Family Size of Women and Children
during the Demographic Transition
David Lam
University of Michigan
Letícia Marteleto
University of Texas
University of Colorado
March 3, 2015
Support for this research was provided by the U.S. National Institute of Child
Health and Human Development.
Family size and cohort size
• This paper is a sequel to previous papers looking at family size and
cohort size during the demographic transition:
• David Lam and Letícia Marteleto, “Stages of the Demographic
Transition from a Child’s Perspective: Family Size, Cohort Size, and
Children’s Resources,” Population and Development Review, June
2008, 34(2): 225-252.
• David Lam and Letícia Marteleto, “Small Families and Large Cohorts:
The Impact of the Demographic Transition on Schooling in Brazil,” in
The Changing Transitions to Adulthood in Developing Countries,
National Academies Press, Washington, DC, 2006, pp. 56-83.
• We showed that family size declines while cohort size increases
during a long period of the demographic transition – 20 to 30 years in
most countries. During this period competition for resources within
families is declining, while competition with cohort members is
increasing.
Number of surviving siblings of 9-11-year-olds and total number
of 9-11-year-olds in population, Brazilian censuses 1960-2000
6.0
250
Number of surviving
siblings of 9-11 year-olds
200
4.0
150
3.0
Total number aged 9-11
in population
100
2.0
1.0
Stage 1, rising
fam ily size and
cohort size
Stage 2, falling
fam ily size and
rising cohort size
Stage 3, falling
fam ily size and
cohort size
0.0
1960
Cohort size (1960=100)
Number of siblings
5.0
50
0
1965
1970
1975
1980
1985
1990
1995
2000
David Lam and Letícia Marteleto, “Stages of the Demographic Transition from a Child’s Perspective:
Family Size, Cohort Size, and Children’s Resources,” Population and Development Review, June 2008.
Purpose of this paper
• How are changes in the family size of children
related to changes in fertility during the
demographic transition?
• This is important if children are competing for
resources with siblings.
• While it may seem obvious that children’s family
size will fall when fertility declines, they do not
need to fall at the same rate or even change in
the same direction.
• We expand on Preston (1976) and study a large
number of countries during the demographic
transition.
• We also look at the inequality in family size,
extending Preston’s results.
Distribution of family size for women
Number of children surviving to women aged 45-49,
Brazil 1960
0.12
Women (mean=4.5)
Density
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Number of children
Children’s family size as a function of women’s family
size
fw(s)=pdf for family size of women aged 45-49
fc(s)=pdf for family size of children of women aged 45-49
sW = mean family size for women aged 45-49
sfW ( s )
sfW ( s )
fC ( s)  n

sW
sf
(
s
)
ds
 W
0
fC ( s )  fW ( s ) if s  sW
fC ( s )  fW ( s ) if s  sW
fC ( s )  fW ( s ) if s  sW
Mean family size of women and children
Number of children surviving to women aged 45-49,
Brazil 1960
0.14
Women
(Mean=4.5)
Children
(Mean=7.1)
0.12
Density
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Number of children
Sam Preston, Family Sizes of Children and Family Sizes
of Women,” Demography 1976
sW = mean family size for women aged 45-49
 W = standard deviation of family size for women aged 45-49
sC = mean family size of their children
n
sW   s fW ( s )ds
fC ( s)
0
n


sfW ( s ) 

sC   s f C ( s )ds   s n
ds 
 sf ( s )ds 
0
0
 0 W

n
n
n
sC 
2
s
 fW (s)ds
0
sW
n
2
2
2
s

s
f
(
s
)
ds

s
 W  W
  W  fW (s)ds
0
0
sW
  W2 
 sW  

 sW 
Sam Preston, Family Sizes of Children and
Family Sizes of Women,” Demography 1976
sW = mean family size for women aged 45-49
 W = standard deviation of family size for women
sC = mean family size of their children
  W2 
sC  sW  

 sW 
(1)
CVW = coefficient of variation of women’s family size ( W / sW )
  W2
sC  sW 1  2
sW


2

s
(1

CV
 W
W)

(2)
Fertility can decline without a decrease in mean family
size for children
Case 1: Before fertility decline
50% of women have 2 children
50% of women have 6 children
Mean family size for women = 1/2*2 +1/2*6
= 4.0
Mean family size for children = 2/8*2 + 6/8*6=0.5+4.5 = 5.0
Case 2: After fertility decline
50% of women have no children
50% of women have 6 children
Mean family size for women = 1/2*0 +1/2*6 = 3.0 (decrease of 1)
Mean family size for children = 6.0
(increase of 1)
Implications of Preston’s result
sC  sW (1  CVW2 )
(2)
• Mean children’s family size is always greater
than mean women’s family size, as long as there
is any variance in fertility
• Fertility decline and family size:
– If CV goes up while mean fertility declines, children’s
family size will decline more slowly than women’s
family size
• Comparing subgroups:
– If a group with higher fertility also has a higher CV,
then the difference in family size of children will be
larger than the difference in family size of women.
Preston’s analysis of U.S. data
• Preston found exactly these two patterns in historical U.S.
data for women aged 45-49
Year
1890
1910
1940
1950
1960
1970
Women's Children's
mean
mean
family size family size
(1)
(2)
4.99
7.78
4.09
7.17
2.66
5.36
2.29
4.91
2.25
4.41
2.71
4.46
Year
1970 White
1970 Nonwhite
Women's Children's
mean
mean
family size family size
(1)
(2)
2.65
4.20
3.16
6.32
Ratio
(2) / (1)
(3)
1.56
1.75
2.02
2.14
1.96
1.65
Ratio
(2) / (1)
(3)
1.58
2.00
CV for
women
(4)
0.75
0.87
1.01
1.07
0.98
0.81
CV for
women
(4)
0.76
1.00
Women’s family size fell
54% from 1890-1950, but
children’s family size fell
only 37%
Due to rising CV
Nonwhite women had 19%
higher family size than white
women, but nonwhite children
had 50% higher family size
than white children
Due to larger CV for nonwhites
Implications for family size during
demographic transition
• “These patterns are a disconcerting
precedent for those concerned with issues
of population quality in less developed
countries; the pace of reductions in family
size for children can be expected to lag
behind that for women in the process of
fertility transition” (Preston 1976: 108).
• One purpose of this paper is to test this
prediction across a wide range of countries.
We extend Preston’s results to look at the
standard deviation of children’s family size
 C = standard deviation of family size for children
 W = standard deviation of family size for women
CVW = coefficient of variation of women’s family size ( W / sW )
SW = skewness of family size for women
 C2  W2 1  CVW (SW  CVW )
(3)
Empirically, skewness is slightly negative at high levels of fertility
and becomes increasingly positive as fertility declines. The term in
brackets tends to be less than 1 at high levels of fertility and greater
than 1 at low levels of fertility.
Increasing skewness causes children’s standard deviation to fall more
slowly than women’s standard deviation as fertility declines.
Number of children surviving to women aged
45-49, Brazil 1960-2010
0.35
Distribution becomes
more skewed as fertility
declines
0.3
Density
0.25
0.2
0.15
1960
1970
1980
1991
2000
2010
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Number of children
Surviving family size of children of women
aged 45-49, Brazil 1960-2010
0.35
This distribution also
becomes more skewed
as fertility declines, but
is shifted to right
compared to distribution
for women.
0.3
Density
0.25
0.2
0.15
1960
1970
1980
1991
2000
2010
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Number of children
Distribution of
surviving family
size for women
aged 45-49 and
children of
women aged
45-49, Brazil
1960-2010
Note that bottom
figure is a
reweighted
version of the top
figure
Women’s family size
Children’s family size
.35
Thailand 1970
Women
.1
.15
.2
Children
0
.05
Distribution of family
size for women
aged 45-49 and
children of women
aged 45-49
.25
.3
Mean for women=6.53
Mean for children=8.21
(ratio 1.26)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Thailand 2000
.3
Women
.25
Children
.1
.15
.2
Mean for women=2.55
Mean for children=3.47
(ratio 1.36)
0
.05
Thailand 1970 and
2000
1
.35
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Empirical Analysis
• We use IPUMS-International census data and
Demographic and Health Surveys
• We use 101 countries, 310 total data sets, including
high-income countries with fertility data
• Scatterplots include both cross-sectional variation
across countries and time series variation within
countries
• We show estimates of OLS regression and Fixed
Effect (FE) regression using only within-country
variation over time.
Summary of datasets with
children ever born variable
Total datasets
Number of countries
Number of countries with
multiple years
Total IPUMS-I DHS
310
144
166
101
59
68
74
41
43
Coefficient of variation in women’s family size, by mean
family size, children ever born to women aged 45-49
1
CV rises as fertility falls
Coefficient of variation
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Slope=-0.051 (0.003)
0.1
b(FE)=-0.026 (0.005)
N=310 (101
countries)
0
1
2
3
4
5
6
Women’s mean family size
7
8
9
Coefficient of variation in women’s family size, by mean
family size, children ever born to women aged 45-49
1
Uruguay 1975
Chile 1960
CV rises as fertility falls
Coefficient of variation
0.9
0.8
0.7
0.6
Ukraine 2007
0.5
Slovenia 2002
0.4
China 1990
Jordan 1990
0.3
0.2
Slope=-0.051 (0.003)
0.1
b(FE)=-0.026 (0.005)
N=310 (101
countries)
0
1
2
3
4
5
6
Women’s mean family size
7
8
9
Skewness in women’s family size, by mean family size,
children ever born to women aged 45-49
2.5
Skewness is negative at high
fertility levels, increases to highly
positive at low fertility levels
2
Skewness
1.5
1
0.5
0
Slope=-0.307 (0.010)
-0.5
b(FE)=-0.271 (0.017)
-1
1
2
3
4
5
6
Women’s mean family size
7
8
9
Mean children’s family size by mean women’s family
size, children ever born to women aged 45-49
Children’s mean family size
10
45-degree line
Children's mean
OLS line
9
8
7
6
5
4
Slope=1.041 (0.017)
3
b(FE)=1.191 (0.029)
2
1
1
2
3
4
5
6
Women’s mean family size
7
8
9
Standard deviation in children’s family size, by mean
number of children ever born to women aged 45-49
Standard deviation of children’s
family size rises slightly with
falling fertility, in spite of the large
decline in the mean
S.D. children’s family size
6
5
4
3
2
Slope=-0.059 (0.022)
1
b(FE)= 0.031 (0.036)
0
1
2
3
4
5
6
Women’s mean family size
7
8
9
Multipliers for mean and standard deviation
sC  sW (1  CVW2 )  sW k
 C2   W2 1  CVW ( SW  CVW )
 C   W 1  CVW ( SW  CVW )
1/2
 C  W m
If k and m are constant, then mean and standard deviation of
children’s family size will decline at same rate as the mean and
standard deviation of women’s family size.
We look at how k and m vary with the mean of women’s family size.
Ratio of children’s mean family size to women’s mean family size,
by mean family size of women aged 45-49, children ever born
k=Children’s mean /Women’s mean
2
Preston was right that children’s
family size falls more slowly than
women’s family size
1.9
1.8
South Africa
2007, 2001, 1996
1.7
1.6
1.5
1.4
1.3
1.2
Slope= -0.060 (0.004)
1.1
b(FE)= -0.028 (0.006)
1
1
2
3
4
5
6
7
Women’s mean family size
8
9
Ratio of children’s mean family size to women’s mean family size,
by mean family size of women aged 45-49, children ever born
Mexico 1960 and China 1982 had
similar fertility levels, but mean family
size of children was 37% higher in
Mexico (2.4 extra siblings)
k=Children’s mean /Women’s mean
2
1.9
1.8
Mexico 1960,
5.16*1.67=8.62
1.7
1.6
1.5
1.4
1.3
1.2
China 1982,
5.36*1.17=6.29
1.1
1
1
2
3
4
5
6
7
Women’s mean family size
8
9
Ratio of children’s mean family size to women’s mean family size,
by mean family size of women aged 45-49, surviving children
k=Children’s mean /Women’s mean
2
Pattern using surviving children is
very similar to pattern using
children ever born
1.9
1.8
1.7
1.6
Slope= -0.059 (0.006)
1.5
b(FE)= -0.040 (0.005)
1.4
1.3
1.2
N=266 (87
countries)
1.1
1
1
2
3
4
5
6
7
Women’s mean family size
8
9
Figure X. Ratio of children's family size to women's family size
B. Colombia
C. Mexico
D. Chile
E. DominicanRepublic
F. Ecuador
G. Panama
H. Peru
1.1 1.2 1.3 1.4 1.5 1.6
1.1 1.2 1.3 1.4 1.5 1.6
A. Brazil
2
3
4
5
6 7
8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2
Mean number of surviving children, women 45-49
3
4
5
6
7 8
Figure X. Ratio of children's family size to women's family size
J. Indonesia
K. Philippines
L. Bangladesh
M. Jordan
N. Morocco
1.1 1.2 1.3 1.4 1.5 1.6
1.1 1.2 1.3 1.4 1.5 1.6
I. Thailand
2
3
4
5
6
7
8 2
3
4
5
6
7
8 2
3
Mean number of surviving children, women 45-49
4
5
6
7
8
Figure X. Ratio of children's family size to women's family size
P. Ghana
Q. Rwanda
R. Tanzania
S. Zambia
T. Zimbabwe
1.1 1.2 1.3 1.4 1.5 1.6
1.1 1.2 1.3 1.4 1.5 1.6
O. Kenya
2
3
4
5
6
7
8 2
3
4
5
6
7
8 2
3
Mean number of surviving children, women 45-49
4
5
6
7
8
Implications for children’s resources
• Suppose some fixed resource, like mother’s time, is divided
by the number of children.
• Suppose women’s family size falls from 8 to 2.
• If children’s family size also fell to 1/4 its original size, then
resources per child would go up 4 times.
• Alternatively, suppose the ratio of children’s family size to
women’s size increases from 1.2 to 1.5 (children’s family
size falls from 9.6 to 3.0).
• Resources per child increase by 3.2 times instead of 4
times. The increase is 20% smaller than it would have
been if children’s family size had fallen as fast as women’s
family size.
Ratio of children’s mean family size to women’s mean family size,
by mean family size of women aged 45-49, children ever born
Increase in ratio from 1.2 to 1.5 when
fertility falls from 7 to 2. This implies
a 20% smaller increase in resources
per child than if ratio remained
constant. (1.2/1.5=0.8)
k=Children’s mean /Women’s mean
2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
1
2
3
4
5
6
7
Women’s mean family size
8
9
“Leakage” in resources per child
sC  sW (1  CVW2 )  sW k
ln( sC )  ln( sW )  ln( k )
 ln( sC )  ln( sW )  ln(k )


t
t
t
If k is constant, then a 10% decline in mean women’s family size will
lead to a 10% decline in mean children’s family size, and a 10%
increase in resources per child. An increase in k by 10% will
completely offset this.
The percentage change in k can be thought of as a “tax” or “leakage”
in the increase in resources per child that would have occurred from
the decline in fertility.
“Leakage” in resources per child –
Regression of log(k) on log(children ever born)
log(CEB-4549)
log(k) using children
ever born
OLS
FE
-0.179
-0.084
[0.012]** [0.021]**
log(Surv-4549)
Constant
0.57
0.419
[0.020]** [0.033]**
Observations
310
R-squared
0.42
Number of countries
310
0.07
101
Standard errors in brackets
* significant at 5%; ** significant at 1%
log(k) using surviving
children
OLS
FE
-0.167
-0.118
[0.017]** [0.017]**
0.523
0.449
[0.026]** [0.026]**
266
0.27
266
0.21
87
Family size of school-aged children
• The children of women aged 45-49 are not
necessarily an interesting group.
– Many of them are not children
– They span a large age range.
• We may be more interested in a particular age
range of children, say school-age children.
• We will focus on children aged 10 (or 9-11).
• We show empirically that the following is a good
approximation for describing the mean family
size of ten-year old children:
sC (10)  sW (2549) 1  CV
2
W (25 49)

(4)
Family size of school-aged children
• Calculate the family size of children aged 9-11:
– Match them to their mothers in the censuses and
DHS surveys
– Take the number of surviving children of their mothers
• Generate the surviving family size of women 2549 using the same reweighting used above
• A comparison shows that these distributions are
very similar in all countries.
• Children aged 9-11 are roughly representative of
the children of women aged 25-49
Family size of children aged 9-11 and
children of women aged 25-49, Brazil 1960
0.16
Children 9-11
0.14
Children of women 25-49
Density
0.12
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
Number of children
10 11 12 13 14 15
7
Mean family size of children aged 9-11 and
children of women aged 25-49
1
2
3
4
5
6
Children 9-11
45-degree line
1
2
3
4
5
6
Mean family size of children of women 25-49
7
Figure 3. Distribution of family size, women 25-49 and children 9-11
3
4
5
6
7
8
9
Number of surviving children
10
.1 .2 .3 .4 .5 .6 .7 .8 .9
1
2
2000
1991
1980
1970
1960
2000
1991
1980
1970
1960
0
Cumulative proportion
1
11
0
1
2
3
4
5
6
7
8
9
Number of surviving children
10
11
0
1
2
3
4
5
6
7
8
9
Number of surviving children
10
.1 .2 .3 .4 .5 .6 .7 .8 .9
2001
1990
1982
1974
2001
1990
1982
1974
0
Cumulative proportion
.1 .2 .3 .4 .5 .6 .7 .8 .9
1
Children 9-11, Ecuador
1
Women 25-49, Ecuador
11
0
1
2
3
4
5
6
7
8
9
Number of surviving children
10
11
0
1
2
3
4
5
6
7
8
9
Number of surviving children
10
11
.1 .2 .3 .4 .5 .6 .7 .8 .9
2000
1984
1980
2000
1984
1973
0
Cumulative proportion
.1 .2 .3 .4 .5 .6 .7 .8 .9
1
Children 9-11, Costa Rica
1
Women 25-49, Costa Rica
0
Cumulative proportion
Large families are
much more common
for children than for
women.
Children 9-11, Brazil
1
.1 .2 .3 .4 .5 .6 .7 .8 .9
0
0
0
Cumulative proportion
Cumulative proportion
Cumulative
distribution of
family size for
women aged 25-49
and children aged
9-11, Brazil,
Ecuador, and Costa
Rica
Women 25-49, Brazil
0
1
2
3
4
5
6
7
8
9
Number of surviving children
10
11
Figure 3. Distribution of family size, women 25-49 and children 9-11
2
3
4
5
6
7
8
9
Number of surviving children
10
2000
1991
1980
1970
1960
0
Cumulative proportion
1
2000
1991
1980
1970
1960
.1 .2 .3 .4 .5 .6 .7 .8 .9
1
Children 9-11, Brazil
1
.1 .2 .3 .4 .5 .6 .7 .8 .9
0
0
11
0
1
3
4
5
6
7
8
9
Number of surviving children
10
11
2
3
4
5
6
7
8
9
Number of surviving children
10
2001
1990
1982
1974
0
Cumulative proportion
1
2001
1990
1982
1974
.1 .2 .3 .4 .5 .6 .7 .8 .9
1
Children 9-11, Ecuador
1
.1 .2 .3 .4 .5 .6 .7 .8 .9
0
11
0
1
2
3
4
5
6
7
8
9
Number of surviving children
10
11
0
0
1
2
3
4
5
6
7
8
9
Number of surviving children
10
11
.1 .2 .3 .4 .5 .6 .7 .8 .9
2000
1984
1980
2000
1984
1973
0
Cumulative proportion
.1 .2 .3 .4 .5 .6 .7 .8 .9
1
Children 9-11, Costa Rica
1
Women 25-49, Costa Rica
Cumulative proportion
2
Women 25-49, Ecuador
0
Cumulative proportion
Cumulative proportion
In Brazil 80% of women
aged 25-49 had less than
four surviving children in
2000;
Only 58% of children were
in families with less than
four surviving children in
2000, similar to the
proportion for women in
1960.
Women 25-49, Brazil
0
1
2
3
4
5
6
7
8
9
Number of surviving children
10
11
In Ecuador in 2001 only 3.2% of women were
in a family with 8 or more children, but 10.6%
of children were in a family with 8 or more
surviving children.
.9
.8
.7
.6
.5
.4
.3
.2
0
0
1
2
3
4
5
6
7
Number of surviving children
8
9
10
11
2001
1990
1982
1974
.1
.1
2001
1990
1982
1974
0
.2
.3
.4
.5
.6
Cumulative proportion
.7
.8
.9
1
Children 9-11, Ecuador
1
Women 25-49, Ecuador
0
1
2
3
4
5
6
7
Number of surviving children
8
9
10
11
Inequality in children’s family size
• Women’s standard deviation falls at slightly lower rate
than the mean
• As a result, children’s mean falls at slightly lower rate
than women’s mean
• But children’s standard deviation falls much more slowly
– it tends to stay roughly constant due to increase in
skewness in women’s family size
• These imply that the coefficient of variation in children’s
family size must increase as mean family size declines
• In general there is a substantial increase in inequality in
children’s family size as mean family size declines
1
Coefficient of variation of surviving family size of children
by mean family size of women age 45-49
.4
.5
.6
.7
.8
.9
Coefficient of Variation
of children’s family size
increases as fertility
declines
.3
Slope= -0.046 (0.005)
.2
b(FE)= -0.045 (0.005)
1
2
3
4
5
6
7
Mean number of children ever born, Women 45-49
8
1
Children 9-11, Brazil
Brazil:
90th percentile fell
from 9 to 7 from
1960 to 2000
.3
.4
.5
.6
.7
.8
.9
If there are fixed resources in families, the
10th percentile child goes from getting 4.5
times as much as the 90th percentile child to
getting 7 times as much. This is in addition to
inequality in the amount of the fixed resource
between small and large families.
2000
1991
1980
1970
1960
0
.1
.2
10th percentile fell from
2 to 1.
So 90/10 ratio rose
from 4.5 to 7
0
1
2
3
4
5
6
7
Number of surviving children
8
9
10
11
.7
.8
.9
1
Children 9-11, Ecuador
.3
.4
.5
.6
Ecuador:
80th percentile fell
from 8 to 6 from
1974 to 2001
2001
1990
1982
1974
0
.1
.2
20th percentile fell
from 4 to 2; 80/20
ratio rose from 2 to 3
0
1
2
3
4
5
6
7
Number of surviving children
8
9
10
11
90/10 and 80/20 ratios for children’s surviving family
size, by mean family size of women 45-49
8
b(FE)= -0.426 (0.082)
P80/P20
3
4
5
6
Slope= -0.325 (0.097)
7
P90/P10
2
Slope= -0.138 (0.026)
1
b(FE)= -0.151 (0.030)
1
2
3
4
5
6
Mean number of children ever born, Women 45-49
7
8
Figure X2. Measures of inequality of children's family size
B. Colombia
C. Mexico
D. Chile
E. DominicanRepublic
F. Ecuador
G. Panama
H. Peru
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
A. Brazil
2
3
4
5
6 7
8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2
Mean number of surviving children, women 45-49
P90/P10
P80/P20
3
4
5
6
7 8
Figure X2. Measures of inequality of children's family size
J. Indonesia
K. Philippines
L. Bangladesh
M. Jordan
N. Morocco
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
I. Thailand
2
3
4
5
6
7
8 2
3
4
5
6
7
8 2
3
Mean number of surviving children, women 45-49
P90/P10
P80/P20
4
5
6
7
8
Figure X2. Measures of inequality of children's family size
P. Ghana
Q. Rwanda
R. Tanzania
S. Zambia
T. Zimbabwe
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
O. Kenya
2
3
4
5
6
7
8 2
3
4
5
6
7
8 2
3
Mean number of surviving children, women 45-49
P90/P10
P80/P20
4
5
6
7
8
Conclusions
• Mean family size of children tends to fall more slowly
than mean family size of women as fertility declines.
• The ratio of mean children’s family size to mean women’s
family size rises from about 1.2 to 1.5 as fertility falls, the
result of an increase in the coefficient of variation in
women’s family size.
• There is roughly a 20% smaller increase in resources per
child during the demographic transition than would be
implied by fertility decline alone.
• Inequality in children’s family size tends to increase with
the decline in fertility, the result of increasing skewness in
women’s family size. The gap in resources per child
between large and small families increases as fertility
declines.