Kinship and Family Support in
Aging Societies
Wolf, D.A.
IIASA Working Paper
WP-86-081
December 1986
Wolf, D.A. (1986) Kinship and Family Support in Aging Societies. IIASA Working Paper. IIASA, Laxenburg, Austria, WP86-081 Copyright © 1986 by the author(s). http://pure.iiasa.ac.at/2780/
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WORKING PAPER
~ A l Y D F A Y I L Y ~ R ' r
IN AGING 90QFllE9
December 1986
WP-86-81
International l n s t ~ t u t e
for Applied Systems Analysis
NOT M)R QUOTATION
WITHOUT THE PERMISSION
OF THE AUTHOR
KINSHIP AND FAMILY 9UPPORT
IN AGING SOCIETiES
December 1986
WP-86-81
Working hpers are interim r e p o r t s on work of the International
Institute for Applied Systems Analysis and have moeived only limited
mvlew. Views or opinions expressed herein do not neoessarfly
represent thase of the Institute or of its National Member
Organizations.
INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS
A-2361 Laxenburg, Austria
This is a revised version of a paper originally presented at the United Nations
International Symposium on Population Structure and Development, held in Tokyo,
Japan f r o m 10-12 September 1986, and to be published in 1987 by the United Nations. This researah was supported in part by G r a n t No. AGO5153 from the U.S.
National Institute on Aging. Important contributions to the research were made by
Nathan Keyfitz, Gun Stsnflo and Jan Bartlema. Helpful comments on an earlier version of the paper w e r e provided by Naohiro Ogawa, S h i m Hoiruchi, Jack Habib and
Shigemi Kono.
The main direction of r e s e a r c h in IIASA's Population Program is population
aging-* phenomenon which a l m o s t all countries in t h e world are experiencing
today. Many social economic consequences of aging f o r society depend on t h e
existing family s t r u c t u r e and i t s f u t u r e evolution.
This p a p e r d e s c r i b e s t h e micro-simulation a p p r o a c h to t h e analysis of t h e kinship patterns. The only d a t a which one needs are t h e data on fertility and mortality. Among o t h e r findings t h e p a p e r shows that, as a r e s u l t of fertility reduction,
t h e links between generations became weaker.
A n a t o l i Yashin
Deputy Leader
Population Program
Contents
I.
INTRODUCTION
11.
INDICATORS OF THE AGING PROCESS
111. DISAGGREGATING THE DEPENDENCY RATIO
Modelling K i n s h i p Patterns
SimulaWons Perf o r n e d
Results
IV. SUMMARY AND CONCLUSIONS
REFERENCES
Appendix T a b l e A
Appendix T a b l e B
KINSHIP AND FAUILY SUPPORT
IN AGING SlOCIETIES
L INTRODUCTION
A general aoncern with the worldwide phenomenon of increasingly aged populations has existed f o r many years. This concern will presumably grow as the
phenomenon continues its progress during the coming decades. I t is generally held
that the aging of the world's population presents serious problems, o r , a t a
minimum, makes necessary significant adjustments in public policies and social and
eoonomic institutions (see,f o r example, United Nations, 1985a). The issue remains
somewhat oontroversial, however: a reoent paper argues that, at least f o r the United States, the burdens implied by the projected increase in the over-65 elderly
a r e exaggerated (Aaron, 1986). Aaron suggests nonetheless that the prospective
increase in the relative size of the over-80 population presents problems that have
received insufficient attention. However problematic the transition to a more elderly world proves to be, t h e r e wan be little doubt that the transition will be aocompanied by important changes in the economic and sooial s t m a t u r e s of many aountries.
This paper addresses issues related to kinship in increasingly w e d populations: patterns of nuclear-family kin, the aonsequences of these patterns, and,
especially, the way in whioh the aged "dependency burden" oan be allmated along
family lines. The perspeotive adopted is that of the 16 oountries affiliated with the
International Institute f o r Applied Systems Analysis (IIASA), all of which are industrialized countries. A s shall be illustrated, the aging phenomenon exhibited in the
IIASA uountries Is r a t h e r different from that of the world as a whole.
%heme countries are: Austria, Bulgaria, Canada, Csechoslovakia. Finland, Prance, the Cerman
Democratic Republic, the German Federal Republic, Hungary, Itoly, Japan, t h e Netherlands, Poland,
Sweden, t h e Unlon of Soviet Socialist Republics, and the United States of America.
Kinship patterns r e p r e s e n t only one of numerous social dimensions t h a t can
be expected to undergo change as a r e s u l t of population aging. As oountries be-
oome m o r e aged, social institutions suoh as the eduoational system and t h e oonoept
of family will ohange. Aspects of s w i a l s t r u a t u r e , such as t h e spatial arrangement
of the population, and t h e d e g r e e and n a t u r e of migration p a t t e r n s , will be affected. With a n increasing s h a r e of t h e lifetime s p e n t at ages c u r r e n t l y r e g a r d e d as
"retirement age", t h e conception of t h e worklife, and possibly of productive aoflvity itself, may undergo change. And, norms and expectations regarding lifetime
upward mobility, and the implied lifetime path of consumption opportunities, will
inevitably be changed as a consequence of new p a t t e r n s of l a b o r availability at
various levels of t h e seniority hierarchy, and the need f o r s u p p o r t o v e r a g r e a t e r
range of years. P e r h a p s uniquely among these s e v e r a l social implications of aging
populations, t h e issue of kinship p a t t e r n s lends itself to a demographic analysis.
Kinship patterns are of p m c t i a a l importance f o r a number of reasons, prominent among which is the issue of s u p p o r t f o r t h e elderly. Family members, espeoially nuclear-family members (spouse, siblings, children) play important roles i n
t h e support f o r t h e elderly in many countries. Support f o r t h e elderly oan take
many forms, including t h e provision of d i r e c t f i ~ n a i a support,
l
the provision of
informal health-care services, and s h a r e d living arrangements. A t t h e m o s t basic
level, t h e complete absenoe of such family members from t h e kinship network
means t h a t the potential f o r s u p p o r t of the elderly from t h i s important s o u r c e i s
nonexistent. However, even given t h e existence of such family members, p a t t e r n s
of s u p p o r t show considerable variation according to t h e number, sexes, ages, and
o t h e r demographic c h a r a c t e r i s t i c s of individual members of t h e kin network. For
example, r e o e n t r e s e a r c h oonducted by Wolf and Soldo (1986) using t h e U.S. 1982
National Long Term Care Survey showed t h a t t h e probability t h a t a given child
provides health care to an elderly, disabled, formerly-married mother, ranges
from n e a r zero to n e a r one according to t h e sex, age, marital and work status of
t h e child, and to t h e corresponding a t t r i b u t e s of any siblings.
The plan of this p a p e r is as follows. In part 11, s e v e r a l aggregate indicators
of the aging process, as experienced by the IIASA countries, are briefly summarized. P a r t I11 p r e s e n t s r e s u l t s from a new a n a l p i s of kinship p a t t e r n , and uses
these r e s u l t s to show how the dependency burden can be disaggregated along family lines. Family linkages between t h e aged and t h e working-age populations are illustrated f o r t h r e e a l t e r n a t i v e demographic soenarios, using a microanalytic simulation technique. P a r t IV summarizes and aoncludes t h e paper.
II. INDICATORS OF THE AGlNC PBOCESS
In o r d e r to provide a context f o r the subsequent analysis. selected demographic indicators f o r t h e IIASA countries as a whole, and f o r t h e world, are shown
in Figures 1-4. The g r a p h s present historical data beginning in 1950, and continue
with projected d a t a through 2025; t h e source f o r t h e projections i s t h e United Nations publication World Population Prospects: Estimates and Projections as As-
sessed in -82.
The d a t a shown f o r t h e IIASA countries as a group in Figures 1-3
are simply weighted totals, with weights based upon 1985 total population figures.
Aocordingly, t h e data f o r IIASA oountries as a whole are heavily influenced by that
of t h e USSR and the US, whioh together receive 53.8 percent of t h e weights used in
t h e calculations.
Figure 1. Total fertility rates f o r IIASA countries and world, 1950-2020.
In general, t h e figures depiot a situation whereby t h e IIASA countries are
f a r t h e r along t h e trend than i s t h e world at Large with r e s p e c t to t h e demographic
determinants of increasingly aged population struoture, In Figure 1,t h e total fer-
tility rate (TFR)i s shown; the IIASA countries, all of which are industrialized, have
much lower fertility rates in t h e recent past, and in t h e projected n e a r future,
than does t h e world at large. F r o m 1980 onwards, the TFR in t h e IIASA countries i s
actually projected to rise somewhat, while t h a t of t h e world as a whole i s projected
to decline sharply. As a consequence, t h e differences between t h e IIASA aountries
and t h e world as a whole w i l l be greatly diminished, although not aompletely eliminated, by 2020. The projected world's TFR for 2020 is at about t h e level shown by
t h e IIASA countries in 1985.
Together, fertility and mortality rates determine t h e a g e composition of t h e
population. Indiaators of mortality rates-life
expectancy at birth (for both sexes
combined)--are pictured in Figure 2. Again, life expectancy in t h e IIASA countries
presently exceeds t h a t of t h e world as a whole, but this gap i s projected to diminish greatly between now and 2020.
Aspects of t h e population age s t r u c t u r e implied by the paths of fertility and
mortality are presented in Figures 3 and 4. In Figure 3 w e see the median a g e of
t h e population. Here, t h e IIASA countries are older at t h e outset than is t h e world
as a whole, but t h e differenae between t h e two grows r a t h e r than diminishes
throughout most of t h e period up to 2025. This, of course, reflects t h e vastly diff e r e n t 'current a g e s t r u c t u r e of the industrialized countries compared to t h e rest
of t h e world. The median age of t h e population of t h e combined IIASA countries,
whiah w a s about 28 y e a r s in 1950, will r i s e to nearly 40 y e a r s by 2025.
Finally, w e see in Ffgure 4 t h e aged dependency ratio, constructed as t h e ratio of persons o v e r 65 to persons 20+4, f o r t h e IIASA countries and t h e world. As
w e would expect, this r a t i o i s higher in t h e IIASA aountries than in t h e world in
'
general at present, and i s projected to remain higher throughout t h e period
covered by t h e projection. The dependency ratio is, in fact, one of t h e principal
indiaators cited in discussions of t h e potential problems posed by population aging.
In t h e following section, this paper examines the dependency burden in g r e a t e r detail.
IIL DISAGGEEGATING TEE DEPENDENCY RATIO
As mentioned before, t h e aged dependenay r a t i o commands considerable attention as a n indiaator of t h e potential problems facing a n increasingly aged population. Computed as t h e ratio of persons 65 and older to persons aged 20 to 64, t h e
ratio is roughly t h e number of r e t i r e e s p e r worker, or potential worker. A s such,
Figure 2.
Life expectancy, for both sexes combined, IIASA countries and world,
1950-2020.
I\U worm
it aan be taken as a proxy f o r the w t i o of the elderly component of the dependent
population to the economically active population. Obviously this interpretation of
the w t i o embodies sevenid simplifying assumptions: it ignores the facts that many
persons over 65 a r e economically active, that many persons over 65 contribute to
their own support. and that many persons under 65 a r e themselves dependent-for
example, as a result of ill health or disability.
Nonetheless, this aged dependency w t i o forms the basis f o r the following discussion. Perhaps the leading mason f o r concern with the ratio lies in the extent
to which current resources are allocated to the support of the aged. There are
t h r e e broad uategories of resources available for the support of the aged: the assets held by the aged themselves; collective resources, the ultimate origin of
which is those currently working; and family members. In most IIASA muntries,
collective resources, provided via programs administered by the state, are a ma-
Figure 3.
Median age of population in IIASA countries and world, 1950-2025.
jor sourae of support for t h e aged. And i t is the prospect of pressure on the
state's resouraes, resulting from a n increase in the size of the recipient populations of these programs-especially, in relation to the size of the working populations f r o m whom t h e resources come--which motivates much of t h e policy concern
about population aging.
One possible response to t h e prospective pressures upon public programs for
the support of t h e aged i s a n attempt to shift some of the potential burden of caring for the aged away from public programs, and onto t h e family (for a policyoriented discussion of this issue, see S c h o r r , 1980).
However, t h e very demographic trends that are producing t h e dramatic ongoing and projected t r e n d s in t h e age s t n a t u r e of the population are also altering
t h e patterns of family networks t h a t can, in theory, s e r v e to substitute f o r the
public (that is, t h e working population as a whole) In providing support for t h e
aged. Reduced fertility rates and i n c r e d n g longevity each influence t h e pattern
of llnkages between members of the aged population and thelr offspring within t h e
working-age population. The study of this pattern requires a model of kinship, to
which w e now turn.
Figure 4.
Aged dependency ratio for IIASA countries and world, 1950-2025.
Podding Kiruhip PatterDemographers have a long tradition of analyzing kinship structures.
At
present, work on this issue c a n be alassified into analytic models and simulation
models. Examples of analytic models include t h e work of Goodman, Keyfitz, and
Pullum (1974, 1975), f u r t h e r elaborated in Keyfitz (1985); Krishnamoorthy (1980);
Pullum (1982); and Joffe and Waugh (1982). The Goodman et al. approach has been
extended and applied by o t h e r s , including Goldman (1978, 1986), Schmueli (1985),
and Bartlema and d e Jong (1985). Simulation analyses of kinship p a t t e r n s have
been reported by s e v e r a l authors, among which are Howell and Lehotay (1978),
Hammel, Wachter and McDaniel (1981). Le Bras and Wachter (1978), and Bartlema
and Winkelbauer (1986). The analytic models, while m o r e elegant formally, are limited with r e s p e a t to t h e goals of t h e present analysis: as so f a r developed, they
are unable to r e p r e s e n t t h e frequency distribution of kin o v e r t h e life cyole. Consequently, the simulation approach i s adopted here.
The advantage of the m i c r d m u l a t i o n methodology used h e r e is t h a t i t gen-
erates observations on hypothetical i n d i v i d u a l s , to which attributes such as sex
and the dates of birth and death are associated. Moreover, each hypothetical individual i s linked to o t h e r individuals, with t h e i r corresponding attributes, in the
s a m e hypothetical population. The results presented below are generated by a new
simulation procedure based upon a continuous-time stochastic event-history proaess; details regarding t h e features of the event-history process, and t h e technique used to simulate the process, can be found in Wolf (1986).
The assumptions underlying t h e simulations reported h e r e are in many
respects identical to those adopted by Goodman et al. (1974). In particular, the
population i s assumed to be stable and homogeneous with respect to rates of dying
and childbearing; birth rates are also assumed not to depend upon parity. Howeve r , in t h e present simulations a minimum interval of exactly 12 months between
births i s assumed. And, t h e simulations employ a two-sex model, in t h e limited
sense t h a t both daughters and sons are born to t h e women in t h e hypothetiad population; t h e r e is, however, no mating or "marriage market". Thus, the simulation
model in its present stage of development can represent the distributions of broth-
ers and sons as w e l l as of s i s t e r s and daughters, but aannot represent spouses and
fathers.
Basiaally, the approach aonsists of simulating lanrily trees which evolve in
aalendar time, and then sampling from t h e resulting population in cross-section to
obtain a picture of the kinship patterns then prevailing. Figure 5 helps to clarify
t h e problem. The horizontal axis in Figure 5 represents aalendar time, set arbit r a r i l y to z e r o at t h e leftmost point. Horizontal line segments shown above the
t i m e axis depict individual lifetimes; t h e left endpoint of a segment represents
one's own date of birth, while the right endpoint of a segment represents one's own
date of death. x's along the segments represent times at which one's ahildren are
born.
Flgure 5 depicts t h e lifetimes of 11 hypothetiaal individuals, labelled a
through k . This i s in faat an e x a e r p t from a family t r e e , sinae individuals b -k are
all desaended from individual a . The vertiaal dashed lines in the figure connect
mothers with t h e i r ahildren. Thus, b and c are a's children; d i s b's child; e and
f are c 's children; and so on. I t follows t h a t d , e , and f are a's grandchildren;
m o r e distant relationships can be additionally derived.
Figure 5.
Pictorial representation of family-tree simulation problem.
A cross-sectional picture of the population pictured in Figure 5 uan be obtained by "sampling" from the population at an arbitrarily ohosen time, shown as t*
in t h e figure. A t t i m e t*, individuals e through i , and k , are alive.
Each
individual's age at the time of the "survey" can readily be determined: f o r example, point z on t h e t i m e axis oorresponds to A's date of birth; therefore. A's age
at the time of the survey is t* -2. Similarly, it is easy to establish how many Wing
kin, in each possible kin relationship, cxan be associated with eaah person living at
time t* . For example, in Figure 5, individual A 's mother (designated as f ), one of
two siblings ever-born (individual f ), and child (individnal k ) are all alive.
The simulations reported below consist of the generation of a large sample of
family t r e e s , each of which begins with a single initial mother o r 'heed". Each
seed produoes offspring, and each of these offspring produoes f u r t h e r offspring.
and s o on, until some Limit (expressed relative to calendar time) is reached. To
each individual is attaohed a life-history, which oonsists of (1)event-history data-
-a sequence of items representing dates of own birth and death, and dates, if any,
of one's children's births-and
(2) "accounting" o r cross referencing data-that
is,
identifying numbers, and references t o t h e identifying numbers of one's mother and
any ahildren. Each such life-history is entered into a data base, which is subsequently "sampled", as depicted in Figure 5, the sample information being then tabulated f o r analysis.
The only input data required in o r d e r to carry out such a simulation are
schedules of birth and death rates, and the r a t l o of males to females among all
births. For t h e simulations reported h e r e , sex-specific vital rates f o r 5-year age
groups were used. The rates w e r e treated as the parameters of a n age-dependent
continuous-time semi-Markovian event-history p r m e s s , a special aase of t h e gen-
eral framework laid out in Wolf (1986). In particular, t h e probability of f i r s t birth
at age a is given by
and t h e probability of a birth at age at,given t h a t t h e r e was a previous birth at
age
Is given by
provided t h a t
9 r + +I.
In (1) and (2) d z ) is t h e death rate f o r females at age z , taken directiy from
the Input data. b*(z) is t h e birth rate at age z , adjusted upward from the observed birth r a t e s d ( z ) - - i n o r d e r to oompensate f o r t h e imposition of a minimum
waiting time of exactly one y e a r between births.
This adjustment is derived as follows. First note that t h e birth rate at exact
age z oan be expressed as
where n, is t h e proportion of women not at risk of childbearing at age z , due to
ahildbirth at some time in t h e preceding 1 2 months. However, the proportion n, is
simply the probability of giving birth between z -1 and z , given by
Thus. (3) can be rearranged, yielding
which allows us to express t h e birth rate f o r those actually at risk in terms of the
observed birth rate.
In most applied demographic analysis the b ( z ) schedule is t r e a t e d as piece-
w i s e constant. The dah used in this analysls included birth rates c o n s h n t o v e r 5y e a r age groups 15-19, 20-24, and s o on. In t h e seaond through fifth y e a r s of any
such group, b**(z) as given by (4) is also constant. In t h e f i r s t y e a r of each
group, however, t h e b** ( z ) transformation is nonconstant. In particular, at age y
such that z < y
= z + & < z + 1,
A constant-rate equivalent to b** ( a ) f o r use on the interval
2.2 + I
can be ob-
h i n e d by integrating b** (a)o v e r this interval, yielding
Equation (6) was used to calculate t h e adjusted birth rates used in t h e simulations
reported below.
Further generality could be incorporated into t h e analysis, f o r example by introducing "duration dependenae" as well as age dependenae, by using parityspecific birth rates. and by taking acaount of persistent intergenerational patterns, suah as positive correlations between t h e fertility behavior of mothers and
t h e i r daughters (see Preston, 1976). or between t h e longevity of parents and t h e i r
offspring (Jaquard, 1982; Hrubec et al., 1984); suah generalizations a r e , however,
beyond t h e saope of t h e present paper.
Simulations Perfoxmed
Three variants of t h e simulation procedure described above w e r e performed
f o r this study. All are based upon period fertility and mortality data f o r t h e Netherlands, supplied by Jan Bartlema (for a r a t h e r different approach to t h e study of
kinship, based upon t h e same data, see Bartlema and Winkelbauer, 1986). The base
run uses a fertility schedule implying a total fertility rate of 2.65, which i s approximately t h e rate prevailing in 1 - 7 0 , and a mortality schedule implying life expeotancies at birth of approximately 78 years f o r women, and 72 y e a r s f o r men
(figures close to those prevailing in the period data f o r 1980). Sinoe t h e simulations produce kin frequencies f o r t h e stable populations implied by the input
parameters, t h e results are to be interpreted as illustrative of a given pattern of
births and deaths, r a t h e r than a representation of a real population.
Two variants upon t h e base simulation were also performed. The first, a lowmortality variant, used age-specific mortality rates uniformly 25 percent lower
than those in t h e base run. This modification implies, in turn, about a 5 percent inorease in life expectancy. This increase i s only slightly higher than t h e projected
increase, by 2020, for the Netherlands as given in t h e United Nations projections.
The second simulation variant, a low-fertility variant, assumes a uniform 40
percent drop in age-specific fertility rates; that is, a drop to a total fertility rate
of approximately 1.6. A d r o p this dramatic was, in fact, attained in t h e Netherlands between 1970 and 1980. According to t h e United Nations projections, t h e to-
tal fertility rate in t h e Netherlands will be only slightly below the 1.6 level f o r the
rest of t h e 20th century, and will again rise, and s u r p a s s this level, e a r l y in t h e
next century. The t w o variant simulations are included in o r d e r to assess t h e likely consequences-with
r e s p e c t to t h e patterns of living kin available to provide
support f o r aged parents--of realistic demographic trends.
Base sirnulortion. The results obtained f o r the base simulation are summarized in Table 1, which presents kin patterns from t h e viewpoint of women. This
table refers to a simulated population containing approximately 30,000 women. The
population was generated by simulating t h e successive offspring of a large number
of "seeds", as explained above, and sampling from t h e resulting population a f t e r
300 y e a r s of simulated evolution. Column (2) of t h e table shows t h e distribution of
t h e cross-sectional population a f t e r 300 years of evolution by %year age groups;
this distribution agrees quite w e l l with t h e stable age distribution obtained when
t h e same vital rates are used to construct a conventional life table. In o t h e r
words, t h e simulation a p p e a r s to have successfully represented t h e stable population implied by the input data.
Table 1. Summary of simulated kinship patterns, base simulation.
Basic result
Key to colusns:
Age group
Proportion o f population i n age group
Proportion i n age group with l i v i n g mother
Average age o f l i v i n g mothers of those i n age group
Hean number o f l i v i n g daughters o f those i n age group
Average age o f l i v i n g daughters o f those i n age group
Proportion i n age group with no l i v i n g daughters
Hean number o f l i v i n g sons o f those i n age group
Average age o f l i v i n g sons o f those i n age group
Proportion i n age group with no l i v i n g sons
Hean number o f l i v i n g children o f those i n age group
Average age o f l i v i n g children o f those i n age group
Proportion i n age group with no l i v i n g children
Existing kinship models, notably that developed by Goodman, Keyfitz and Pullum (1974), yield Information such as that shown in columns (3) and (5) of the table:
t h e mean numbers, respectively, of living mothers and daughters of living m e m b e r s
of t h e stable population. The expected patterns a p p e a r h e r e as well: at birth,
everyone's mother i s alive (in this simulated population, no one under t h e a g e of 5
has lost t h e i r mother); t h e proportion with a living mother declines steadily, slowly
at f i r s t , and more rapidly in t h e middle ages, reaching z e r o in t h e 80-84 a g e group.
Column (5) shows t h a t t h e mean number of daughters exhibits a n inverted-u
s h a p e o v e r t h e lifetime: t h e mean becomes positive in t h e earliest a g e group exhibiting fertility behavior-the
15-19 a g e g r o u p - a n d rises to i t s maximum at approx-
imately t h e oompletion of childbearing.'
Thereafter, t h e Alean number of living
daughters drops, reflecting mortality among t h e daughters. The mean number of
sons [aolumn (8)] and of all children [column (11)] behave exactly as does t h e mean
number of daughters.
However, t h e miorosimulation approach to studying kinship permits us to go
beyond t h e use of a v e r a g e values, viewing t h e living-kin phenomenon in considerably g r e a t e r detail. Of p a r t i c u l a r i n t e r e s t are columns (7), (lo), and (13) which
p r e s e n t information on t h e frequency distribution of living offspring by age. In
t h e base simulation t h e proportion of women with n o living children r e a c h e s i t s low
of 0.04 in t h e 40-44 a g e group, remaining virtually unchanged at t h a t level through
t h e 70-74 a g e group. There i s an indication that t h e proportion childless begins to
r i s e r a t h e r rapidly among t h e oldest-old, especially those 90 and over. This must
remain a r a t h e r tentative conclusion, since so few members of t h e simulated population fall into these a g e groups. For example, t h e proportion childless in the 9599 a g e group (0.19) is based upon a sample of 2 1 hypothetical women; in a random
sample from a r e a l population yielding t h e same results, a 95-peroent confidence
interval f o r t h e t r u e proportion childless would r a n g e from 0.022 to 0.358. Moreover, t h e oonclusion i s of little significance in pop&tions
with t h e s t r u o t u r e of
t h a t depicted in Table 1;in such a population less than one p e r c e n t of t h e population falls into t h e 90-and-over category. However, if p r e s e n t demographic trends
oontinue t h e oldest-old groups will greatly increase in relative terms, and t h e i r
unique family situation w i l l take on added significance.
Also of i n t e r e s t i s t h e data provided in column (12) of Table 1: t h e a v e r a g e
age of t h e living children available to t h e population by age group. This a v e r a g e
is, of course, inoreasing o v e r t h e life cyole. N o t e t h a t , on t h e average, t h e child r e n of t h e "oldest-old" are themselves approaching retirement age.
%here are aorne minor irregularities In column (5)-and elsewhere in Table 1-reflecting the inevitable presence of HontbCarlo "suapllng error" in the dmulation; even a simulated population of
over 30,000 la "small" for purposes of some of the diaaggregated statistics shown in Table 1.
Table 1 advances somewhat o u r understanding of t h e constmints faced by a
society which wishes to turn to the family as a source of support f o r the aged population. As w e oonsider successively older ages, an increasing proportion of the
elderly a r e without living offspring; among those with living offspring, the average
age of the offspring i s itself approaohing, or within, t h e bounds of t h e aged
category.
However, w e can gain additional insights into t h e problem by taking f u r t h e r
advantage of the microsimulation approaoh, and tabulating t h e simulated population along family lines. Table 2 does this, in a r a t h e r simple way. taking account
only of t h e mother-child relationship. Two age groups are reoognized: 20-64 and
85 plus, t h e two groups used in calculating t h e aged dependency ratio. In Table 2
members of t h e aged group are tabulated aceording to the number of living ohild r e n they have. Only women are counted in t h e tabulation of t h e aged group. Those
in the 20-64 age group are tabulated aooording to (1) whether t h e i r mother is alive
a d 65 or older, and (2) the size of t h e i r "sibship"-that
is, t h e number of broth-
ers and s i s t e r s they have, plus one (for themselves). Both men and women are included in t h e tabulation of t h e 20-64 group. sinoe both sexes represent potential
souroes of support f o r t h e i r elderly mothers.
In Table 2, a woman i n t h e 65+ age category will be counted twice if h e r moth-
er i s alive; onoe as one of t h e ahildren of h e r noth her, and once as an aged mother
herself, classified according to the number of living children (age 20+) s h e has.
The table i s arranged such t h a t as we r e a d down the oolumns, w e encounter ohild r e n at increcrstng risk of being responsible f o r t h e o a r e of an elderly mother,
and w e encounter mothers with a demOQStng pool of child-resouroes to osll upon
f o r support. Thus. in column (I),which shows the number of children aocording to
t h e existelme of a n aged mother and the size of sibship, w e see that 69.8 percent of
ohildren 20-64 do not have a n aged mother. This can mean e i t h e r t h a t t h e i r mother
is alive but less than 65 y e a r s old, or that their mother i s not alive. The next fig-
ure in oolumn (1) is f o r children with an aged mother, and from sibships of five or
more. Such ohildren, beoalm~ethey have several brothers and/or sisters, b e a r
proportionately less of t h e burden of parental oare than do children from smaller
s i bships-at
least, on average. Moving down this oolumn, w e see that 2.4 percent of
all persons aged 20-64, in t h e simulated population, are only ahildren-more
cisely. only Ltving children-with
a living mother 85 or older.
pre-
Table 2. Cross-tabulation of aged mothers and working-age children, base simulation.
Population Group
Children
Mothers
Age 65+
Age 2084
(1)
(2)
(3)
(4
(5)
Number
Proportion
of 20-64
Group
CumulaUve
Number
Proportion
of Total
Proportion
of Total
(6
(7)
(8)
Number
Proportlon
of Total
Cumulatlve
Proportlon
of Total
21442
.698
.698
-
-
-
-
-
Mother 65+;
slbshlp = 5+
1107
.036
-734
13
-012
300
.075
-075
slbshlp = 4
2208
.072
.808
36
.016
570
.I43
218
737
.024
20
.027
775
.I95
.B55
-
-
-
-
176
.044
.999
30699
1.00
N o living mother 65+
sibshlp = 3
slbshlp = 2
elbshlp = 1
N o Hvlng ahildren
Total
1.00
-
180
3976
1.00
In reoognition of t h e f a c t that those 65 or older may not be forced to rely exclusively on family members under 65, columns (4) and (5) of Table 2 show the
numbers of "old siblings": these are children, aged 65 or more, of a living mother.
In all cases, of oourse, t h e living mother i s at least 80 y e a r s old. The numbers are
also expressed as ratios to t h e number of w o r k i n g w e children in each sibship [in
column (5)]. The "old sibling" group ranges in size from 1.2 percent to 2.7 percent
of t h e oorresponding "young sibling" group.3 In o t h e r words, the pool of &ndolder siblings, available to assist w o r k i n g w e children in t h e care and support of
aged mothers, i s relatively small.
Columns (6) and (7) present t h e distribution of aged mothers acoording to the
number of living children. The largest single group are those with t w o living child r e n (28 percent of t h e total); a A t h e r small 4.4 percent of t h e women 65 or older
have no living children.
The figures given in Table 2 allow us to construct an aged dependency ratio
t h a t i s family-based, as w e l l as the usual population-based dependency ratio. Thus,
we c a n establish t h e boundaries of family-based support f o r t h e aged population.
This in turn should be of considerable interest to those who seek to use the instruments of public policy to encourage a shift of responsibility f o r the support of the
elderly away from t h e s t a t e , and onto the family.
First, the oonventional aged dependency r a t i o f o r the simulated population
represented in Table 2 i s readily oomputed as 3976-the
size of t h e 65+
population4ivided by 30699 in t h e w o r k i n g w e group, yielding a ratio of 0.13. In
o t h e r words, if t h e prevailing policy f o r this population dictated that the workingage population shared fully and equally t h e burden of support of the aged, and if
t h e aged all received a n equal level of support, then each w o r k i n g w e individual
would be required to provide .13 units of support f o r t h e aged (ignoring, in this artificial situation, t h e existenae of aged men).
A t t h e opposite extreme, w e might envision a s y s t e m whereby the state provides no support f o r the elderly, and requires any such support to aome from family members. However improbable such a scheme may seem, i t is instructive to examine t h e distribution of t h e aged dependency burden in such a situation. First, i t
i s apparent that between 4 and 5 peroent of the aged, under this extreme policy,
%he "older/younger" distinction i s not npproprlate in the came of only children; the relevant row
of Table 2 tells ue that of all llvlng only chlldren with a mother of 65 or older, 737 were ln t h e 2064 age group, and 20 were in the 65+ age group.
have access to no support from the working-age population whatsoever. Moreover,
nearly 70 percent of t h e working-age population b e a r s none of the aged dependenay burden whatsoever. Among those working-age individuals who do have an aged
parent, the dependency r a t i o is quite high: i t is 3976 minus 176 (or, t h e number of
aged with a t least one living working-age offspring) divided by 30699 minus 21422
(or, t h e number of working-age children with a living aged mother), or 0.41.
An intermediate scheme f o r t h e provision of support to the aged population
can also be examined. Imagine, f o r example, t h e following simple scheme: the
state provides a minimum level of support to all members of t h e aged population;
those with no family members to call upon receive only this minimum. Those aged
with working-age f d l y members reaeive a standard supplement to t h e minimum,
t h e cost of which i s shared within working-age "sibships". Thus, a working-age individual with a n aged parent to support, but with no working-age siblings, must
contribute a full s h a r e of the supplemental support allowance; a working-age individual with a n aged parent, and with one working-age sibling, need contribute only
half a s h a r e of t h e supplemental support allowanae; and so on. In this plan, aged
with many offspring are no b e t t e r off than aged with few offspring.
Each of the t h r e e hypothetical support systems described above-the
population-based scheme, t h e family-based scheme, and t h e mixed scheme-implies
a different distribution of t h e aged dependency burden across t h e working-age population. These distributions are represented pictorially, as Lorenz curves, in
Figure 6. In this figure t h e horizontal axis represents cumulative proportions of
t h e working-age population, and the vertical axis represents cumulative proportions of the support burden borne by this population. The working-age population
i s ordered, by individual, according to t h e s h a r e of t h e support burden individually borne. The ordering i s from the lowest to the highest s h a r e s of the aged supp o r t burden borne. Thus, in t h e extreme family-only scheme, eaah of t h e nearly 70
percent of the working-age population without living aged parents bears none of
t h e support burden, and comes f i r s t in the a r r a y . Next c o m e children from the
largest "sibshipsf', since they m u s t provide the smallest fraation of a unit of support; last c o m e only-children (that is, only-working-age ahildren) with a living
aged parent, eaah of whom i s fully responsible f o r the support of t h e i r parent.
This scheme is represented by the lowest of t h e t h r e e lines graphed in Figure 6,
t h e data f o r which can be found in columns (3)--representing the horizontal axis,
cumulative proportion of children by support burden borne--and (6)--representing
the cumulative amount of support burden borne--of Table 2.
Figure 6.
Distribution of aged dependency burden under alternative support
schemes: base simulation.
The uppermost line shown in Figure 6 shows the distribution of t h e aged
dependency burden under t h e population-based support scheme: this is a scheme
characterized by complete equality, and hence i t appears as a 45-degree straight
line. The middle line represents a mixed system, in which one-half of a "standard
unft" of support fs collectively provided, while family members s h a r e equally in the
provision of t h e remaining half of t h e standard unit.
Even this intermediate
scheme dfstributes the burden of support f o r the elderly r a t h e r unequally, as indicated by the divergence of t h e line from t h e 4 5 4 e g r e e line of uomplete equality.
The distributions shown in Figure 6, i t must be remembered, r e f e r only to t h e
support burden borne by the working-age population. The distribution of support
received by the aged themselves under the t h r e e schemes i s a completely different
matter, although the relative patterns of inequality in the provision and reueipt of
support are the s a m e across schemes: the population-based scheme confers equal
s h a r e s of the burden across the entire working-age population, and bestows equal
benefits across the aged population.
A t the o t h e r extreme, the strictly family-
based scheme distributes both the support burden, and the provision of support,
m o s t unequally: a majority of the working-age population bears no support burden,
and a small minority (about 4 percent) of the aged population receives no support.
The mixed scheme is intermediate, with respect to both the working-age and the
aged population.
W e have seen how prevailing population parameters constrain the scope f o r
shifting the burden of support f o r the aged from the state to the family. How does
this picture change, if at all, when w e consider the situation under alternative
demographic scenarios?-that
is, in the case of increased life expectancy and re-
duced fertility, both of which are expected t o take place? For a n answer to this
question, w e can examine the patterns implied by each of the variant simulations
described earlier.
kriant s i m u l a t i o n s . The reduced-mortality and reduced-fertility variant
simulations allow us to explore the partial effects of ongoing demographic trends
t h a t are being experienced in both IIASA and non-IIASA countries.
Tables A and B-identical
Appendix
in format to Table 1-present details of the kinship pat-
terns generated by the t w o variant simulations. The most important change caused
by a drop in mortality rates is a r i s e in the proportion of the population with a living mother. This r i s e f i r s t becomes apparent in the 25-29 age group, and is on the
o r d e r of a 50-100 percent increase f o r those approaching retirement age.
A comparison of the reduced-fertility scenario to the base simulation reveals
a substantial increase in the proportion of the population over 65, and in the proportion childless at virtually all ages 15 and over. However, while t h e r e are
dramatic changes with respect to offspring, t h e r e is essentially no change with
respect to parents: the proportion with a living mother is about the same, at all
ages, as in the base simulation.
Key findings from all t h r e e simulations are displayed in Table 3. For each indicator shown, the reduced-mortaiity simulation differs very little from t h e base
simulation. Recall that in this alternative scenario, life expectancy at birth w a s
given a modest five percent increase. Accordingly, under the alternative scenario
the proportion of the population over 65 shows a modest increase: from 0.13 to
0.15. Correspondingly slight changes can be found f o r each of the o t h e r indica-
tors shown.
Table 3. Summary of kinship indicators for t h r e e alternative simulations.
Base
Low-mortality
variant
Low-fertllity
variant
Proportion of population aged 65+
.13
.I 5
.23
Proportlon of working-aged population
without aged parents
.70
.66
Proportion of aged population without
working-age offspring
.04
.05
Population-based aged dependency ratio
.I3
-13
.21
Family-based aged dependency ratio
.41
.37
.53
In contrast, t h e reduced-fertility simulation produces dramatic shifts in the
age and kinship structure of t h e population. Again, this simulation assumes fertility rates t h a t are 40 percent lower at all ages than in t h e base simulation. A s a
result, t h e proportion of t h e population in t h e age 65+ group rises significantly,
from 0.13 to 0.23. A s already mentioned, however, the proportion of the workingage population with a living aged mother changes little--a d r o p from 0.70 to 0.66while t h e proportion of t h e aged population without working-age offspring is greatly increased, from about 0.04 to 0.17.
Both t h e population-based dependency ratio-the
r a t i o of elders to t h e
working-age population--and t h e family-based dependency ratio-the r a t i o of eld-
ers with working-age offspring to working-age individuals with a living aged
parent--are distinctly higher in the simulated reduced-fertility world. The former
exhibits a 62-percent increase, while the latter exhibits a m o r e modest 3 0 p e r c e n t
increase.
Y e t within t h e working-age population, t h e distribution of relutive
s h a r e s of parental support obligations i s almost indistinguishable across all t h r e e
simulations; illustrations of this distribution, analogous to that shown in Figure 6
f o r the base simulation, are virtually identical in appearance, and hence are not
shown.
The m o s t striking contrasts suggested by t h e t h r e e sets of results, then, pertain to t h e LmeLs of dependency burdens, and the gross, overall patterns of potential kin-support linkages between t h e aged and working-age populations. Reduced
fertility not only raises t h e aged dependency ratio, i t r a i s e s t h e proportion of eld-
ers with no working-age offspring to call upon ( o r f o r t h e state t o t u r n to); i t increases t h e average number of aged parents p e r working-age adults with living
aged parents, but daes not particularly affect t h e proportion of working-age
adults with a living aged parent.
W e close this section with a reminder t h a t t h e simulation model used in t h e
analysis, like all models, omits c e r t a i n elements of t h e phenomenon being studied.
Since t h e model used daes not incorporate nuptiality, t h e existence of husbands
and f a t h e r s cannot be taken into account. Accordingly c e r t a i n qualifications must
be placed on t h e analysis. Spouses are in f a c t a leading s o u r c e of support f o r t h e
dependent elderly. By omitting spouses, w e ignore a potential sourae of support
f o r t h e older women in t h e population. Even more, however, we ignore a potential
demand upon t h e older women: namely, t h e demands of aaregiving to t h e i r own
aged spouse. Similarly, from t h e perspective of w o r k i n g e e children o u r ignoring
of f a t h e r s means t h a t w e o v e r s t a t e t h e extent of dependency among t h e i r mothers.
However, w e
ignore a n additional (but empirically minor) c l a i m upon t h e
working-age children: t h e existenoe of widowed fathers.
IV. SUMMARY AND CONCLUSIONS
To summarize, this p a p e r has examined t h e aged dependency burden issue at a
microanalytic level, at t h e level of individual kin-network ties. Aggregate population data f o r t h e r e c e n t past, and projections f o r t h e aoming decades, reveal patt e r n s of low fertility and rising life expectancy f o r t h e world as a whole, and f o r
t h e IIASA countries in particular. These trends in vital rates will, in turn, lead t o
increasingly aged population s t r u c t u r e s , with a higher r a t i o of o v e r 4 5 people to
working-age-defined as t h e 2 0 4 4 age group-people.
This p a p e r h a s presented findings from simulation analyses designed to reveal
the p a t t e r n of linkages between individuals within t h e aged and t h e working-age
populations. For t h e r a t h e r simple models used h e r e , t h e only necessary input
data w e r e age-specific schedules of fertility and mortality. Yet the type of information generated by t h e model is not generally available: f o r those countries
which maintain complete population r e g i s t r y systems, such as t h e Scandinavian
countries, kin-linkage information could be extracted with some effort; in o t h e r
countries, data on kinship linkages has, on only a few occasions, been obtained in
sample surveys.
The principal finding of t h e analysis w a s a pronounced lack of overlap of t h e
aged and t h e working-age populations, with r e s p e c t to nuclear-family kinship ties.
Using data which imply a stable population similar in s t r u c t u r e to t h e Netherlands
in 1984, w e find t h a t nearly 70 percent of t h e working-age population does not
have a living aged parent, while about 4 percent of t h e aged population has no
offspring in t h e working-age group. Further reductions in mortality will tend to
exacerbate this lack of overlap only slightly, while reductions in fertility on a
scale t h a t has actually been observed i n s o m e industrialized nations will significantly exacerbate t h e situation.
A tabulation of t h e working-age and aged populations according to t h e existence of living kin in e a c h age group helps to define t h e extreme bounds f o r t h e
use of family members as a n alternative to collective support of t h e elderly. Demographic realities preclude t h e use of t h e family as t h e sole source of support f o r
t h e elderly, since some of t h e aged population i s without working-age family
members to turn to f o r support. Mixed schemes of support f o r t h e aged can be
used to combine collective and kin-based responsibility f o r supporting t h e aged
population; the resulting public policy problem involves tradeoffs among the following t h r e e factors: t h e adequacy of support given t h e worst-off aged, the burden placed on t h e public budget by t h e universal component of t h e aged-support
scheme, and t h e burden placed on those with aged parents by t h e family-based
component of t h e aged-support scheme. To each possible solution to t h e policy
problem t h e r e corresponds t w o distributional analyses, one pertaining to t h e supp o r t burden borne by t h e working-age population (illustrated, f o r example, in Fig-
ure 6) and one pertaining to t h e benefits enjoyed by t h e aged population.
The analysis presented in this p a p e r is, of course, only a f i r s t step. More
complicated demographic models can easily be envisioned. However, a more complete analysis m u s t g o beyond demography, and take account of t h e incentive eff e c t s of public policies. Attempts to compel a shift of t h e burden of supporting t h e
aged away from t h e public budget and onto family members may, in the long run, influence t h e very behaviors t h a t give rise to kinship patterns in t h e f i r s t place.
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Appendix Table A
Summary of Simulated Kinship Patterns, Variant Simulation:
Reduced-Mortality Scenario
Reduced Mor t a l i tv Regime
Key t o columns:
(1)
(2)
(3)
(4)
(5)
(6)
(71
(8)
(9)
(10)
(11)
(12)
(13)
Age group
Proportion o f population i n age group
Proportion i n age group n i t h l i v i n g rother
Averageageoflivingmothersofthoseinagegroup
Mean nunber of l i v i n g daughters o f those i n age group
Average age of l i v i n g daughters o f those i n age group
Propor tion i n age group n i th no l i v i n g daughters
Mean nunber of l i v i n g sons o f those i n age group
Average age o f l i v i n g sons of those i n age group
Proportion i n age group n i t h no l i v i n g sons
Hean nunber o f l i v i n g children o f those i n age group
Average age o f l i v i n g children o f those i n age g r w p
Proportion i n age group with no l i v i n g children
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