixties. In fact, the now in force and the minimum old age pension,
working age population in the demographic which we also assume is index linked.
scenario we have chosen here only shows a
slight decline. If we assume there is no productivity growth
and no pension plan reform, there is a very large
What will this change mean in terms of increase in the equilibrium contribution rate for
equilibrium contribution rates or pension our fictitious pension plan. We have calculated
benefits under a given pension plan? Our this rate by dividing aggregate pension
projection does not relate to a real pension plan, payments by aggregate gross occupational
but to a single pension plan that we assume income. The resulting increase is more rapid
covers the whole population. This plan followsthan that in the demographic ratio (see Chart
the same rules as France’s general pension plan VII). This is because a growing proportion of
with two variants: one with and one without thethe population is accumulating more and more
effects of the reforms introduced in 1993. In thepensionable years of service under the pension
first case, the reference wage used to calculate plan. The increase is smaller if we continue to
pension entitlements is still the average wage assume there is no reform but we factor in a 1%
up to the social security earnings ceiling for theincrease in occupational income each year. The
10 best years and the number of years of service order of the magnitude of the effect is easily
required for entitlement to a full pension before explained. Pensions follow earnings with a lag
Chart VIIChart VI
Indicator of change in the overall contributionVery long term change in the ratio of persons
rate: impacts of productivity assumption andaged 60 or more to persons aged 20 to 60
the 1993 reform (base 1990 = 100)
Source: microsimulation. Source: microsimulation.
INSEE Studies no. 37, August 1999 9of about 20 years since pension entitlements are in 1991, is attenuated by generation effects.
calculated on the basis of the 10 highest paiTdhis means that today’s pensioners with low
years, which for the sake of simplicity we benefits (pensioners who retired in the early
assume are the last 10 years at work, and nineteen seventies) are being replaced by
because average seniority in the firm is aboutgenerations of pensioners now going into
10 to 15 years upon retirement. Each annualretirement with better benefits.
percentage point of growth in occupational
income therefore produces a gap of about 20%A further decline is created by the 1993
between the average pension and the averagereforms. These reforms do not concern the
wage and thus an equivalent drop in the oldest pensioners, who will still be unaffected
apparent contribution rate required for by the changes in entitlements in 2020.
instantaneous equilibrium of the pension However, the youngest pensioners will see their
system without cutting benefits. relative income drop by about 5%, which is in
line with the saving observed in equilibrium
In comparison to these trends, the reform contribution rates.
introduced in 1993, which mainly involved the
switch to calculating pension entitlement on the
basis of the 25 highest paid years, produces a Projecting pension inequality
savings of about 5 percentage points in the
contribution rates in the very long run. ThisThe preliminary results suggest that the model
order of magnitude of the effect is more or less works well for projections of conventional
consistent with the other figures available aggregates and for evaluating one particular
(Commissariat général du plan, 1995; dimension of pension inequality, which is
Hamayon, 1995), at least up through the inequality between age groups or generations.
intermediate period until 2020. It is also fairly easy to use the model to evaluate
inequality between the sexes, as long as we are
But, no matter what their origin, savings in able to make stable assumptions about
contribution rates inevitably lead to changes inwomen’s labour force participation rates and
the allocation of resources between age groupsoccupational earnings.
and a weakening of pensioners’ relative
economic position. If there is a rise in This leaves the unresolved question of vertical
productivity, the replacement rate will declineinequality in pensions, meaning inequality
(since pensions are caculated on the basis of a between people of the same age and same sex
sequence of past earnings and not the last wageup and down the social ladder, and how this
earned) and the growing gap between pensioninequality will be affected by various reform
payments and wages will affect the oldest
pensioners most severely. On the other hand,
the switch to the calculating entitlement on the Chart VIII
basis of the 25 highest-paid years will Men’s income by age (wages and/or pensions)
especially weaken the relative position of the in 1991 and 2020 with and without reform, with
youngest pensioners, at least at first, since the 1% annual increase in occupational income*
change in rules only affect payments to new
The change in the relative situations of income
earners and pensioners can be illustrated by
relative income indicators for each age group.
Such indicators can be obtained by
standardising age income curves to the same
average of 100, for all dates and all projection
assumptions (see Chart VIII). We can see that
the savings in contribution rates produced by
1% annual growth and no reform between 1991
and 2020 corresponds to a preliminary decline
* The chart shows the curve of men’s average income by age.
in the pensioners’ relative position. However,
It combines basic pensions with occupational income. The cur
we should mention that the decline in the ves are centred on an average value of 100. Supplementary
pension benefits are not included in the simulation.relative position of the oldest pensioners in
Source: microsimulation.2020, compared to that of the oldest pensioners
10 INSEE Studies no. 37, August 1999