Kinship and Family Support in Aging Societies

W O R K I N G P A P E R

~ A l Y D F A Y I L Y ~ R ' r IN AGING

^90QFllE9

December 1986 WP-86-81

I n t e r n a t i o n a l 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 h p e r s are interim r e p o r t s on work of t h e International Institute for Applied Systems Analysis

and

have moeived only limited mvlew. Views or opinions expressed herein do not neoessarfly r e p r e s e n t thase

of

t h e Institute

or

of i t s 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 Na- tions. This researah was supported in part by

G r a n t

No. AGO5153 from t h e U.S.

National Institute on Aging. Important contributions

to

the research

were

made by Nathan Keyfitz, Gun Stsnflo and Jan

Bartlema.

Helpful comments on a n

earlier

ver- sion 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 i s population aging-* phenomenon which

a l m o s t

all c o u n t r i e s in t h e world are experiencing today. Many social economic consequences of aging f o r s o c i e t y depend on t h e existing family s t r u c t u r e a n d 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 kin- s h i p p a t t e r n s . The only d a t a which one needs are t h e data o n f e r t i l i t y a n d mortal- ity. Among o t h e r findings t h e p a p e r shows t h a t , as a r e s u l t of f e r t i l i t y reduction, t h e links between g e n e r a t i o n s became weaker.

A n a t o l i Yashin Deputy L e a d e r Population P r o g r a m

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 R e s u l t s

IV. SUMMARY AND CONCLUSIONS REFERENCES

A p p e n d i x T a b l e A A p p e n d i x 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 popu- lations has existed f o r many years. This concern will presumably grow as the phenomenon continues i t s 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 Un- ited 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 eld- erly world proves

to

be, t h e r e wan be little doubt that the transition will be aocom- panied by important changes in the economic and sooial s t m a t u r e s of many aoun-

tries.

This paper addresses issues related

to

kinship in increasingly w e d popula- tions: 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 indus- trialized countries. A s shall be illustrated, t h e aging phenomenon exhibited in the IIASA uountries Is r a t h e r different from t h a t 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 s o c i a l dimensions t h a t

can

be e x p e c t e d

to

undergo change as a r e s u l t of population aging. A s 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 , s u c h as t h e s p a t i a l 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 affect- ed. 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, a n d possibly of productive ao- flvity 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 h i e r a r c h y , 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 t h e s e 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, prom- inent among which is the issue of s u p p o r t f o r t h e elderly. Family members, espe- oially nuclear-family members (spouse, siblings, children) play important roles i n t h e s u p p o r t f o r t h e e l d e r l y in many countries. S u p p o r t f o r t h e e l d e r l y oan take many forms, including t h e provision of d i r e c t f i ~ n a i a l s u p p o r t , the provision of informal health-care s e r v i c e s , 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 s u c h 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, e v e n given t h e existence of s u c h 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, s e x e s , a g e s , 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 C a r e S u r v e y 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 s e x , a g e ,

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 a n y siblings.

The plan of this p a p e r is as follows. In part 11, s e v e r a l a g g r e g a t e indicators of the aging p r o c e s s , as e x p e r i e n c e d by the IIASA countries,

are

briefly

summar-

ized. 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 , a n d uses these r e s u l t s

to

show how the dependency burden c a n be disaggregated along fami- ly lines. Family linkages between t h e a g e d and t h e working-age populations are il- l u s t r a t e d f o r t h r e e a l t e r n a t i v e demographic soenarios, using a microanalytic simu- lation technique. P a r t IV summarizes and aoncludes t h e p a p e r .

II.

INDICATORS

OF THE

AGlNC

PBOCESS

In o r d e r

to

provide

a

context f o r the subsequent analysis. selected demo- graphic 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 p r e s e n t historical d a t a 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 Na- tions 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 t h a t of t h e USSR and the US, whioh together receive 53.8 p e r c e n t 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 t r e n d 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 s t r u o t u r e , In Figure 1, t h e total f e r -

tility

rate (TFR)

i s shown; t h e IIASA countries, all of which

are

industrialized, have much lower fertility

rates

in t h e r e c e n t 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, t h e

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 g r e a t l y diminished, although not aompletely elim- inated, by 2020. The projected world's TFR for 2020 is

at a b o u t

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

b i r t h (for both s e x e s 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 g a p i s projected

to

dimin- ish g r e a t l y between now and 2020.

Aspects of t h e population a g e s t r u c t u r e implied by t h e paths of fertility and mortality

are

presented in Figures 3 and 4. In Figure 3

w e

see t h e 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, r e f l e c t s t h e vastly dif- f e r e n t 'current a g e s t r u c t u r e of t h e industrialized countries compared

to

t h e

rest

of t h e world. The median a g e 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 r a t i o , constructed as t h e ra- tio 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

' g e n e r a l

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 f a c t , 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 p a p e r examines t h e dependency burden in g r e a t e r de- tail.

IIL

DISAGGEEGATING

TEE

DEPENDENCY RATIO

As mentioned before, t h e aged dependenay r a t i o

commands

considerable

at-

tention

as

a n indiaator of t h e potential problems facing a n increasingly aged popu- lation. 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 dis- cussion. 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 as-

sets 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 popula- tions of these programs-especially, in relation

to

the size of the working popula- tions 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

car-

ing for the aged away from public programs, and onto t h e family (for a policy- oriented 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 ongo- ing 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

Patter-

Demographers have a long tradition of analyzing kinship s t r u c t u r e s . A t p r e s e n t , work on t h i s 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 r e p o r t e d by s e v e r a l a u t h o r s , 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

lim- ited with r e s p e a t

to

t h e goals of t h e p r e s e n t 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. Con- sequently, the simulation a p p r o a c h i s adopted h e r e .

The advantage of t h e 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 a t t r i b u t e s such as sex and the dates of birth and death are associated. Moreover, e a c h hypothetical indi- vidual i s linked

to

o t h e r individuals, with t h e i r corresponding attributes, in t h e s a m e hypothetical population. The r e s u l t s presented below are generated by a new simulation procedure based upon a continuous-time stochastic event-history pro- aess; details regarding t h e features of t h e event-history process, and t h e tech- nique used

to

simulate t h e process, can be found in Wolf (1986).

The assumptions underlying t h e simulations r e p o r t e d h e r e are in many r e s p e c t s identical

to

those adopted by Goodman

et

al. (1974). In particular, t h e population i s assumed

to

be stable and homogeneous with r e s p e c t

to

rates of dying and childbearing; birth

rates

are also assumed not

to

depend upon parity. Howev- e r , in t h e p r e s e n t 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 po- pulation; t h e r e is, however, no mating or "marriage market". Thus, the simulation model in its p r e s e n t stage of development can r e p r e s e n t t h e distributions of broth- ers and sons as w e l l as of s i s t e r s and daughters, but aannot r e p r e s e n t 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 p a t t e r n s then prevailing. Figure 5 helps

to

clarify t h e problem. The horizontal axis in Figure 5 r e p r e s e n t s aalendar time,

set

a r b i - t r a r i l y

to

z e r o

at

t h e leftmost point. Horizontal line segments shown above t h e t i m e axis depict individual lifetimes; t h e left endpoint of

a

segment r e p r e s e n t s one's own d a t e of birth, while t h e r i g h t endpoint of

a

segment r e p r e s e n t s one's own d a t e of death.

x's

along t h e segments r e p r e s e n t 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 f a a t

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 t h e 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 t h e population pictured in Figure 5 uan ^{be ob-} tained by "sampling" from t h e population

at

a n a r b i t r a r i l y 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

t h e time of the "survey" can readily be determined: f o r exam- ple, 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 i s

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 r e p o r t e d below consist of the generation of a l a r g e 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 i s 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 r e f e r e n c e s 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 subse- quently "sampled", as depicted in Figure 5, t h e sample information being then tabu- lated 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 r a t e s , and t h e r a t l o of males

to

females among all births. For t h e simulations r e p o r t e d h e r e , sex-specific vital

rates

f o r 5-year age groups

were

used. The

rates

w e r e t r e a t e d as t h e 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

a g e a is given by

and t h e probability of a b i r t h

at

age at, given t h a t t h e r e was a previous birth

at

a g e 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

a g e z , taken directiy from t h e Input data. b * ( z ) is t h e b i r t h

rate at

age z , adjusted upward from t h e ob- served 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 t h a t t h e birth

rate at

e x a c t a g e

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, t h e proportion

n,

is simply t h e probability of giving b i r t h between

z

-1 and z , given by

Thus. (3) can be r e a r r a n g e d , yielding

which allows

us to

e x p r e s s t h e birth

rate

f o r those actually

at

risk in terms of t h e observed birth

rate.

In

m o s t

applied demographic analysis t h e 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 5- y e a r a g e 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 t h a t 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 r e p o r t e d below.

F u r t h e r generality could b e incorporated into t h e analysis, f o r example by in- troducing "duration dependenae" as well as a g e dependenae, by using parity- specific birth rates. and by taking acaount of persistent intergenerational pat- terns, 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 p a r e n t s 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 p r e s e n t paper.

Simulations Perfoxmed

Three variants of t h e simulation procedure described above w e r e performed f o r this study. A l l are based upon period fertility and mortality data f o r t h e Neth- erlands, 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 ap- proximately t h e

rate

prevailing in 1 - 7 0 , and

a

mortality schedule implying life ex- peotancies

at

birth of approximately 78 y e a r s f o r women, and 72 y e a r s f o r men (figures close

to

those prevailing in t h e period data f o r 1980). Sinoe t h e simula- tions produce kin frequencies f o r t h e s t a b l e populations implied by the input parameters, t h e r e s u l t s

are to

be interpreted as illustrative of a given

pattern

of b i r t h s 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 f i r s t ,

a

low- mortality variant, used age-specific mortality

rates

uniformly 25 p e r c e n t lower than those in t h e base run. This modification implies, in turn, about

a

5 p e r c e n t in- o r e a s e in life expectancy. This increase i s only slightly higher than t h e projected increase, by 2020, for t h e Netherlands

as

given in t h e United Nations projections.

The second simulation variant,

a

low-fertility variant, assumes a uniform 40 p e r c e n t d r o p in age-specific fertility r a t e s ; t h a t is,

a

d r o p

to

a

total

fertility

rate

of approximately 1.6. A d r o p this dramatic was, in fact, attained in t h e Nether- lands between 1970 and 1980. According

to

t h e United Nations projections, t h e to- tal fertility

rate

in t h e Netherlands w i l l be only slightly below the 1.6 level f o r t h e

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 like- ly 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

summar-

ized in Table 1, which p r e s e n t s kin patterns from t h e viewpoint of women. This table refers

to a

simulated population containing approximately 30,000 women. The population w a s generated by simulating t h e successive offspring of

a

l a r g e 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 y e a r s of evolution by %year a g e groups;

this distribution a g r e e s 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 popula- tion implied by t h e input data.

Table 1. Summary of simulated kinship patterns, base simulation.

Basic r e s u l t

Key t o 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 t h a t developed by Goodman, Keyfitz and Pul- lum (1974), yield Information such as t h a t 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 t h i s 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 d a u g h t e r s 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 g r o u p exhi- biting f e r t i l i t y 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.' T h e r e a f t e r , t h e Alean number of living d a u g h t e r s drops, reflecting mortality among t h e daughters. The mean number of sons [aolumn (8)] and of all children [column (11)] behave e x a c t l y as does t h e mean number of daughters.

However, t h e miorosimulation a p p r o a c h

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 consider- a b l y 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), a n d (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 b a s e simulation t h e p r o p o r t i o n 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 g r o u p , remaining virtually unchanged

at

t h a t level through t h e 70-74 a g e group. T h e r e 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 o v e r . This must remain a r a t h e r tentative conclusion, since so few members of t h e simulated popu- lation fall into t h e s e a g e groups. For example, t h e proportion childless in t h e 95- 99 a g e g r o u p (0.19) i s 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

r e s u l t s , a 95-peroent confidence i n t e r v a l f o r t h e t r u e p r o p o r t i o n childless would r a n g e from 0.022

to

0.358. More- o v e r , t h e oonclusion i s of l i t t l e 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 t h a n one p e r c e n t of t h e popula- tion falls into t h e 90-and-over category. However, if p r e s e n t demographic t r e n d s oontinue t h e oldest-old g r o u p s will g r e a t l y i n c r e a s e in r e l a t i v e terms, a n d t h e i r unique family situation w i l l take o n 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 c h i l d r e n available

to

t h e population by age group. This a v e r a g e is, of c o u r s e , inoreasing o v e r t h e life cyole. N o t e t h a t ,

on

t h e a v e r a g e , t h e chil- d r e n of t h e "oldest-old"

are

themselves approaching r e t i r e m e n t age.

%here are aorne minor irregularities In column (5)-and elsewhere in Table 1-reflecting the inev- itable presence of HontbCarlo "suapllng error" in the dmulation; even a simulated population of over 30,000 l a "small" f o r 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

t u r n

to

t h e family as a source of support f o r the aged po- pulation. A s w e oonsider successively older ages, an increasing proportion of t h e elderly a r e without living offspring; among those with living offspring, t h e average age of t h e 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 popula- tion 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

t h e number of living ohil- d r e n they have. Only women

are

counted in t h e tabulation of t h e aged group. Those in t h e 20-64 a g e group

are

tabulated aooording

to

(1) whether t h e i r mother is alive a d 65

or

older, and (2) t h e 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

in- cluded in t h e tabulation of t h e 20-64 group. sinoe both s e x e s r e p r e s e n t 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+ a g e 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

t h e number of living children (age 20+) s h e has.

The table i s a r r a n g e d such t h a t as

we

r e a d down t h e oolumns,

w e

encounter ohil- d 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 t h e number of children aocording

to

t h e existelme of a n aged mother and t h e size of sibship, w e see t h a t 69.8 percent of ohildren 20-64 d o 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

t h a t t h e i r 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

m o r e .

Such ohildren, beoalm~e they have s e v e r a l b r o t h e r s and/or s i s t e r s , b e a r proportionately less of t h e burden of parental oare than d o children from

smaller

s i bships-at least, on average. Moving down this oolumn, w e

see

t h a t 2.4 percent of all persons aged 20-64, in t h e simulated population, are only ahildren-more pre- cisely. only Ltving children-with a living mother 85 or older.

Table 2. Cross-tabulation of aged mothers and working-age children, base simulation.

Population Group

Children Mothers

Age 2084 Age 65+

(1) (2) (3) (4 (5) (6 (7) (8)

CumulaUve Proportion Cumulatlve

Proportion Proportion of 20-64 Proportlon Proportlon Number of Total of Total Number Group Number of Total of Total

N o living mother 65+ 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

sibshlp = 3

slbshlp = 2

elbshlp = 1 737 .024 1.00 20 .027 775 .I95 .B55

N o Hvlng ahildren

- - - - -

^{176 .044 .999}

Total 30699 1.00 180 3976 1.00

In reoognition of t h e f a c t t h a t those 65 or older may not be forced

to

rely ex- clusively on family members under 65, columns (4) and (5) of Table 2 show t h e 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 p e r c e n t

to

2.7 percent of t h e oorresponding "young sibling" group.3 In o t h e r words, t h e pool of &nd- older 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) p r e s e n t t h e distribution of aged mothers acoording

to

t h e number of living children. The l a r g e s t single group

are

those with

t w o

living chil- d r e n (28 percent of t h e total); a A t h e r small 4.4 p e r c e n t 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 t h e 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 t u r n should b e of considerable i n t e r e s t

to

those who s e e k

to

use t h e instru- ments of public policy

to

encourage a s h i f t of responsibility f o r t h e support of t h e elderly away from t h e s t a t e , and onto t h e family.

First, t h e oonventional aged dependency r a t i o f o r t h e 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 t h a t t h e working- age population s h a r e d fully and equally t h e burden of support of t h e 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 b e required

to

provide .13 units of support f o r t h e aged (ignoring, in this ar-

tificial 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 t h e

state

pro- vides no support f o r t h e elderly, and r e q u i r e s any such support

to

aome from fami- ly members. However improbable such

a

scheme may seem, i t is instructive

to ex-

amine t h e distribution of t h e aged dependency burden in such

a

situation. First, i t i s a p p a r e n t t h a t between 4 and 5 peroent of t h e 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 20- 64 age group, and 20 were in the 65+ age group.

have access

to

no support from the working-age population whatsoever. Moreover, nearly 70 p e r c e n t of t h e working-age population b e a r s none of t h e aged dependen- ay burden whatsoever. Among those working-age individuals who do have an aged parent, t h e 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 s h a r e d within working-age "sibships". Thus, a working-age in- dividual with a n aged p a r e n t

to

support, but with no working-age siblings, must contribute a full s h a r e of t h e supplemental support allowance;

a

working-age indi- vidual 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 t h e 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 po- pulation. These distributions

are

represented pictorially, as Lorenz curves, in Figure 6. In this figure t h e horizontal axis r e p r e s e n t s cumulative proportions of t h e working-age population, and t h e vertical axis r e p r e s e n t s cumulative propor- tions of t h e support burden borne by this population. The working-age population i s o r d e r e d , by individual, according

to

t h e s h a r e of t h e support burden individual- ly borne. The ordering i s from t h e lowest

to

t h e highest s h a r e s of t h e aged sup- p o r t burden borne. Thus, in t h e extreme family-only scheme, eaah of t h e nearly 70 p e r c e n t of t h e working-age population without living aged parents b e a r s none of t h e support burden, and comes f i r s t in t h e a r r a y .

Next

c o m e children from t h e largest "sibshipsf', since they

m u s t

provide t h e

smallest

fraation of a unit of sup- port; 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 t h e support of t h e i r parent.

This scheme is represented by t h e lowest of t h e t h r e e lines graphed in Figure 6, t h e d a t a 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 t h e cumulative amount of s u p p o r t 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 a p p e a r s as a 45-degree s t r a i g h t line. The middle line r e p r e s e n t s 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 t h e elderly r a t h e r unequally, as indi- cated 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 s u p p o r t burden borne by t h e working-age population. The distribution of support received by t h e aged themselves under t h e t h r e e schemes i s a completely different matter, although t h e relative p a t t e r n s of inequality in t h e provision and reueipt of

support are t h e

s a m e

across schemes: the population-based scheme confers equal s h a r e s of the burden across t h e e n t i r e working-age population, and bestows equal benefits across t h e 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 b e a r s no support burden, and a small minority (about 4 percent) of t h e aged population receives no support.

The mixed scheme i s intermediate, with respect

to

both the working-age and the aged population.

W e have seen how prevailing population parameters constrain t h e scope f o r shifting the burden of support f o r the aged from t h e

state to

t h e family. How does this picture change, if

at

all, when w e consider t h e situation under alternative demographic scenarios?-that is, in t h e

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 t h e patterns implied by each of t h e variant simulations described e a r l i e r .

kriant s i m u l a t i o n s . The reduced-mortality and reduced-fertility variant simulations allow us _to explore t h e partial effects of ongoing demographic trends t h a t are being experienced in both IIASA and non-IIASA countries. Appendix Tables A and B-identical 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 d r o p in mortality

rates

i s a r i s e in t h e proportion of the population with a liv- ing mother. This r i s e f i r s t becomes a p p a r e n t in t h e 25-29 age group, and i s on t h e 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 t h e proportion of t h e population o v e r 65, and in the pro- portion childless

at

virtually a l l ages 15 and over. However, while t h e r e are dramatic changes with respect

to

offspring, t h e r e i s essentially no change with r e s p e c t

to

parents: t h e proportion with a living mother i s about t h e 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 in- dicator shown, t h e 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 p e r c e n t increase. Accordingly, under the alternative scenario t h e proportion of the population o v e r 65 shows a modest increase: from 0.13

to

0.15. Correspondingly slight changes can be found f o r each of t h e o t h e r indica-

tors

shown.

Table 3. Summary of kinship indicators for t h r e e alternative simulations.

Low-mortality Low-fertllity

Base variant 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 a g e and kinship

structure

of t h e population. Again, this simulation assumes fertili- ty rates t h a t are 40 p e r c e n t 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 a g e 65+ group r i s e s significantly, from 0.13 to 0.23. A s already mentioned, however, t h e proportion of t h e working- age population with a living aged mother changes little--a d r o p from 0.70

to

0.66- while t h e proportion of t h e aged population without working-age offspring is great- ly increased, from about 0.04

to

0.17.

Both t h e population-based dependency r a t i o - t h e r a t i o of elders

to

t h e working-age population--and t h e family-based dependency r a t i o - t h e 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 t h e simulated reduced-fertility world. The former exhibits a 62-percent increase, while t h e

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

t h a t shown in Figure 6 f o r t h e base simulation,

are

virtually identical in appearance, and hence

are

not shown.

The

m o s t

striking c o n t r a s t s suggested by t h e t h r e e sets of results, then, per- tain

to

t h e LmeLs of dependency burdens, and the gross, overall patterns of poten- tial kin-support linkages between t h e aged and working-age populations. Reduced

fertility not only raises t h e aged dependency r a t i o , 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 in- creases t h e a v e r a g e number of aged p a r e n t s p e r working-age adults with living aged parents, but d a e s not particularly a f f e c t t h e proportion of working-age adults with

a

living aged p a r e n t .

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 d a e s not i n c o r p o r a t e nuptiality, t h e existence of husbands and f a t h e r s cannot b e taken into account. Accordingly c e r t a i n qualifications must b e placed on t h e analysis. Spouses are in f a c t

a

leading s o u r c e of s u p p o r t f o r t h e dependent elderly. By omitting spouses, w e ignore a potential s o u r a e of s u p p o r t f o r t h e o l d e r women in t h e population. Even more, however, we ignore a potential demand upon t h e o l d e r 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 e x t e n t 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 f a t h e r s .

IV. SUMMARY AND

CONCLUSIONS

To summarize, this p a p e r h a s examined t h e aged dependency burden issue

at

a microanalytic level,

at

t h e level of individual kin-network ties. Aggregate popula- tion data f o r t h e r e c e n t past, and projections f o r t h e aoming decades, r e v e a l pat- t 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 t r e n d s in vital

rates

will, in t u r n , 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 a g e group-people.

This p a p e r h a s presented findings from simulation analyses designed

to

r e v e a l 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 infor- mation g e n e r a t e d by t h e model i s 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 b e e x t r a c t e d with some e f f o r t ; in o t h e r countries, d a t a 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 d a t a which imply a s t a b l e 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 p e r c e n t of t h e working-age population does not have a living aged p a r e n t , while about 4 p e r c e n t of t h e aged population has no offspring in t h e working-age group. F u r t h e r reductions in mortality will tend

to

e x a c e r b a t e this lack of overlap only slightly, while reductions in fertility on

a

scale t h a t h a s actually been observed i n s o m e industrialized nations will signifi- cantly e x a c e r b a t e t h e situation.

A tabulation of t h e working-age and aged populations according

to

t h e ex- istence of living kin in e a c h a g e 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 s u p p o r t of t h e elderly. Demo- g r a p h i c realities preclude t h e

use

of t h e family as t h e

sole

s o u r c e of s u p p o r t f o r t h e elderly, since some of t h e aged population i s without working-age family members

to

t u r n

to

f o r support. Mixed schemes of s u p p o r t f o r t h e aged c a n b e used

to

combine collective and kin-based responsibility f o r supporting t h e aged population; t h e resulting public policy problem involves tradeoffs among t h e fol- lowing t h r e e factors: t h e adequacy of s u p p o r t given t h e worst-off aged, t h e bur- den 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 p a r e n t s 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 sup- p 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 c a n easily b e envisioned. However, a

more

com- plete analysis

m u s t

g o beyond demography, and t a k e account of t h e incentive ef- f 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 t h e long run, in- fluence t h e v e r y behaviors t h a t give rise

to

kinship p a t t e r n s in t h e f i r s t place.

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a

Burden Not a Burden? The Elderly in A m e r i c a . The Brookings Review, Summer 1986, pp. 17-24.

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UP:

A 2 b o - S ~ model of Kin-Counts. WP-86-69. Laxenburg, Austria: International Institute f o r Applied Systems Analysis.

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Younger

and Older Sisters. h o g r a p h y 15:499-507.

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2000: The Chickens Come Home

to

Roost. In S.B. Keisler, J.M. Morgan, and V.K. Oppenheimer (eds.), Aging: Social Change. N e w York: Academic Press.

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a

Galton-Watson Proaess. Journal o f d p p l i e d ProbabiLity 19:767-775.

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Wachter, E.A. Hammel and P. Laslett (eds.), S a t i s t i c a l S u d i e s of Historical Social S r u c t u r e . N e w York: Aaademic

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Dgmography 13:105-114.

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a

Stable Population.

Dwroography 19549-566.

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at

the XIIIth International Congress of Gerontology, N e w York, July 1985.

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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) Age group

(2) Proportion o f population i n age group (3) Proportion i n age group n i t h l i v i n g rother

(4) A v e r a g e a g e o f l i v i n g m o t h e r s o f t h o s e i n a g e g r o u p ( 5 ) Mean nunber o f l i v i n g daughters o f those i n age group (6) Average age of l i v i n g daughters o f those i n age group (71 Propor t i o n i n age group n i th no l i v i n g daughters (8) Mean nunber o f l i v i n g sons o f those i n age group (9) Average age o f l i v i n g sons o f those i n age group (10) Proportion i n age group n i t h no l i v i n g sons

(11) Hean nunber o f l i v i n g children o f those i n age group (12) Average age o f l i v i n g children o f those i n age g r w p (13) Proportion i n age group with no l i v i n g children

-

- O ~ C - C - N - N - C . - W ~ O C U ~ - ~

CQ o - r ~ - a c o ~ c o w ~ W c o ~ r - h ~ - a m m

-

d d d d d d d d d d d d d d d d d d d d d

m m m m U u - O * O * O ' J * O r - h . ~ ~ ~ r + ~ - O O

-

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

-

N d d d d d d d d d d d d d d d d d d d d d

- W L w L W L w a

s . r l . r l g

s !q ^z-gs z.s; z.5

O + d w =J w + =J w + 3 a + L L L r n E r n L C r n L C r n L e n o o a a aao aao aao

n n L C L n E L n C L n w 0 0 w a a w 0 ~ ~ 0 ~ w 0

Z h h S ~ Z h P l h P l h