Income Trajectories in Retirement in Portugal
Maria Clara Murteira
Faculdade de Economia da Universidade de Coimbra
Av. Dias da Silva, 165
3004

512 COIMBRA
–
PORTUGAL
e

mail:
murteira@fe.
uc.pt
1
ABSTRACT
The aim of this paper is to analyse the income trajectories in retirement of
pensioners receiving a state pension in Portugal. The availability of longitudinal data
regarding individual incomes allows us to examine the income dynamics
both on
retirement and during the retirement period. The empirical research developed below is
based on longitudinal data from the social security administration files on wages and
retirement pensions. It has been used a dataset of approximately 53500 reco
rds relating
to old age pensioners: men and women of four generations who retired in 1985, 1990,
1995 and 2000. The individual records contain information on age, sex, contribution
periods, the date of the first contribution, the date of retirement, gross
earnings and
pension incomes.
First the analysis is developed following the income trajectories of men and
women of four generations considering the hypothesis that the inequalities in the current
level of pension income may be due to a generational effec
t. The individuals of different
generations faced different circumstances in their life courses as they lived in different
socio

economic environments. This fact may have had an influence on the level of
pension received during retirement.
Second the inco
me trajectory of each group of pensioners is followed taking
three variables into account: the final remuneration, the first pension income and the
pension in December 2001. In the first part, I focus on comparisons of the income
distributions of the three
variables for each group of pensioners (the individuals are
categorised according to both sex and generation) using dominance analysis. The
Lorenz criterion of dominance is used for making inequality comparisons. Since the
means of the income distribution
s change I also follow the first and second order
dominance criteria to compare the income distributions. Then I examine income
mobility within each group on retirement and during the retirement period. In the
second part, I follow the income trajectories
both on and during retirement for each
group in order to examine the changes in relative income positions, while taking
average earnings in Portugal as a reference.
2
1.
Introduction
The aim of this paper is to analyse income trajectories in retirement for
pen
sioners receiving state pensions in Portugal. The study of the pension income
received by the pensioners of today is regarded as fundamental, especially in the case of
Portugal, because most retired people get very low payments, for various reasons: low
re
corded levels of earnings, incomplete contributory history, failure to record earnings,
etc.
since the pension system has not yet reached a state of maturity.
The following research is based on a dataset provided by the Centro Nacional de
Pensões (Nationa
l Pensions Centre). The dataset includes nearly 53500 records relating
to old age pensioners: men and women who retired in 1985, 1990, 1995 and 2000. The
data are individual and longitudinal, and they include records of pay and pensions (first
pension and
pension in 2001) and some characteristics of the pensioners’ contribution
histories.
Based on this source of information, two themes were examined. First, the
income trajectories of men and women of different generations, contemporaneous in
December 2001,
were analysed. The hypothesis that inequalities at the level of the
pension processed on this date may be due to a generational effect is accepted.
Secondly, the income dynamics for the pensioner groups in the transition to retirement
and during the retir
ement period were studied. First, the income change in these two
income transitions was examined following dominance analysis and income mobility
analysis. Next, the significance of the income fall that occurs on retirement and the
evolution of the pension
level during the retirement period were assessed on the basis of
a relative income concept.
2.
The equal treatment of generations by the pension system
Economic studies often treat generations as statistical entities, defined by precise
references

cohor
ts of individuals born in the same year

and not as historic entities, as
if the life courses took the same pattern, from generation to generation. Even
longitudinal studies very often do not incorporate the historic perspective, ignoring the
relationship
between individual times and the collective time. Life courses are therefore
deeply influenced by the social history in which they are inscribed. Each generation is
born in its own time, it knows specific circumstances and leaves its successors a
3
differen
t world. A generation may be defined as a community of time and place.
The fact that generations have different destinies has been remarked on by a
number of authors. Kant and Herzen have observed that the efforts of preceding
generations revert unilatera
lly to succeeding generations, seeing a form of injustice in
this fact. Rawls takes a different view: he does not see the different fate of generations
as unjust, but a natural fact, inherent to human development. Justice is related, rather, to
“how insti
tutions deal with natural limitations and the way they are set up to take
advantage of historical possibilities” (Rawls, 1972: 291)
1
.
If a generation is defined as a community of time and place, the circumstances
that mark out the economic and social cont
ext in which each generation is inscribed are
environmental aspects, which are beyond the control of individuals, but which define
the range of possibilities and alternatives available to them. Accepting that the
intergenerational context is marked by the
inequality of paths, opportunities and
achievements, it is hard to find a basis on which to defend the equal treatment of
generations by the pension system. The changes in the variables (demographic,
economic and institutional) that affect the environment
in which the life courses occur
and in individual behaviours can result in considerable differentiations in average
pension levels between generations.
On the other hand, not all the features of an individual path can be ascribed to
the collective past of
the generation belonged to. In addition to the inequalities that can
be seen between succeeding generations, intra

generational inequalities also occur,
since the individuals in a generation share a social and historic context, but are not an
undifferenti
ated whole. The inter

individual differentiation within a generation can be
more telling than the inter

generational differentiation. The unit of analysis relevant to
the study of inequalities is not the generation, but the individual.
1
This is why justice between generations is a singular philosophical
object which, according to the
author, “[it] subjects any ethical theory to severe if not impossible tests” (Rawls, 1972: 284).
Fundamentally, relations between successive generations pose an essential problem to ethical theories,
which are not found in t
he setting of direct interpersonal relations: the non

reciprocity of rights and duties
that raises the problem of responsibility in relation to future generations. “We can do something for
posterity but it can do nothing for us” (Rawls, 1972: 291).
See als
o Hans Jonas
, Le principe
responsabilité, Une éthique pour la civilisation technologique
.
4
3.
The income dynam
ic in the transition to retirement and during retirement
The income dynamics for the pensioner groups in the transition to retirement and
during the retirement period were studied. In order to develop this analysis, the income
trajectories in retirement
of pensioners receiving a Portuguese state pension are
followed. The availability of longitudinal data from the social security administration
files on earnings and retirement pensions allows the analysis of the income dynamics
both on retirement and durin
g the retirement period. The income trajectory of each
group of pensioners (the individuals are categorised according to both sex and
generation) is followed, taking three variables into account: the final remuneration, the
first pension income and the pen
sion income in December 2001.
First, the change occurring in the income distribution
2
of each subgroup of
individuals in these two income transitions was examined following dominance analysis
and income mobility analysis. Next, the significance of the inc
ome fall that occurs on
retirement and the evolution of the pension level during the retirement period were
assessed on the basis of a relative income concept
3
(the relative income position). The
relative income position is defined as the average levels of
earnings (or pensions) of
each group divided by the average earnings in the economy in the same period.
In this
way the effect of the two income transitions on their relative income position is
analysed.
4.
The database used
The empirical research develop
ed below is based on longitudinal data from the
social security administration files on wages and retirement pensions. It has been used a
dataset of approximately 53500 records relating to state pensioners: men and women
who retired in 1985, 1990, 1995 and
2000. Although I had all the records relating to the
retired people in those years, I have used only the records relating to the individuals
who retired with the legal age of retirement. The pensioners considered in each group
were born and retired the sa
me years.
2
In this part we considered real incomes. Values for remunerations and pensions have been referenced to
December 2001.
3
In this part we considered nominal incomes.
5
The individual records contain information on age, sex, contribution periods, the
date of the first contribution, the date of retirement, gross earnings and pension
incomes.
The data used come from the information collected regularly by the Centr
o
Nacional de Pensões to calculate pension benefits. The amount of earnings is that
declared by the employer or by the beneficiary (in the case of the self

employed) for the
purpose of calculating contributions (gross remunerations); the amount of the pens
ions
corresponds to the sums actually processed and received (gross pensions).
5. Methodology
5.1. The income trajectories of different generations
First, the longitudinal evolution of earnings is analysed, to compare the income
trajectories of the diff
erent generations. I followed the evolution of the remuneration
levels, the reference remuneration levels (taken into account for calculating the amount
of the pension for the statutory pension
4
),
the first pension and the fixed pension in
December 2001,
of the men and women in the generations considered.
Next, I followed a cross

section analysis, combining all the pensioner groups, to
compare the average pensions of the various groups at one moment when they are
contemporaneous, December 2001. The fact th
at life courses occurred in different
historical periods, marked by different circumstances, could explain the disparities in
the situation between generations with respect to the average amount of resources
available in retirement. To examine this issue,
the independen
t

samples T tests were
carried out to compare difference in average pension levels (in December 2001) for
different groups.
Finally, to identify how important inter and intra

generational inequalities are,
the eight pensioner groups were gat
hered. The inequality of the distribution of the
pension on December 2001 was measured and decomposed by groups, based on the
Theil indexes of inequality, T and L. Theil has shown that in a population consisting of
individuals who are grouped in a mutually
exclusive way (in our case, by generation,
sex, etc.), overall inequality may be expressed as the sum of two terms: the
“within

group” component, or the weighted sum of the inequality value of the various
4
The statutory pension results from applying the calculation rules.
6
groups; and the “between

group” component, which a
rises from variations in the
average income levels between groups.
When the population consists of
n
individuals, T and L are translated by the
following formulas:
n
1
i
i
n
1
i
y
ln
n
1
L
e
yi
ln
yi
n
1
T
The same indexes can be translated by the follo
wing expressions, according to
the Theil decomposability:
ln
s
T
s
T
G
1
g
g
g
G
1
g
g
g
and
ln
n
n
L
n
n
L
G
1
g
g
g
G
1
g
g
g
within

group ineq.
between

group ineq. within

group ineq. between

group ineq.
In the expressi
on for T, the weight appearing in the between

group inequality
component is the part of the income of the group,
n
n
s
g
g
g
, and T
g
stands for the
Theil (T) index of group
g
,
g
=1,..., G. In the expression for L, the weight appearing in
the within

group is the part of the population of each group,
n
n
g
, and L
g
is the Theil (L)
index of group
g
,
g
=1,…,G. We can see that the total inequality may be expressed as the
sum of the two terms: the inequality between groups (inequality betwee
n sexes and
generations), and the inequality that is found within each group (within

group
inequality).
5.2. The income dynamic in retirement
To study the income dynamic in pensioners’ retirement, we evaluated the
distributional effects occurring in the
transition to retirement and during retirement.
Comparisons are drawn between the distribution of the three variables (last
remuneration, first pension and pension in December 2001), of each group of
individuals, using dominance criteria. The income mobil
ity within each group is also
examined.
7
Then the evolution of the relative income position of each group in the transition
to retirement and during retirement is analysed, taking as reference the average
remuneration level in the economy.
5.2.1. The inc
ome dynamics in the transition to retirement and during retirement
A) Dominance analysis
To analyse how does the income distribution change (of each group) in the
transition to retirement and during retirement, first the Lorenz dominance criterion was
use
d to establish inequality comparisons. Bearing in mind that the distributions being
studied have different levels of average income, they were then compared using first
and second order dominance criteria.
B) Income mobility
Income mobility in the two in
come transitions was also analysed. Three mobility
concepts were used: mobility as time independence; the aggregate income movement,
and mobility as equalization of longer

term incomes.
Time independence
A measure of income mobility could be calculated on
the basis of the existing
correlation between the initial and final income (or logarithm of income). Origin
dependence expresses the correlation between the initial income and the final income of
the individuals of each generation and sex, making it possi
ble to see if the inequality of
the initial situations is attenuated by the income mobility effect, or if, on the contrary,
the initial situations continue to determine the final situations. Origin independence
would be desirable if it attenuates the inequ
ality of an initial situation.
The time independence measures calculated are based on the Pearson correlation
coefficients. A correlation coefficient is an indicator of income mobility: the nearer its
value is to zero, the greater the income mobility; a va
lue close to one would express
income immobility.
The correlation coefficients and the mobility measures derived from them are
used to analyse the dependence of the first pension in relation to the last remuneration,
and the dependence of the pension in 2
001 in relation to the first pension and the last
remuneration.
8
The aggregate income movement
The analysis of the aggregate income movement was developed by Fields and
Ok (1996, 1999a). The transformation of the distribution from x into y is seen as the
transformation of a personalised vector of incomes of n individuals, x, at moment
t
in
the income vector of those same individuals, y, at moment
t+k
. The total income
movement may be given by the sum of the absolute values of the individual changes of
inc
ome (Fields and Ok, 1996):
n
n
1
i
i
i
1
n
R
y
,
x
y
x
)
y
,
x
(
d
Per capita
income change measures are used to assess the aggregate movement
of income, because they make it possible to compare groups of different sizes. The
measures of income changes
as a percentage of initial income are also used, because
they report the total movement of income in relation to the initial income:
n
/
y
x
)
y
,
x
(
m
n
1
i
i
i
1
n
n
1
i
i
n
1
i
i
i
1
n
x
/
y
x
)
y
,
x
(
p
By using these measures we can identify the origi
n of mobility: if this results
from exchanges of position between individuals (within each group), or from structural
factors (like a rise or fall in total income). Measures m
n
1
and p
n
1
are decomposed to
distinguish the two sources of mobility. The measure
s of aggregate income movement
satisfies the additive decomposition, and so its total value is equal to the addition of the
component given by the transfer of income between individuals (exchange) and the
component given by the rise or fall in income (stru
ctural).
When the income transition involves growth of the total income, as happens in
the transition of the first pension to the 2001 pension, decomposition for all groups will
be as follows:
)
y
,
x
(
G
n
1
)
y
,
x
(
T
n
1
m
1
n
)
y
,
x
(
G
x
1
)
y
,
x
(
T
x
1
p
n
1
i
i
n
1
i
i
1
n
with
xi
yi
:
i
i
i
)
y
x
(
.
2
)
y
,
x
(
T
and
n
1
i
i
n
1
i
i
x
y
)
y
,
x
(
G
.
If an income transition involves a fall in total income, as happens in the
transition from the last remuneration to the first pension, we get:
9
)
y
,
x
(
'
G
n
1
)
y
,
x
(
'
T
n
1
m
1
n
)
y
,
x
(
'
G
x
1
)
y
,
x
(
'
T
x
1
p
n
1
i
i
n
1
i
i
1
n
,
with
yi
xi
:
i
i
i
)
x
y
(
.
2
)
y
,
x
(
'
T
and
n
1
i
i
n
1
i
i
y
x
)
y
,
x
(
'
G
.
Then the measures of
per capita
income movement are calculated, where this is
expressed in logarithms (Field and Ok, 1999a),
n
/
x
ln
y
ln
)
y
,
x
(
m
n
1
i
i
i
2
n
Mobility as equalizati
on of longer

term incomes
We also used the measure of mobility as equalization of longer

term incomes, P,
developed by Fields (2002). Based on personalised income vectors, the index shows the
extension to which mobility causes incomes over the long term to
be less unequally
distributed than in the initial year. It is taken that long

term income corresponds to the
average income of the initial and final periods under analysis. The value of P is given
by:
)
y
(
I
)
m
(
I
1
P
1
LC
LC
,
where I
LC
is an inequality index
that verifies the Lorenz properties. To determine P, the
inequality index associated with the average income distribution of the initial and final
periods and the inequality index associated with the initial period are calculated. The
maximum value of P w
ill be 1, obtained when I
LC
(m) =0, that is, when the income
mobility produces the perfect average income equalization of the periods being
analysed. The index, P, is equal to 0 when income mobility has no effect on the
equalization of the average income (I
LC
(m)= I
LC
(y
1
)). The index, P, can be negative
when income mobility produces a greater differentiation of the average income (I
LC
(m)=
I
LC
(y
1
)). To see whether income equalization occurs in each of the income transitions
considered, the inequality indexes (
Gini and Theil indexes) were calculated for the
initial distribution and for the average income distribution of the initial and final
periods.
10
5.2.2. The relative income position
Afterwards the relative income position is examined for each group, ta
king as
reference the average remuneration in the economy. The evolution of the relative
income position of each group of individuals in the transition to and during retirement is
analysed. This allows us to compare the relative income of each group at dif
ferent
points in time. We used the Average Remuneration (base)
5
for the total men and women
as a term of reference. The relative income position (RIP) is thus defined:
RIP
i
t
=
t
t
i
)
W
(M
on
remunerati
Average
y
The purpose of this procedure is to ass
ess the significance of both the fall in
income that occurs on retirement and the evolution of income during retirement. In this
way we can see the effect of the two income transitions on the relative situation of
pensioners, since the evolution of their i
ncome is analysed in relation to the average
remuneration in the economy.
The evolution of minimum pension levels is also analysed in relation to the same
variable.
6. Results
6.1. The income trajectories of different generations
The evolution of the a
verage remunerations, the reference remuneration
(remuneration considered for the calculation of the pension
6
), the statutory pension, the
first pension and the pension in December 2001, for the men and women of the
generations considered, is shown in the
charts below.
5
The definitive value of average remuneration in 2002 had not been determined when this article was
prepared. The figure given is an approximate calculation of the effective value, base
on the amount
estimated by DEEP, in September 2004, for average earnings in 2002 (M+W), for mainland Portugal.
6
To calculate the reference remuneration, up to 1994, were considered the non

revalued remunerations of
the best five years in the last ten wor
king years. After 1994, to calculate the reference remuneration the
remunerations revalued of the best ten years of the last fifteen were considered.
11
Chart 1A Average values for earnings, reference remunerations, first pension
in 2001
Men
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
110000
120000
130000
140000
150000
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
srr
pe
pmr
p01
year
earnings and pensons  average values
1985
1990
1995
2000
Chart 1b Average values of remunerations, reference remuneration, first pension and pension
in December 2001
Women
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
110000
120000
130000
140000
150000
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
srr
pe
pmr
p01
year
remunerations and pensions  average values
1985
1990
1995
2000
12
The series of values for the average remunerations of each generation is
followed by a point that represents the respective nominal reference remuneration
(which serves as the calcu
lation base for the pension). The corresponding real reference
remuneration is shown later, designated “srr”, followed by the representation of the real
average statutory pension, “pe”, the real average first pension, “pmr” and the average
pension in Decem
ber 2001, “p01”.
The comparative analysis of individuals of the same sex from different
generations allows us to conclude that the older generations were in a relatively worse
situation in 2001, for a number of reasons: remuneration levels in the years pre
ceding
retirement; contributory careers, and regulatory aspects. These circumstances all
influenced the amount of the first pension and the subsequent income trajectory. The
older generations received lower real remuneration in the years before they retire
d, and
so they had a lower average reference remuneration
7
. This fact, together with the lower
contributory careers, explains the lower average values of the first pension
8
. The
subsequent indexing of pensions did not have any effect on the relative classi
fication of
the groups, which was the same at the end of 2001.
The gender differentiation of paths among pensioners retiring in each year, was
noted. The men and women retiring in the same year exhibited quite distinct paths in
terms of contributory career
s, remuneration levels and pension levels. The men always
had substantially higher average reference remuneration and first pension levels than the
women. At the time they retired, on average, the women received a pension
significantly higher than the valu
e of the respective statutory pension, thanks to the
rules that guarantee minimum levels.
The independent

samples T tests
were carried out to see if there are significant
differences in the average pension levels among the groups of individuals in December
2001. Table 1 in Appendix 1 summarises the results. The tests show that the different
7
This aspect is partly due to th
e fact that, up to 1994, the remuneration used as the pension calculation
base was not revalued, which has put the generations that retired before then in a relatively worse
situation in relation to those who have retired since that year. In addition, the
steady growth in real
remuneration in the period under analysis has favoured the generations retiring later.
8
The type of data used means that certain prudence is required when interpreting the results. Some years
after retirement, we find individuals fro
m the generation with lower mortality rates and higher incomes
included in the group of individuals belonging to the older generations. This effect is more significant the
older the generations.
13
means between groups of men of different generations are statistically significant. In the
case of women, the equal average pension hypothesis for retired females is onl
y
accepted in 1990 and 1995; all the other differences are statistically significant. The fact
that life courses have occurred in different historic periods, marked by different
circumstances may explain the differences between generations in terms of the
average
amount of resources available in retirement. The difference in means between groups of
retired men and women in each year are statistically significant
9
.
Finally, the eight subgroups of pensioners were gathered to measure and
decompose the inequali
ty of pension distribution at a point in time when they are
contemporaneous (December 2001). The values of the Theil (L and T) indexes were
calculated for pension distribution at this time and were decomposed by subgroups.
The joint observation of the gro
ups of men and women (Table 2a in Appendix 1)
shows that the total inequality is due mainly to within

group inequality (76.2% of L or
82.5% of T) and a lesser part to between

group differentiation (23.8% of L or 17.5% of
T). As the within

group inequality
component is large, this means that the individuals of
each sex and generation share a social and historic context but are not an homogeneous
whole. The between

group component, despite being relatively small, nevertheless has
some significance.
This decom
position does not enable precise conclusions to be drawn about
inequality between generations, since the between

group inequality also expresses the
inequality from generation to generation. So it is convenient to compose new groups of
individuals from dif
ferent generations, grouped by sex. Tables 2b and 2c in Appendix 1,
give the inequality indexes calculated and the respective decomposition by generation.
For the men, the aggregate inequality can be ascribed almost exclusively to
within

group component
(95.6% for L and 95.6% for T) and only a very small part to
between

group component (5.8% for L and 4.4% for T). For the women, the aggregate
inequality can be ascribed almost solely to the within

group component (96.7% for L
and 97.7%for T) and only a ver
y small part to between

group component (3.3% for L
and 2.3% for T). In both cases, the aggregate inequality in pension distribution in 2001
9
These results reveal important inequalities of paths and s
ituation between retired men and women in
each year. The gender difference was a clear expression of intra

generational inequality. In the case
studied here, we can only talk about gender inequality in the same generation in 2000. The reasoning does
not ap
ply to those retiring in other years, since men and women retiring in other years do not belong to
the same generation as the legal minimum retirement age was different for men and women.
14
is attributable, above all, to within

group component, with only a small part attributable
to between

group compone
nt (generational).
The results confirm that the male and female groups of each generation are not
all undifferentiated, and that it is within

group inequality

which expresses the inter

individual differences of situation

that determines the greater pa
rt of total inequality.
The unit of analysis relevant for the study of inequalities does not appear to be the
generation.
6.2. The income dynamic in retirement
6.2.1. The
dominance analysis and income mobility analysis
A) Distributions Comparisons accord
ing to dominance analysis
The Tables below summarise the results inequality comparisons based on the
Lorenz dominance criteria and distribution comparisons based on the first and second
order dominance criteria.
Table 1
–
Inequality comparisons by the Lor
enz dominance criteria
Lorenz dominance criteria
ur

pp
pp

p01
ur

p01
1985
H
p01
L
pp
p01
L
ur
M
pp
L
ur
p01
L
pp
p01
L
ur
1990
H
p01
L
pp
p01
L
ur
M
pp
L
ur
p01
L
pp
p01
L
ur
1995
H
p01
L
pp
p01
L
ur
M
pp
L
ur
p01
L
pp
p01
L
ur
2000
H
pp
L
ur
p01
L
pp
p01
L
ur
M
pp
L
ur
p01
L
pp
p01
L
ur
(a)
ur

last remuneration; pp

first pension; p01

pension in 2001
The inequality comparisons
according to the Lorenz dominance criteria do not
allow an inequality ranking of the distributions of the last remuneration and the first
pension for men retiring in 1985, 1990 and 1995. For the other groups, inequality
decreases with the transition to ret
irement. The transition to retirement involves,
however, a fall in average income. So, the comparison of the distributions of the last
15
remuneration and the first pension are inconclusive according to the first and second
order dominance criteria.
During th
e retirement period, inequality in the pension distribution of all the
groups falls and real average income rises. The pension in 2001 has first order
dominance over the first pension and, therefore, second order dominance.
Table 2

Comparison of the di
stributions by the first and second order dominance criteria
1
st
order dominance criteria
2
nd
order dominance criteria
ur

pp
pp

p01
ur

p01
ur

pp
pp

p01
ur

p01
1985
H
p01
DPO
pp
p01
DSO
pp
M
p01
DPO
pp
p01
DSO
pp
p01
DSO
ur
1990
H
p01
DPO
pp
p01
DSO
pp
M
p01
DPO
pp
p01
DSO
pp
p01
DSO
ur
1995
H
p01
DPO
pp
p01
DSO
pp
M
p01
DPO
pp
p01
DSO
pp
2000
H
p01
DPO
pp
p01
DSO
pp
M
p01
DPO
pp
p01
DSO
pp
It was also found that the pension distribution in 2
001 is less unequal than the
distribution of the last remuneration, for all the groups. Bearing in mind the evolution of
average income, however, the dominance criteria allows us to conclude that the 2001
pension only exhibits second order dominance over t
he last remuneration for women
retiring in 1985 and 1990.
B) Income mobility
Time Independence
The results relating to the analysis of time independence can be found in Appendix
2, in Tables 1a and 1b. All the correlations (of incomes or the logarithm of
incomes) are
found to be statistically significant, and so, in all cases, the null hypothesis of statistical
independence can be rejected, with a high degree of probability. This means that time
dependence or reduced income mobility may be an issue in thr
ee cases: between the
first pension and the last remuneration; between the pension in 2001 and the first
pension, and also between the pension in 2001 and the last remuneration. These results
16
suggest that the observable inequalities in pension distributio
n

of the first pension and
the pension in 2001

within each group under analysis, reflect the inequality in the
remuneration distribution.
The correlation coefficients between the last remuneration and the first pension
and between the first pension an
d the 2001 pension are smaller for the women. A
greater proportion of women get far lower pensions, and frequently benefit from a series
of redistributive mechanisms designed to raise the levels of the very lowest pensions: as
with rules that establish min
imal levels for pensions and periodic or extraordinary
increases that guarantee a higher relative growth for the lowest pensions. These
mechanisms help to reduce the dependence of final income from the initial income.
Aggregate income movement
The result
s of the analysis of the aggregate income movement are summarised in
Tables 2a and 2b in Appendix 2.
In the transition to retirement the
per capita
income flux was more significant
for the men than for the women retiring in each year.
Per capita
income mov
ement is
less for the older generations. Income flux as percentage of initial income has quite
significant values in the transition to retirement, representing 34% and 49% of the
average amount of the last remuneration in the case of men and between 49% an
d 69%
of the average value of the last remuneration for women. Income movement as a
percentage of initial income is more significant for the women and for the older
generations. The measure m
n
2
expresses a high income flux relative to the amount of the
las
t remuneration, more significant in the case of women and for the older generations.
The decomposition of aggregate income movement shows the structural effect
caused by the fall in real income in the case of men and the presence of a significant
exchange
component in the case of women, due to the redistributive effects caused by
the regular improvements that raise the pension up to the minimum level.
In the income transition that occurs during the retirement period, the
per capita
income flux is more sign
ificant in the older generations, which was expected, since the
periods elapsing between the observations of the two variables differ according to the
generation. Income movement as a percentage of the initial amount (first pension),
varies as a function o
f the date when the pension started, and is higher in the older
generations. The women retiring in each year exhibit a higher income movement as a
percentage of the initial pension amount than men retiring in the same years. The
17
measure m
n
2
expresses a rel
ative income movement that is more significant in the older
generations than was expected. The indicator is higher in the female groups than in the
male groups who leaved the labour force in each year.
Income movement, either
per capita
or as a percentage
of initial income, is
fundamentally the outcome of the structural component

the global increase in income
that occurred between the receipt of the first pension and the year 2001
–
being the
exchange component very small.
Mobility as equalization of
longer

term incomes
To see if income equalisation occurred in each of the income transitions
considered, the same inequality indexes (the Gini and Theil Indexes) were calculated for
the initial distribution and for the average income distribution in the i
nitial and final
periods. The values of P
G
, P
T
referring to the two income transitions are given in Tables
3a. and 3b. in Appendix 2.
It was found that income mobility had an income equalising effect, in the
transition to retirement, for almost all groups.
The income mobility that occurred during
retirement continued to have an equalising effect on incomes for all groups.
6.2.2. The relative income position
The analysis of the relative income position of the pensioners in the groups
analysed (Chart in Ap
pendix 3) showed a significant fall in the relative income position
in the transition to retirement, more important in the male groups. The fall in real
income in the transition to retirement is due to structural factors. It expresses, on the
one hand, th
e immaturity of the pension system, as many of the individuals in the
groups analysed only joined the system late and did not have the chance to build up full
contributory careers. On the other hand, precarious integration in the labour market
causes a lac
k of pay records, and this, together with low remuneration levels, helps to
explain the low amounts of the first pension.
A trend is also seen for the relative position to decline during retirement in the
male groups. In the female groups, pension indexat
ion generally produces not very
expressive variations in the relative income position.
These results prove that the pension indexation mechanism is inadequate
according to the standards of adequacy that we consider desirable. Old age pensions are
18
meant to
ensure an income to replace individual earnings. So, guaranteed pension levels
must take as reference the earned income that is lost when individuals reach the legal
retirement age. And so there should not be any significant drop in income on retirement:
the first pension should be a certain percentage of the last remuneration in order to
safeguard the standard of living reached, within the possible limits. The subsequent
evolution of pension levels should prevent a relative decline in the economic situati
on
of pensioners, since a determined parity of the living standards between pensioners and
working people, that happens as soon as they retire, can later be changed by pension
indexing mechanisms.
With respect to the indexation mechanism for minimum pensi
on values (Table 4
in Appendix 2), it was found that the minimum pension value grew in real terms, but the
minimum payment levels didn’t keep pace with the growth in average earnings in the
economy. The minimum pension level grew in real terms in almost ev
ery year in the
studied period. But the quotient between the minimum pension amount and the average
remuneration was greater at the beginning of the 1990s than in the following decade.
This evolution occurred despite the minimum pension levels have raised
above
average levels in the last years, since periodic and extraordinary increases of pensions
have followed the principle of positive discrimination, which involves a higher relative
increase for the lowest pensions.
7. Conclusion
First, the analysis h
as shown that there is a statistically significant differentiation
of income trajectories and in the average pension levels established at the end of 2001,
between the various generations of men and women, probably expressing what Rawls
(1972) called “a na
tural fact, inherent to human development”. On one hand, since the
intergenerational context is marked by the inequality of income paths, we find no basis
to defend the equal treatment of generations by the pension system. On the other hand,
the decomposit
ion of the inequality in pension distribution at the end of 2001 shows that
it is very largely due to the within

group inequality component (inter

individual
inequalities). So, the unit of analysis relevant to the study of inequalities is probably the
indi
vidual not the generation.
Then, it is worth highlighting some results of the income dynamic analysis. In
the transition to retirement, there is a fall in real average income for all the subgroups of
19
individuals, significant falls in the relative income p
osition, more important in the male
groups. Income distributions become less unequal for some groups. Income mobility
has a significant exchange effect on the female groups, but only a structural effect on
the male groups. During the retirement period, ine
quality in the income distribution of
the groups falls and real average income rises. The trend is still seen for the relative
income position in the male groups to decline. For all the groups, income mobility has
only a structural effect.
The system does
not radically correct the inequality pattern established in the
labour market, since the initial and final pension distribution reflects the inequality
pattern of remuneration distribution. However, the redistributive mechanisms

like the
regulatory impro
vements that raise the pension above its statutory level, and positive
differentiation of increases

are important because they raise the guaranteed amounts
for those with the lowest incomes, leading to a certain degree of income mobility.
20
References
ATKINSON, Anthony B. (1995),
Incomes and the Welfare State: Essays on Britain and
Europe
, Cambridge, Cambridge University Press.
ATTIAS

DONFUT, Claudine (1988),
Sociologie des Générations
, Paris, PUF.
BUCHINSKY, M., FIELDS, G., FOUGÈRE,
D.
e
KRAMARZ
, F.
(2003), “Ranks or
Francs? Earnings Mobility in France: 1967

1999”, CREST,
mimeo.
CHAMPERNOWNE, David G. e COWEL, Frank A. (1998),
Economic inequality and
income distribution
, Cambridge, Cambridge University Press.
COWELL, Frank A. (2000),
“Measurement of Inequality”,
in
A. B. Atkinson e F.
Bourguignon (eds.),
Handbook of Income Distribution
, Amsterdam, Elsevier Science:
87

166.
COWELL, Frank A. e KUGA, Kiyoshi, (1981a) “Additivity and the Entropy Concept:
An Axiomatic Approach to Inequality
Measurement”,
Journal of Economic Theory
25,
1: 131

143.
FIELDS, Gary
(2002), “Does Income Mobility Equalize Longer

Term Incomes? New
Measures of an Old Concept”, Cornell University,
mimeo.
FIELDS, Gary S.
(2001),
Distribution and Development: A New Look
at the Developing
World
, Russell Sage Foundation.
FIELDS, Gary S.
e
OK, Efe A.
(1996), “The Meaning and Measurement of Income
Mobility”
, Journal of Economic Theory
71: 349

377.
FIELDS, Gary S.
e
OK, Efe A.
(1999a), “Measuring Movement of Incomes”,
Economic
a
66: 455

471.
FIELDS, Gary S.
e
OK, Efe A.
(1999b), “The Measurement of Income Mobility: An
Introduction to the Literature.”
i
n
J. Silber (ed.)
Handbook of Income Inequality
Measurement
, London, Kluwer Academic Publishing: 557

596.
FOSTER, James E. (1983)
, “An Axiomatic Characterization of the Theil Measure of
Income Inequality”,
Journal of Economic Theory
, 31, 105

121.
JONAS Hans (1990)
, Le principe responsabilité, Une éthique pour la civilisation
technologique
, Paris, CERF.
RAWLS, John
(1972),
A Theory
of Justice
, Cambridge Mass., Harvard University
Press.
21
ANEX 1
Table 1. Independent

samples T tests
Levene
test
Equality
Var
.
95%
Confidence
Interval
F
Sig.
Test
t
df
S
ign
l.
(bilat.)
M
ean
diff
.
Lower
bound
Upper
bound
H 1985
H 1990
256,432
0,000
Variâncias
diferentes
14,482
10475,4
0,000
11522,31
9
962,7
13081,9
H 1985
H 1995
654,742
0,000
Variâncias
diferentes
26,484
13601,8
0,000
22602,16
20929,4
24275,0
H 1985
H 2000
779,514
0,000
Variâncias
diferentes
35,790
14884,2
0,000
31347,53
29630,7
33064,4
H 1990
H 1995
220,590
0,000
Variâncias
dif
erentes
12,008
16081,5
0,000
11079,86
9271,3
12888,4
H 1990
H 2000
373,317
0,000
Variâncias
diferentes
31,012
17373,3
0,000
19825,22
17975,9
21674,6
H 1995
H 2000
33,022
0,000
Variâncias
diferentes
8,810
20949,9
0,000
8745,36
6799,6
10691,2
M 1985
M 1990
145,289
0,000
Variâncias
diferentes
12,650
8028,1
0,000
4078,29
3446,3
4710,3
M 1985
M 1995
107,109
0,000
Variâncias
diferentes
12,484
6906,4
0,000
4452,87
3753,7
5152,1
M 1985
M 2000
137,660
0,000
Variâncias
diferentes
22,524
12217,9
0,000
7
136,24
6515,2
7757,3
M 1990
M 1995
0,227
0,634
Variâncias
iguais
0,902
9668,0
0,367
374,58

439,6
1188,8
M 1990
M 2000
5,115
0,024
Variâncias
diferentes
7,972
12607,0
0,000
3057,94
2306,1
3809,8
M 1995
M 2000
6,577
0,010
Variâncias
diferentes
6,50
0
10696,7
0,000
2683,36
1874,2
3492,5
H 1985
M 1985
908,447
0,000
Variâncias
diferentes
27,791
4928,7
0,000
14799,88
13755,9
15843,9
H 1990
M 1990
1261,554
0,000
Variâncias
diferentes
33,036
8828,8
0,000
22243,90
20924,0
23563,8
H 1995
M 1995
1596,
225
0,000
Variâncias
diferentes
43,568
13072,2
0,000
32949,17
31466,8
34431,6
H 2000
M 2000
2823,948
0,000
Variâncias
diferentes
51,051
14179,8
0,000
39011,17
37513,3
40509,0
22
Table 2.A
–
Pension in 2001: Theil indexes (L e T)
–
M+W
n
g
/n
y
g
/y
μ
g
/μ
Theil indexes
L
T
1985
H
0,07576
0,06644
0,87705
0,08828
0,1
1037
M
0,06762
0,04385
0,64844
0,01862
0,02258
1990
H
0,12087
0,12752
1,05504
0,14274
0,17722
M
0,09510
0,06766
0,71144
0,04304
0,05794
1995
H
0,18332
0,22478
1,22619
0,19056
0,23746
M
0,08614
0,06178
0,71723
0,04625
0,06460
2000
H
0,20967
0,28542
1,36128
0,18977
0,23427
M
0,16152
0,12254
0,75868
0,05065
0,07285
within

grup inequality
0,11618
0,16800
between

grup inequality
0,03632
0,03558
total inequality
0,15251
0,20358
Table 2.B
–
Pension in 2001: Theil indexes (L e T)

Men
n
g
/n
y
g
/y
μ
g
/μ
Theil indexes
L
T
1985
H
0.12848
0.09436
0.73438
0.08828
0.11037
1990
H
0.20500
0.18110
0.88341
0.14274
0.17722
1995
H
0.31091
0.31922
1.02671
0.19056
0.23746
2000
H
0.35561
0.40533
1.13983
0.18977
0.23427
within

grup inequality
0.16734
0.
21326
between

grup inequality
0.01034
0.00988
total inequality
0.17768
0.22315
Table 2.C

Pension in 2001: Theil indexes (L e T)

Women
n
g
/n
y
g
/y
μ
g
/μ
Theil indexes
L
T
1985
M
0.16478
0.14822
0.89953
0.01862
0.02258
1990
M
0.23173
0.22870
0.
98692
0.04304
0.05794
1995
M
0.20990
0.20884
0.99495
0.04625
0.06460
2000
M
0.39359
0.41423
1.05245
0.05065
0.07285
within

grup inequality
0.04268
0.06027
between

grup inequality
0.00144
0.00142
total inequality
0.04412
0.06168
23
ANEX 2
Table 1a
–
C
orrelation coeficients of incomes, r de Pearson, and 1

r
N
r
1

r
r
t

1
pp
p01
r
t

1
pp
p01
1985
H
4042
r
t

1
1
0,907
0,879
r
t

1
0
0,093
0,121
pp
0,907
1
0,972
pp
0,093
0
0,028
p01
0,879
0,972
1
p01
0,121
0,028
0
M
3608
r
t

1
1
0,766
0,669
r
t

1
0
0,234
0,331
pp
0,766
1
0,920
pp
0,234
0
0,08
p01
0,669
0,920
1
p01
0,331
0,08
0
1990
H
6449
r
t

1
1
0,919
0,910
r
t

1
0
0,081
0,090
pp
0,919
1
0,988
pp
0,081
0
0,012
p01
0,91
0,988
1
p01
0,09
0,012
0
M
5074
r
t

1
1
0,809
0,793
r
t

1
0
0,191
0,207
pp
0,809
1
0,967
pp
0,191
0
0,033
p01
0,793
0,967
1
p01
0,207
0,033
0
1995
H
9781
r
t

1
1
0,902
0,902
r
t

1
0
0,098
0,098
pp
0,902
1
0,993
pp
0,098
0
0,007
p01
0,903
0,993
1
p01
0,097
0,007
0
M
4596
r
t

1
1
0,795
0,785
r
t

1
0
0,205
0,215
pp
0,795
1
0,981
pp
0,205
0
0,019
p01
0,785
0,981
1
p01
0,215
0,019
0
2000
H
11187
r
t

1
1
0,903
0,903
r
t

1
0
0,097
0,097
pp
0,903
1
0
,998
pp
0,097
0
0,002
p01
0,903
0,998
1
p01
0,097
0,002
0
M
8618
r
t

1
1
0,801
0,798
r
t

1
0
0,199
0,202
pp
0,801
1
0,996
pp
0,199
0
0,004
p01
0,798
0,996
1
p01
0,202
0,004
0
rt

1
–
last remuneration; pp
–
first pension income; p01
–
pension income in December 2001
24
Table 1b

Correlation coeficients of log incomes, r(ln) de Pearson and 1

r(ln)
r (ln)
1

r(ln)
N
r
t

1
pp
p01
r
t

1
pp
p01
1985
H
4042
r
t

1
1
0,786
0,689
r
t

1
0
0,214
0,311
pp
0,786
1
0,912
pp
0,214
0
0,088
p01
0,689
0,912
1
p01
0,311
0,088
0
M
3608
r
t

1
1
0,507
0,439
r
t

1
0
0,493
0,561
pp
0,507
1
0,843
pp
0,493
0
0,157
p01
0,439
0,843
1
p01
0,561
0,157
0
1990
H
6449
r
t

1
1
0,824
0,793
r
t

1
0
0
,539
0,478
pp
0,824
1,000
0,941
pp
0,176
0
0,242
p01
0,793
0,941
1
p01
0,207
0,242
0
M
5074
r
t

1
1
0,461
0,522
r
t

1
0
0,247
0,265
pp
0,461
1
0,758
pp
0,539
0
0,019
p01
0,522
0,758
1
p01
0,478
0,242
0
1995
H
9781
r
t

1
1
0,753
0,735
r
t

1
0
0,247
0,265
pp
0,753
1
0,981
pp
0,247
0
0,019
p01
0,735
0,981
1
p01
0,265
0,019
0
M
4596
r
t

1
1
0,413
0,395
r
t

1
0
0,587
0,605
pp
0,413
1
0,948
pp
0,587
0
0,052
p01
0,395
0,948
1
p01
0,605
0,052
0
2000
H
11187
r
t

1
1
0,792
0,787
r
t

1
0
0,208
0,213
pp
0,792
1
0,996
pp
0,208
0
0,004
p01
0,787
0,996
1
p01
0,213
0,004
0
M
8618
r
t

1
1
0,478
0,471
r
t

1
0
0,522
0,529
pp
0,478
1
0,994
pp
0,522
0
0,006
p01
0,471
0,994
1
p01
0,529
0,006
0
25
Table 2a
–
per capita
income movement and decomposition, % movement and e decomposition, log
income movement
per capita
–
Transition to retirement
n
m
n
1
T’xy/n
G’xy/n
p
n
1
T’xy/∑x
G’xy/∑x
m
n
2
1985
H
4042
37902,4
692,7
37209,6
0,49
0,01
0,48
0,77
M
3608
20689,6
11079,4
9610,2
0,69
0,37
0,32
1,14
1990
H
6449
39781,5
1173,0
38608,5
0,41
0,01
0,40
0,56
M
5074
25173,7
18746,2
6427,5
0,61
0,45
0,15
0,98
1995
H
9781
42
928,7
3402,4
39526,3
0,39
0,03
0,36
0,51
M
4596
25282,3
14918,4
10363,8
0,52
0,30
0,21
0,81
2000
H
11187
41574,9
5076,8
36498,1
0,34
0,04
0,30
0,39
M
8618
26618,5
19356,1
7262,4
0,49
0,35
0,13
0,69
Table 2b
–
per capita
income movement and decom
position, % movement and e decomposition, log
income movement
per capita
–
Transition during the retirement period
n
m
n
1
Txy/n
Gxy/n
p
n
1
Txy/∑x
Gxy/∑x
m
n
2
1985
H
4042
17489,6
370,7
17118,9
0,44
0,01
0,43
0,56
M
3608
21449,1
54,6
21394,5
1,04
0,00
1,04
0,80
1990
H
6449
10019,8
586,3
9433,5
0,17
0,01
0,16
0,25
M
5074
11075,2
91,2
10984,0
0,32
0,00
0,31
0,32
1995
H
9781
8779,5
102,1
8
677,5
0,12
0,00
0,12
0,17
M
4596
7790,9
0,0
7790,9
0,20
0,00
0,20
0,20
2000
H
11187
2174,5
1084,7
1089,9
0,02
0,01
0,01
0,03
M
8618
1915,4
169,8
1745,6
0,04
0,00
0,04
0,04
26
Table 3
–
P(Fields

Gini) and P(Fields

Theil)
Transition r
t

1

pp
Transition pp

p2001
Transition r
t

1
–
p2001
P(G)
P(T)
P(G)
P(T)
P(G)
P(T)
1985
H

0,03963

0,06522
0,27859
0,43348
0,18400
0,29709
M
0,26575
0,46986
0,42001
0,63941
0,51400
0,76414
1990
H
0,00214
0,00147
0,13415
0,21820
0,10861
0,17359
M
0,31388
0,50804
0,16431
0,32249
0,41227
0,63787
1995
H
0,03066
0,06026
0,06962
0,11602
0,08619
0,14672
M
0,30336
0,48996
0,03269
0,16159
0,36032
0,56684
2000
H
0,07373
0,27985
0,01270
0,02039
0,08334
0,29174
M
0,33125
0,50658
0,02896
0,04054
0,3
4595
0,52493
27
Table 4
–
Minimum pension value
Minimum
pension value
(vmp)
Dec
t

1
vmp Dec
t

1
/
Average remuneration (base)
t
Real growth rate
(vmp)
1985
5500
0,223

0,162
1986
6900
0,229
0,123
1987
11500
0,321
0,52
3
1988
13000
0,317
0,031
1989
14600
0,323

0,003
1990
17000
0,334
0,027
1991
20000
0,339
0,056
1992
22800
0,325
0,047
1993
24700
0,308
0,017
1994
26200
0,294
0,008
1995
27600
0,287
0,012
1996
29000
0,293
0,019
1997
30100
0,287
0,016
1998
31300
0
,291
0,013
1999
32600
0,287
0,018
2000
34000 (a)
0,288
0,015
2001
36000 (a)
0,293
0,015
2002
38000 (a)
0,275 (b)
0,019
(a)
–
lowest minimum value; (b)

estimated value.
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