Stages of the Demographic Transition from a Child’s Perspective:
Family Size, Cohort Size, and Children’s Resources
David Lam
University of Michigan
[email protected]
Letícia Marteleto
University of Michigan
[email protected]
January 2006
Population Studies Center Research Report 06-591
_____________
David Lam is Professor of Economics and Research Professor in the Population Studies Center at the
University of Michigan. Letícia Marteleto is a researcher in the Population Studies Center at the
University of Michigan. Support for this research was provided by the U.S. National Institutes of Health
(NICHD Grant Number R01HD031214, Fogarty International Center Grant Number D43TW00657), the
Mellon Foundation and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq),
Brazil. A previous version of this paper was presented at the XXV International Population Conference of
the International Union for the Scientific Study of Population, Tours, France, July 2005.
Stages of the Demographic Transition from a Child’s Perspective:
Family Size, Cohort Size, and Children’s Resources
Abstract
This paper provides a new characterization of stages of the demographic transition, describing it
from a child’s perspective. These stages describe the sequence of changes in family and cohort sizes that
affect children’s resources. In Stage 1, falling mortality produces increases in surviving family size and in
the size of birth cohorts. In Stage 2, falling fertility overtakes falling mortality to produce declining family
size, but population momentum causes continued growth in cohort size. In Stage 3, falling fertility
overtakes population momentum to produce declining cohort size. We apply our framework to census
microdata for Brazil, Kenya, Mexico, and Vietnam, focusing on children aged 9-11. Brazil was still in
Stage 1 during the 1960s, was in Stage 2 from roughly 1970 to 1982, and has been in Stage 3 since 1982,
the year in which the largest birth cohort was born. Mexico and Vietnam have also entered Stage 3, with
declines in both the family size of children aged 9-11 and in the absolute number of 9-11 year-olds.
Kenya also experienced declines in children’s family size between 1989 and 1999, but will not experience
the declining cohort size for at least another decade.
Child’s Perspective on Stages of the Demographic Transition, Page 1
INTRODUCTION
The demographic transition has played itself out with a great deal of regularity in developing
countries over the last fifty years. Looking at a broad set of countries, a relatively simple stylized
version of the demographic transition is consistent with the empirical experience of most of the
developing world. The transition can be thought of as beginning with large and sustained declines in
death rates, especially infant and child mortality. The immediate effect of these declines in infant and
child mortality is an increase in the number of surviving children at the family level and an increase in
the total number of children at the population level. These declines in mortality are eventually
followed by the second key element of the transition – a decline in fertility. The timing and pace of
this fertility decline has varied considerably across countries, and has provided rich research material
for several generations of demographers. These changes in fertility eventually have effects on both
family size and the size of cohorts. It is these changes in family size and cohort size over the course of
the demographic transition that are the focus of this paper. This paper develops a new characterization
of stages of the demographic transition, viewing the demographic changes from a child’s perspective.
As we will show empirically below, there can be dramatic changes in the numbers of siblings and the
size of cohorts along the course of the demographic transition. These changes are not always in the
same direction, however, as a result of the complex interaction of population momentum with falling
fertility and mortality.
We focus on three stages of the demographic transition from a child’s perspective, each with
different implications for resource competition at the family and population level. In the first stage,
falling infant and child mortality lead to increasing numbers of surviving children within families and
to increases in the size of birth cohorts. This is the stage in which rapid population growth begins, as
evidenced at both the family and population levels. In the second stage, falling fertility overtakes
falling mortality to produce declining family size, but cohort size continues rising due to population
momentum. In the third stage, falling fertility overtakes population momentum to cause declines in
the absolute size of birth cohorts. Children, especially school-age children, compete for resources at
both the family and the population level. Children born in what we define as the first stage of the
demographic transition face increasing competition for resources at both levels. Children born in the
second stage face increasing competition at the population level, but have decreasing numbers of
siblings. Children born in the third stage experience declines in both cohort size and family size.
The paper begins by presenting a simple model to illustrate the dynamics of cohort size and
family size during the demographic transition. We then analyze the sequence of stages in several
countries, documenting the fact that cohort size and family size move in opposite directions for as
long as two or three decades in many countries. We look in particular detail at the case of Brazil,
where we have detailed census microdata back to 1960. We use these data to look at changes in
family size from the perspective of school-age children. Brazil entered Stage 2 of the transition before
1970, and entered Stage 3 around 1982, when the largest birth cohort was born. We have shown in
previous work that the resulting decline in the size of the school-age population in the 1990s is
associated with large improvements in schooling outcomes (Lam and Marteleto, 2005). Brazil is
typical of many Asian and Latin American countries that have already entered Stage 3 of the
transition. We also look in detail at Kenya, Mexico, and Vietnam, taking advantage of large census
Child’s Perspective on Stages of the Demographic Transition, Page 2
microsamples that permit us to focus on cohort size and family size from the perspective of children
in narrow age groups. We show that the number of siblings of children aged 9-11 fell in all of these
countries between the two most recent censuses. This suggests that all of these countries have entered
Stage 2, with children competing for resources with fewer siblings in the household.
RESEARCH ON COHORT SIZE, FAMILY SIZE, AND SCHOOLING
Numerous researchers have considered the possible effects of family size and cohort size on
resources available to children, with particular focus on their impact on schooling. The recent
National Academy of Sciences’ report, Growing up Global, provides a review of this literature
(Lloyd, 2005). Without attempting to thoroughly review this large literature, we briefly discuss some
of the key studies that have looked at the impact of cohort size and family size on children’s
resources.
Negative effects of rapid growth of the school-age population on schooling outcomes have
frequently been mentioned as one of the potential negative consequences of rapid population growth
(Jones 1971; World Bank 1984). Empirical evidence of a negative impact of the size of the school-age
population on school outcomes has been mixed, however. In one of the most comprehensive analyses
of the issue, Schultz (1987) analyzed the economics of school finance resulting from changes in the
size of the school-age population relative to the adult population. Using aggregate cross-national data
on age structure, school enrollments, and school expenditures, Schultz found no significant effect on
school enrollment rates of the proportion of the population in school age, although he did find a
negative relationship between the proportion of the population in school age and public school
expenditures per child. Kelley (2001) notes that several other studies based on cross-country data also
suggest that there is no impact of relative cohort size on the share of national budgets allocated to
schooling, although most of these studies do not look directly at schooling outcomes. In the case of
Brazil, which we will focus on extensively below, Birdsall and Sabot (1996) cite Brazil’s rapid
increase in the number of children at school ages in the 1970s and 1980s as a potential cause for the
poor educational performance of the 1980s. Lam and Marteleto (2005) show that sharp declines in the
growth rate of the school-age population in Brazil help explain the large increases in school
enrollment in the 1990s, with the enrollment of older school-age males from poorer households
appearing to be most affected by rapid growth of the school-age population.
In addition to the literature on cohort size, an even larger literature looks at the impact of family
size on schooling outcomes. As pointed out in the reviews by Lloyd (1994) and Kelley (1996), this
literature has produced mixed results. Most empirical studies on educational attainment in developing
countries have found that children from large families attain less schooling than children with fewer
siblings (Ahn, Knodel, Lam, and Friedman 1998; Knodel and Wongsith 1991; Lam and Marteleto,
2005, Marteleto 2001; Parish and Willis 1993, Patrinos and Psacharopoulos 1997, Psacharopoulos and
Arriagada, 1989). This is often attributed to a dilution of resources, with a smaller share of financial
and interpersonal resources allocated to each child in larger families. Some studies, however, have
found a positive association between family size and education (Chernichovsky 1985; Hossain 1988;
King et al 1986; Mueller 1984), a result that Kelley (1996) argues could be theoretically plausible if
Child’s Perspective on Stages of the Demographic Transition, Page 3
there were large economies of scale in the production of human capital within families. As
emphasized in the review by King (1987), whatever the relationship between family size and
schooling observed in the data, giving a causal interpretation to the association is difficult, since
fertility and children’s schooling are choices made jointly by parents.
The purpose of this paper is not to provide any new evidence on the impact of cohort size or
family size on children’s outcomes, but to analyze how cohort size and family size change during the
demographic transition. While there has been considerable discussion of the impact of changes in
family size and cohort size on children’s resources in developing countries, there has been
surprisingly little discussion of the actual dynamics of changes in family size and cohort size that
typically take place during the demographic transition. In most of the literature on the impact of
cohort size and family size on children’s outcomes, the discussion suggests that cohort size and family
size will move together, following the path of overall population growth. As we will show below,
both empirical evidence and simple models of the underlying population dynamics make it clear that
family size and cohort size may move in opposite directions for as long as several decades once
fertility begins to fall. Understanding these dynamics can provide a clearer picture of how the
competition for resources allocated to children changes during the demographic transition, with
important implications for those countries that have only recently begun to experience fertility
decline.
DYNAMICS OF FAMILY SIZE AND COHORT SIZE
In this section we present a stylized model of the demographic transition that demonstrates
several important points about how family size and cohort size change in response to the typical
changes in fertility and mortality that characterize the transition. One goal of this model is to think
about how the changes in fertility and infant mortality that drive the demographic transition translate
into changes in the family size experienced by children. A second goal is to think about how these
changes interact with population momentum to affect the cohort size experienced by these same
children. Given the strong non-stationary of vital rates, age structure, and population growth during
the demographic transition, the link between vital rates in a current year and measures such as
numbers of siblings of children born in that year and total number of births in that year is complex.
It is beyond the scope of this paper to develop a complete model of these dynamics, but a simple
model demonstrates a number of important key points. To begin we assume for simplicity that a
woman has all of her births at the mean age of childbearing μ. This implies that all of the children
born in a given year are born to women age μ , that the cohort Total Fertility Rate (TFR) for these
women is equivalent to the period TFR, which we will denote f, and that f is also the average
completed family size for women who give birth in that year. In the limiting case in which there is no
variance in fertility across women, f will also be the average completed family size for children born
in that year. As pointed out by Preston (1976), and as discussed in more detail below, if there is
variance in fertility across women, then the average family size of children will be larger than the
average family size of women.
Child’s Perspective on Stages of the Demographic Transition, Page 4
Let s(t) represent surviving family size for children born in year t, let f(t) represent the number of
children born per woman who give birth in year t, and let p(t) represent the probability of survival to
some age such as the age of attending school for children born in year t. Surviving family size is
simply the product of the fertility rate and the survival rate in a simple multiplicative relationship
s (t ) = f (t ) p (t )
(1)
Looking at change over time, we take the natural logarithm of (1) and differentiate with respect to
time to get:
∂ ln s (t ) ∂ ln f (t ) ∂ ln p(t )
=
+
∂t
∂t
∂t
(2)
Equation (2) simply states that the rate of change in surviving family size is the sum of the rate of
change in the fertility rate and the rate of change in the survival probability. Since during most of the
demographic transition the fertility rate will be declining while the survival probability is increasing,
the net change in surviving family size at any given point in the transition is ambiguous, depending on
the relative magnitudes of the two changes. While a more complete model of the age profile of
fertility would greatly complicate Equation (2), it would not change the basic point that declining
fertility competes with increasing survival to determine the evolution of surviving family size during
the transition.
We can continue with this simple model to introduce the dynamics of cohort size. The actual
number of births in year t, which we will denote N0(t), will depend on the number of women in
childbearing age in year t and the number of surviving children born to each woman of childbearing
age. In our model the number of women of childbearing age in year t is simply the number of women
age μ in year t, which we will denote Nμ(t). We can therefore express the number of surviving
children born in year t as:
N0 (t ) = Nμ (t ) s(t ) = Nμ (t ) f (t ) p(t ) .
(3)
Assuming for simplicity that all surviving births also survive to the age of childbearing, we can link
current numbers of childbearing age women to past births and modify Equation (3):
N0 (t ) = Nμ (t ) s(t ) = N0 (t − μ ) f (t ) p(t ) .
Equation (4) makes the simple but fundamentally important point that current numbers of surviving
births are the product of cohort size one generation in the past multiplied by current fertility and
survival rates. As above, it is useful to take logs and differentiate with respect to time and think about
the dynamics in terms of growth rates:
(4)
Child’s Perspective on Stages of the Demographic Transition, Page 5
∂ ln N0 (t ) ∂ ln N μ (t ) ∂ ln s(t )
=
+
∂t
∂t
∂t
(5)
The role of population momentum is now clearly evident in Equation (5). The first term on the righthand size is the growth rate of the childbearing age population in year t, or equivalently (given our
assumptions), the growth rate of numbers of births μ years prior. While the growth rate of the
childbearing age population is affected by fertility and mortality one generation back, it is not affected
by current fertility and mortality, and hence need not move in the same direction as current family
size. During the demographic transition the two terms on the right-hand side of Equation (5) can
clearly move in opposite directions. In particular, surviving family size will start to decline if fertility
falls faster than infant mortality, but the childbearing age population may continue to increase due to
population momentum.
Equation (5) provides a useful framework for thinking about the dynamics of family size and
cohort size during the demographic transition. Assume that before the transition begins we have a
stationary population, with constant numbers of surviving births in every year, N0(t)= N0(t-1)= N0(t-
μ), or equivalently, ∂Nμ (t ) / ∂t = 0 in Equation (5). We can characterize the beginning of the
demographic transition as an unexpected increase in the survival probability, ∂p (t ) / ∂t > 0 in some
year t1. Since this will not cause any change in the childbearing age population for the first μ years, all
effects on numbers of surviving children work through the increase in survival probabilities. This
increase in child survival must increase both the average size of families, s, and the number of births
born in each year, N0, during the initial years of the transition. From the perspective of children, the
generations born in some initial set of years after year t1 experience both an increase in surviving
numbers of siblings and an increase in the size of their cohorts relative to previous years. This begins
what we call Stage 1 of the demographic transition from a child’s perspective.
Following the standard pattern of the demographic transition, we now assume that with some lag
there begins a sustained decline in fertility, ∂f (t ) / ∂t < 0 beginning in some year t2. Recalling
Equation (2), surviving family size may either continue to increase or begin to decline, depending on
whether fertility falls fast enough to offset the increase in child survival. It is entirely an empirical
question whether and for how long surviving family size continues to increase after fertility begins to
decline. We assume that at some point, possibly quite a few years after the onset of fertility decline,
fertility begins to fall fast enough to offset increased child survival, leading to decreasing family size.
Once the decline in surviving family size begins, it need not (and generally will not) imply a decline
in the number of surviving births in the population. As Equation (5) reminds us, population
momentum resulting from the rapid growth in cohort size during the first stage of the transition will
cause continued growth in the childbearing population for at least one generation in the future. While
it is not a mathematical necessity that cohort size continues to grow after family size has begun to fall,
the typical empirical pattern is one in which there is continued growth in total numbers of births for
some period after family size has begun to decline. This is what we call Stage 2 of the demographic
transition from a child’s perspective. Children born in this period experience declining family size but
increasing cohort size relative to previous cohorts. They compete with fewer siblings at home, but
Child’s Perspective on Stages of the Demographic Transition, Page 6
compete with more children of the same age in the overall population. This stage begins when the
sum of fertility growth and survival growth in Equation (2) becomes negative.
Assuming that declines in fertility continue to be faster than increases in child survival, the stage
is set for an eventual reduction in the impact of population momentum. Stage 1 of the transition from
a child’s perspective is a race between falling fertility and falling mortality to determine when
surviving family size begins to fall. Stage 1 ends when falling fertility overtakes falling mortality and
family size declines. As Equation (5) makes clear, Stage 2 is similarly a race between falling fertility
and population momentum to determine when the absolute number of births in the population begins
to fall. Stage 2 ends when falling fertility overtakes population momentum to produce a decline in the
absolute number of births.
It is important to add that the stages as we have defined them may not always be sharply defined.
Family size might begin to decline but then rise again if the rate of decline in infant and child
mortality once again overtakes the rate of decline in fertility. Similarly, the absolute number of births
may reach a peak, decline for a few years, then rise again as “waves” of population momentum work
their way through the childbearing population. We may therefore see a long flat peak or oscillations
around a turning point in both family size and cohort size, rather than sharply defined peaks. We will
see, however, that the basic stages as we have defined them are fairly clearly evident for countries
undergoing the demographic transition during recent decades, even if the boundaries between stages
are not always sharply defined.
FAMILY SIZE OF CHILDREN AND FAMILY SIZE OF WOMEN
The model described above is a useful simplification of the dynamics of family size and cohort
size during the demographic transition, and allows us to see a number of key points about these
dynamics. The family size variables f(t) and s(t) in the model can be thought of as the mean total
family size and mean surviving family size for women. They are also the mean family size for
children only in the limiting case in which all women have exactly the same number of children. Once
we allow variance in fertility across women we immediately introduce the important distinction made
by Preston (1976) between family size of women and family size of children. This is an important
issue to introduce in our analysis, and we will see below that it can be important in understanding the
evolution of family size from a child’s perspective during the demographic transition.
Preston derived expressions for the mean family size for women of a given age, say 45-49, and
contrasted this with the mean family size for the children of those women. If sW is the mean surviving
family size for women and sC is the mean surviving family size of their children, Preston showed that
⎛ σ W2 ⎞
sC = sW + ⎜
⎟,
⎝ sW ⎠
where σ W is the standard deviation of family size for women. A convenient restatement of this result
for our purposes is:
(6)
Child’s Perspective on Stages of the Demographic Transition, Page 7
⎛
sC = sW ⎜ 1 +
⎝
σ W2 ⎞
= sW (1 + CV 2 ) ,
2 ⎟
sW ⎠
(7)
where CV is the coefficient of variation of surviving family size for women. As noted by Preston,
mean family size for children will be greater than mean family size for women as long as there is any
variation in women’s fertility. Looking at historical data from the United States, Preston observed that
the variance in fertility falls more rapidly or less rapidly than mean fertility during different stages of
fertility decline, causing movements in children’s family size that may differ in important ways from
movements in fertility. In a recent application to Cambodia, Neupert (2005) shows that the mean
family size of children is about 25% higher than the mean family size of women aged 45-49 in 1998.
Extending Preston’s result to our application, if we continue to assume that all women have all of
their children at age μ, but some women have more children than others, then Equation (7) provides
an exact characterization of the relationship between the family size of children born in a given year
and the family size of women who give birth in that year. More realistically, we must recognize that
the children born in a given year have mothers who span a wide age range. If we are interested in
tracking something like the mean family size of school-age children, the problem becomes more
complicated than in Preston’s results. When Preston analyzed the children of women age 45-49, for
example, these children would have spanned an age range of at least 25 years, from as young as 5 to
as old as 30. If we are interested in the mean family size of children age 10 in 1980, the mothers of
those children could have ranged in age from roughly 25 to 49, representing the experience of a wide
range of cohorts. Assume that we can define a group of women who could be considered the potential
mothers of children who are age 10 in 1980. All women age 25 to 49 in 1980 might be considered to
have been at risk of having a 10-year-old child in 1980 (although women in the middle of the age
range are much more likely to have done so than those on the extremes), so this is one logical
candidate for the relevant group of women. We can then analyze how the mean family size of women
age 25-49 in 1980 compares to the mean family size of children age 10 in 1980.
Note that the family size of the mothers of children aged 10 will correspond almost exactly to the
family size of the children themselves. When we take children of a single age we do not observe the
phenomenon discussed by Preston. Preston’s result is driven by the fact that a broad age group of
children (such as children of women aged 45-49) will over-represent children born in large families.
Mothers with eight children will have eight times as many children included in the calculation of
children’s mean family size as mothers with one child. This will not happen in a sample of 10-yearold children. With the minor exception of twins and other multiple births, each mother of a 10-year
old child will have only one 10-year-old child, so the family size of 10-year-old children will be the
same as the family size of the mothers of 10-year-old children. These mothers, however, are not a
random sample of all women. They over-represent women with large numbers of children, since those
women are more likely to have children of any given age1. If we want to understand how changes in
1
To take the extreme case, women with no children are never represented in the group of mothers of
children of any given age. More generally, the mothers of any group of children of a given age will be
more likely to include mothers with large numbers of children.
Child’s Perspective on Stages of the Demographic Transition, Page 8
the family size of 10-year-old children compare to changes in fertility, we cannot look simply at the
mothers of those children, but must look at the fertility of women of a broader age range. If we
consider an approximate childbearing span of age 15 to 40, then women aged 25 to 49 would be an
approximate representation of the potential mothers of 10-year-old children in a given year. We can
then compare how changes in the fertility of women aged 25-49 compares to changes in the family
size of children aged 10.
As we will demonstrate below, empirically it turns out to be the case that the relationship
between the mean family size of 10-year-old children and the mean family size of women aged 25-49
can be roughly approximated by the following variation on Equation (7):
sC (10) ≈ sW (25−49) ⎡⎣1 + CVW2 (25−49) ⎤⎦ .
(8)
Equation (8) states that the mean surviving family size of children aged 10 is roughly equal to the
product of the mean surviving family size of women aged 25-49 and a term equal to 1 plus the
squared coefficient of variation in family size for women aged 25-49. Unlike Preston’s result, or its
restatement in Equation (7), this is not an exact equality since children aged 10 do not represent all
children born to women aged 25-49. They are just one single-year age group drawn out of the children
of these women. The intuition behind the expression is in some ways the inverse of the logic behind
Preston’s result. When we look at children of a single year of age, their mothers are not a random
sample of all women, but are overly representative of women who have large numbers of children.
The larger the variance in women’s fertility, the larger the gap between the average family size of
children and the average family size for all women. Although Equation (8) is not an exact equality, it
turns out empirically to be a simple and surprisingly accurate approximation, and provides a
convenient way of summarizing the relationship between trends in fertility and trends in children’s
family size.
DATA
Fundamental to our analysis is an interest in both macro-level and micro-level demographic
changes during the demographic transition. We will present data at both levels in the following
sections. Macro-level data on cohort size and age structure are more readily available than micro-level
data on family size. Estimates of age distributions such as those made by the United Nations
Population Division provide a reasonably accurate picture of changes in cohort size back to 1950
(United Nations Population Division 2005). We will use these data to describe the trends in the size of
the population aged 9-11, including projections for future decades. The 9-11 age group is used for our
analysis at both the macro and micro level for several reasons. We want to focus on a narrow age
range of children that would be likely to be affected by both family size and cohort size. Age 10 is a
somewhat arbitrary but quite interesting age because it represents an age at which most children
would be expected to be in school. We use the 9-11 age group rather than age 10 alone in order to
reduce problems that might result from age misreporting or small cell sizes. We prefer 9-11 over a
Child’s Perspective on Stages of the Demographic Transition, Page 9
broader group such as age 7-14 in order to focus on something that is closer to a single birth cohort,
providing a better match to the model discussed above.
In order to look at changes in family size we require micro data from censuses or surveys at
multiple points during the demographic transition in a given country. Since we will focus on the
number of siblings for children aged 9-11, we need large data sets in order to generate large cell sizes
at this age. Our analysis draws on large public use census samples from several countries. We pay
special attention to Brazil, where we have excellent micro-samples of the census for 1960, 1970,
1980, 1991, and 2000. We also use census data taken from the Integrated Public Use Microsamples –
International (IPUMS-I) project of the University of Minnesota (Sobek et al. 2002). From the IPUMSI web site we use census samples from Mexico (1990 and 2000), Kenya (1989 and 1999) and Vietnam
(1989 and 1999). While the census data for Mexico, Kenya, and Vietnam do not let us go as far back
in the demographic transition as we can for Brazil, they do allow us to look in detail at recent changes
in family size in these countries, as viewed from the perspective of school-aged children.
Our choice of countries is driven by the availability of large census samples, and is admittedly
not a representative sample of countries. These countries are used in order to explore the dynamics of
cohort size and family size using high quality data, and not because they are necessarily the most
typical or representative countries. It is important to note, however, that these are large countries that
reflect a considerable range of demographic experience. Brazil and Mexico reflect many of the major
features of the demographic transition in Latin America, with Brazil having had an earlier and faster
fertility decline. Vietnam has a unique history that makes it not entirely typical of southeast Asia, but
the fertility decline there has been similar to much of the region, though with a later onset of rapid
fertility decline than, say, China or Thailand. Kenya’s late fertility decline is similar to much of
Africa, as is its continued rapid growth in the size of birth cohorts.
TRENDS IN FERTILITY AND INFANT MORTALITY
As background for our analysis of cohort size and family size, it is useful to review the trends in
fertility and infant mortality for our four countries. Figure 1 shows the Total Fertility Rate and the
probability of infant survival for Brazil, Kenya, Mexico, and Vietnam based on U.N. estimates
(United Nations Population Division 2005). The infant survival rate, which could be thought of as a
measure of p(t) in Equation (1), is calculated as one minus the infant mortality rate, where the infant
mortality rate is expressed as the proportion of births that die before age one. While the basic trends in
fertility and mortality shown in Figure 1 are well known, several points are worth noting in the
context of the framework just presented. Fertility in all of these countries is high and relatively stable
through the 1950s and 1960s, followed by a period of rapid fertility decline and a subsequent leveling
off. The probability of infant survival shows much more constant rates of change over the four
decades shown, even in spite of having an upper asymptote of one. The growth rate of infant survival
is steady but fairly slow, around 0.2 to 0.3 percent per year in most of the countries shown between
1955 and 2000, taking the average rate of change between the five year periods provided in the U.N.
data. This compares to growth rates of fertility that begin around zero, fall to as fast as -4 to -5 percent
per year during the period of most rapid fertility decline, then level off.
Child’s Perspective on Stages of the Demographic Transition, Page 10
The bottom panel of Figure 1 shows estimates of the rate of change in surviving family size.
These are calculated by calculating the annual rate of change for fertility and survival and plugging
them into Equation (2) above, which shows the predicted growth rate in surviving family size as the
sum of the growth rate of fertility and the growth rate of survival.2 As seen in Figure 1, this prediction
implies positive growth of surviving family size in the 1950s and 1960s for all four countries, turning
to a decline in family size in the 1970s and 1980s. In all four countries family size reaches its
maximum rate of decline in the 1980s or 1990s, moving back toward zero by the 1995-2005 period.
This slowing of the rate of decline in family size results from the slowing in the rate of decline in
fertility.
TRENDS IN COHORT SIZE
As our model above demonstrates, the evolution of cohort size need not follow the evolution of
family size during the demographic transition. In looking at cohort size we will look at the size of a
cohort at age 9-11 rather than at the size of a cohort at birth. Figure 3 presents U.N. estimates and
projections of the number of 9-11 year-olds in each country from 1950 to 2030, using 1950=100 as a
benchmark for each country. Brazil shows a peak in the 9-11 cohort around 1995, corresponding to a
peak in births ten years earlier. The peak number of 9-11 year-olds was around 2000 in Vietnam and
2005 in Mexico. Kenya is far off the scale of the other countries (and is shown using a different
scale), with a predicted peak in the 9-11 population around 2025 that is ten times the number of 9-11
year-olds in 1950.
Comparing these patterns to the predicted change in family size shown in Figure 1, the implied
peak in the number of births comes 10 to 30 years after the year in which we predict that surviving
family size would have started to decline. The explanation for this delay is population momentum
driven by growth in the size of the childbearing population. It should also be noted in Figure 2 that the
size of the 9-11 population (or the size of any other age group) does not necessarily have a single
peak. In both Mexico and Kenya, for example, it appears that the number of births begins to decline,
but then increases again for some period of time. This is not surprising, given the theoretical dynamics
shown above. As falling fertility competes with population momentum, it is easy for the total number
of births to increase even after a period in which it was decreasing, and even though fertility continues
to fall. The number of women of childbearing age will grow at somewhat uneven rates due to the
patterns in numbers of births lagged one generation. Even if fertility falls at a fairly steady rate, an
increase in the rate of growth of the childbearing population could case the number of births to begin
increasing again after an initial period of decline.
Like the cases of Brazil, Mexico, and Vietnam in Figure 3, many developing countries have
already experienced their peak birth cohort. This is the case in almost all East Asian and Latin
American countries. Kenya represents an important case in which birth cohorts will continue to grow
for several decades, a situation that applies to many countries in Africa and South Asia. Since the
2
The growth rates of family size in the bottom panel of Figure 1 are for the 10-year period
surrounding each point. For example, the point for 1955 is based on the rates of growth of fertility and
child survival between the 1950-55 period and the 1955-60 period.
Child’s Perspective on Stages of the Demographic Transition, Page 11
absolute size of the school-age population will begin to decline roughly ten years after the largest
cohort has been born, it is clear that many developing countries, especially those in Latin America and
Asia, have been in a period of declining, or at least roughly constant, school-age populations for a
decade or more. It is more difficult to be sure when family size began to decline in all of these
countries, especially when measured from the perspective of children of some particular age. Getting
beyond crude approximations such as those presented in Figure 1 requires microdata at the household
level, preferably covering a large period of the demographic transition. In the following sections we
draw on large census samples from Brazil, Kenya, Mexico, and Vietnam to look in detail at how
family size changes during the demographic transition, and how these changes compare to changes in
cohort size.
THE DEMOGRAPHIC TRANSITION IN BRAZIL
The case of Brazil is particularly interesting to examine. Brazil’s demographic transition is fairly
typical of those observed throughout the developing world, and is documented with excellent census
data. Table 1 provides an overview of Brazil’s demographic transition based on census data from
1940 to 2000. As shown in the first row of Table 1, the Total Fertility Rate for all Brazil was around
6.2 from 1940 to 1960, declining rapidly to 4.4 in 1980, 2.7 in 1991, and 2.3 in 2000. Brazil’s rapid
fertility decline occurred during a period of a far-reaching social change that included periods of both
rapid economic growth and economic crisis (Wood and Carvalho 1988, Martine 1996, Lam and
Duryea 1999). Table 1 also shows the considerable regional variation in the pace of fertility decline.
The poorer north and northeast regions have consistently had the highest fertility rates and began
fertility decline later than the higher income south and southeast regions. In 1970, the southeast’s TFR
had fallen to 4.6, while the TFR for the northeast remained at 7.5. In 1991, the regional differences
persisted as the southeast showed a TFR of 2.4 and the northeast had a TFR of 4.0. By 2000 the TFR
for the southeast had declined to slightly below replacement level at 2.0, with a TFR for the northeast
of 2.6. This regional unevenness in fertility decline reflects patterns in socio-economic development.
The TFR in the more developed southeast and south regions is similar to those of high-income
countries, while the higher TFR in the north and northeast regions reflects the lower income,
education, and industrialization levels of those regions.
Table 1 also shows the population size and annual growth rates for the country from 1940 to
2000. Brazil experienced rapid population growth during the second half of the 20th century, with the
annual growth rate peaking at 3% in the 1950-60 period. In the 1970-1980 period the growth rate was
still about 2.5% per year, but was clearly on the decline. The annual growth rate fell to 1.9% in the
1980-91 intercensal period, and to 1.6% in the 1991-2000 period. As seen in the last row of Table 1,
Brazil more than quadrupled its total population over this period, from 41 million in 1940 to 169
million in 2000.
The dramatic changes in fertility rates and population growth rates shown in Table 1 are
associated with large changes in the size of birth cohorts. As shown in Figure 2, the number of 9-11
year-olds more than doubled between 1950 and 1975, reflecting the size of birth cohorts ten years
prior. Taking overlapping age distributions from the Brazilian censuses from 1960 to 2000, Lam and
Child’s Perspective on Stages of the Demographic Transition, Page 12
Marteleto (2005) find that the largest birth cohort was born in 1982. The rate of increase in the size of
birth cohorts varies over time, with much slower growth in the 1960s than in the 1970s. These
changes in the pace of the increase in cohort size are the result of the complex interaction between
falling fertility rates and increasing numbers of women in childbearing age. The decline in cohort size
after the peak in the early 1980s is also uneven, with cohort size actually increasing again in the
1990s, producing the increase in the size of the 9-11 age group around 2005 in Figure 2. This is not
due to an increase in fertility, which falls rapidly throughout the 1970s, 1980s and 1990s, but to an
increase in women of childbearing age as an “echo” of the rapid cohort growth of the 1970s.
The changes in fertility and mortality that caused the changes in cohort size shown in Figure 2
also caused large changes in family size. The changes in family size do not simply track changes in
cohort size, however. Family size begins to decline well before the largest birth cohort is born, a
pattern that can be expected in all countries during the demographic transition. We can use micro data
from the Brazilian censuses to track changes in family size from a child’s perspective over the course
of the demographic transition. As noted in the theoretical discussion above, it is important to
recognize that trends in fertility, which are essentially trends in the family size for women, are not the
same as trends in the family size for children. As we will see empirically, and as originally explained
by Preston (1976) it is possible for the family size of women and the family size of children to change
at much different rates, and even to move in opposite directions.
Table 2 explores these issues using Brazilian census data from 1960 to 2000. The first row looks
at family size for women aged 45-49, the same age group used by Preston for his analysis of historical
patterns in the United States. The mean number of children ever born to women aged 45-49 fell from
5.9 in 1960 census to 3.6 in 2000, a decline of 39%. Looking at Line 5 of Table 2, the mean number
of surviving children for these women fell from 4.4 to 3.3 over the same period, a decline of 25%. As
pointed out by Preston, the mean family size for the children of these women will be larger than the
mean family size for the women as long as the variance of family size for women is non-zero.
Columns 6-10 of Table 2 show the standard deviation of family size. For women aged 45-49 the
standard deviation falls from 4.6 to 2.6 for children ever born, and from 3.4 to 2.4 for children
surviving, from 1960 to 2000.
As shown in Equation (7), the mean family size for children, c , is equal to the mean family size
for women, x , multiplied by 1 plus the squared coefficient of variation of family size for women.
Columns 11-15 show the coefficient of variation from 1960 to 2000, and Columns 16-20 show the
mean family size of children. For women aged 45-49, the C.V. stays surprisingly constant across
years (around 0.8), implying that the mean family size for children is a fairly constant multiple of the
mean family size for women, about 1.6. The C.V. does drop between 1960 and 1980, however, then
returns to roughly its initial level, a pattern we will see repeated for other age groups. The mean
family size for children of women aged 45-49 was 9.6, falling to 5.9 by 2000, counting all children
ever born. It is interesting to note that the levels for 1980 are similar to the levels reported by Preston
for the United States in the 1890 census. Preston estimated a mean family size for women aged 45-49
of 5.0, and a mean family size for their children of 7.8, a ratio of 1.6. The equivalent numbers in Table
2 for Brazil in 1980 are 5.4 and 8.1, a ratio of 1.5.
Child’s Perspective on Stages of the Demographic Transition, Page 13
The same exercise can be done for women of any age. Row 2 looks at women aged 25-29. We
look at these women because they are the lower range of the women we will include in our sample of
potential mothers of 9-11 year-olds. An interesting feature of the fertility experience for these young
women is that the coefficient of variation is very similar in 1960 and 2000, implying once again that
the ratio of women’s family size and children’s family size is about the same in the two years. The
C.V. declines considerably between 1960 and 1980, however, with important consequences for the
mean family size of children. Although the average fertility of women aged 25-29, as measured by the
mean number of children ever born, is almost unchanged from 1960 to 1970 to 1980, the standard
deviation falls from 2.4 to 1.8. This causes mean family size for women in these age groups to fall by
one full sibling, from 4.7 to 3.8. A similar pattern is observed for surviving family size for these
younger women, looking at Row 6 of Table 2.
The mean family size of women aged 25-29 is obviously an incomplete measure of their eventual
family size, but it is a very relevant dimension of resources for a 10-year-old whose mother is in this
age range. More generally, suppose we are interested in the family size of all children aged 9-11,
rather than in the family size of children whose mothers are in a given age range. Row 3 of Table 2
looks at all women aged 25-49, a group that will encompass most of the mothers of children aged 911, as well as mothers of children of many other ages. As shown in Columns 16-20, the mean family
size of children of mothers aged 25-49 fell from 7.6 in 1960 to 4.4 in 2000. Row 4 shows that the
mean family size of children aged 9-11 fell from 7.4 in 1960 to 4.1 in 2000. The mean family size of
children aged 9-11 is very similar in every year to the mean family size of children of mothers aged
25-49. This provides empirical support for the approximation given above in Equation 8, and suggests
that this age group of women is a useful benchmark for analyzing the relationship between changes in
fertility and changes in the family size of children aged 9-11.
The consistency between the family size of children aged 9-11 and the family size of children of
women aged 25-49 is even more evident when we look at surviving family size in Rows 6 and 7 of
Table 2. The patterns are demonstrated graphically in Figure 3, which shows the family size of
children aged 9-11 from 1960 to 2000. Surviving family size of children aged 9-11 (that is, the mean
number of living children for the mothers of children aged 9-11 at the time of the census) falls from
5.9 in 1960 to 5.4 in 1980 to 3.8 in 2000. As clearly seen in Figure 3, this is almost indistinguishable
from the mean family size for the children of women aged 25-49 across the five censuses. This
consistency gives us a convenient way to compare changes in fertility with changes in the family size
for children. We will use the mean family size of women aged 25-49 as an indicator of mean fertility
at the time our focal children were born, and will compare this to the mean family size of children
aged 9-11.
Row 4 of Table 2 indicates that fertility decline was already reducing the family size of children
between the 1960 and 1970 censuses. The number of children ever born in the families of children
aged 9-11 declined by 0.3 between 1960 and 1970. Looking at Row 8, the number of children
surviving in these families shows a different pattern however, with an increase of 0.1 in the number of
children surviving to the mothers of 9-11 year-olds. While this increase in surviving siblings is very
small, it suggests that Brazil was still in what we would call Stage 1 of the demographic transition in
Child’s Perspective on Stages of the Demographic Transition, Page 14
1970 – falling infant and child survival was leading to increasing family size, even though fertility had
already begun to decline.
Looking at changes from 1970 to 1980, the declines in children ever born are substantially larger
than the 1960-70 declines. Children aged 9-11 in 1980 had almost one fewer sibling ever born than
their counterparts in 1970. These declines were large enough to cause a 0.6 decline in the number of
surviving siblings. The fact that the number of siblings ever born declined by about 0.9, while the
number of surviving children declined by only 0.6, indicates that falling infant and child mortality
continued to have an important impact on family size in the 1970s. The total family size for 9-11 yearolds continues to decline rapidly over the next two decades, with a decline of 1.3 between 1980 and
1991 and 0.8 between 1991 and 2000. Children aged 9-11 in 1991 had one full sibling less than their
counterparts in 1980, with a further decline of 0.6 siblings between 1991 and 2000. The net impact of
declining fertility over these four decades was to cause the surviving family size of 9-11 year-olds to
fall by 2.1 children between 1960 and 2000, a decline of 35%.3
As demonstrated in Figure 3 and Table 2, changes in children’s family size do not directly track
changes in the family size of women. Between the 1970 and 1980 censuses, for example, the mean
number of surviving children to women aged 25-49 fell by only 0.15, while the mean family size of
children aged 9-11 fell by over half a sibling, 0.55 (twice as large a percentage decrease). The
explanation for the faster decline in family size for children resulted from the fact that the standard
deviation in women’s fertility fell faster than the mean, suggesting that fertility declines were more
rapid among those with the highest fertility. The coefficient of variation in women’s family size
reached its lowest level – 0.75 – in the 1980 census, indicating that the standard deviation in fertility
declined faster than the mean between 1960 and 1980, while the standard deviation declined more
slowly than the mean between 1980 and 2000. As a result, the mean family size of children declined
faster than mean fertility between 1960 and 1980, but declined more slowly than fertility from 1980 to
2000.
As shown in Table 1, fertility decline began earlier in Southeast Brazil than it did in the much
poorer Northeast. It is therefore interesting to look at how the family size of children changed in the
two separate regions. Similarly, it is interesting to look at children from poorer versus richer socioeconomic backgrounds, which we will proxy using mother’s education. Table 3 shows the mean
family size of women aged 25-49 and children aged 9-11 for these separate groups. It also shows the
coefficient of variation for both measures, and the percentage change in mean family size for the
intercensal periods. Looking at the first two rows, the mean number of children ever born to women
aged 25-49 in the Northeast was 5.0 in 1960 (note that this includes incomplete fertility for the
younger women in this age group, and is should not be thought of as a measure of completed fertility).
The mean number of children ever born into the families of children aged 9-11 was 8.6 in 1960, with
the difference between 8.6 and 5.0 reflecting relatively high dispersion in the family size of women.
Comparing children ever born to surviving children for the Northeast, we see high rates of infant
and child mortality. The mean number of surviving children to women aged 25-49 in 1960 was 3.5,
implying a survival rate of only 70%. The mean surviving family size for children aged 9-11 in the
3
Note that this could also be expressed as a 42% decline in the mean number of siblings.
Child’s Perspective on Stages of the Demographic Transition, Page 15
Northeast in 1960 was 6.3. This number increased to 6.5 in 1970. The primary reason for the rise in
the family size for 9-11 year-olds was increased infant and child survival. The number of children
ever born to women aged 25-49 was almost constant between 1960 and 1970, while the number of
surviving children increased from 3.5 to 3.9 births. The coefficient of variation in mean surviving
births to women declined between 1960 and 1970, a trend that in and of itself would have slightly
reduced the mean family size of children. The increase in mean family size of women was large
enough to offset this, however, leading to the increase of 0.2 siblings for children aged 9-11 between
1960 and 1970.
Northeast Brazil, then, appears to have clearly been in a period of increasing family size in the
1960s, viewed either from the perspective of women or children. Cohort size was also increasing
rapidly, implying that children were facing increased competition for resources at both the macro and
micro levels. The situation in the richer Southeast was somewhat different. Fertility was considerably
lower, with women aged 25-49 reporting 3.8 children ever born, about 25% below the level in the
Northeast. Surviving family size for women aged 25-49 was 3.1 births, which generated a surviving
family size for children aged 9-11 of 5.6. The family size of children in the Southeast declined slightly
between 1960 and 1970, suggesting that the Southeast had already entered the phase of declining
family size.
In the 1970-80 period we see a decline in surviving family size of children in the Northeast, from
6.5 to 6.2, indicating that the Northeast moved into Stage 2 of the transition sometime between 1970
and 1980. Declines in children’s mean family size are quite rapid after 1980. The mean surviving
family size of children aged 9-11 in the Northeast fell by 11% between 1980 and 1991 and by 17%
between 1991 and 2000, with a total decline over the 1960-2000 period of 28%. Declines in family
size in the Southeast are larger over the entire period, with a decline of 40% in mean surviving family
size of 9-11 year-olds between 1960 and 2000. Thinking of this as the number of siblings rather than
family size, this represents a decline from 4.6 to 2.4 siblings in the Southeast, a decline of 48%.
Table 3 also compares the trends in family size for mothers with high and low education. Low
education is defined as less than four years of schooling, while high education is four years or more.
Four years is roughly the median schooling for women aged 30 in 1980, and will be used as the cutoff
for low education in all of the countries analyzed below. As shown by Lam and Duryea (1999), there
is a strong negative relationship between women’s schooling and fertility in Brazil, with increases in
women’s schooling playing a major role in Brazil’s fertility decline. We use it here as a summary
indicator of socioeconomic status that reflects a number of variables in addition to mother’s
schooling, including husband’s schooling, family income, and regional differences.
We see a number of striking patterns when we look at changes in family size by separate
education groups. Figure 4 demonstrates these patterns graphically, showing the trends in surviving
family size for women and children in both socio-economic groups. Looking at the top two lines in
Figure 4, which show the mean family size of 9-11 year-olds, we see that between 1960 and 1970
surviving family size increased for children in the low socioeconomic group, but decreased for
children in the high socioeconomic group. After 1970 family size fell for both groups, but fell at a
much faster rate for the high education group. Mean family size for the low-SES children fell by
roughly 1 child between 1960 and 2000, while it fell by 2 children for the high-SES children. As
Child’s Perspective on Stages of the Demographic Transition, Page 16
shown in Table 3, this is a 40% decline for the high-SES group, compared to 16% for the low-SES
group.
To see the role of declining fertility in explaining these declines in children’s family size, we can
look at the mean family size of 25-49 year-old women in the bottom two lines in Figure 4. The
decline in women’s mean family size was actually very similar for the two groups, with a 17% decline
for low-SES women and an 18% decline for high-SES women. The explanation for why such similar
declines in fertility could lead to very different declines in children’s family size is seen in the
coefficients of variation in women’s family size in Table 3. The C.V. for low-SES women was 0.79 in
1960 and 0.81 in 2000, implying that the ratio of women’s family size to children’s family size was
almost identical in the two years. The C.V. for high-SES women, however, fell from 0.98 in 1960 to
0.77 in 2000. Recalling from Equation (7) that mean family size of children is equal to mean family
size of women multiplied by 1+CV2, this implies that the ratio of women’s mean family size to
children’s mean family size fell from 1.96 to 1.60. This generates an additional 23% decline in mean
family size of children beyond the decline caused by the decline in mean family size of women.
Figure 5 shows the distribution of family size in detail in each census. The top panel shows the
frequency distribution for the numbers of siblings of children aged 9-11. The bottom panel shows the
cumulative distribution, showing the percentage of children with x or fewer siblings. The figure
provides a clear picture of the evolution of small families in Brazil. Looking at the top panel, the peak
of the distribution moved from 4 siblings in 1960 to 1 sibling in 2000. The percentage with 3 siblings
stays roughly constant across the five censuses, with the percentage above 3 falling rapidly over time.
Looking at the cumulative distribution in the bottom panel, we see that in 1960 and 1970 (which are
virtually indistinguishable) the median number of siblings was well below five, while only about 20%
had less than three siblings. By 2000 these proportions had reversed, with only about 20% having five
or more siblings, while over 50% had less than three. Over 25% of 9-11 year-olds had only one
sibling in 2000, compared to 7% in 1960. Looking across the five censuses, some of the largest
changes in family size of 9-11 year-olds take place between the 1980 and 1991 censuses. These reflect
the rapid declines in fertility in Brazil between 1970 and 1981, declines that far offset the
improvements in infant and child survival during that period.
Figure 6 combines the census estimates of cohort size and family size for children aged 9-11 in
the five censuses from 1960 to 2000. The figure presents a concise summary of our interpretation of
the stages of the demographic transition from a child’s perspective. As noted above, the number of
surviving siblings rises slightly between the 1960 and 1970 censuses. The total number of 9-11 yearolds in the population increases by about 30% between 1960 and 1970. From the perspective of 10
year-olds, Brazil was still in Stage 1 of the demographic transition between 1960 and 1970, with both
family size and cohort size increasing. Between 1970 and 1980 the number of surviving siblings
declined, while the total number of 9-11 year-olds in the population continued to grow, increasing by
19% during the decade. Although we cannot pinpoint the turning point, which could have occurred
either during the 1960s or 1970s, Brazil is clearly well into Stage 2 of the demographic transition
from the perspective of 10 year-olds by 1980, with falling numbers of siblings and rising cohort size.
These trends continue between the 1980 and 1991 censuses. Ten year-olds in 1991 had one fewer
sibling than ten year-olds in 1980, but the total number of ten year-olds in the population increased by
Child’s Perspective on Stages of the Demographic Transition, Page 17
30%, almost as large as the increase of the 1960s. With the largest cohort born in 1982, the number of
9-11 year-olds declined between the 1991 and 2001 census, a decline of about 10%. The timing of the
entry into our Stage 3 of the demographic transition is much easier to see than the boundary between
Stage 1 and Stage 2, since it only requires identification of the year in which the largest cohort is born.
From the perspective of a 10 year-old, 1992 marks the year in which there is both a decline in the
absolute number in the population as well as a (continuing) decline in the average number of siblings.
CHANGING FAMILY SIZE IN KENYA, MEXICO, AND VIETNAM
We can do the same kind of analysis on other countries for which we have multiple censuses or
large surveys. We use the large public use census samples for Kenya, Mexico, and Vietnam provided
through the IPUMS-International project, each of which has a recent pair of censuses ten years apart.
In each country we present estimates for the total population followed by breakdowns between rural
and urban populations and breakdowns by whether the mother has four or more years of schooling. As
in our Brazil results, we show the mean family size of children aged 9-11 and the mean family size of
women aged 25-49, using both the total number of children ever born and the number surviving at the
time of the census.
Table 4 shows results for Kenya. Looking at the overall family size for children aged 9-11, we
see that in spite of Kenya’s late fertility decline, declines in the number of siblings were clearly
evident between the 1989 and 1999 censuses. Total family size for children fell from 7.0 to 6.2, while
surviving family size fell from 6.2 to 5.6, declines of 11.6% and 10.4% respectively. The percentage
declines in mean family size for women aged 25-49 were similar to the percentage declines in mean
family size for children, suggesting that the overall decline in fertility drove the decline in mean
family size of children. The 10% increase in the coefficient of variation in women’s family size (both
children ever born and children surviving) explains why mean family size for children fell at a slightly
lower rate than did mean family size for women.
Breaking down the results by rural-urban location and mother’s education, we see declines in
family size in every group. Surviving family size for 9-11 year-olds fell by 9.6% in rural areas and
8.4% in urban areas, with slightly higher declines in family size of women aged 9-11. The smallest
declines in family size are observed in the group with low mother’s education, where surviving family
size for 9-11 year-olds fell by 3.5%. Looking over all of the declines in Table 4, we see fairly similar
declines in mean family size for women and children in most groups. This suggests that the decline in
mean family size for children was driven by broad declines in fertility, with only a small role played
by changes in the variance in women’s fertility. As shown in Figure 2, the absolute number of
children aged 9-11 was still increasing in Kenya between 1989 and 1999. Census estimates indicate
that the absolute number of 9-11 year-olds in 1999 was 33% higher than the number in 1989, an
annual growth rate of 2.9%. According to our typology, then, Kenya was clearly in Stage 2 of the
demographic transition in the 1990s, with cohort size still increasing while family size was clearly on
the decline.
Table 5 shows results for Mexico. The mean surviving family size of 9-11 year olds fell from 5.1
to 4.7 between 1990 and 2000, a decline of about 8%. The decline in surviving fertility for women
Child’s Perspective on Stages of the Demographic Transition, Page 18
aged 25-49 was only 0.1 births, a 4% decline, with a fall in the coefficient of variation explaining the
other 4% of the decline in mean family size of children. Declines in family size are observed in both
rural and urban areas, and for children of both high education and low education mothers. Note that
the smaller declines in family size within educational groups demonstrate that rising women’s
education contributes substantially to the decline in fertility over the period in which these children
were born. As shown in Figure 2, the number of 9-11 year-olds in Mexico was relatively flat between
1990 and 2000, part of a long flat peak that extends from around 1985 to 2005. Mexico, then,
represents a case in which family size of 9-11 year-olds was clearly falling after 1990, while cohort
size was relatively flat.
Table 6 shows results for Vietnam. The mean surviving family size for 9-11 year-olds in 1989
was 4.5, lower than Kenya and Mexico and about the same as Brazil. In spite of this already low level,
Vietnam had the most rapid decline in family size during the 1990s, a decline of 23%. Similar
declines are observed in rural and urban areas, and by education group. Women’s mean family size
falls at a slightly slower rate, with declines in the coefficient of variation contributing part of the
decline in mean family size of children. As shown in Figure 2, the number of 9-11 year-olds reached a
peak in Vietnam around 2000, indicating that 9-11 year-olds in the 2000 census were still
experiencing small increases in cohort size, but were experiencing fairly significant declines in family
size compared to 1990.
Figure 7 shows the detailed distribution of numbers of siblings of children aged 9-11 in Kenya,
Mexico, and Vietnam. We show the cumulative distributions for these comparisons, showing the
percentage of children who have x or fewer siblings. These cumulative distributions clearly
demonstrate the decline in family size over time in each country, and the large differences between
countries. Looking at the distribution for Kenya in the top panel, 56% of 9-11 year-olds had five or
more siblings in 1989. This fell to 45% in 1999. The percentage with seven or more siblings fell from
28% to 21% over the decade, while the percentage with less than four siblings increased from 28% to
40%. Mexico already had significantly smaller family sizes than Kenya in 1989, and the declines in
Mexico in the 1990s were smaller than those observed in Kenya. The percentage of 9-11 year-olds
with five or more siblings in Mexico fell from 38% to 33% over the decade, while the percentage with
less than three siblings grew from 30% to 37%.
Vietnam had by far the smallest families of the three countries shown in 1989, with only 26% of
9-11 year-olds having five or more siblings in 1989. Vietnam nonetheless shows some of the largest
declines in family size over the decade, with the percentage of 9-11 year-olds having five or more
siblings falling to 12% in 1999, about 1/4 of the percentage with five or more siblings in Kenya. The
percentage with less than three siblings in Vietnam increased from 34% to almost 60% between 1989
and 1999, a dramatic emergence of small families. The distribution of family size in Vietnam in 1999
is similar to that observed in Brazil in 2000, with the percentage having one sibling or less at 32% in
Brazil and 34% in Vietnam.
The overall picture shown in Figure 7 is a clear shift toward smaller families in each of the quite
diverse countries shown, viewed from the perspective of school-age children. While this should
perhaps not be surprising, given the fertility decline underway in each country, several points should
be noted. First, fertility decline must compete with declines in infant and child mortality to determine
Child’s Perspective on Stages of the Demographic Transition, Page 19
the number of surviving siblings. Only by looking directly at numbers of siblings for children of a
given age can we see the net effect of these two offsetting demographic trends. The second point is
that there is a complex relationship between the Total Fertility Rate estimated in a given year and the
average number of siblings of children born in that year. In addition to the fact that the family size of
children born in a given year is affected by fertility rates over 20-30 years, family size from children’s
perspective can look quite different than family size from women’s perspective. Only direct analysis
of micro data can answer the question of whether the number of siblings of school-age children is
increasing or decreasing over a given period. A third point is that it is important to look at the changes
in the complete distribution of numbers of siblings, changes that are difficult to predict based on
fertility rates alone. One of the patterns evident in Figure 7 is that the biggest changes in numbers of
siblings are taking place at the largest family sizes. This means that children in these countries are
significantly less likely to have large numbers of siblings.
STAGES OF THE DEMOGRAPHIC TRANSITION
Returning to our stylized characterization of stages of the demographic transition from a child’s
perspective, the previous section documents that the four countries we look at – Brazil, Kenya,
Mexico, and Vietnam – all moved into Stage 2 of the transition long enough ago that we see a clear
decline in the number of surviving siblings for children age 9-11 when we compare the two most
recent censuses. In Brazil, where we have census data back to 1960, we can see a movement from
Stage 1, with rising family size and rising cohort size, into Stage 2, with falling family size and rising
cohort size, some time in the 1960s or 1970s. For the other countries it is impossible to tell when they
moved from Stage 1 to Stage 2 in the absence of comparable micro data for earlier years. In all cases
we know that there had to be a Stage 1 period, since there had to be a period in which net family size
increased in order to create the rapid population growth and resulting population momentum that is
typical of these countries. We also know that all four countries moved from Stage 1 into Stage 2 by at
least the 1990s, and probably some time before that.
Brazil, Mexico, and Vietnam have all recently reached the peak in the number of children aged
9-11. In the case of Brazil and Mexico this is a relatively long, flat peak in which the number of 9-11
year-olds remains roughly constant over 20 to 30 years. This peak comes after a period of rapid
growth in the number of 9-11 year-olds, and marks a transition into what we call Stage 3 of the
demographic transition from a child’s perspective. While those born in Stage 2 faced falling family
size but increasing cohort size, those born in Stage 3 experience declines in both family size and
cohort size. In the case of Kenya, cohort size will continue to increase for at least two decades.
School-aged children in Kenya are currently experiencing declines in the number of siblings but
increases in the absolute number of children.
Declines in the absolute numbers of births have come later than the decline in surviving family
size in all four of the countries we consider, as suggested by our model and our typology of stages of
the demographic transition. It is important to keep in mind that this sequence of changes is not a
mathematical necessity, though we believe the typical pattern of the demographic transition is likely
Child’s Perspective on Stages of the Demographic Transition, Page 20
to always produce continued increases in cohort size for one or two decades after family size begins to
fall.
CONCLUSIONS
While the demographic transition has been heavily analyzed and discussed, we believe that
researchers have failed to recognize one of the most interesting and important features of the
population dynamics that drive the transition. While the basic empirical regularities of falling
mortality, falling fertility, and resulting patterns in population growth rates are well known, little
attention has been paid to the implications of these changes on the dynamics of family size and cohort
size. These dynamics turn out to have a number of intriguing features, the most important of which is
the tendency for family size and cohort size to move in opposite directions during a significant part of
the demographic transition.
We have proposed a characterization of the demographic transition from a child’s perspective
that has three stages. Children born in Stage 1 face increases in both family size and cohort size, the
result of falling infant and child mortality. Children born in Stage 2 experience declining family size,
as falling fertility overtakes falling mortality, but face continued increases in cohort size as the result
of population momentum. Children born in Stage 3 experience declines in both cohort size and family
size. Using a simple model of the demographic transition, we demonstrate the key components of
these stages – a race between falling fertility and falling mortality in Stage 1, and a race between
falling fertility and population momentum in Stage 2. This model suggests that Stage 2 is likely to be
a typical feature of the demographic transition, potentially lasting for one or two decades.
Using unusually rich census data for Brazil, we have shown that the country was still in Stage 1
during the 1960s, was in Stage 2 from roughly 1970 until about 1982, and has been in Stage 3 since
1982, the year in which the largest birth cohort was born. Using data for the most recent two censuses
from Kenya, Mexico, and Vietnam, we show that the average number of siblings of 9-11 year-olds
declined in all three countries. Analysis of the distribution of number of siblings shows that these
declines are driven in large part by substantial declines in the number of 9-11 year-olds with large
numbers of siblings. For Mexico and Vietnam, these declines in family size occurred during a period
in which cohort size was either decreasing or remaining roughly constant. These countries therefore
seem to have entered our Stage 3 of the demographic transition. Kenya seems to be clearly still in
Stage 2, with rising cohort size combining with falling family size.
The implications of these changes in family size and cohort size depend on the interaction
between these variables and outcomes such as schooling, health, and eventually labor market
experience. As noted above, an extensive literature has explored these relationships, and it is beyond
the scope of this paper to provide new evidence on those links. The goal of this paper has been to
provide new insights into the underlying population dynamics affecting the competition for resources
at the family and population levels. We believe this framework will help increase our understanding
of the changes that have taken place in many developing countries during recent decades and in
planning for the needs of young people in the decades to come.
Child’s Perspective on Stages of the Demographic Transition, Page 21
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Child’s Perspective on Stages of the Demographic Transition, Page 23
Table 1. Total Fertility Rates by Regions, Total Population and Annual Growth
Rates, Brazil, 1940-2000
YEAR
Total Fertility Rates
Brazil
North
Northeast
Southeast
South
Center-West
Total Population (millions)
1940
1950
1960
1970
1980
1991
2000
6.16
7.17
7.15
5.69
5.65
6.36
41.23
6.21
7.97
7.5
5.45
5.7
6.86
51.94
6.28
8.56
7.39
6.34
5.89
6.74
70.07
5.76
8.15
7.53
4.56
5.42
6.42
93.14
4.35
6.45
6.13
3.45
3.63
4.51
119.00
2.70
4.00
4.00
2.40
2.30
2.90
146.83
2.31
3.05
2.60
2.00
2.25
2.34
169.54
Annual Intercensal Growth Rate
Source: IBGE (1996; 2002), Wong (2000).
2.31
2.99
2.85
2.45
1.91
1.60
Child’s Perspective on Stages of the Demographic Transition, Page 24
Table 2. Measures of family size for women and children, Brazil 1960 to 2000
Variable and
Mean family size
Standard Deviation
age group
1960 1970 1980 1991 2000 1960 1970 1980 1991 2000
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9) (10)
Family size ever
born
1. Women 45-49
5.9 5.7 5.4 4.5 3.6 4.6 4.4 3.8 3.5 2.9
2. Women 25-29
2.5 2.6 2.4 1.7 1.5 2.4 2.3 1.8 1.6 1.4
3. Women 25-49
4.3 4.3 3.9 2.9 2.5 3.8 3.6 3.1 2.6 2.2
4. Children 9-11
7.4 7.1 6.2 4.9 4.1 3.7 3.6 3.4 3.2 2.9
Surviving family
size
5. Women 45-49
6. Women 25-29
7. Women 25-49
8. Children 9-11
4.4
2.1
3.3
5.9
4.5
2.2
3.5
6.0
4.5
2.2
3.4
5.4
3.9
1.6
2.6
4.4
3.3
1.5
2.3
3.8
3.4
1.9
2.8
2.8
3.4
2.0
2.9
2.8
3.1
1.6
2.6
2.8
2.8
1.4
2.2
2.6
2.4
1.3
1.9
2.5
Coefficient of Variation
Mean family size of children
1960 1970 1980 1991 2000 1960 1970 1980 1991 2000
(11) (12) (13) (14) (15) (16) (17) (18) (19) (20)
0.79
0.93
0.89
0.49
0.77
0.90
0.84
0.51
0.71
0.74
0.79
0.55
0.78
0.95
0.91
0.64
0.80
0.94
0.88
0.69
9.6
4.7
7.6
9.1
4.7
7.4
8.1
3.7
6.3
7.2
3.2
5.3
5.9
2.9
4.4
0.78
0.91
0.86
0.46
0.75
0.88
0.81
0.47
0.69
0.73
0.75
0.52
0.74
0.92
0.85
0.59
0.75
0.92
0.83
0.64
7.0
3.8
5.7
7.0
3.9
5.9
6.7
3.3
5.3
6.0
2.9
4.5
5.1
2.7
3.9
Child’s Perspective on Stages of the Demographic Transition, Page 25
Table 3. Measures of family size for women ages 25-59 and children aged 9-11,
by region and mother's education, Brazil 1960-2000
Variable
and age
Sample
Mean
Coefficient of variation
Percentage change in mean
1960 1970 1980 1991 2000 1960 1970 1980 1991 2000 60-70 70-80 80-91 91-2000 60-2000
Family size ever born
1. Women 25-49 Northeast
2. Children 9-11 Northeast
5.0
8.6
5.1
8.2
5.0
7.5
3.8
6.4
3.0
5.1
0.88
0.46
0.82
0.47
0.74
0.50
0.88
0.57
0.90
0.66
3.2%
-4.2%
-1.6% -23.8%
-8.7% -14.8%
-21.8% -39.5%
-20.1% -40.4%
3. Women 25-49 Southeast
4. Children 9-11 Southeast
3.8
6.7
3.7
6.4
3.3
5.4
2.4
4.1
2.1
3.5
0.91
0.51
0.87
0.53
0.79
0.57
0.88
0.62
0.85
0.65
-0.4% -10.6% -26.7%
-5.3% -15.1% -24.6%
-12.4% -42.9%
-13.9% -47.8%
5. Women 25-49 Low education
6. Children 9-11 Low education
4.9
7.8
5.0
7.6
4.9
7.0
3.9
6.4
3.4
5.7
0.81
0.46
0.76
0.47
0.70
0.50
0.83
0.54
0.85
0.59
2.4%
-3.1%
-2.6% -19.1%
-8.0% -8.2%
-13.5% -30.2%
-10.5% -26.8%
7. Women 25-49 High education
8. Children 9-11 High education
2.9
5.9
3.0
5.6
2.8
4.7
2.3
3.6
2.1
3.2
1.04
0.58
0.95
0.57
0.79
0.60
0.83
0.59
0.80
0.62
2.8% -5.5% -19.7%
-6.3% -16.3% -22.3%
-7.7% -28.0%
-12.1% -46.4%
Surviving family size
9. Women 25-49 Northeast
10. Children 9-11 Northeast
3.5
6.3
3.9
6.5
4.0
6.2
3.3
5.5
2.7
4.6
0.89
0.45
0.81
0.45
0.72
0.48
0.83
0.53
0.85 12.5%
0.61 2.6%
11. Women 25-49 Southeast
12. Children 9-11 Southeast
3.1
5.6
3.2
5.5
3.0
4.9
2.3
3.8
2.1
3.4
0.87
0.48
0.84
0.50
0.77
0.55
0.84
0.58
0.83
0.62
13. Women 25-49 Low education
14. Children 9-11 Low education
3.7
6.2
4.0
6.3
4.1
6.0
3.4
5.6
3.1
5.1
0.79
0.44
0.74
0.45
0.68
0.48
0.80
0.51
0.81
0.55
15. Women 25-49 High education
16. Children 9-11 High education
2.5
5.1
2.7
5.0
2.6
4.3
2.1
3.4
2.0
3.1
0.98
0.53
0.90
0.53
0.77
0.57
0.79
0.54
0.77
0.58
4.1% -18.7%
-5.0% -10.8%
-17.5% -21.4%
-16.8% -27.7%
4.4% -6.0% -23.8%
-1.1% -11.7% -21.8%
-10.1% -32.8%
-11.7% -39.7%
8.8%
2.1%
2.0% -16.6%
-5.2% -6.2%
-10.3% -16.9%
-8.0% -16.5%
7.7% -2.3% -17.3%
-2.5% -13.8% -20.4%
-6.0% -18.2%
-10.6% -40.2%
Note: Low education is women with under 4 years of schooling; high education is women with 4 or more years of schooling
Child’s Perspective on Stages of the Demographic Transition, Page 26
Table 4. Family size for women 25-49 and children 9-11, Kenya 1989 and 1999
Variable and
age group
Sample
Mean family size
1989
1999
Percent
change
Coefficient of variation
1989
1999
Percent
change
Family size (ever born)
Women 25-49 All Kenya
Children 9-11
All Kenya
5.64
7.01
4.86
6.19
-13.9%
-11.6%
0.56
0.43
0.61
0.46
9.9%
7.3%
Surviving family size
Women 25-49 All Kenya
Children 9-11
All Kenya
4.87
6.19
4.26
5.55
-12.4%
-10.4%
0.56
0.41
0.61
0.45
9.9%
8.6%
Family size (ever born)
Women 25-49 Rural
Children 9-11
Rural
Women 25-49 Urban
Children 9-11
Urban
Women 25-49 Low education
Children 9-11
Low education
Women 25-49 High education
Children 9-11
High education
5.97
7.18
4.07
5.63
6.36
7.59
4.81
6.21
5.31
6.42
3.65
5.20
6.07
7.22
4.26
5.57
-11.2%
-10.5%
-10.3%
-7.6%
-4.6%
-4.9%
-11.3%
-10.2%
0.52
0.42
0.69
0.48
0.51
0.41
0.58
0.43
0.56
0.44
0.73
0.52
0.52
0.40
0.63
0.47
7.2%
5.7%
5.3%
8.1%
0.9%
-0.5%
9.2%
8.7%
Surviving family size
Women 25-49 Rural
Children 9-11
Rural
Women 25-49 Urban
Children 9-11
Urban
Women 25-49 Low education
Children 9-11
Low education
Women 25-49 High education
Children 9-11
High education
5.13
6.32
3.62
5.13
5.29
6.53
4.37
5.72
4.64
5.74
3.25
4.70
5.14
6.31
3.84
5.08
-9.6%
-9.2%
-10.3%
-8.4%
-2.9%
-3.5%
-12.3%
-11.2%
0.52
0.40
0.68
0.46
0.53
0.40
0.57
0.41
0.56
0.43
0.72
0.50
0.53
0.40
0.63
0.46
6.9%
7.1%
6.4%
8.4%
0.6%
0.4%
10.6%
10.8%
Note: Low education is women with under 4 years of schooling; high education is women with 4 or more
years of schooling
Child’s Perspective on Stages of the Demographic Transition, Page 27
Table 5. Family size for women 25-49 and children 9-11, Mexico 1990 and 2000
Variable and
age group
Sample
Mean family size
1990
2000
Percent
change
Coefficient of variation
1990
2000
Percent
change
Family size (ever born)
Women 25-49
All Mexico
Children 9-11
All Mexico
4.1
5.6
3.8
5.1
-7.0%
-7.9%
0.67
0.55
0.62
0.57
-6.4%
3.9%
Surviving family size
Women 25-49
All Mexico
Children 9-11
All Mexico
3.7
5.1
3.6
4.7
-4.2%
-7.8%
0.66
0.51
0.59
0.53
-11.4%
3.0%
Family size (ever born)
Women 25-49
Rural
Children 9-11
Rural
Women 25-49
Urban
Children 9-11
Urban
Women 25-49
Low education
Children 9-11
Low education
Women 25-49
High education
Children 9-11
High education
5.4
6.7
3.7
5.0
5.6
6.8
3.3
4.5
4.7
6.0
3.3
4.4
5.4
6.6
3.2
4.2
-12.2%
-10.2%
-10.0%
-12.3%
-3.1%
-2.1%
-3.2%
-5.5%
0.57
0.47
0.67
0.57
0.55
0.47
0.65
0.54
0.58
0.50
0.60
0.59
0.52
0.46
0.58
0.56
0.8%
7.7%
-10.1%
4.0%
-5.7%
-0.9%
-11.1%
2.8%
Surviving family size
Women 25-49
Rural
Children 9-11
Rural
Women 25-49
Urban
Children 9-11
Urban
Women 25-49
Low education
Children 9-11
Low education
Women 25-49
High education
Children 9-11
High education
4.7
6.0
3.4
4.7
4.9
6.1
3.1
4.3
4.3
5.5
3.1
4.1
4.9
6.0
3.1
4.0
-7.9%
-8.9%
-7.5%
-12.4%
0.2%
-1.7%
-1.2%
-6.4%
0.59
0.45
0.67
0.53
0.57
0.45
0.66
0.51
0.55
0.47
0.57
0.54
0.50
0.44
0.55
0.52
-6.5%
6.1%
-15.1%
2.2%
-11.8%
-1.1%
-15.9%
0.3%
Note: Low education is women with under 4 years of schooling; high education is women with 4 or more
years of schooling
Child’s Perspective on Stages of the Demographic Transition, Page 28
Table 6. Family size for women 25-49 and children 9-11, Vietnam 1989 and 1999
Variable and
age group
Sample
Family size (ever born)
Women 25-49
All Vietnam
Children 9-11
All Vietnam
Surviving family size
Women 25-49
All Vietnam
Children 9-11
All Vietnam
Mean family size
1989
1999
Percent
change
Coefficient of variation
1989
1999
Percent
change
3.5
4.8
2.8
3.6
-19.7%
-24.5%
0.63
0.46
0.60
0.50
-4.5%
9.5%
3.3
4.5
2.7
3.5
-17.4%
-22.6%
0.61
0.44
0.58
0.48
-4.7%
9.7%
Family size (ever born)
Women 25-49
Rural
Children 9-11
Rural
Women 25-49
Urban
Children 9-11
Urban
Women 25-49
Low education
Children 9-11
Low education
Women 25-49
High education
Children 9-11
High education
3.9
5.1
3.1
4.2
4.8
5.9
3.1
4.3
3.2
4.0
2.5
3.1
4.0
4.9
2.6
3.3
-16.4%
-21.5%
-19.8%
-27.1%
-16.1%
-16.3%
-14.8%
-22.1%
0.59
0.42
0.67
0.50
0.54
0.40
0.61
0.44
0.56
0.46
0.60
0.52
0.55
0.43
0.57
0.47
-3.8%
9.0%
-10.6%
3.6%
2.2%
9.0%
-7.1%
6.2%
Surviving family size
Women 25-49
Rural
Children 9-11
Rural
Women 25-49
Urban
Children 9-11
Urban
Women 25-49
Low education
Children 9-11
Low education
Women 25-49
High education
Children 9-11
High education
3.6
4.8
2.9
4.0
4.3
5.4
2.9
4.1
3.1
3.8
2.4
3.0
3.7
4.6
2.6
3.2
-13.8%
-19.3%
-18.1%
-25.7%
-13.6%
-14.2%
-13.1%
-20.7%
0.57
0.41
0.65
0.48
0.53
0.39
0.60
0.43
0.55
0.44
0.58
0.49
0.53
0.41
0.55
0.46
-4.3%
9.0%
-10.4%
3.7%
0.3%
7.4%
-7.0%
6.6%
Note: Low education is women with under 4 years of schooling; high education is women with 4 or more
years of schooling
Child’s Perspective on Stages of the Demographic Transition, Page 29
Figure 1. Total Fertility Rate, Infant Survival Probability, and Predicted Growth Rate of Family
Size, Brazil, Kenya, Mexico, and Vietnam, 1950-2005
Total Fertility Rate
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1950
Kenya
Vietnam
Mexico
Brazil
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
Probability of Infant Survival
1.00
0.98
0.96
0.94
0.92
0.90
Kenya
Vietnam
Mexico
Brazil
0.88
0.86
0.84
0.82
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2000
2005
Predicted Annual Growth Rate of Surviving Family Size
4.0%
3.0%
2.0%
1.0%
0.0%
-1.0%
-2.0%
-3.0%
-4.0%
-5.0%
-6.0%
1950
Kenya
Vietnam
Mexico
Brazil
1955
1960
1965
1970
1975
1980
1985
1990
1995
Child’s Perspective on Stages of the Demographic Transition, Page 30
Figure 2. Population Aged 9-11, Brazil, Kenya, Mexico, Vietnam, 1950-2030
United Nations Estimates and Medium Variant Projections (1950=100)
400
300
1400
1200
250
1000
200
800
150
600
100
400
50
200
0
1950
0
1960
1970
1980
1990
Year
2000
2010
2020
2030
Kenya
Brazil, Mexico, Vietnam
350
1600
Vietnam
Mexico
Brazil
Kenya
Child’s Perspective on Stages of the Demographic Transition, Page 31
Figure 3. Family size for children ages 9-11 and women
ages 25-49, Brazil 1960 to 2000
8
7
Mean family size
6
5
4
3
2
1
0
1960
Total family size, children 9-11
Surviving family size, children 9-11
Surviving family size, children of women 25-49
Children ever born, women 25-49
Surviving children, women 25-49
1970
1980
1990
2000
Child’s Perspective on Stages of the Demographic Transition, Page 32
Figure 4. Family size of children ages 9-11 by mother's
education, Brazil 1960 to 2000
7
Surviving family size
6
5
4
3
2
Children 9-11, low mother's education
1
Children 9-11, high mother's education
Women 25-49, low education
Women 25-49, high education
0
1960
1970
1980
1990
2000
Child’s Perspective on Stages of the Demographic Transition, Page 33
Figure 5. Distribution of Numbers of Surviving Siblings of Children Ages 9-11,
Brazil 1960-2000
Percentage with x siblings
30
1960
1970
25
1980
1991
2000
Percentage
20
15
10
5
0
0
1
2
3
4
5
6
7
8
9
Number of Siblings
Percentage with x or fewer siblings
100
90
Cumulative Percentage
80
70
60
50
40
2000
1991
1980
1970
1960
30
20
10
0
0
1
2
3
4
5
Number of Siblings
6
7
8
9
Child’s Perspective on Stages of the Demographic Transition, Page 34
Figure 6. Number of surviving siblings and total number in population of 9-11 year-olds,
Brazilian censuses 1960-2000
250
6.0
Stage 1, rising family
size and cohort size
Stage 3, falling family
size and cohort size
Stage 2, falling family size
and rising cohort size
200
4.0
150
3.0
100
2.0
50
1.0
Number of surviving siblings of 9-11 year-olds
Number age 9-11 in population
0.0
1960
0
1965
1970
1975
1980
Year
1985
1990
1995
2000
Cohort size (1960=100)
Number of siblings
5.0
Child’s Perspective on Stages of the Demographic Transition, Page 35
Figure 7. Distribution of Numbers of Siblings of Children Ages 9-11,
Kenya, Mexico, and Vietnam
(percentage with x or fewer siblings)
Kenya, 1989 & 1999 Census
100
80
70
60
50
40
30
1999
20
1989
10
0
0
1
2
3
4
5
6
7
8
9
Number of Siblings
Mexico, 1990 & 2000 Census
100
90
80
70
60
50
40
30
2000
1990
20
10
0
0
1
2
3
4
5
6
7
8
9
Number of Siblings
Vietnam, 1989 & 1999 Census
Cumulative Percentage
Cumulative Percentage
Cumulative Percentage
90
100
90
80
70
60
50
40
30
20
10
0
1999
1989
0
1
2
3
4
5
Number of Siblings
6
7
8
9