Transitions Between

Childlessness and First Birth:

Three Generations of

U.S.Women

Series 2, Number 153 August 2011
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Kirmeyer SE, Hamilton BE. Transitions between childlessness and first birth: 

Three generations of U.S. women. National Center for Health Statistics. 

Vital Health Stat 2(153). 2011. 

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Transitions between childlessness and first birth : three generations of U.S.

women.

p. ; cm.— (Vital and health statistics. Series 2 ; no. 153) (DHHS publication ;

no. (PHS) 2011–1353)

‘‘August 2011.’’

Includes bibliographical references.

ISBN-13: 978–0–8406–0646–4

ISBN-10: 0–8406–0646–X

1. Fertility—United States—Statistics. 2. Birth intervals—United States—

Statistics. I. National Center for Health Statistics (U.S.) II. Series: Vital and

health statistics. Series 2, Data evaluation and methods research ; no. 153.

III. Series: DHHS publication ; no. (PHS) 2011–1353.

[DNLM: 1. Reproductive Behavior—United States—Statistics. 2. Birth

Intervals—United States—Statistics. 3. Fertility—United States—Statistics.

4. Longitudinal Studies—United States—Statistics. W2 A N148vb no.153 2011]

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Series 2, Number 153

Transitions Between Childlessness

and First Birth: Three Generations of

U.S.Women

Data Evaluation and Methods Research

U.S. DEPARTMENT OF HEALTH AND HUMAN SERVICES

Centers for Disease Control and Prevention

National Center for Health Statistics

Hyattsville, Maryland

August 2011

DHHS Publication No. (PHS) 2011–1353
National Center for Health Statistics

Edward J. Sondik, Ph.D., Director

Jennifer H. Madans, Ph.D., Associate Director for Science

Division of Vital Statistics

Charles J. Rothwell, M.S., Director
Contents 

Abstract ................................................................................................. 1 

Introduction .............................................................................................. 1 

Methods ................................................................................................. 1 

Data Sources ........................................................................................... 1 

Data Quality............................................................................................ 2 

Analytic Methods ....................................................................................... 2 

Measures .............................................................................................. 2 

Results and Discussion ..................................................................................... 3 

Patterns of First-birth Probabilities (qx) ...................................................................... 3 

Number in Cohort Remaining Childless, by Age (lx) ........................................................... 4 

Distribution of First Births by Mother’s Age (bx) ............................................................. 4 

Expectation of Number of Years to be Childless in the Future (ex) ................................................ 5 

Degree of Concentration of First Births...................................................................... 6 

Importance of Childlessness in the Demographic Context of the 20th Century ...................................... 7 

Trends by Parity Distribution in the 20th Century ............................................................. 7 

Cohort TFRs, 1950–2005 ................................................................................. 7 

Postponement and Recuperation of Fertility .................................................................. 8 

Relationship of Childlessness to TFRs....................................................................... 9 

Conclusion ............................................................................................... 11 

References ............................................................................................... 11 

Appendix. Technical Notes .................................................................................. 16 

Figures

1.	 Probability of having a first birth, by age and birth cohort of mother: United States, 1910, 1935, and 1960 .......... 3 

2.	 Cumulative probability of having a first birth, by age and birth cohort of mother: United States, 1910, 1935, 

and 1960 .......................................................................................... 4 

3.	 Number of women remaining childless, by age and birth cohort of mother: United States, 1910, 1935, and 1960...... 5 

4.	 Distribution of first births, by age and birth cohort of mother: United States, 1910, 1935, and 1960 ................ 6 

5.	 Average number of years expected to remain childless, by age and birth cohort of mother: United States, 1910, 

1935, and 1960 ..................................................................................... 7 

6.	 Lorenz curves of first births and Duncan Index of Concentration, by birth cohort: United States, 1910, 1935, 

and 1960 .......................................................................................... 8 

7.	 Parity distribution at completed fertility of birth cohorts: United States, 1900–1960.............................. 9 

8.	 Percent distribution of the number of children ever born, by birth cohort of mother: United States, 1910, 1935, 

and 1960 .......................................................................................... 10 

9.	 Total fertility rates at completed fertility of birth cohorts: United States, 1950–2005 ............................. 10 

10.	 Proportion childless and total fertility rate at completed fertility, by birth cohorts: United States, 1910–1960 ......... 11 

iii
Text Tables

A.	 Cumulative probability of first birth, by selected age and birth cohort of women: United States, 1910, 1935, 

and 1960 .......................................................................................... 4 

B.	 Proportion of women childless, by selected age and birth cohort of women: United States, 1910, 1935, and 1960 ..... 5 

C.	 Mean, median, modal, and maximum number of first births (bx), by birth cohort of women: United States, 

1910, 1935, and 1960................................................................................ 6 

D.	 Expected number of years childless, by selected age interval and birth cohort of women: United States, 1910, 1935, 

and 1960 .......................................................................................... 7 

E.	 Gini Concentration Ratio and Duncan Index of Concentration, by birth cohort of women: United States, 

1910, 1935, and 1960................................................................................ 8 

F.	 Total fertility rates, by selected age group and birth cohorts of women: United States, 1930, 1940, 1950, 1960, 

1970, and 1980 ..................................................................................... 9 

Detailed Tables

1.	 Maternity table for the 1910 birth cohort, by age of mother ................................................ 13 

2.	 Maternity table for the 1935 birth cohort, by age of mother ................................................. 14 

3.	 Maternity table for the 1960 birth cohort, by age of mother ................................................. 15 

iv
Transitions Between Childlessness

and First Birth: Three Generations

of U.S. Women

by Sharon E. Kirmeyer, Ph.D.; and Brady E. Hamilton, Ph.D.,

Division of Vital Statistics

Objective

This report analyzes the patterns of

childlessness, and conversely, the

first-birth patterns of three birth cohorts

of American women. For this report, a

cohort refers to women born in the

same year. The cohorts compared were

women born in 1910, 1935, and

1960—who, consequently, turned 25

during the Great Depression, the Baby

Boom, and lastly, the post-Baby Boom

period. The purpose of the report is to

explore the differences in fertility

characteristics of these three

generations of women and to consider

those differences in light of the social

and economic conditions at the time.

Methods

Life table methodology, including the

probability of having a first birth, the

number of women remaining childless,

and the expected number of years to

remain childless, was applied to each of

the three birth cohorts for comparison.

Techniques extended from life table

functions were also used and included

measures of first-birth concentration as

well as comparisons between childlessness and the total fertility rate (TFR).

Data were based on the Centers for

Disease Control and Prevention’s

National Center for Health Statistics

tables on cohort fertility.

Results

Of the three birth cohorts studied,

the women born in 1910 had the

highest proportion childless and a low

TFR. In contrast, the women born in

1935 had both the lowest proportion

childless and the highest TFR. The

fertility of women who were born in

1960 is characterized as intermediate to

the other cohorts in terms of

childlessness, but is distinct with both

lowest levels of childbearing and oldest

ages of first births. First-time

childbearing is more concentrated (that

is, least spread out) by age of mother

for the 1910 and 1935 cohorts than the

1960 cohort. Finally, data for all U.S.

birth cohorts 1910–1960 suggest that

the greater the proportion childless in a

cohort, the lower the TFR.

Keywords: birth cohorts • cohort

fertility • life table methods • zero parity

Introduction

Both the timing of the first birth

and the percentage childless have

profound consequences for society.

These include the demand for schools

and housing, as well as the development

and utilization of women in the labor

force. Moreover, the lives of women

who become mothers are significantly

different from those who do not. To

give birth (and to raise a child) results

in a transition to parenthood, with

immediate and generally permanent

implications (1). In industrialized

societies, parenthood affects the

acquisition of material goods (such as

choice of place of residence, housing

type, and consumable goods) (2). When

and if women become mothers, they can

encounter opportunity costs (for

example, those that limit education, the

ability to work full-time, the possibility

to obtain higher professional attainment,

promotions, and higher incomes) (3).

In nonindustrialized societies, rather

than material or maternal opportunities,

the degree of kin availability—that is the

presence of children and the children’s

spouses—is of great importance for the

elderly. Consequently, the proportion of

women with any offspring is key to

the well-being of families in these

societies (2).

Childlessness has increasingly

become an acceptable lifestyle in North

America and Europe. However, lifestyle

decisions are only one of the reasons for

having a child. Not having a child may

be due to postponement of childbearing,

rather than early sterility (such as

premature menopause). Intervening

factors leading to childlessness include

partners’ availability and intentions, life

course events, subfecundity, and

unplanned events (1).

This report presents three strongly

contrasting patterns of childlessness (and

their complement, descriptions of first

childbirth) and discusses the context in

which these patterns occurred in the

United States. In addition, this report

discusses previously unknown

relationships between individual

functions of childlessness and the larger

demographic context.

Methods

Data Sources

The patterns of childlessness

examined in this report used U.S. birth

cohort data, not period data. A birth

cohort for this report is a group of

women born in the same year and who

share the same general or common

experiences, at successive ages, during

their reproductive lives.

Within this report, the experiences

of three cohorts of women are followed

over consecutive years through their

respective reproductive lives. In

contrast, analysis of period data includes

the observation of many cohorts within

a given time interval (1 year, for

example), with mixed and different

experiences of their reproductive lives.

The data for this report come from

publications based on U.S. vital

statistics data: ‘‘Fertility Tables for Birth

Cohorts by Color: United States,

1917–1973’’ (4), Centers for Disease

Control and Prevention’s National

Center for Health Statistics (NCHS)

Page 1
Page 2 [ Series 2, No. 153

tables from the vital statistics of the

United States (5,6), and the recent

NCHS Internet release, ‘‘Cohort Fertility

Tables for All, White, and Black

Women: United States, 1960–2005’’ (7).

The selection of these three birth

cohorts was based on several criteria.

The cohorts chosen experienced their

prime childbearing years under differing

social, economic, and demographic

conditions, and were evenly spaced from

each other. The birth cohorts selected

were 1910, 1935, and 1960, which are

spaced 25 years apart. This spacing is

close to the mean length of a generation,

which empirically has a mode of 27–28

years (8). Moreover, these cohorts had

data for essentially their complete

reproductive lives; that is, ages 15–49.

Note that the data for the 1960 cohort

are only available through age 45.

However, this was deemed acceptable

because the cohort had essentially

completed its childbearing.

In essence, the data represent three

generations of women who experienced

markedly different conditions. The

earliest cohort of women spent their

prime childbearing years (ages 20–35)

during the Great Depression (1929 to

the start of World War II), the second

during the post-World War II economic

recovery and the ‘‘Baby Boom’’ years

(1946–1964), and the third during a

period of social and economic

liberalization (which began in the late

1960s) with relatively low and definitely

delayed fertility (1973–2005).

Data for the 1910 and 1935

cohorts were taken from earlier

sources (4–6) and data for the 1960

cohort were from the most recent

source (7).

Data Quality

Note that the data in this report

encompass a period where birth

registration completeness improved to

become effectively universal. Three

nationwide tests of birth registration

completeness estimated that of all births

occurring in the United States,

92.5 percent in 1940, 97.9 percent in

1950, and 99.2 percent in 1964–1968

were registered (9). Accordingly, births

for earlier data years were adjusted for

underregistration. The quality (as well as

classification) of live birth order and age

of mother also improved, with relatively

few births imputed for live birth order

and age of mother not stated. For a

detailed discussion on the adjustment of

births and imputation of missing data,

see references 4 and 7.

Analytic Methods

The life table method is most

commonly applied to mortality data to

analyze the probability of dying in a

particular time period such as 1 year

and to estimate a variety of statistics

such as the average expectation of life

at birth. However, life tables can also be

used to study how long it takes for any

event to happen. Some examples of

reproductive health applications include:

estimating the average time to

conceive (10), gauging pregnancy

outcomes (11), measuring the mean

duration of breastfeeding (12),

evaluating contraceptive use

duration (13), cumulating birth

probabilities within first marriages (14),

and measuring the duration of

cohabitation, marriage, divorce, and

remarriage (15). This is the first time,

the authors believe, that life tables have

been used to formally examine and

compare patterns of childlessness. The

tabular data (4–7) produce functions that

relate to both childlessness and first

birth; as such, the tables are referred to

in this report as ‘‘maternity tables.’’

Several maternity table functions

that are used in the analysis are briefly

discussed in the next section. The

complete maternity tables are included

as Tables 1–3. Unlike standard life

tables, which range from birth to the

oldest measureable age, the maternity

table starts at age 15 and ends at age 49.

These ages typically represent the

beginning and end points of the

reproductive period. As seen in

Tables 1–3, less than 1 percent of first

births occur after age 45 (i.e., column

bx, births).

Measures

As noted earlier, the life table

method is most commonly applied to

mortality data to analyze the probability

of dying within a given time interval

and to estimate other duration functions.

Its applications are common in survival

analysis, medical trials, and a number of

reproductive health topics. The life

table—or in this case, the ‘‘maternity

table’’—functions were calculated in a

spreadsheet format using Excel, wherein

the calculations from one table column

become the basis for the next. The

following describes the most basic

functions.

Size of maternity table’s initial

cohort, or ‘‘radix’’—For purposes of

comparison, each cohort in the maternity

table is standardized to 100,000 at age

15 (expressed as l

15 in formal terms).

Probability of having a first birth at

age x (the qx values)—Represent the

probability or chance that a woman who

is childless on her xth birthday will have

a child before reaching her xth + 1

birthday.

Number of first births occurring at

age x (the bx values)—Represent the

number of first births who are born to a

woman at age x.

Number of childless women at age x

(the l

x values)—Represent the number of

women who are still childless on their

xth birthday.

Cumulative probability of having a

first birth by age x—Derived by

subtracting the l

x value from the radix

and dividing that difference by the radix

to obtain a cumulative indicator of the

probability of first births in a cohort.

Number of years expected to remain

childless from a given age to age 50

(the ex values)—Represent the average

time remaining in a woman’s

reproductive life that she would expect

to be childless. It has a well-known

counterpart in life tables: the expectation

of life.

A more detailed description of the

functions is provided in the ‘‘Technical

Notes.’’ Two other related functions are

described below.

Indicators of dispersion (Gini

Concentration Ratio and Duncan Index

of Concentration)—Represent two

measures of spread (or dispersion) in

volume and timing of childbearing. Both

depend on the Lorenz curve of

cumulative dependent variables. While

most known for indicating economic

and geographic inequality, they have

also been used to reflect maternal and
child health inequality (16,17). Both

measures indicate the concentrations of

first births by age of mother. The

differences in the two indices are

discussed below.

Lifetime total fertility rate by birth

cohort (TFR)—The age-cohort-specific

central fertility rates (f

x) are summed

over a cohort’s 35-year reproductive

period to provide the completed fertility

rate for that birth cohort, expressed as

number of births per 1,000 women

(aged 15–50).

Results and Discussion

The birth cohort of 1910 turned 25

in 1935, during the Great Depression. At

that time, many marriages were delayed

due to the lack of employment

opportunities for men. The average age

of marriage increased and a record

number of women never married (18).

Women at age 25 remained childless for

more years than did those in the other

cohorts during comparatively better

economic times; they expected 14 years

of future childlessness compared with 11

years for women born in 1935 and

1960.

The birth cohort of 1935 turned 25

in 1960, at the height of the prosperity

that contributed in part to the Baby

Boom. At this post-World War II time,

the economy had grown rapidly and

headed to full employment and high

wages. Men with only a high school

education could earn enough money to

support a family (19). Prior to World

War II, few attained higher levels of

education. Post-World War II, the G.I.

Bill assisted veterans in both obtaining

higher education and supporting a

family. At the same time, women were

staying at home, having at least two

children. This was due both to

their husbands functioning as the sole

provider in the household and to social

and workplace discrimination, which

curtailed the employment of married

women and, particularly, mothers (19).

The birth cohort of 1960 turned 25

in 1985, during a period of increasing

educational attainment and sustained

labor force participation for women.

There were legally enforced

improvements in opportunities for

women. Also at this time, there were

changes in the service sector in the U.S.

economy (especially for professional,

managerial, sales, and technical

services) (20), which favored the

employment of women. Just as

importantly during this time, modern

methods of contraception became widely

available (21,22).

Patterns of First-birth

Probabilities (qx)

During each year of a childless

woman’s reproductive life, there is some

probability that she will give birth. If

she does not, she remains childless and

has the opportunity in the succeeding

year to have a birth. The shapes of

first-birth probabilities differ greatly

among the three cohorts. They are

distinguished by overall magnitude of

the first-birth curve, its symmetry, and

the peak age to give birth (Figure 1).

Of the three cohorts, the 1910

cohort’s attainment of motherhood was

the lowest. The greatest probability or

likelihood to have a first birth at a given

age was 114 births per 1,000 (or 6,126

of 53,737 childless women). This peak

of first births occurred at age 23

(Table 1). Put another way, 11.4 percent

of childless women born in 1910 had a

first birth at age 23. The greatest

number of first births occurred early in

the reproductive period. The

probabilities for first births dropped

rapidly after age 25. This is not

unexpected given that the United States

was deep into the Great Depression at

this time.

The birth cohort of 1935 entered

prime childbearing years during the

economic prosperity of the late 1950s

and early 1960s. This cohort had the

highest overall fertility and lowest level

of childlessness. The highest first-birth

probability occurred at age 24 when

about 15 percent of women still

childless had their first child (Table 2).

The probability curve was similar to that

of the 1910 cohort, but first-birth

probabilities were higher than those of

the 1910 cohort until age 39.

The initial slope of first-birth

probabilities for the 1960 cohort (to

age 20) was not as steep as those of

the previous cohorts. After age 20, the

probabilities remained fairly constant

for 10 years. The cohort’s highest

probability of having a first child

occurred comparatively late, at age 29,

with the chance that 1 out of 10

childless women would have their

first child (Table 3). Overall, the

1910 cohort 1935 cohort 1960 cohort

Probability of first birth 

0.000 

0.020 

0.040 

0.060 

0.080 

0.100 

0.120 

0.140 

0.160 

15 20 25 30 35 40 45 49 

Age in years 

SOURCE: CDC/NCHS, National Vital Statistics System. 

Figure 1. Probability of having a first birth, by age and birth cohort of mother:

United States, 1910, 1935, and 1960

Series 2, No. 153 [ Page 3
Page 4 [ Series 2, No. 153

Table A. Cumulative probability of first birth, by selected age and birth cohort of women:

United States, 1910, 1935, and 1960

Age of women in years

18.......................

22.......................

25. . . . . . . . . . . . . . . . . . . . . . .

30. . . . . . . . . . . . . . . . . . . . . . .

35. . . . . . . . . . . . . . . . . . . . . . .

49. . . . . . . . . . . . . . . . . . . . . . .

Birth cohort

1910 1935 1960

0.087

0.397

0.576

0.723

0.778

0.803

Cumulative probability of first birth

0.108 0.093

0.457 0.329

0.663 0.482

0.825 0.686

0.869 0.794

0.886 0.844

first-birth probability curve for the

1960 cohort shifted considerably to Cumulative probability of first birth 

15 20 25 30 35 40 45 49 

Age in years 

SOURCE: CDC/NCHS, National Vital Statistics System. 

0.000 

0.100 

0.200 

0.300 

0.400 

0.500 

0.600 

0.700 

0.800 

0.900 

1.000 

1910 cohort 1935 cohort 1960 cohort

Figure 2. Cumulative probability of having a first birth, by age and birth cohort of mother:

United States, 1910, 1935, and 1960

the older ages relative to those of the

earlier cohorts.

Table A compares the cumulative

first-birth probabilities at important ages.

Among them are: age 18, when high

school is generally completed; age 22,

when college is completed; and age 35,

when motherhood has essentially been

initiated. For these three ages, the 1935

cumulative birth probabilities were the

highest (0.108 at age 18 and 0.869 at

age 35). The 1960 cohort’s cumulative

probability was relatively high at age 18

(0.093), but quickly dropped below

those of other cohorts at age 25.

However, at age 35, women born in

1960 had a higher probability of having

had a first birth than the 1910 cohort

(Figure 2).

Number in Cohort

Remaining Childless, by

Age (l

x)

Because the size of the initial

cohort is set at 100,000, the number of

women in column l

x (Tables 1–3) at age

49 represents the number out of the

original 100,000 who remain childless at

that age.

As illustrated in the inset of

Figure 3, about 19,700 out of the

100,000 women of the 1910 cohort

remained childless at the end of their

reproductive period. That is, 0.197 of

that cohort were still childless at age 49.

For the 1935 cohort, the relative

proportion was 0.114, and for the most

recent cohort, 1960, it was 0.156. These

figures correspond well with the

proportions childless found in the

National Fertility Survey (23) and the

National Surveys of Family Growth (3).

In the last 10 years of their

reproductive periods, the proportions

childless in the three cohorts were

approximately equally spaced (Figure 3).

This was not true at earlier ages. Due to

the postponement of first births by the

women in the 1960 cohort, a relatively

large number of the 1960 cohort were

childless at younger ages. It was not

until women in the 1960 cohort were

aged 33 that they crossed under the

‘‘survival curve’’ of the women in the

1910 cohort. From that age forward, a

relatively larger proportion of the 1910

cohort than the 1960 cohort was

childless at each age (Figure 3 and

Table B).

Distribution of First Births

by Mother’s Age (bx)

As shown in Table B, a substantial

number of women did not have children

by the time they concluded their

reproductive years. However, approximately 80 percent to 90 percent of the

women in all three cohorts did have at

least one birth. The distributions of first

births vary by peak, shape, and overall

magnitude of first births for these three

cohorts of 100,000 women. These

differences are shown in Figure 4 and

Table C.

The fewest first births were born to

women in the 1910 cohort. For each

100,000 women who entered their

reproductive period in 1925, 80,300

became mothers between ages 15 and

49 (Table A). It was at age 19 that the

greatest numbers of births occurred; that

is, 81 births per 1,000 women (or 8,100

per the original 100,000 women born in

1910). Of the 1910 cohort, one-half of

the first births were born to women

before age 21.1 and the other one-half at

later years (Tables A and C).

Many more first births occurred to

women in the 1935 cohort than in the

1910 cohort: approximately 88,600 of

the 100,000 women in the 1935 cohort

within their 35-year reproductive period.

This level is 10 percent higher than that

of the 1910 birth cohort. It was at age
20, the peak age for first births, when

92 births per 1,000 took place for

women born in 1935. One-half were

born before age 20.8 for the 1935 cohort

and the other one-half at later years

(Tables A and C).

The number of first births born to

women in the 1960 cohort was

intermediate to those in the 1910 and

1935 cohorts (roughly 84,400 women

had a first birth compared with 80,300

and 88,600). But the volume of first

births is not the only distinguishing

characteristic of this cohort. The peak of

the distribution is 63 births per 1,000, a

peak that is about two-thirds the number

of births that occurred in the 1935

cohort table (also at age 20). The shape

of this distribution is markedly different

as well: the decline in numbers of first

births is particularly more attenuated

than it was for the earlier cohorts. This

moderate level extends into older years.

The midpoint is about 2 years older for

the 1960 cohort than that of the 1935

cohort (Table C).

Series 2, No. 153 [ Page 5

Number of women 

15 20 25 30 35 40 45 49 

Age in years 

NOTE: Based on initial cohort of 100,000 women aged 15. 

SOURCE: CDC/NCHS, National Vital Statistics System. 

1910 cohort 1935 cohort 1960 cohort

0 

10,000 

20,000 

30,000 

40,000 

50,000 

60,000 

70,000 

80,000 

90,000 

100,000 

Figure 3. Number of women remaining childless, by age and birth cohort of mother: United

States, 1910, 1935, and 1960

Table B. Proportion of women childless, by selected age and birth cohort of women:

United States, 1910, 1935, and 1960

Birth cohort

Age of women in years 1910 1935 1960

18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22...................................

25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

l

x /100,000

0.913 0.892 0.907

0.606 0.543 0.671

0.424 0.337 0.518

0.277 0.175 0.314

0.222 0.131 0.206

0.197 0.114 0.156

Expectation of Number of

Years to be Childless in the

Future (ex)

A woman may give birth in the first

12 months of her reproductive life—that

is, at age 15—or she may have her first

birth at the end of the maternity table

when she is in her 40s. However, it is

most likely that she will have her first

birth, if she does become a mother, in

her 20s. It is not only of interest

whether a woman will or will not

become a mother: a discrete outcome. It

is additionally of interest to know the

average number of years that she

remains childless during the period

when she could potentially have a child.

This is an important statistic because it

speaks to the opportunity costs a woman

may have in completing her education

and job training during years when her

childbearing potential is comparatively

high.

The average number of years a

childless woman at a given age is

expected to remain childless is shown in

Figure 5. This measure is a function of

both the birth probabilities at a given

age (qx) and the number of women who

remain childless at that age (l

x). The

expected childless years begin to decline

sharply when the number of childless

women remains fairly constant: around

age 35 for each of the three cohorts

(Figure 3). Thereafter, with each year of

life, the expected number of childless

years decreased annually by

approximately 1 year (Figure 5).

The 1910 cohort had the highest

overall level of childlessness and thus

the average number of years expected to

be childless followed the highest curve

of the three cohorts. It reached a high of

15.4 years at age 30 (Table D).

For ages 15–30, the 1935 cohort

had substantially lower levels of

childlessness compared with the 1910

cohort, although the shapes of the

curves were similar (Figure 5).

At age 15, women of the 1910

cohort anticipated being childless for an

average of 13.4 years; those of the 1935

cohort, 10.8 years. After age 30, the two

curves followed similar patterns.

The childless-years curve remained

rather flat for the 1960 cohort as the

first-birth probability curve was quite

wide (as in Figure 1). As seen earlier in

Figure 3, the number of women

remaining childless stayed fairly

constant up to age 35. This is when the

average expected number of childless

years dropped constantly with each

increasing year of age (Figure 5).
Page 6 [ Series 2, No. 153 Number of first births 

15 20 25 30 35 40 45 49 

Age in years 

NOTE: Based on initial cohort of 100,000 women aged 15. 

SOURCE: CDC/NCHS, National Vital Statistics System. 

1910 cohort 1935 cohort 1960 cohort

1,000 

2,000 

3,000 

5,000 

6,000 

7,000 

8,000 

9,000 

10,000 

4,000 

0 

Figure 4. Distribution of first births, by age and birth cohort of mother: United States, 1910,

1935, and 1960

Table C. Mean, median, modal, and maximum number of first births (bx), by birth cohort of

women: United States, 1910, 1935, and 1960

Birth cohort

Summary indicators of first birth, by cohort 1910 1935 1960

Mean age at first birth ...................... 22.7 22.1 24.2

Median age at first birth ..................... 21.1 20.8 22.7

Modal (most common) age at first birth ............ 19.0 20.0 20.0

Maximum number of first births (bx) at any age ....... 8,102.0 9,241.0 6,289.0

Degree of Concentration of

First Births

Another way to view the

distribution of first births relative

to age of women is in terms of

concentration (2). Concentration analysis

generally studies the degree to which a

certain proportion of producers (in this

case, women of fertile ages) dominate a

market (here, first-born children). The

greater the degree of concentration (as

measured by the Gini or Duncan

indices, for example), the greater is the

concentration of first births among

women in particular age groups.

Lorenz curves provide a visually

interpretable basis for comparing these

two indicators of concentration. The

Lorenz curves in Figure 6 map the

cumulative proportion of first births of a

cohort to the cumulative proportion of

years exposed to childbearing. The

points on the Lorenz curve represent

statements like ‘‘in the first 35 percent

of 1935 cohort’s reproductive years (that

is, by age 27.25), 90 percent of the first

births were produced.’’ A 45-degree

diagonal line that runs from 0 through

100 percent shows the condition of

equal distribution, where the probability

distribution of having a first birth holds

constant across ages. That is, by age

32.5 (the midpoint between ages 15 and

50), 50 percent of women would have

had their first birth.

Several Lorenz curves can be

mapped on the same graph regardless of

the total number of events occurring as

the Lorenz curve and its related

indicators are independent of scale.

Accordingly, Figure 6 plots first-birth

concentrations for each of the fertility

cohorts even though the cumulative

number of first births in the maternity

tables is different for each cohort (80.3,

88.6, and 84.4 thousand first births).

To easily compare the information

of concentration (or inequality) shown

in the Lorenz curves, the Gini ratio can

be used. It is the index associated with

the proximity of the Lorenz curve to the

diagonal line of equality. The Gini

concentration quotient is the ratio of the

area that lies between the Lorenz curve

and the line of equality to the total area

below the line of equality (24). The ratio

range is 0–1. The higher the coefficient,

the greater is the concentration or

inequality. Table E shows the ratios for

the cohorts of 1910 and 1935 to be

similar (0.534 and 0.563, respectively),

but the ratio for 1960 is notably lower

at 0.447. This lower figure illustrates the

greater dispersion in age of first births

for the most recent cohort.

As stated earlier, indicators from the

Lorenz curves provide concrete

information about the pacing of first

births. At 50 percent of cumulative years

exposed (to age 32.5), the cumulative

proportions of first births were fairly

similar (in 1910, 95 percent of first

births; in 1935, 97 percent; and in 1960,

90 percent). But at a cumulative

25 percent of years exposed (to age 23),

the differences in cumulative

proportions of first births are markedly

different (in 1910, 65 percent; in 1935,

68 percent; and in 1960, 52 percent).

This is another way of expressing the

lower concentration of first births for

the 1960 cohort (Figure 6).

A second indicator of concentration,

the Duncan index, is also shown in

Figure 6 (25). Geometrically, this index

is the maximum vertical distance from

the diagonal line to the curve, showing

the exact point where there are the

greatest deviations between the diagonal

line and the Lorenz curve. It is

calculated by subtracting at each age the

value of the diagonal from the value of

the Lorenz curve. The greatest

difference indicates the age where the

concentration is highest.

As illustrated by the lengths of

these vertical lines in Table E, the

cohorts of 1910 and 1935 have the

greater indices of concentration (0.491

and 0.523), and the 1960 cohort index
Number of years 

15 20 25 30 35 40 45 49 

Age in years 

NOTE: Refers to number of years women may expect to remain childless from current age to end of reproductive period. 

SOURCE: CDC/NCHS, National Vital Statistics System. 

1910 cohort 1935 cohort 1960 cohort

0.0 

2.0 

4.0 

6.0 

8.0 

10.0 

12.0 

14.0 

16.0 

18.0 

Figure 5. Average number of years expected to remain childless, by age and birth cohort of

mother: United States, 1910, 1935, and 1960

Table D. Expected number of years childless, by selected age interval and birth cohort of

women: United States, 1910, 1935, and 1960

Birth cohort

Age interval of women in years 1910 1935 1960

15–50 ................................

30–50 ................................

13.4

15.4

ex

10.8

14.3

13.6

12.0

has the lesser value (0.401). These

values may be compared as they are

based on the same number of years a

woman is exposed to childbearing.

The Duncan calculations reinforce

the Gini calculations. The greatest

vertical difference for the 1910 cohort

has a value of 0.506 out of a maximum

of 1.0; the horizontal position is at the

cumulative age proportion of 37 percent

or 27 years. For 1935, the point of

highest concentration is also at age 27,

but the vertical measure of concentration

is higher, at 0.542. In 1960, it is at age

31 that the vertical distance is the

greatest, with a distance of 0.422. In

sum, the 1935 cohort has the highest

concentration and the 1960 the lowest;

additionally, the 1960 cohort has a

Duncan index occurring at the oldest

age (age 31).

Importance of Childlessness

in the Demographic Context

of the 20th Century

Childlessness is but one aspect of a

cohort’s fertility behavior. There are, of

course, those women who have had one,

two, three, four, and even higher

parities. It is the totality of the

distribution of these parities that

produce cohorts’ TFRs. Moreover, the

TFR at the end of the reproductive

period is not the only indicator of

concern. The timing of childbearing

(whether predominately early or late,

concentrated or dispersed) marks broad

trends in five decades of childbearing.

One interesting illustration of this is the

pattern of the TFR with respect to the

proportion childless for the cohorts

(1910, 1915, 1920, etc.), from 1910

through 1960.

Series 2, No. 153 [ Page 7

Trends by Parity

Distribution in the

20th Century

Figures 7 and 8 show relative

frequencies of zero- and higher-order

completed parity for all cohorts

(Figure 7) and the three cohorts

(Figure 8). The low completed fertility

of the 1910 cohort shown in Figure 9

was due to the higher proportion of

women who had zero, one, or two

children. In fact, the proportion childless

stayed historically high for women born

in 1910–1915. The high TFR of the

1935 cohort was due to a combination

of the historically lowest levels of

childless and parity-one women and the

highest levels of women with four or

more children (37 percent), than had

been seen in the birth cohorts of

1900–1960. The cohort of 1960

sustained a TFR close to 2.0. This level

began before 1995 (Figure 9). It was

characterized by distinctively high levels

of women with two children

(35 percent) and moderate parities of

zero, one, and three. The 1960 cohort

had historically low levels of completed

fertility of four or more children. The

percent distribution for the parity for

these three cohorts is clearly shown in

Figure 8.

Cohort TFRs, 1950–2005

The cohort TFR is measured 50

years after the birth of the cohort when

women have essentially completed their

childbearing. TFR is the average number

of children born to women by the end

of their reproductive years. Figure 9

provides the TFRs for the years

1950–2005. During this period of

interest, the TFRs of the 1910 and 1960

cohorts were located near two low

points in the curve and the 1935

cohort’s TFR was near a high point. As

noted, childlessness is an important

component of the TFR; the high

childlessness of 1910 and 1960 and low

childlessness of 1935 influence the

corresponding TFRs.
Cumulative proportion of first births 

Cumulative proportion of years exposed 

NOTE: Vertical lines represent Duncan Index of Concentration. 

SOURCE: CDC/NCHS, National Vital Statistics System. 

1910 cohort 1935 cohort 1960 cohort

0.70 

0.00 

0.10 

0.20 

0.30 

0.40 

0.50 

0.60 

0.80 

0.90 

1.00 

0.00 0.20 0.40 0.60 0.80 1.00 

Figure 6. Lorenz curves of first births and Duncan Index of Concentration, by birth cohort:

United States, 1910, 1935, and 1960

Table E. Gini Concentration Ratio and Duncan Index of Concentration, by birth cohort of

women: United States, 1910, 1935, and 1960

Measures of dispersion

Gini Concentration Ratio .....................

Duncan Index of Concentration ................

Birth cohort

1910 1935 1960

0.534 0.563 0.447

0.491 0.523 0.401

Page 8 [ Series 2, No. 153

In general terms, the lifetime

reproductive experience of women born

in 1910 began in 1925, a time only a

few years before the beginning of the

Great Depression. Due to economic

considerations, there was a sudden drop

in marriages, down 20 percent in 1932

from that of 1929 (26). The difficult

economic circumstances of the Great

Depression coupled with the decline in

marriage lowered the probabilities that

women would normally have a first-,

second-, or higher-order birth. World

War II affected the mid-childbearing

years both in terms of uncertainty and in

terms of large numbers of potential

fathers being away from home, which

further suppressed completed fertility

rates. Some demographers concluded

that the children who were postponed

were, in the end, never born (18).

In contrast, the women of the 1935

cohort started their reproductive ages in

1950. World War II had ended; the

members of the Armed Forces and

employees of war-related industries had

returned home to start or to resume

married life, and the economy

prospered (19).

There was a dramatic jump in the

number of marriages, with a 42-percent

increase in 1 year alone (1945–

1946) (26). In addition to the rapid

growth in the economy, families were

aided by the G.I. Bill. This legislation

and its supplements were sufficient for

Veterans to live singly or married (27).

The prosperity that it ensured led to

early and nearly universal marriage and

parenthood. With such means of

support, it was not necessary to

postpone family formation.

As shown above, completed parity

distributions were markedly different from

those of the pre-World War II period. In

addition, almost all of the women in the

1935 cohort who had children went on to

have a second-, third-, or higher-order

birth (Figure 7) (7).

For a variety of reasons, cohort

fertility fell after 1980, which was

reflected in the 1960 cohort’s fertility

characteristics. Some of these reasons

included delaying first births (28),

delayed marriage (29), a major decline

of completed parity for black

women (7), the widespread availability

of coitus-independent means of fertility

control (21,22), and the substantial

numbers of women who entered the

labor force (30). Less educated women

also became more likely to stay

childless (31). It has been observed that

women with initial desires to remain

childless diverged by educational

attainment (32). More educated women

found that they could combine

motherhood with a professional life.

Postponement and

Recuperation of Fertility

Cohort fertility analysis provides the

ability to study major timing trends in

childbearing. The last century showed

trends of postponement and then

recuperation in timing of births. The

terms ‘‘postponement’’ and

‘‘recuperation’’ are dual measures of

magnitude and timing of fertility.

Postponement

An essential aspect of trends in

low-fertility countries during the past

one-half of a century has been

postponement of childbearing.

Childbearing postponement takes place

in the form of a fertility decline among

young women, which is a combination

of actual postponement as well as a

decline in the number of births. What

proportion of the fewer births were

actually postponed becomes apparent

only when the respective generation

reaches the end of its childbearing age

and it is clear how many of the

‘‘postponed’’ births were born later in

the life of these women. For a more

detailed discussion of this issue, see

section 2.6 in Frejka and Sardon (33).

Postponement of childbearing

started among the cohorts of the 1940s

of the United States, Canada, and

Northern and Western Europe. Table F

shows that the average number of

children borne by American women

prior to their 27th birthday had peaked

for the 1940 birth cohort at 1.927. But

that number had halved for the 1980
Proportion per 1,000 women 

Birth cohort 

SOURCE: CDC/NCHS, National Vital Statistics System. 

Parity 0 Parity 1 Parity 2 Parity 3 Parity 4 or more

0 

100 

200 

300 

400 

1900 1910 1920 1930 1940 1950 1960 

Figure 7. Parity distribution at completed fertility of birth cohorts: United States, 1900–1960

birth cohort (i.e., through age 26). The

childbearing delay, again shown in

Table F, had slowed down among birth

cohorts of the 1970s in the United

States in both relative and absolute

terms.

Recuperation

Childbearing recuperation is the

phenomenon of increase in age-specific

cohort rates in the later childbearing

ages of 27 and over. Less attention has

been paid in the literature to this

phenomenon although there are

considerable data. Due to the length of

the window in Table F, there are fewer

time periods in the overview of

recuperation or ‘‘catching up.’’ As seen

in Table F, the cumulative fertility rates

for ages 27–40 for the 1930 birth

cohorts dropped below one. For the

1960 birth cohort, there had been a

robust recuperation of fertility in the

older ages such that the annual rates of

change in the preceding decade had

been positive: 2 percent.

Relationship of

Childlessness to TFRs

As seen earlier, trends in

childlessness affect the completed

cohort fertility rate, but trends in the

distributions of births for other parities

Series 2, No. 153 [ Page 9

affect the completed fertility rate as

well. Taken together, these factors

produce a shift in the relationship

between childlessness (y axis in

Figure 7) and completed fertility (TFR,

y axis in Figure 9), with two major

segments produced in the observed

trends (Figure 10). The first segment is

for the 1910–1935 birth cohorts and the

second is for the 1935–1960 birth

cohorts (the calendar year 1980 is the

point of inflection).

The observation has been that an

elevated percentage of women who are

childless contributes to low levels of

completed fertility (34). The proportion

childless has been mapped by other

authors (35,36), showing that the higher

the percentage childless, the lower the

TFR. However, these examples used

cross-sectional TFRs and proportions

childless from numerous countries at

various points. The data shown in this

report (Figure 10) are less ambiguous

than those of other analysts: the data

were from one country (the United

States) and represent a continuous series

of completed fertility from 1950 through

2005.

As seen in other publications, there

was a general but loose negative

relationship between proportion childless

and the TFR. When least squares

regression was applied to the data in

Figure 10, a negative relationship

between proportion childless and

fertility was also measured. Namely,

the TFR declined by one child for

a 7.5-percent increase in the proportion

of childless women.

Table F. Total fertility rates, by selected age group and birth cohorts of women: United States, 1930, 1940, 1950, 1960, 1970, and 1980

Birth cohort

Total fertility rates, by age group and birth cohort 1930 1940 1950 1960 1970 1980

Postponement up to age 26

Cumulated age-specific cohort rates ............. 1.795 1.927 1.165 0.995 0.978 0.948

Annual rates of change of percent ............... - - ­ 0.710 –5.032 –1.577 –0.172 –0.312

Corresponding span of birth cohorts ............. . . . 1930–1940 1940–1950 1950–1960 1960–1970 1970–1980

Recuperation from 27th to 40th birthday

Cumulated age-specific cohort rates ............. 1.389 0.849 0.834 0.988 - - ­ --­

Annual rates of change of percent ............... - - ­ –4.923 –0.178 1.694 - - ­ --­

Corresponding span of birth cohorts ............. . . . 1930–1940 1940–1950 1950–1960 1960–1970 1970–1980

. . . Category not applicable.

- - - Data not available.

SOURCE: SOURCE: Frejka T, Sardon JP. Contemporary childbearing trends in low-fertility countries: A long-term perspective. Marrakech, Morocco: XXVI IUSSP International Population Conference. 2009.
Page 10 [ Series 2, No. 153

Figure 8. Percent distribution of the number of children ever born, by birth cohort of

mother: United States, 1910, 1935, and 1960 Percent 

Number of children 

SOURCE: CDC/NCHS, National Vital Statistics System. 

1910 cohort 1935 cohort 1960 cohort

0 

5 

10 

15 

20 

25 

30 

35 

40 

0 1 2 3 4 or more 

NOTE: Based on total fertility rates for women aged 45–49. 

SOURCE: CDC/NCHS, National Vital Statistics System. Rate per 1,000 women 

Year cohort completed fertility 

0 

1,500 

2,000 

2,500 

3,000 

3,500 

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 

1910 cohort 1935 cohort 1960 cohort 

(estimated) 

Figure 9. Total fertility rates at completed fertility of birth cohorts: United States, 1950–2005

However, given the presence of a

continuous series of data points, the

outcomes are even more informative.

Figure 10 depicts an annual plotting of

the proportion of 1,000 women at age

50 who are childless, by the

corresponding TFRs. Each point in

Figure 10 represents a birth cohort that

can also be defined as the year that

cohort reaches age 50. The figure shows

how the TFR and the percentage

childless changes over time.

Starting with the cohort of 1910 for

which the TFR was 2.3 and more than

20 percent of the cohort was childless at

age 50, each successive cohort through

the cohort of 1935 had a higher TFR

and lower percentage childless. The

cohort of 1935 had a TFR of 3.2 with

less than 10 percent of the cohort

remaining childless. Cohorts after 1935

had decreasing TFRs and increasing

percentages childless with the lowest

completed cohort TFR occurring in the

1956 cohort (1.99) with the proportion

childless at 16 percent. The horizontal

ranges in TFRs are similar; however, the

magnitudes of the slopes describing the

trends between the cohorts of 1910 and

1935, and 1935 and 1960, are

substantially different. The relationship

between the TFR and percentage

childless is much stronger between the

1910 and 1935 cohorts (slope equals

13 percent) than it is between the 1935

and 1960 cohorts (slope equals

6 percent). Only one-half the change in

percentage childless was needed in

recent years to produce the same

amount of change in the TFR as in

earlier years. In other words, the TFR

would increase by one child when the

proportion childless decreases by

13 percent in the 1910–1935 cohort

segment, and for the 1935–1960 cohort

segment, the TFR would increase by

one child when the proportion childless

decreases by 6 percent.

A demographic explanation may be

given for these differential slopes. As

can be seen in Figures 7 and 8, between

the 1910 and 1935 cohorts, the

proportion childless dropped greatly as

the proportion of women of high parity

rose to historically high levels.

While the 1960 cohort had lower

completed fertility than did the 1910

cohort, the percentage childless was

lower. The differences in final levels

were greatly affected by achieved

parities of four or more, so that the

overall fertility of women in these

earlier cohorts with their greater family

size was less affected by the proportion

of childless women than the later

cohorts with their smaller family size.

Hence, in these series, the TFR depends

not only on the percentage childlessness,

but on the entire fertility distribution.

There is little variation in data

points around the long-term trends

represented by the long segments in

Figure 10. The amount of variation

explained by the least squares equations

linking childlessness and completed

cohort fertility is quite high: 82 percent

for the more recent segment of years

and 92 percent for the previous ones.

These tight relationships imply strict

trends in U.S. demographic history that

were reversed when a series of events

related to post-World War II prosperity
1910 (1955) 

1915 1920 

1940 

1925 1930 1935 (1980) 

1945 

1950 

1960 (2005) 

1955 

NOTES: Year cohort completed fertility in parentheses. Based on proportion childless and total fertility rate for women aged 45–49. 

SOURCES: CDC/NCHS, National Vital Statistics System and Table 186 of reference 7. Proportion childless per 1,000 women 

Rate per 1,000 women 

0 

50 

100 

150 

200 

250 

2,000 2,200 2,400 2,600 2,800 3,000 3,200 

Figure 10. Proportion childless and total fertility rate at completed fertility, by birth cohorts:

United States, 1910–1960

reversed the decline in fertility that had

been occurring for decades.

An economic interpretation for the

childlessness–TFR relationship has been

noted. Once a family has a child, it may

go on to have more children because

any goods are substitutable. For

example, goods can be passed on from

one child to the next, a car can hold

three children as well as it can hold one,

two children may share a house as

easily as may one, etc. (2). It has been

further observed that in recent times,

once having had one child, the

probabilities to have additional ones

have remained fairly high (1).

Conclusion

Current low and late fertility and

increased childlessness has been

observed in all of Europe and in much

of North America. This ‘‘second

demographic transition’’ (37) is

consistent with an observed increase in

individual autonomy and a growth in

gender equality. At the same time, there

is the increase in socioeconomic

activities competitive with childbearing.

In the United States, education and

career have been reported as important

factors in women’s decisions to delay

marriage and motherhood. From 1970 to

2005, the female labor force

participation rate increased by

37 percent and the percentage of women

having completed four or more years of

college had more than tripled (38).

Studies (1,3) found that older women

are childless for both voluntary and

involuntary reasons; age is the primary

explanatory variable for involuntary

childlessness for older women due to

subfecundability and decreased partner

availability. In the United States,

childlessness may have plateaued (3) or

may continue to rise as this country

adopts more of the demographic and

social attributes recently seen in

Europe (39).

In sum, the various indicators for

the transitions to first birth for the 1910,

1935, and 1960 birth cohorts are closely

tied to the social, economic, and

historical features of the periods during

which these women spent their

childbearing years. The 1910 cohort

passed the important portion of its

childbearing years during the Great

Depression. Average age of marriage

increased while a record number of

women never married. Of the three

cohorts, the 1910 cohort had the largest

proportion of women who did not have

children. As well, the largest proportion

of these women had only one birth,

contributing to the low TFR of 2.35.

The 1935 cohort passed its principal

reproductive years during the prosperous

post-World War II era. Men were often

sole bread earners and many factors

kept women in the home with their roles

circumscribed to motherhood. These

Series 2, No. 153 [ Page 11

women married young, began their

childbearing young, and were the cohort

among the three to have the least

childlessness.

The 1960 birth cohort moved

through a very different socioeconomic

era. The obstacles to educational and

employment opportunities were

eliminated. Along with the availability

of modern contraception, ‘‘choice’’ in

whether and when to become mothers is

shown by the first-birth probability curve.

This concentration curve is far flatter than

that of the other two cohorts. The

proportion of women who had first births

is intermediate and the concentration

measures of first births are the lowest. The

TFR of the 1960 cohort (2.00) is among

the century’s lowest.

What will the future hold for the

next generation, the birth cohort of

1985? It began its childbearing years in

a society socially divided on means and

financing of fertility regulation.

Childbearing outside of marriage has

increased significantly (40): the

percentage of births occurring outside of

marriage has increased from

33.2 percent in 2000 when the cohort

was aged 15, to 41 percent in 2009. The

cohort moved into its key childbearing

years during a significant recession;

fertility dropped in 2009 to replacement

levels (40). A repeat of the current study

could be made in 10 years, using similar

measures, providing better insight on the

socioeconomic factors affecting the

first-birth transitions of the 1985 cohort.

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Series 2, No. 153 [ Page 13

Table 1. Maternity table for the 1910 birth cohort, by age of mother

Number of Number of Number of Number of

Probability of Number of first births childless childless years expected

giving birth to childless occuring to person-years person-years to remain

Age of woman first child at women at women at lived at lived from childless from

in years age x age x age x age x age x to age 50 age x to age 50

x qx l

x bx Lx Tx ex

15. . . . . . . . . . . . . . . . . . . . . . . 0.0118 100,000 1,180 99,410 1,343,336 13.43

16. . . . . . . . . . . . . . . . . . . . . . . 0.0269 98,820 2,658 97,491 1,243,926 12.59

17. . . . . . . . . . . . . . . . . . . . . . . 0.0507 96,162 4,875 93,724 1,146,435 11.92

18. . . . . . . . . . . . . . . . . . . . . . . 0.0765 91,286 6,983 87,795 1,052,711 11.53

19. . . . . . . . . . . . . . . . . . . . . . . 0.0961 84,303 8,102 80,252 964,917 11.45

20. . . . . . . . . . . . . . . . . . . . . . . 0.1059 76,201 8,070 72,167 884,664 11.61

21. . . . . . . . . . . . . . . . . . . . . . . 0.1104 68,132 7,522 64,371 812,498 11.93

22. . . . . . . . . . . . . . . . . . . . . . . 0.1134 60,610 6,873 57,173 748,127 12.34

23. . . . . . . . . . . . . . . . . . . . . . . 0.1140 53,737 6,126 50,674 690,954 12.86

24. . . . . . . . . . . . . . . . . . . . . . . 0.1092 47,611 5,199 45,011 640,280 13.45

25. . . . . . . . . . . . . . . . . . . . . . . 0.1030 42,412 4,368 40,227 595,269 14.04

26. . . . . . . . . . . . . . . . . . . . . . . 0.0963 38,043 3,664 36,212 555,041 14.59

27. . . . . . . . . . . . . . . . . . . . . . . 0.0747 34,380 2,568 33,096 518,830 15.09

28. . . . . . . . . . . . . . . . . . . . . . . 0.0692 31,812 2,201 30,711 485,734 15.27

29. . . . . . . . . . . . . . . . . . . . . . . 0.0638 29,610 1,889 28,666 455,023 15.37

30. . . . . . . . . . . . . . . . . . . . . . . 0.0568 27,721 1,575 26,934 426,357 15.38

31. . . . . . . . . . . . . . . . . . . . . . . 0.0494 26,147 1,292 25,501 399,424 15.28

32. . . . . . . . . . . . . . . . . . . . . . . 0.0417 24,855 1,036 24,337 373,923 15.04

33. . . . . . . . . . . . . . . . . . . . . . . 0.0366 23,818 872 23,383 349,586 14.68

34. . . . . . . . . . . . . . . . . . . . . . . 0.0305 22,947 700 22,597 326,204 14.22

35. . . . . . . . . . . . . . . . . . . . . . . 0.0252 22,247 561 21,966 303,607 13.65

36. . . . . . . . . . . . . . . . . . . . . . . 0.0203 21,686 440 21,466 281,641 12.99

37. . . . . . . . . . . . . . . . . . . . . . . 0.0162 21,246 344 21,074 260,174 12.25

38. . . . . . . . . . . . . . . . . . . . . . . 0.0126 20,902 263 20,770 239,101 11.44

39. . . . . . . . . . . . . . . . . . . . . . . 0.0164 20,638 338 20,469 218,331 10.58

40. . . . . . . . . . . . . . . . . . . . . . . 0.0117 20,300 238 20,181 197,861 9.75

41. . . . . . . . . . . . . . . . . . . . . . . 0.0081 20,062 163 19,981 177,680 8.86

42. . . . . . . . . . . . . . . . . . . . . . . 0.0050 19,900 99 19,850 157,699 7.92

43. . . . . . . . . . . . . . . . . . . . . . . 0.0033 19,800 65 19,768 137,849 6.96

44. . . . . . . . . . . . . . . . . . . . . . . 0.0019 19,735 37 19,716 118,081 5.98

45. . . . . . . . . . . . . . . . . . . . . . . 0.0010 19,698 20 19,688 98,365 4.99

46. . . . . . . . . . . . . . . . . . . . . . . 0.0005 19,678 10 19,673 78,677 4.00

47. . . . . . . . . . . . . . . . . . . . . . . 0.0000 19,668 0 19,668 59,004 3.00

48. . . . . . . . . . . . . . . . . . . . . . . 0.0000 19,668 0 19,668 39,336 2.00

49. . . . . . . . . . . . . . . . . . . . . . . 0.0000 19,668 0 19,668 19,668 1.00

0.0000 Quantity more than zero but less than 0.00005.
Page 14 [ Series 2, No. 153

Table 2. Maternity table for the 1935 birth cohort, by age of mother

Number of Number of Number of Number of

Probability of Number of first births childless childless years expected

giving birth to childless occuring to person-years person-years to remain

Age of woman first child at women at women at lived at lived from childless from

in years age x age x age x age x age x to age 50 age x to age 50

x qx l

x bx Lx Tx ex

15. . . . . . . . . . . . . . . . . . . . . . . 0.0167 100,000 1,670 99,165 1,075,746 10.76

16. . . . . . . . . . . . . . . . . . . . . . . 0.0349 98,330 3,432 96,614 976,581 9.93

17. . . . . . . . . . . . . . . . . . . . . . . 0.0604 94,898 5,732 92,032 879,967 9.27

18. . . . . . . . . . . . . . . . . . . . . . . 0.0879 89,166 7,838 85,248 787,934 8.84

19. . . . . . . . . . . . . . . . . . . . . . . 0.1116 81,329 9,076 76,791 702,687 8.64

20. . . . . . . . . . . . . . . . . . . . . . . 0.1279 72,252 9,241 67,632 625,896 8.66

21. . . . . . . . . . . . . . . . . . . . . . . 0.1376 63,011 8,670 58,676 558,264 8.86

22. . . . . . . . . . . . . . . . . . . . . . . 0.1440 54,341 7,825 50,428 499,588 9.19

23. . . . . . . . . . . . . . . . . . . . . . . 0.1483 46,516 6,898 43,067 449,160 9.66

24. . . . . . . . . . . . . . . . . . . . . . . 0.1497 39,618 5,931 36,652 406,093 10.25

25. . . . . . . . . . . . . . . . . . . . . . . 0.1469 33,687 4,949 31,213 369,441 10.97

26. . . . . . . . . . . . . . . . . . . . . . . 0.1401 28,738 4,026 26,725 338,228 11.77

27. . . . . . . . . . . . . . . . . . . . . . . 0.1257 24,712 3,106 23,159 311,503 12.61

28. . . . . . . . . . . . . . . . . . . . . . . 0.1095 21,606 2,366 20,423 288,344 13.35

29. . . . . . . . . . . . . . . . . . . . . . . 0.0927 19,240 1,784 18,348 267,922 13.93

30. . . . . . . . . . . . . . . . . . . . . . . 0.0776 17,456 1,355 16,779 249,573 14.30

31. . . . . . . . . . . . . . . . . . . . . . . 0.0652 16,102 1,050 15,577 232,794 14.46

32. . . . . . . . . . . . . . . . . . . . . . . 0.0529 15,052 796 14,654 217,218 14.43

33. . . . . . . . . . . . . . . . . . . . . . . 0.0449 14,256 640 13,936 202,564 14.21

34. . . . . . . . . . . . . . . . . . . . . . . 0.0379 13,616 516 13,358 188,628 13.85

35. . . . . . . . . . . . . . . . . . . . . . . 0.0336 13,100 440 12,879 175,271 13.38

36. . . . . . . . . . . . . . . . . . . . . . . 0.0285 12,659 361 12,479 162,391 12.83

37. . . . . . . . . . . . . . . . . . . . . . . 0.0245 12,299 301 12,148 149,912 12.19

38. . . . . . . . . . . . . . . . . . . . . . . 0.0200 11,997 240 11,877 137,764 11.48

39. . . . . . . . . . . . . . . . . . . . . . . 0.0131 11,757 154 11,680 125,887 10.71

40. . . . . . . . . . . . . . . . . . . . . . . 0.0072 11,603 84 11,562 114,207 9.84

41. . . . . . . . . . . . . . . . . . . . . . . 0.0048 11,520 55 11,492 102,645 8.91

42. . . . . . . . . . . . . . . . . . . . . . . 0.0036 11,464 41 11,444 91,153 7.95

43. . . . . . . . . . . . . . . . . . . . . . . 0.0024 11,423 27 11,410 79,709 6.98

44. . . . . . . . . . . . . . . . . . . . . . . 0.0012 11,396 14 11,389 68,300 5.99

45. . . . . . . . . . . . . . . . . . . . . . . 0.0000 11,382 0 11,382 56,911 5.00

46. . . . . . . . . . . . . . . . . . . . . . . 0.0000 11,382 0 11,382 45,528 4.00

47. . . . . . . . . . . . . . . . . . . . . . . 0.0000 11,382 0 11,382 34,146 3.00

48. . . . . . . . . . . . . . . . . . . . . . . 0.0000 11,382 0 11,382 22,764 2.00

49. . . . . . . . . . . . . . . . . . . . . . . 0.0000 11,382 0 11,382 11,382 1.00

0.0000 Quantity more than zero but less than 0.00005.
Series 2, No. 153 [ Page 15

Table 3. Maternity table for the 1960 birth cohort, by age of mother

Number of Number of Number of Number of

Probability of Number of first births childless childless years expected

giving birth to childless occuring to person-years person-years to remain

Age of woman first child at women at women at lived at lived from childless from

in years age x age x age x age x age x to age 50 age x to age 50

x qx l

x bx Lx Tx ex

15. . . . . . . . . . . . . . . . . . . . . . . 0.0181 100,000 1,810 99,095 1,363,438 13.63

16. . . . . . . . . . . . . . . . . . . . . . . 0.0312 98,190 3,064 96,658 1,264,343 12.88

17. . . . . . . . . . . . . . . . . . . . . . . 0.0467 95,126 4,442 92,905 1,167,685 12.28

18. . . . . . . . . . . . . . . . . . . . . . . 0.0591 90,684 5,359 88,004 1,074,779 11.85

19. . . . . . . . . . . . . . . . . . . . . . . 0.0706 85,325 6,024 82,313 986,775 11.56

20. . . . . . . . . . . . . . . . . . . . . . . 0.0793 79,301 6,289 76,156 904,462 11.41

21. . . . . . . . . . . . . . . . . . . . . . . 0.0810 73,012 5,914 70,055 828,306 11.34

22. . . . . . . . . . . . . . . . . . . . . . . 0.0824 67,098 5,529 64,334 758,251 11.30

23. . . . . . . . . . . . . . . . . . . . . . . 0.0820 61,569 5,049 59,045 693,917 11.27

24. . . . . . . . . . . . . . . . . . . . . . . 0.0841 56,521 4,753 54,144 634,872 11.23

25. . . . . . . . . . . . . . . . . . . . . . . 0.0885 51,767 4,581 49,477 580,728 11.22

26. . . . . . . . . . . . . . . . . . . . . . . 0.0918 47,186 4,332 45,020 531,252 11.26

27. . . . . . . . . . . . . . . . . . . . . . . 0.0966 42,854 4,140 40,784 486,232 11.35

28. . . . . . . . . . . . . . . . . . . . . . . 0.0994 38,714 3,848 36,790 445,447 11.51

29. . . . . . . . . . . . . . . . . . . . . . . 0.0997 34,866 3,476 33,128 408,657 11.72

30. . . . . . . . . . . . . . . . . . . . . . . 0.0975 31,390 3,061 29,860 375,529 11.96

31. . . . . . . . . . . . . . . . . . . . . . . 0.0892 28,330 2,527 27,066 345,669 12.20

32. . . . . . . . . . . . . . . . . . . . . . . 0.0808 25,803 2,085 24,760 318,603 12.35

33. . . . . . . . . . . . . . . . . . . . . . . 0.0718 23,718 1,703 22,866 293,843 12.39

34. . . . . . . . . . . . . . . . . . . . . . . 0.0645 22,015 1,420 21,305 270,976 12.31

35. . . . . . . . . . . . . . . . . . . . . . . 0.0567 20,595 1,168 20,011 249,672 12.12

36. . . . . . . . . . . . . . . . . . . . . . . 0.0498 19,427 967 18,943 229,661 11.82

37. . . . . . . . . . . . . . . . . . . . . . . 0.0420 18,460 775 18,072 210,717 11.42

38. . . . . . . . . . . . . . . . . . . . . . . 0.0342 17,684 605 17,382 192,645 10.89

39. . . . . . . . . . . . . . . . . . . . . . . 0.0265 17,080 453 16,853 175,263 10.26

40. . . . . . . . . . . . . . . . . . . . . . . 0.0212 16,627 352 16,451 158,410 9.53

41. . . . . . . . . . . . . . . . . . . . . . . 0.0149 16,274 242 16,153 141,960 8.72

42. . . . . . . . . . . . . . . . . . . . . . . 0.0101 16,032 162 15,951 125,806 7.85

43. . . . . . . . . . . . . . . . . . . . . . . 0.0063 15,870 100 15,820 109,855 6.92

44. . . . . . . . . . . . . . . . . . . . . . . 0.0038 15,770 60 15,740 94,035 5.96

45. . . . . . . . . . . . . . . . . . . . . . . 0.0026 15,710 41 15,690 78,295 4.98

46. . . . . . . . . . . . . . . . . . . . . . . 0.0013 15,669 20 15,659 62,606 4.00

47. . . . . . . . . . . . . . . . . . . . . . . 0.0000 15,649 0 15,649 46,947 3.00

48. . . . . . . . . . . . . . . . . . . . . . . 0.0000 15,649 0 15,649 31,298 2.00

49. . . . . . . . . . . . . . . . . . . . . . . 0.0000 15,649 0 15,649 15,649 1.00

0.0000 Quantity more than zero but less than 0.00005.
Page 16 [ Series 2, No. 153

Appendix. Technical Notes

Sources of Data

The birth probabilities shown in this

report were obtained from ‘‘Cohort

Fertility Tables for All, White, and

Black Women: United States,

1960–2005’’ (7), ‘‘Fertility Tables for

Birth Cohorts by Color, United States,

1917–1973’’ (4), and ‘‘Vital Statistics of

the United States, 1974’’ and for

1999 (5,6).

The ‘‘Cohort Fertility Tables for

All, White, and Black Women: United

States, 1960–2005’’ (7) were recently

released as a revision and extension of

the cohort fertility measures (central

birth rates, cumulative birth rates, parity

distributions, and birth probabilities)

published in the other, older reports.

Detailed information on the computation

of birth probabilities and the other

measures may be found in the

‘‘Technical Appendix to the Cohort

Fertility Tables for All, White, and

Black Women: United States,

1960–2005’’ (41).

Description of Life

Table Functions

Age of woman (x)—Identifies the

cohort with the year of the date on

which the woman’s birth occurred.

Because these women retain this

designation throughout their

childbearing years, there is a fixed

relationship between the cohort

identification year, the age of the

member of the cohort (column x), and

the calendar or data year to which the

fertility measure refers.

Probability of giving birth to a first

child at age x—Indicates the probability

or chance that a childless woman

changes her status to being a mother

within a specific year and is the single

most important function in the maternity

table. The transition from being

childless to being a mother is the first

and, obviously, most important step in a

woman’s fertility career (31), affecting

nearly all social, economic, and

emotional aspects of a woman’s life.

The year begins exactly at a woman’s

birthday and concludes when she reaches

her next birthday (Figure 1 and

Tables 1–3, column qx). These probabilities permit the calculation of the other

functions in the maternity tables.

Cumulative percentage of having a

first birth at age x—Calculated by

subtracting the number of women who

have had a first birth and dividing the

difference by 100,000 (using column l

x

in Tables 1–3). This function is

fundamental in the development of

cohort fertility analysis. Whelpton (42)

relied on this function for short- to

medium-range fertility projections.

Cumulative percentage of first births at

ages 18, 22, and 40 provided robust

estimates of final childlessness.

As noted, not all women have a

first birth in their lifetimes. Accordingly,

the cumulative probability of having had

at least one (first) birth by the end of

the reproductive period is approximately

80 percent to 90 percent (Figure 2).

Number of the birth cohort

remaining childless—Focuses on how

long a cohort of women stay in the state

of childlessness. The maternity tables in

this report use a standard 100,000 as the

number of childless women who enter

the table at the beginning of their

reproductive lives. Each year some

women give birth, which decreases the

size of the remaining childless cohort.

This function depicts the size of the

childless population at any given age

(up to age 50). As noted, not all women

give birth in their lifetimes. Related to the

complement of the previous measure,

10 percent to 20 percent of women in the

birth cohorts remained childless (Figure 3

and Tables 1–3, column l

x).

Number of first births occurring to

women at age x—Shows the number of

first births occurring within a given age

interval. The number of first births is

influenced by the size of the pool of

childless women, the percentage of

women in a sexual relationship in that

pool, and the probability of giving birth

to a first child for members of that age

class at risk of childbearing (Figure 4

and Tables 1–3, column bx).

Number of years expected to remain

childless from age x to the end of the

reproductive period—Is parallel to the

‘‘life expectancy’’ function in a

mortality-oriented life table. However,

instead of average number of years of

life expected to live in the future, this

function estimates the average number

of years a woman expects to remain

childless from a specific age to the end

of her reproductive period. For example,

the women at age 15 in the 1910 birth

cohort may expect, on the average, to

remain childless for 13.4 years; that is, a

woman can expect to have her first birth

by age 28.4. While some women will

remain childless to the end of their

reproductive period, the majority will

give birth before then (Figure 5 and

Tables 1–3, column ex).

The Lorenz (concentration)

curve—Included to show the

concentration of first births by age. The

graph illustrates the dispersion of first

births over the range of the reproductive

lives of women rather than the central

tendency of first births over the range

(e.g., the average age of first birth). In

this, the Lorenz curve permits the

measure of skewness or ‘‘tilt’’ of the

first-birth curve. The women in the 1935

cohort were considered to be young

when they had their first births, whereas

the members of the 1960 cohort, by

comparison, were much older.

Figure 6 shows Lorenz curves in

addition to a diagonal line at 45 degrees,

which indicates an even distribution of

births by age. The further the Lorenz

curve deviates from the 45-degree

diagonal line, the more concentrated is

the age distribution of first births. If the

number of first births was equal in each

age group—that is, the distribution

curve lies on the diagonal line—the

distribution curve would represent a

complete lack of concentration. If all

first births took place in a single age

interval, the distribution curve would

represent the maximum, or 100 percent,

concentration of births at one age. Two

measures of concentration related to the

Lorenz curve discussed in this report are

the Gini Concentration Ratio and the
Duncan Index of Concentration.

Numerically, the Duncan index is

different from the Gini index as the

Duncan is affected by the number of

age classes.

Distribution of children ever born,

or parity, by birth cohort—Refers to a

distribution of all women in a cohort by

the number of children ever born alive

to those women up to a specified

age—generally up to age 49. The

proportions may be expressed on a per

1,000 basis (per mille, for greater

precision) (Figure 7), or as a percentage

(Figure 8) (4,7). This measure is

important to describe the household,

which may be large or small, and to

describe at what ages women give birth

and in which various orders.

Cohort total fertility rate

(TFR)—Refers to the average completed

fertility of women in a cohort

(Figure 9). It takes into account the

cumulative fertility rates over all ages,

not just the rate of first births. This

summary indicator is not included in the

maternity table, but is used in this report

to show the impact of childlessness

relative to completed fertility of a

cohort (4,7). The TFR based on the

cohort fertility data is considered to be

the ‘‘truer’’ measure of fertility than the

TFR based on period data; the latter is

complicated by the overlap in timing of

cohort rates.

General Probability of

Birth (nqx)

The probability of birth estimates

the likelihood that a woman who has

attained parity n (either zero, one, two,

three, four, five, six, seven, or higher)

by age i will have another (n + 1)th

birth before reaching the end of that age

interval; that is, before age i + 1. The

birth probabilities are computed using

the central birth rates and the parity

distributions (41).

The formula for the probability of

zero parity—that is, women having their

first birth—is:

0 1 0 BP = BR / PD • 1,000.0, i,y i,y i,y

where

BP0 = probability of a childless i,y

woman at age i having a live

birth in year y,

BR1	 = first-order central birth rate of i,y

women at age i in year y,

and

PD0	 

i,y = proportion of childless women

at age i in year y.

The formulae for computing the

birth probabilities of higher parities

(one, two, three, four, five, six, seven,

or higher), as well as the computed

probabilities, are available

elsewhere (41).

Note that the probabilities shown in

Tables 1–3 are specific to those women

born in 1910, 1935, and 1960 ‘‘at risk’’

of having their first birth. As mentioned,

the probabilities show the likelihood of

first birth between the beginning of an

age interval and before reaching the end

of that age interval. For example, the

probability of a first birth for women in

the 1960 cohort in the age interval

20–21 is 0.0793 (Table 3). This means

that for every 1,000 women who reach

their 20th birthday without having given

birth, 79.3 of them will give birth before

reaching their 21st birthday.

It is assumed that births are evenly

distributed across the single-year age

interval under consideration. Across age,

the probability of first birth rises with

age of mother, peaking sometime in the

20s, and then declines. The probability

of dying, in comparison, generally

increases with age. This is an important

distinction for the final age group in the

life tables. With traditional mortalityrelated life tables, everybody within this

age group dies; that is, the probability of

dying equals one ( nqx = 1.000).

However, the probability of first birth

for the final age group of the birth

cohort is less than one, so that some

women remain childless throughout

their lives.

Short Definitions of Life

Table Functions and

Formulae

Age- and cohort-specific, parity

zero, birth probabilities for women at

ages 15–49—Refers to the probability

or chance that a childless woman, at age

i, will have a first birth within the year.

Series 2, No. 153 [ Page 17

0 q , i,y

where

q0 = probability that a first birth

occurs within 1 year,

i = age of woman,

and

y =	 year

(See general formula for probability of

birth, nqi

, above.)

Age- and cohort-specific number of

childless women at ages 15–49—Refers

to the number of women at age i from

the original cohort who have yet to have

any children at the beginning of year y.

l

i

0

,y

,

where

l

0 =	 the number of women who

have not had any children,

i = age of woman,

and

y =	 year.

0 0 0 l

i+l,y = li,y • qi+l,y

(Often the cohort is set to have an initial

magnitude like 100,000.)

Age- and cohort-specific number of

first-born children for women at ages

15–49—Refers to the number of first

births occurring to women, at age i,

within year y.

bi

0

,y ,

where

b0 =	 the number of first-born 

children, 

i = age of woman,

and

y =	 year.

0 0 0 bi,y = qi,y • l

i,y

Age- and cohort-specific number of

childless years for women at ages

15–49—Refers to the number of

childless years lived by women at age i

in year y, taking into account the

decrease of childless women as the

cohort ages in the year.

L0 , i,y

where

L0

i,y = the number of childless years

lived by childless women at age i
Page 18 [ Series 2, No. 153

and

L0

i,y = is calculated for all ages for

each cohort.

0 0 0 L = (0.5) • l + (0.5) • l i,y i,y i+l,y

Cohort-specific number of years

childless from current age to age

50—Refers to the number of childless

years from age i to the end of

reproductive period.

0 Ti,y

where

T0 = the total number of childless i,y

years lived over exact age i by

women in the cohort

and

T0 = Σ50 L , that is, the sum of i,y i=x x,y

childless women-years from

age x to age 50.

Age- and cohort-specific expected

number of years to be childless for

women at ages 15–49—Refers to the

average number of years a woman at

age i in year y expects to remain

childless.

0 e , i,y

where

e0 = the average number of years

expected to remain childless

between ages x and 50,

i = the age of woman x,

and

y = year.

0 0 0 e = T / l i,y i,y i,y

Cohort TFR—Refers to the average

completed fertility of women in a given

birth cohort at the end of their

reproductive period.

TFR ,

y

where

TFR = the average completed fertility

of women in a cohort at age 50

and

TFR = Σ8+ CumBR is the sum of y n=1 i,y

cumulative birth rates from

parity one to eight or higher.

Cumulative birth rates—Refers to

the sum of central fertility rates from

age 15 to the current age.

CumBR,

where

n n n CumBRi+1,y+1 = CenBRi,y + CumBRi,y

i = age,

y = year,

and

n =	 parity.

To repeat, the TFR takes into

account the cumulative fertility rates for

all parities, not just the rate for a birth

order one. (With the TFR, the emphasis

is usually on rates for all ages.)

Indicators of Concentration

Lorenz curve—Is a graphical

representation of various types of

inequality, where the x axis represents

the cumulative proportion of an

independent variable such as time,

population, etc., and the cumulative

proportion on the y axis of a dependent

variable, such as income or, for this

report, first births. The curve is convex,

and is graphed between 0.0 and 1.0. As

an example, it could be said that a curve

may show that 45 percent of the women

in the population had 70 percent of its

children.

Gini Concentration Ratio—The

graph containing the Lorenz curve also

holds a diagonal line at 45 degrees; that

is, where x = y. This line is called the

‘‘line of perfect equality.’’ If the Lorenz

curve lies precisely on the diagonal line,

then all members of the horizontal axis

have an equal distribution on the y axis.

A perfectly unequal distribution would

be one in which one person has the

entire amount of the item measured and

everyone else has none.

Theoretically, the Gini ratio (G) is a

ratio of areas that lies between the line

of perfect equality and the Lorenz curve

to total area under the line of equality.

G = A/B,

where

A =	 the area between the line of

perfect equality and the Lorenz

curve

and

B = the area under the line of

equality.

If the function is known, the ratio

may be easily found with integration.

However, as when working with

discrete points, the ratio can be

approximated as follows:

G n = 1–Σ (X – X ) • (Y + Y ), k=1 k k–1 k k–1

where

Xk = horizontal point,

Yk =	 vertical point,

and

k = sequence of each point.

Duncan Index of Concentration—

Refers, geometrically, to the maximum

vertical distance from the diagonal line

of equality to the Lorenz curve.

Algebraically, the index is simply

the sum of values of

|X – Y |. k k

As such, it is equivalent to the

Index of Dissimilarity, which is the sum

of the positive differences between the

two percent distributions. The value of

the concentration index depends upon

the size of the set of geographic units

used.

Δ =	 Duncan Index of Concentration

and

n = 1⁄2Σ |X – Y |, k=1	 k k

where

Xk = horizontal point,

Yk = vertical point,

and

k =	 sequence of each point.

The computation of the Duncan

index provides the point where the

concentration is greatest. It is calculated

by subtracting the individual values

between the line of equality from the

Lorenz curve. Its largest value indicates

the age at greatest concentration.
Vital and Health Statistics

Series Descriptions

ACTIVE SERIES

Series 1.	 Programs and Collection Procedures—This type of report

describes the data collection programs of the National Center

for Health Statistics. Series 1 includes descriptions of the

methods used to collect and process the data, definitions, and

other material necessary for understanding the data.

Series 2.	 Data Evaluation and Methods Research—This type of

report concerns statistical methods and includes analytical

techniques, objective evaluations of reliability of collected

data, and contributions to statistical theory. Also included are

experimental tests of new survey methods, comparisons of

U.S. methodologies with those of other countries, and as of

2009, studies of cognition and survey measurement, and final

reports of major committees concerning vital and health

statistics measurement and methods.

Series 3.	 Analytical and Epidemiological Studies—This type of

report presents analytical or interpretive studies based on vital

and health statistics. As of 2009, Series 3 also includes

studies based on surveys that are not part of continuing data

systems of the National Center for Health Statistics and

international vital and health statistics reports.

Series 10.	 Data From the National Health Interview Survey—This

type of report contains statistics on illness; unintentional

injuries; disability; use of hospital, medical, and other health

services; and a wide range of special current health topics

covering many aspects of health behaviors, health status, and

health care utilization. Series 10 is based on data collected in

this continuing national household interview survey.

Series 11.	 Data From the National Health Examination Survey, the

National Health and Nutrition Examination Surveys, and

the Hispanic Health and Nutrition Examination Survey—

In this type of report, data from direct examination, testing,

and measurement on representative samples of the civilian

noninstitutionalized population provide the basis for (1)

medically defined total prevalence of specific diseases or

conditions in the United States and the distributions of the

population with respect to physical, physiological, and

psychological characteristics, and (2) analyses of trends and

relationships among various measurements and between

survey periods.

Series 13.	 Data From the National Health Care Survey—This type of

report contains statistics on health resources and the public’s

use of health care resources including ambulatory, hospital,

and long-term care services based on data collected directly

from health care providers and provider records.

Series 20.	 Data on Mortality—This type of report contains statistics on

mortality that are not included in regular, annual, or monthly

reports. Special analyses by cause of death, age, other

demographic variables, and geographic and trend analyses

are included.

Series 21.	 Data on Natality, Marriage, and Divorce—This type of

report contains statistics on natality, marriage, and divorce

that are not included in regular, annual, or monthly reports.

Special analyses by health and demographic variables and

geographic and trend analyses are included.

Series 23.	 Data From the National Survey of Family Growth—These

reports contain statistics on factors that affect birth rates,

including contraception and infertility; factors affecting the

formation and dissolution of families, including cohabitation,

marriage, divorce, and remarriage; and behavior related to

the risk of HIV and other sexually transmitted diseases.

These statistics are based on national surveys of women and

men of childbearing age.

DISCONTINUED SERIES

Series 4.	 Documents and Committee Reports—These are final

reports of major committees concerned with vital and health

statistics and documents. The last Series 4 report was

published in 2002. As of 2009, this type of report is included

in Series 2 or another appropriate series, depending on the

report topic.

Series 5.	 International Vital and Health Statistics Reports—This

type of report compares U.S. vital and health statistics with

those of other countries or presents other international data of

relevance to the health statistics system of the United States.

The last Series 5 report was published in 2003. As of 2009,

this type of report is included in Series 3 or another series,

depending on the report topic.

Series 6.	 Cognition and Survey Measurement—This type of report

uses methods of cognitive science to design, evaluate, and

test survey instruments. The last Series 6 report was

published in 1999. As of 2009, this type of report is included

in Series 2.

Series 12.	 Data From the Institutionalized Population Surveys—

The last Series 12 report was published in 1974. Reports

from these surveys are included in Series 13.

Series 14.	 Data on Health Resources: Manpower and Facilities—

The last Series 14 report was published in 1989. Reports on

health resources are included in Series 13.

Series 15.	 Data From Special Surveys—This type of report contains

statistics on health and health-related topics collected in

special surveys that are not part of the continuing data

systems of the National Center for Health Statistics. The last

Series 15 report was published in 2002. As of 2009, reports

based on these surveys are included in Series 3.

Series 16.	 Compilations of Advance Data From Vital and Health

Statistics—The last Series 16 report was published in 1996.

All reports are available online, and so compilations of

Advance Data reports are no longer needed.

Series 22.	 Data From the National Mortality and Natality Surveys—

The last Series 22 report was published in 1973. Reports

from these sample surveys, based on vital records, are

published in Series 20 or 21.

Series 24.	 Compilations of Data on Natality, Mortality, Marriage, and

Divorce—The last Series 24 report was published in 1996.

All reports are available online, and so compilations of reports

are no longer needed.

For answers to questions about this report or for a list of reports published

in these series, contact:

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Centers for Disease Control and Prevention

3311 Toledo Road, Room 5412

Hyattsville, MD 20782

1–800–232–4636

E-mail: cdcinfo@cdc.gov

Internet: http://www.cdc.gov/nchs
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DHHS Publication No. (PHS) 2011–1353, Series 2, No. 153