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WHAT HAPPENED DURING THE BABY BOC4?

NEW ESTIMATES OF AGE- AND PARITY-SPECIFIC

BIRTH PROBABILITIES FOR ANERICAN WC4EN

Warren Sanderson

Working Paper No. 23

CENTER FOR ECONOMIC ANALYSIS OF HUMAN BEHAVIOR AND SOCIAL INSTITUTIONSNational Bureau of Economic Research, Inc.261 Madison Avenue, New York, N.Y. 10016

December, 1973Preliminary; Not for Quotation

NBER. working papers are distributed informally and in limitednumber for comments only. They should not be quoted without written

permission.

This report has not undergone the review accorded official NBERpublications; in particular, it has not yet been submitted for approvalby the Board of Directors.

The research reported herein was performed pursuant to grants fromthe Ford Foundation and from the National Institute of Child Health andHuman Development, National Institutes of Health (U.S. Dept. of Health,Educatton, and Welfare). The opinion8 expressed herein are those of theauthor and do not necesaai1y reflect the views of the grantors.

• WHAT HAPPENED DURING THE BABY- BOOM?NEW ESTIMATES OF AGE—AND PARITY-'

SPECIFIC BIRTH PROBABILITIESFOR MiERICAN WON

by

Warren C, SandersonStanford University

The baby boom is over and, with fertility in the United

States currently below replacement level, it may well be saia that a

birth dearth is already upon us. Graph 1 shows the U. S. general

fertility rate1 from 1909 through 1968.2 The secular movement of this

rate is clearly downward. However, this secular decline was interrupted

by a period in the l95Os when fertility was both relatively high and

increasing. The peak general fertility rate during the baby boom occurred

in 1957 and subsequently fertility has fallen every year thereafter with

the exceptions of 1969 and l97O, This recent fertility history presents

a problem for economists and other interested in fertility. Is the

current low level of fertility but a trough in a long cycle which is

destined to produce yet another baby boom or is it a manifestation of a

continued secular decline in fertility? To put the same problem in

somewhat different terms: is a baby boom an anomalous or systematic

phenomenon.

.Although in recent years, there have been important advances

in the economic theory of fertility,4 these contributions have not yet

been sufficiently articulated to throw much light on the course of

—2—

postwar fertility changes. It is the main purpose of this paper to

examine in detail the pattern of fertility fluctuations n the United

States since the Second World War and to define, with someprecision,

the questions these patterns raise for students of fertility behavior,

Towards this end I present new estimates of age— and parity-.specific

monthly birth probabilities for cohorts of native white women born in

the twentieth century. These data lend themselves to numerous uses, only one

of which is pursued here——the close analysis of the structure of fertility

changes after 1950, What they reveal in that connection are hitherto

unrecognized patterns of fertility variation across age and parity groups

during the baby boom, Perhaps the most startling finding is that, although

aggregate fertility measures reach their "baby boom" peak in 1957, the

birth probabilities often do not, Looking across groups of women of

different ages one finds that probabilities of second and higher order

births reached a peak level during the years 1953—1955 as frequently as

in the years 1956—1958. The probabilitjes of second through fourth order

births for young women consistently reached their peak during the period

1959—1961. In addition, the new data pertaining to lower order births

show that before the Second World War temporal variations in birth pro-

babilities were quite similar across age groups. After the War, that is

to say during the height of the Baby Bàom, a marked structural change

occurred and the positive correlation across age groups disappeared,

To aid further analysis of the mass of birth probability data,

I have "decomposed" the time series for different birth orders into an

-.3—

"age", a "current year", and a "cohort" component. For each of the

birth orders, this trio of components allows us to disentangle the

distinct influences which intertwined themselves, giving rise to the

observed birth probabilities. This analysis shows that the cohort

influences were very important in creating the pattern of first birth

probability fluctuations in the baby boom period. The strength of this

source of influence progressively diminished in the case of higher order

births, however. The current year components for first birth probabilities

exhibit a time profile which is unlike those for higher order births in

that its peak precedes 1957 while the peaks of the current year components

for higher order births all occur in 1957, In view of the absence of

uniformity in the temporal patterns exhibited by the various birth

probability series, it may be reassuring to note that the familiar move—

ment to a 1957 peak does emerge in the current year components for each

of the birth orders save the first.

While the behavior of the current year components by themselves

would have promoted a cyclical swing in aggregate fertility paralleling

the one in the postwar period, the amplitude of that movement would have

been much smaller. Since the current year effects had to work against

the anti—natal influence of the changing age structure of the population,

were it not for the "cohort" influence already noticed the outcome

may not even have qualified as the "Baby Bubble" much less

the "Baby Boom".

0

Birth Probabilities.

Patterns of fertility variations will be analyzed, in this

study, using data, estimated by the author, on age— and party—specif Ic

birth probabilities for cohorts of native5 white wOmen born after 1899.

Birth probabilities were first measured for the United States by Wheipton

in his pioneering book, Cohort Fertility, published in 1954. There

Wheipton presented annual age— and parity—specific birth probabilities

for native white women for the years 1920 through 1950.6 Whelptonts

original work spawned further efforts at measuring birth probabilities7

and birth probabilities for all U. S. women are now regularly published

in Vital Statistics of the United States.. Since the first year for which

these data are reported is 1956 those interested in the behavior of time

series fertility measures are left in something of a quandry. There is

one study on birth probabilities of native white women for the years 1920

through 1950 using one methodology and another for all U. S. women covering

the perixl 1956—1968 using a somewhat different methodology. In order to

facilitate the interpretation of time series trends it is preferable to study

the birth probabilities of native white women rather than those of all U. S.

women and so, with an improved methodology,8 I have, re—estimated some of

Wheipton's birth probabilities for native white women and extended his series

through 1966.

Annual age— and parity—specific birth probabilities are of interest

for a number of reasons. Chief among their attractions is that a birth prob-

ability is a period fertility measure which is consistent with economic decision—

making models of fertility. It is implausible to think of the total fertility

rate or the net reproduction rate as being the outcome of a household decision—

making process. However, birth probabilities may, quite plausibly, be considered

as outcome of such a process as Michael (1973) has already demonstrated.

—5—

cAnother attraction of the birth probability data used in this

paper is that they allow the investigator tofollow cohorts of women

over their life cycles and study the processes through which their

completed family sizes are attained. Also, birth probabilities, parti-

cularly monthly birth probabilities like those presented here, are parameters

in mathematical models of fertility and contraception developed by

10demographers.

Conceptually, an age— and parity—specific monthly birth probability

is a rather simple affair. Let us consider, for example, a highly simplified

computation of the monthly birth probability of thirty year old native white

women who have had exactly two previous births having a third birth in

1960. This particular monthly probability is, by the way, about 1.2

percent or on an annual basis about 13.8 percent. For ease of exposition, 0let us assume that all these women were born on January 1, 1930, so that

each of them spends the full twelve months in which she is 30 in the

calendar year 1960. In addition, let us assume that all of these women

had their second births before they were 29 (ie. before the calendar

year 1959). If we were to consider the possibility of second births

occurring in 1959, in this simplified example, then the women who had

had such births would not be, on the average, at risk of having a third

child for a full twelve months in 1960. Neglecting mortality, we may write:

(1) B = N - N(1-p)'2

where B is the number of third births to 30 year old native white women in

1960, N is the number of 30 year old native white women who are capable

0

—6.-

of having a third birth at the beginning of 1960, and p Is the

monthly birth probability we are seeking. From Equation 1, it may

be readily seen that:

N 1/12(2) p=1_(-j!)

The two major components of all birth probabilities are data on age—

and parity—specific births and age— and parity—specific num1ers of

women at risk of having a birth.

When monthly birth probabilities are actually computed, we

cannot take for granted that all women are born on January 1st, nor that

all previous births have occurred sufficiently long before the period of

interest that current birth risk status is unaffected, nor can mortality

be neglected. In addition, in estimating birth probabilities we must

obtain data on births by parity and single years of age for native white

women, and estimates of women capable of having a birth of a given order,

aggregated according to whether .they have had their last birth more than

one year11 before the period of interest or not, - When these

complications are added to the computation, the birth probabilities can

no longer be calculated directly and must obtained using an iterative

procedure. This procedure is discussed in more detail in Appendix I.

Looking at the aggregated birth probabilities presented in

Appendix ii and the underlying disaggregated birth probabilities, one can

see what is a rather remarkable fact: birth probabilities often do not

—7—

120

have th.eir baby boom peak in 1957. Table 1 summarizes data on the

year in which our 205 age— and parity—specific birth probability

scries have their baby boom peaks. Out of the 205 series, 43 or about

21 percent of them peak in 1957, and 70, or about 34 percent of them

peak in the period 1956—1958.

Table 1: Number of Birth Probability Series PeakingWithin the Given Time Interval,

Years Birth Orders

Total1st 2nd 3rd 4th 5th 6th 7th 8th +

1950—1952 6 5 0 0 8 3 1 9 32

1953—1955 3 4 8 11 10 8 10 4 58

1956—1958 15 7 7 7 7 12 10 5 70

(1957) (15) (4) (4) (4) (4) (5) (5) (2) (43)

1959—1961 3 13 12 9 0 1 1 2 41

1962—1966

Total

•3 0 1 0 0 0 0 0 4

30 29 28 27 25 24 22 20 205

Source: Sanderson (1974).

It is clear from Table 1 that the 1957 peak was most common for first births.

In fact, if we consider only second and higher order births, we find that

the seine number of series peak in 1953—1955 as do in 1956.4958. It is also

interesting to note with regard to Table 1 that peaks occurring after the

D56—1958 period are not coon except for second, third, and fourth order

births, The observation that birth probabilities do not generally peak in

1957 suggests the important question: what regularities, if any, exist in

the post—war movements of birth probabilities.

0

0

—8—

One important and striking regularity in the pattern of

birth probabilities is shown by the first birth probabilities of women

27 years old and younger. All the first birth probabilities of women

15 through 27 years old rise in the 'fifties to a peak in 1957. These

ages account for 13 of the 15 first birth probability series which peak

in 1957. The other series which peak in 1957 do so more or less unsystem—

atically. For example, the four ages for which there are peaks in third

order birth probabilities in 1957 are 31, 32, 43, and 44 and the five ages

in which there are peaks in sixth order birth probabilities are 31, 36, 37,

41, and 43. Thus, the first birth probabi1ities of women 27 and under

form the only coherent set of birth probabilities which peak in the same

year as the crude birth rate.'4 The timing of the fluctuations of these

first birth probabilities was an important determinant of the timing of

the baby boom fertility peak. Although in 1957 first births to

native white women 15 to 27 accounted for only about 25 percent of all

births to these women, the decline in the first births to women 15 to 27

accounted for about 50 percent of the decline in all births from 1957 to

1958,

As can be seen from Appendix Graph i-i in Appendix II, the

fact that first birth probabilities for young women tended to peak in the

same year as the crude birth rate does not mean that their patterns of change

in the 'fifties were similar to one another. By 1957, the first birth

probabilities for women 15 to 19 years of age had increased about 31 percent

over their 1950 level, those of women 20 to 24 had increased about 38 per—

cent over their 1950 level, but those of women 25 to 29 increased to only

10 percent above their 1950 level. The first birth probabilities of women

15 to 19 fell somewhat more rapidly from its peak than the first birth

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'—9—

jprobabilities of women 20 to 24 and the first birth probabilities

J of women 25 to 29 fell the least.

The first birth probabilities for women orer 27 years old'

behaved quite differently in the postwar period from those of their

younger sisters. It can be seen from Appendix Graph 1—2 that the first

birth probabilities of women in the 30—34, 35—39, and 40—44 year old age

grouçsbegan to fallin the fifties before 1957. The differences in the

behavior of the first birth probabilities of women of different ages

can be clearly seen in Graph 2, where we have plotted the first birth

probabilities of women aged 20, 26, and 32. This graph shows that,

although before World War II the first birth probabilities of these women tended

to move similarly, in the postwar period their first birth probabilities show

a rather remarkable divergence. This considerable dissimilarity of the

patterns of change of first birth probabilities by age groups is an im-

portant feature of the baby boom and any thorough explanation of postwar

fertility variations must come to grips with it. We shall return to this

question later in the paper.

Second birth probabilities to women 16—19, 20—24, and 25—29

are plotted in Appendix Graph 11—1. All three age' groups show a substantial

increase in their second birth probabilities over the course of the 'fifties.

However, unlike the first birth probabilities of women of the same ages, the

second birth probabilities do not reach their maximum in 1957, but rather

in 1960 or 1961. Thus the baby boom peaks in second birth probabilities

for these women lag their first birth probability peaks by about three

years. Another interesting aspect of this graph is the difference in the

of first and second birth probabilities to women 25 to 29 years.

• —10-.

• 0The first birth probabilities of these women are almost constant from

1951 through 1956, but during the sie period their second birth prob—

abilities rise by about 25 percent. This difference in the behavior

of first and second birth probabilities during the baby boom raises

another interesting question and we shall also return to it below.

Appendix Graph 11—2 shows the second birth probabilities

of women 30—34, 35—39, 40—44. Like the first birth probabilities of

these women and in sharp contrast with the second birth probabilities of

younger women, the second birth probabilities of these women tend to peak before

1957. The baby boom peak of second birth probabilities to 30—34 year olds

lags the peak of first birth probabilities by two years, but the peaks of

first and second birth probabilities to women 35—39 and 40—44 occur in

the same year.

It can be seen from Appendix Graphs 111—1 and 111—2 that the

patteriof third birth probabij.tjes appear to be similar to those of second

birth probabilities. Third birth probabilities for women below 30 tend

to peak around 1960 and third birth probabilities for women 35—39 and

40—44 tend to peak before 1957. In this case, third birth probabilities

for women 30—34 peak in 1957. In fact, as can be seen from Graph 3, as

e move from first through third births the time profile of birth probabilities

of 30—34 year old women looks more like the time profiles for younger

women.

Although the fourth birth probabilities of women 20—24 peak

in 1961 and those for women 25—29 in 1960, their rise over the decade

of the 'fifties is considerably smaller than the lower order birth prob-

abilities of women the same age. For example, third order birth probabilities

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—11—

for women 20—24 rose over 30 percent from 1950 to 1960, whereas

fourth birth probabilities to these women rose less than 7 percent

during the decade. For women 25—29 the rise in thirdbirth prob—

abilities was about 33 percentand for fourth birth probabilties only

about 15 percent. The fourth birth probabilities for women over 30 roáe

more rapidly in the first half of the baby boom decade than the fourth

birth probabilities of younger women. Indeed, as a practical matter

it appears that the fourth birth.probabilities of women 30—34 and

40—44 peaked in 1957.15

With fifth and higher order births, post—1957 peaks in the

aggregated birth probabilities presented in Appendix II disappear and

the age patterns of the birth probabilities become somewhat less regular.

The fifth birth probabilities for women 25—29 peak in 1952, their sixth

probabilities in 1953, their seventh birth probabilities in 1954, and

their eighth and higher birth probabilities in 1956. The fifth, sixth

and seventh birth probabilities for women 30—34 peak in 1956, and

the eighth—plus birth probabilities peak a year later.

—12—

Component Analysis.

We have seen above that fertility behavior in the postwar

period was far from being uniform. All birth probabilities did not

rise in the 'fifties to a peak in 1957 and decline thereafter, but rather

they showed a number of different patterns. How are we to understand

these patterns? In order to make some sense Out of the multiplicity

of fertility series, we must introduce at least a modicum of analytic

structure. In this.pursuit, we shall posit the following representation

of birth probabilities:

(3) ln(pk2.) = + + +Cijk2,

where is the monthly birth probability of birth order 2.. for

women of age i in year j , (the index k represents the year in which

these women were born and can be derived from a knowledge of i and j ),

is the age component, 8. is the current year component, k2. is

the cohort component, and c. . . is a random disturbance term assumedijk2..

to be independently normally distributed with mean zero and cohort variance

This is a rather broad decomposition because we do not need to

know precisely what the current year or cohort influences on birth probabilities

of a given order are in order to measure their contribution to variations

in birth probabilities. The decomposition proposed here is roughly in

the spirit of Easterlin's analysis. In his article on the baby boom

in historical perspective,16 he explains the fertility variations of

native white urban women using variations in the unemployment rate and

—13--

L•

changes in the rate of growth of the size of the group of males 20 to

29 years of age. The influence in the first of these factors would be

recorded as variation in the current year component in the proposed

decomPOsition, and the latter, since it is a reflection of relative

cohort size, would be recorded as variation in the cohort component.

The Easterlifl—FUChs intergenerational relative income hypothesis17 may

also be easily represented in our proposed framework because parental

income levels, in as much as they affect tastes, are likely to have

influences which remain with cohorts throughout their whole reproductive

span, and therefore influences which can be captured as changes in cohort

components. The suggested decomposition, broadens somewhat the Easterlin

hypotheses since separate age, current year, and cohort components are

estimated for each birth order. Separate cohort components, for example,

allow for the intergenerational relative income effect, if it is present, to

affect the birth probabilities differently for different birth orders.

However, along with certain advantages, the birth probability

decomposition in Equation 3 has certain disadvantages. One has to do with

the interaction between cohort and current year components. Given the

specification in Equation 3, temporal patterns of birth probabilities of

women of differing ages, parity held constant, are allowed to differ only

because of the variations in the cohort components. Thus certain sorts of

influences on fertility may not be correctly captured in this analysis.

The influence of benefits after World War II may be one of these.

We do not maintain the total absence of such influences on fertility, but

rather that they.e of minor importance compared with those influences which

are correctly measured.

—14—

Another disadvantage of the proposed decomposition is the

econometric difficulty of thoroughly disentangling the age, current year

and cohort components. We can rewrite Equation 3 as follows:

A** y**(4) [lnpJ Z a LIAr] + Z + z ÷ Ic]

•r=A* r s=y* tc*

where [lnp] is a column vector of observations on the natural logarithms

of birth probabilities of order L , its general element being ln(pj.k,)

where [Ar] is a dummy variable vector which is unity if the age referred

to in the corresponding element of the observation vector is r and zero

otherwise, -

where [Ye] is a dummy variable vector which is unity if the year referred

to in the corresponding element of the observation vector is year s and

zero otherwise,

where I C11 is a dummy variable vector which is unity if the cohort referred

to in the corresponding element of the observation vector is t , and zero

otherwise,where [c] is a vector of random numbers assur-ec to be generated

independently from a normal distribution with mean zero, and constant variance,

and where A* , and A** represent the first and last ages used in the

analysis, and * and ** , and C* and C** have similar meanings

for current years and for cohorts. -

Equation 4 cannot be estimated directly because of linear de-

pendencies between the age, current year, and cohort dummies. Indeed, since

an age and a cohort are associated with each observation we must have:

C**(5) E [Ar] = z

icir=A* t=c*

Therefore, we can write:

(6) [A4] = Z ICJ — E[Ar]tC r=A*

r+j

Substituting Equation 6 into Equation 4, we obtain:

A** c**(7) [1np)

— cx z)IA] + zs2."s1 + E ()Ic ]+[c]

r=A* i t=c* -i trj

However, since each observation is associated with a current year and a

cohort component, we must have:

Y** c**(8) E [Y] = E

[ce]t=c*

Therefore, we can write:c**

(9) 1k = E [Ce] — E[Y5]

t=C* s=Y*s+k

Substituting Equation 9 into Equation 7 we obtain

(10) 1n[p] = E (cc _cc.)[Ar] + z sLk1's + Z (y+:i t+8k)[cir=A*r tC*

r+j s+k

There is one more linear dependency in the remaining dummy variable vectors.

A person who is of age 3 in year k was born in year k—j, which we

call year m . The linear dependency can be expressed as follows:

0

—16—

/(11) Z (j-r)[A I + Z (s—k)I\ J = 't—iu)IC ]

r=A* r s=Y* t fl t

r+J s+k

Therefore, we can write

A**(12) IC I

= (j—r)[A ] + E :jy (t•Ifl)1n r=A*1m) r (n—rn) s t

rj t+n

(n+in)

Substituting the value of [C] in EqudLion 12 into Equati,.n 10, we obtain

A**r I(13) [lnp] = r=A1Jd1 kZ

)'n2)jIA]

r+J

+(a+k')} ILs1

s+k

+tC*

[Cr) + [c) (nu).

t+n

Equation 13 is estimable, and we can ideirify the raj2) s8k2)and the if we knew (a.Q+8kZ+() Let us denote this latter sum by Xp,

Clearly we cannot use the goodneof fit Lo help us determine X , since the

regression coefficients are not affected by its value and further there is no

observed birth probability for the combination of age j , current year k18

and cohort n. Therefore, in order to estjjnae the component differences

-17—

we must use some additional information to compute the

We have estimated Equation 13 for the first four birth orders.

For birth orders one through three, we used ages 18 through 39, omitting

age 30, current years 1920 through 1966 omitting 1960 and the var—affected

years of 1942 through 1947, and cohorts 1900 through 1946, omitting women

born in 1931. In terms of the notation of Equation 13, j = 30, k= 1960

m = 1930, and n = 1931. For birth order four we followed the pattern of

the first three birth orders except that ages 22 through 39, current

years 1924 through 1966, and cohorts 1900 through 1942 were used. This

procedure yielded three regressions with 107 dummy variables and 705

observations each and one regression with 95 dummy variables and 595

observations. The results of these computations are reported in Appendix Ill.

Before the results of these regressions can be used we must com-

pute the We know that the decline in birth probabilities from

1930 to 1933 ought not to be attributed to a fortuitous configuration of

age and cohort components, but rather to a decline in the curreit year

component. Similarly the increase in birth probabilities from 1933 to

1934 ought to be accounted for mainly be an increase in the current year

component. Let us denote the coefficient of [Y] in Equation 13 by

• Then we can write:

(14) l933 — l930, =D1933'

-D1930 £

+ 3XL

and

(15) 81933,t - Big34,=

D1933-

D1934 £

—18--

• If estimates could be made of l933,& l93O8l933,L 81934,Z

or indeed any current year component difference, then the value of

could be estimated. Any estimate of current year components drawn from

observed data must be confounded with age and cohort influences, There

is no way around this problem. The tack taken here is to try to mini-

mize the effects of age and cohort influences by choosing to estimate

current year component differences using observed data for years for

which there is a priori information that changes in current year

conditions were of speical importance in explaining fertility variations.

The estimate used for 1933,2. —193O,

is

di.& E n(p l933,k, 1fl(Pi,193O,k33)

where. k = 1933 — I • The estimate used for l933R. 1934 is

d2,Lmn(pil933k) — ln(Pjl934k÷l)

19

where k = 1933 — i once more, The criterion we used to determine

X was;

oMinize {4(D1933 - + 3X — d1 L)}2 + {D1933

—l934,L

-

in essence, this criterion allows the selection of that X& whose implications

for current year components fit most closely the notions that the declines in

birth, probabilities from 1930 to 1933 and the subsequent increases to 1934

were mainly due to changes in current year components.

Given the values of X computed from the criterion above, we

have computed the current year component differences 8196O,Zand

the cohort component differences —193l,L . The current year

component differences are shown in Graphs 4, 6, 8, and 10, and cohort component

differences in Graphs 5, 7, 9, and 11. The data shown in these graphs are

sensitive to the criterion chosen to estimate the and by no means

ought the plotted data to be interpreted as being precise. However, the

general patterns shown by the component differences remain given any plausible

criterion of which we are aware.

Graph 4 shows the current year component differences for first

births. It is somewhat surprising to note that the current year component

for first births does not peak in 1957, but earlier in the baby boom

decade. How then are we to understand the first birth probabilities of

women 15 through 27, all of which peak in 1957? The answer can be found

—20—

by turning to Graph 5. Here we can see that the cohort component was

rising after the middle of the l92Os. It is the rise, particularly

the increase for women born in the Depression which is the main cause

of the increase in first birth probabilities for young women during

the baby boom. The rather large differences in the behavior of first

birth probabilities by age group which we noted earlier in the paper

can be traced directly to variations in the cohort components.

Clearly, if we are to understand the increase in first births

over the course of the baby boom, we must focus our attention on the large

upward movement of the cohort component which occurred across the

Depression. Apparently relative cohort size has some impact on this

component because the small cohort of 1919 has a relatively large corn—

ponent and the relatively large cohort of 1921 a comparatively small one.

The year 1917 for which the cohort component has a local trough is also

a year in which the birth series has a local peak9 Nonetheless, the sheer

size of the change in the cohort component over the Depression relative

to previous changes suggests that some other factors were also at work.

Perhaps one of the other factors is the Easterlin—Fuchs intergenerational

relative Income effect. However, it is not evident that these two factors

taken together would imply a 1941 peak in the cohort component. In any

case, one thing is clear from Graph 5, cohort components have been the

source of a considerable portion of the variability in first birth probabilities

over the baby boom.

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—21—

Looking at Graphs 6, 8, and 10, one can see a C00fl pattern

in the current year components; one that is different from that in

Graph 4. In Graph 4, we found that the current year càmponent for first

births did not rise in the'f if ties to a peak in 1957. In Graphs 6, 8,

and 10, we see that the currentyear components for second through fourth

births do rise in the 'fifties to a peak in 1957. It is in part this

this difference between the behavior ofthe current year component for

first and for higher order births which explains why birth probability

patterns differ by order for women of the same age, the phenomenon we

observed in Graph 3 above. This clear differentiation between the current

year components of first births and higher order birthsduring the baby

boom period is an important observation.It suggests that students of

fertility might profitably study first and subsequent births separately.

Considering the cohort cQmpQnnts of second through fourth

births, it can be seen that the rise in the cohort component over the

Depression which was so prominent with respect to first births becomes

• significantly attenuated as birth order increases.In Graph 11, which shows

the cohort components for fourth births, the rise over the Depression is so

small as to be almost nonexistent.Thus it appears that at least some

cohort influences affectfertility by primary affecting low order births.

We are now in a position to systematize the observations we made

on the patterns of birthprobability changes over the baby boom. Most of the

age differentiation in the patterns of birthprobabilities may be explained by

c:

—22—

a coton pattern in the cohort components. Cohort components tended to have

a declining phase in the 'twenties followed by an increasing phase beginning

in the middle or late 'twenties. This pattern raised the fertility of

younger women in the 'fifties and làwered the fertility of older women.

The increasing phase of the cohort component clearly grew smaller in

amplitude as birth order increased and it is possible that the reverse

happened with respect to the decreasing phase. Most order differentiation

in the patterns of birth probabilities by age occurs between first and

subsequent births due to the change in the pattern of current year

components from one which is relatively flat from 1952 through 1957 and which

falls thereafter to a pattern for second and higher order births which is

more rounded and which peaks in 1957. The less rapid fall from 1957 to 1960

in this latter pattern accounts for why the interaction between it and the

cohort components produces peaks around 1960 rather than the earlier

peaks in the first birth probabilities of young woman.

In this paper we have presented data on monthly birth probabilities

for native white women which are age.- and parity—specific,

We have considered the patterns of variation shown by these probabilities

over the baby boom and demonstrated that these patterns may be illuminated

by decomposing the birth probabilities into age, current year, and cohort

components. It is hoped that the data presented here and the questions

which hve been raised will aid in the development of models and data which

will deepen our understanding of the intricate processes of fertility change

over time.

—23-'

APPENDIX I

The Methodology of the Creation of Birth Probabilities.

As an example, we shall relate in detail the creation of the

monthly probability of 30 year old women having their second birth in 1950.

First, we assume that women are only born on the first day of, every

Donth. This assumption makes our computations managable without neglecting

the substantial variations in monthly births which have occurred. Women

who report having a second birth at age 30 in 1950 may have been born

between February 1, 1919 and December 1, 1920. In other words, the

women may have any one of twenty—three monthly birthdays. Let us call

women born on February 1, 1919 members of cohort one, women born on

March 1, 1919 members of cohort two, and so on. Women born on December 1,

1920 are members of cohort 23. In order to determine the birth probability

we must know how many women are capable of having a second birth at age

30 in 1950 and how many months these women spend as 30 year olds in

1950. We have assumed in the birth probability computations that a

woman was not capable of having a birth until twelve months after her

last one except in the case of twins.

The assumption that, except in the case of twins, a woman

was not capable of having a birth in less than twelve months after her

last one, forces us to divide those women capable of having a second

birth at age 30 'in 1950 into two groups, those who nve had their first

birth more than a year before they turn 30 in 1950 and those who have

had their first birth within a year of the date on which they turn 30 in

o

—24—

1950. Let us consider, for example, those women of cohort 12

(i.e. those born on January 1, 1920) who are capable of having a second

birth at age 30 in 1950. Some of these women had their first birth when

they were 20 in 1949. If their births were distributed uniformly over

the year 1949, these women would have, on average, six months of 1950

in which they were capable of having a second child. Women who had their

first birth before they were 29 in 1949 would have a full twelve months

of 1950 in which they were capable of having a second child.

Let us define N11 through N231 as the numbers of

women in cohorts 1 through 23 who have had their first child before

age 29 in 1949 and N12 through N232 as the niunbers of women in

cohort 1 through 23 who had their first birth at age 29 in 1949. If

these numbers of women are known and the total number of second births

to 30 year old women in 1950, called B , is known, we can write the

following equation in which p is the monthly probability of having a

second birth.

—2 —

c2 23 2 12 2 23

(1) B —N1.(l — p)i/i —

N1(1 — )(24—i)/ji—i 11 j1 i1 j—l i—13 -,

Equation 1 is not easily solved forp in general. However since we know

that p is generally quite small, often around 0.02, a Taylor series

expansion of the terms involving (1 — p) in which we delete all terms above

the quadratic one will yield a good approximation.

In general, we can write

(2)2

We can rewrite equation 2as follows

(1— p)fl (1 — q)+ n(l— q)fl_lq- l)(l -

() - p[n(1 - q)fl_l + (q)(n)(n - 1)(l - q)2]+ 2[()(fl — l)(i. — g)']p

2

Let us make thefollowing definitions:

F(q, a) (1 q)fl + (n)(1 — q)fllq +)(n - 1)(l - q)fl2(g)22

C(q, n) n(l - q)fl + (q)(n)(n - l)(l - q)n2 and

H(q, a) -2

- n-2

0

—26—

Equation 1 may now be written

2 23 2 12

B — N 4[F(q, i/j) — pG(q, i/j) + p2H(q, i/i)]

jw]. i1 j1 i1

223N(F(q,

241) - pG(q, 24 - i) + p2H(q,

24 -

j—li=13 '

Writing equation 5 in the standard form of a quadratic equation we obtain

r2 12 2 23NH(q, i/j) + N..H(q,

24-1)]j=1 i=1 ' j=1 i=13 13 3

r2 12 223(6) + p N.G(q, ifj)

- N. .G(q,24, -

1)j=i. =i j=1 i=13 13 3

2 23 2 12 2 23

+ N. — N..F(q, i/j) — N.4F(q,2 5—B 0.j=i j=i j=1 i=1 j=1 i=13

Equation 6 can be easily solved for p and its solution clearly depends

on the initial value of q which is chosen. In the computation of the

birth probabilities q was initially set at 0.05. After p was computed

by solving equation 6, the new p was introduced as the value of q and

p was computed once again. Through experinentation it was found that the

value of p almost always converged to its true value after two iterations.

—27-.

CThe underlying birth data for the years 1915 through 1946

are implicit in Wheipton (1954), and data for the years 1947 through 1966

are derived from the relevant issues of Vital Statistics of the United

States. The data on the number of women capable of having a birth

of a given order at a given age in a given year and essentially derived,

simultaneously with the birth probabilities. For example, we assume that

women do not give birth to children before the age of 15. Therefore,

once we have computed first birth probabilities for 15 year old women,

we can determine the number of months of exposure to having a second

birth 16 year old women have in the subsequent year. For more details

on this procedure see Sanderson (1974) Appendix A.

0

APPENDIX II

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APPENDIX III

• —1—

TAFLE A—].THE MONTHLY PUBAILITY (IN PERCENT) OF HAVINC A EIPTHNATIVE WHITE WOMEN, 1920—1966, FOR SELECTED AGE GROUPS

FIRST BIRTHS

Y1R 15—19 20—24 25—29 30—34 35—39 40—441920 0.389 :

1921 0.4221922 0.3721923 0.3721924 0.407 0.868 . : .

1525 0.395 0.835 .

1926 0.380 0.8091927 0. 375 0.8061928 0.359 0.7771929 0.342 0.742 0.5561930 0.352 0.759 0.5741921 0.322 0.712 0.5661932 0.305 0.674 3.5351933 0.282 0.625 0.5031934 0.300 0.672 0.534 0.26219.35 0.210 C.701 0.556 0.2791936 0.304 0.705 3.571 0.2941937 0.320 0.731 0.607 0.3131938 0.235 0.762 0.651 0.3411939 0.212 0.743 0.659 0.356 0.1231943 0.202 0.772 0.731 0.372 0.1311941 0.25 0.889 0.796 0.411 0.1451942 0.363 1.106 0.985 0.494 0.173 ,

1943 0.361 1.027 0.896 0.481 0.1821944 0.313 0.919 0.772 0.425 0.180 0.0351945 0.297 0.Rod 0.753 0.424 0.186 0.3371946 0.357 1.231 1.143 0.571 0.224 0.3421947 0.521 1.556 1.389 0.659 0.253 0.0451948 0.516 1.367 1.181 0.547 0.215 0.0401949 0.500 1.309 1.115. 0.533 0.203 0.0391950 0.484 1.245 1.345 0.518 0.190 0.0381951 0.538 1.385 1.109 0.547 0.189 0.0371952 0.536 1.428 1.118 0.562 0.189 0.0381953 0.557 1.445 1.102 0.553 0.187 0.3391954 0.576 1.521 1.106 0.554 0.199 0.0391955 0.575 1.567 1.10€ 0.518 0.202 0.0371956 0.IO 1.666 1.120 0.500 0.198 0.0341957 0.32 1.721 1.154 0.493 0.202 0.0371958 0.612 1.688 1.125 0.473 0.194 0.0341959 0.599 1.674 1.392 0.463 0.185 0.0371S€0 0.75 1.660 1.078 0.456 0.174 0.03719€]. 0.55 1.631 1.067 0.435 0.165 0.0371962 0.530 1.539 1.031 0,413 0.153 0.03519€3 0.516 1.469 1.008 0.408 0.145 0.0331S€4 0.492 1.417 1.052 0.446 0.170 0.04019€5 0.460 1.295 1.001 0.435 0.168 0.037196 0.452 [.295 1.013 3.433 0.158 0.033

—2—

TABLE A—iTHE MflNTHLY PPflE3ABILITY (IN PERCENT) OF HAVING A BIRTHNATIVE WHITE OMEN, 1920—1966, FOR SELECTFD AGF GROUPS

SECOND BIRTHS

YEAR 16—19 20—24 25—29 30—34 35—39 40—441920 3.C771921 3.2411922 3.1661923 3.4341924 3.423 2.6501925 3.74 2.5201q26 3.436 2.4561c7 3.438 2.4121928 3.278 2.2911929 3.260 2.199 1.2011930 3.196 2.226 1.2101931 2.C28 2.151 1.1721932 2.792 2.099 1.1221923 2.791 2.002 1.0741934 2.880 2.104 1.116 0.5731935 2.E45 2.047 1.109 0.5651936 3.026 2.084 1.139 0.5691S37 3.106 2.132 1.135 0.5841938 3.119 2.217 1.202 0.6241939 3.155 2.144 1.199 0.641 0.2341940 3.564 2.212 1.257 0.694 0.2481941 3.593 2.317 1.323 0.729 0.2621942 3.596 2.568 1.503 0.825 0.2911943 3.466 2.720 1.675 0.925 0.3361944 2.€82 2.320 1.534 0.907 0.367 0.0591945 2.604 1.949 1.513 0.981 0.402 0.0631946 3.315 2.688 1.850 1.073 0.427 0.0681947 4.201 2.984 2.071 1.122 0.432 0.0701q48 4.552 2.961 1.947 1.041 0.400 0.0681949 4.61.1 2.964 1.958 1.049 0.387 0.0671950 4.640 3.007 2.014 1.082 0.379 0.0661951 4.608 3.274 2.141 1.122 0.388 0.0691952 4.649 3.504 2.265 1.163 0.393 0.0691953 4.769 3.712 2.335 1.174 0.396 0.0701954 4.c93 3.897 2.444 1.211 0.410 0.0701955 5.C83 4.021 2.517 1.180 0.413 0.0o71956 5.420 4.21) 2.634 1.180 0.407 0.0b91957 5.462 4.370 2.761 1.182' 0.401 0.0651958 5.420 4.342 2.764 1.148 0.387 0.0641959 5.395 4.430 2.763 1.142 0.369 0.0651960 5.478 4.415 2.765 1.147 0.360 0.0641961 5.539 4.354 2.715 1.149 0.359 0.0631962 5.455 4.206 2.638 1.108 0.331 0.0601963 5.C93 4.029 2.531 1.103 0.333 0.091.964 4.649 3.747 2.463 1.082 0.330 0.0541965 4.C97 3.264 2.284 1.037 0.315 O.O'51966 3.589 2.955 2.158 0.962 0.306 0.051

TABLE A—iTtE MONT'-iLY PRflbABILITY (IN PERCENT) OF HtV!NG A BIRTHN4TIVF WHITE WOMEN, 1920—1966, FOR SELECTEP AGF GP)UPS

THIRD 8IRTHS -

YEAR 18—19 20—24 25—29 30—34 35—39 40—441923 5.9961921 6.1551922 5.4151923 5.5951924 4.114 3.4381925 4.121 3.2291926 4C54 3.0721927 4.241 3.0021928 3.931 2.8591929 3.830 2.691 1.3691930 3.157 2.725 1.3601931 3.520 2.612 1.2861932 3.582 2.544 1.2581923 3.394 2.480 1.192j.934 3.567 2.584 1.228 0.6121935 3.688 2.549 1.181 0.5871936 3.834 2.519 1.159 0.567!937 3.985 2.589 1.153 0.5621.938 3.924 2.679 1.203 0.5691929 3.72 2.556 1.174 0.567 0.2501940 5.531 2.650 1.202 0.588 0.2511941 5.C80 2.649 1.221 0.606 0.2571942 4.687 2.665 1.289 0.648 0.2791943 4.977 2.918 1.467 0.761 0.3201944 4.427 2.689 1.423 0.786 0.344 0.0691945 3.469 2.227 1.316 0.809 0.374 0.0751946 4.191 2.536 1.379 0.833 0.384 0.0741947 4.882 2.785 1.469 0.840 0.382 0.0751948 4.887 2.932 1.410 0.787 0.353 0.0731949 5.504 3.032 1.416 0.771 0.345 0.0701950 4.E51 3.017 1.445 0.792 0.342 0.0681951 A.53 3.09o 1.531 0.8J8 0.354 0.0711952 4.çôô 3.123 1.620 0.892 0.376 0.0761953 5.179 3.167 1.641 0.901 0.378 0.0751954 5.536 3.311 1.708 0.911 0.383 0.0791955 5.540 3.300 1.755 0.908 0.384 0.0791956 5,698 3.557 1.812 0.912 0.380 0.07919.57 5.673 3.70 1.882 0.923 0.371 0.0771958 5.586 3.596 1.874 0.906 0.352 0.0711959 5.€52 3.697 1.900 0.893 0.339 0.0701960 5.136 3.729 1.920 0.880 0.325 0.0671961 5.36 3.680 1.896 0.875 0.317 0.0651962 5.591 3.565 1.820 0.829 0.296 0.0601963 4.S79 3.311 1.736 0.807 0.282 0.0571964 4.773 3.024 1.653 0.788 0.275 0.0541965 4.CÔQ 2.512 1.462 0.724 0.256 0.0491966 3.6B5 2.161 1.288 0.655 0.235 0.045

C

—4—

TABLE 4—1THE MONTHLY PRVB.\BILLTY ( IN PFRCFNT) OF HAVING A BIRTHNT1VC WHIE flMEN, 1920—1966, FCJR SELECTr) AGF GROUPS

FOURTH BIRTHS

YFR 20—24 25—29 30—34 35—39 40—441924 4.511925 4.317 .

1926 4.3921927 4.4381S28 4.C90 .

1929 3.885 1.9271930 4.C53 1.9421921 2.E11 1.8621932 3.714 1.3551923 3.64 1.8331934 3.912 1.856 0.8951935 3.975 1.793 0.8501936 4.c,22 1.748 0.8101937 4.196 • 1.751 0.8021938 4.C96 1.799 0.7981929 3.737 1.724 0.784 0.3611940 3.998 1.730 0.804 0.3541941 3.508 1.758 0.819 0.36519(2 3.436 1.737 0.843 0.3781943 3.853 2.011 0.976 0.4371944 3.809 1.948 3.995 0.463 0.1021945 • 3.226 1.718 0.984 0.491 0.1131946 3.49 1.772 0.994 0.488 0.1091947 3.749 1.726 0.965 0.490 0.1141948 3.887 1.658 3.901 0.460 0.1091949 4.260 1.718 0.395 0.446 0.1051950 4.016 1.746 0.901 0.444 0.1061951 4.C71 1.849 • 0.946 0.465 0.1111952 3.47 1.908 1.013 0.489 0.1141953 3.906 1.903 1.026 0.505 0.120194 4.c94 1.938 1.053 0.513 0.1221955 4. 120 1.93 7 1.050 0.537 0.1211956 4.234 1.964 1.051 • 0.496 0.1201957 4.236 1.994 1.052 0.499 0.1221958 4.156 1.976 1.028 0.471 0.1151959 4.308 2.008 1.014 0.460 0.113lSC 4.269 2.013 0.990 0.447 0.108lYél 4.281 1.988 0.975 0.421 0.10619e2 4.C44 1.897 0.909 0.388 0.098lS3 3.708 1.778 0.875 0.368 0.087194 3.367 .1.65? 0.831 0.353 0.082l95 2.827 1.400 0.735 0.315 0.074196 ?.515 1.170 0.639 0.279 0.066

—5—

TALF A—iTI MnNTHLY PRG3ABILITY (TN PCfT) CF 1AVING BIRTHNTIVF WHITE WOMEn, 1920—1966, FOR SELECTED AG GPOUPSFIFTH BIRTHS

YR 21-24 25—29 30—34 35—39 40—441924 3.c591925 3.9161926 4.C311927 3.960

3.9471929 3.926 2.5471930 3.898 2.5681931 3.676 2.4711932 3.691 2.4741933 3.49 2.3971934 3.921 2.494 1.2681)35 3.972 2.449 1.2081936 3. e35 2.370 1661937 3.769 2.427 1.1501938 3.917 2.426 1.1561939 3.804 2.304 1.107 0.5201940 4.605 2.351 1.097 0.5141941 4.463 2.378 1.131 0.5101942 4.400 2.3?0 1.150 0.5201943 4.948 2.632 1.320 0.5921944 4.572 2.483 1.323 0.611 0.1531945 3.808 2.232 1.299 0.651 0.15819'iô 4.289 2.425 1.303 0.653 0.1641947 4.35 2.322 1.243 C.640 0.1661948 4.690 2.243 1.157 0.599 0.1561949 5.513 2.295 1.117 0.586 0.154iso 5.118 2.309 1.118 0.591 0.1551951 4.c57 2.442 1.157 0.604 0.1581952 5.C29 2.505 1.234 0.638 0.1681953 4.936 2.481 1.255 0.642 0.1741954 4.912 2.498 1.293 0.653 0.1841955 4.831 2.438 1.307 0.654 0.1891956 4.736 2.418 1.308 0.651 0.1811957 4.894 2.420 1.292 0.653 0.1781958 4.922 2.368 1.246 0.627 0.1741959 4.869 2.352 1.228 0.627 0.16519f0 4.E86 2.336 1.200 0.606 0.1661961 4.906 2.386 1.169 0.591 0.1621962 4.738 2.240 1.099 0.537 0.1451963 4.17 2.067 1.033 0.502 0.1401964 3.57 1.883 0.955 0.466 0.1271965 3.233 1.566 0.835 0.415 0.118l96 2.809 1.316 0.711 0.357 0.100

0

—7—

TABLE —1THF MONTHLY P ABILITY (IN PERCENT) CF HAVIN( BIRTHNATIVE WF1IT CMN, 1923—1966, F0 SELEC

SIXTH BIRTHSTED AG GROUPS

YFAR 23—24 25—29 30—34 35—39' 43—411

1924 8.1791925 7.481c26 6.651927 6.292 .

1928 • 6.1561929 5.91 3.343190 5.563 3.3811931 5.716 3.2491922 5.558 3.3261933 5.520 3.1361934 5.€33 3.295 1.92219:35 6.439 3•33q 1.82319:36 5.340 .320 1.7371937 5.343 3.407 1.7321c38 6.194 3.311 1.7101939 5.571 3.153 1.665 0.8141940 7.43 3.246 1.665 0.8001941 6.E99 3.319 1.649 0.1831942 6.649 3.110 1.641 0.795 .

1943 7.403 3.424 1.881 0.8761944 6.691 3.289 1.910 0.908 0.2381945 5.409 2.964 1.827 0.930 0.2491946 6.671 3.439 1.895 0.949 0.2481947 6.C64 3.208 1.732 0.934 0.2451948 5.c59 3.195 1.630 0.856 0.232.1949 6.269 3.325 1.593 0.854 0.2201950 5.€45 3.225 1.586 0.836 0.2251951 5.516 3.310 1.605 0.857 0.2401952 5.103 3.301 1.680 0.854 0.2431953 4.808 3.338 1.682 0.866 0.2481954 5.C19 3.273 1.771 0.875 0.2691955 5.277 3.245 1.786 0.898 0.2641956 5.413 3.214 1.796 0.903 0.2651957 5.541 3.163 1.789 0.911 0.2711958 5.254 3.037 1.703 0.897 0.2551959 5.297 3.135 1.702 0.891 0.2551960 5.370. 3.115 1.643 0.855 0.2531961 5.134 3.082 1.614 0.853 0.2381962 4.c84 2.923 1.502 0.770 0.2231963 4.487 2.650 1.409 0.731 0.214L964. 3.867 2.388 1.291 0.663 0.2041965 3.242 1.981 1.106 0.583 0.1761966 2.E16 1.639 3.925 0.493 0.159

• —8—

TA11 A—ITHE MONTI-1LY P#OEAILTTY (IN PERCENT) OF HAVINC BIRTHNATIVE VHTTE WOMEN, 120—1966, FUR SELECTEfl AGE GRUPS

SEVENTH BIRTHS

Yn/R 25—29 10—34 35—39 40—44I92 4.1031930 4.2071921 4.C521932 3.coOI3 3.321934 3.987 2.4311935 4. 121 2.3511936 4.263 2.2791937 4.217 2.298198 4.398 2.3211939 4.196 2.226 1.1151940 4.Il 2.241 1.095I4l 4.579 2.225 1.1051942 4.355 2.237 1.0711943 4.773 2.490 1.2391944 4.655 2.569 1.250 0.3331545 4.C94 2.464 1.313 0.3551946 5.C59 2.478 1.338 0.34515'i7 4.502 2.333 1.277 0.3451948 4.323 2.220 1.178 0.3301949 4.457 2.254 1.16S1 0.3151950 4.400 2.176 1.136 0.3231951 4.358 2.242 1.116 0.3281952 's.225 2.183 1.123 0.3421S3 4.407 2.186 1.159 0.342194 4.537 2.225 1.214 0.3501955 4.494 2.329 1.199 0.3441956 4.381 2.331 1.203 0.3661957 4.365 2.328 1.191 0.371

4.C55 2.267 1.179 0.3561959 4.179 2.215 1.186 0.3631960 4.C'4 2.176 1.155 0.3461961 3.c9 2.126 1.137 0.3521962 3.779 1.978 1.054 0.3201963 3.416 1.842 0.974 0.3021964 2.c84 1.670 0.913 0.2811965 2.443 1.403 0.769 0.2491966 2.124 1.162 0.663 0.218

—9—

TARLE A—iTHE 1OtTHLY PRr),A8jLITY (TN PERCENT) 1F HAVIt\G 4 BIRTHNAT IVF WilliE WIMEN, 1920—1966, FOR .SELFCTE) AG GROUPS

FIGHTH+ BIRTHS

27—29 30—34 35—39 40—441929 4.6571930 4.65119211922 4.7801923 4.7761924 4.936 3.3581q35 5.352 3.3901936 5.796 3.3301927 5.339 3.4501938 5.219 3.4351929 5.C47 3.242 2.1581940 5.33 3.424 2.184191 5.4)4 3.353 2.1691942 5.22 3.266 2.1371943 5.748 3.578 2.3731944 5.133 3.613 2.434 0.8311945 4.689 3.4'i6 2.427 0.8681S46 5.345 3.635 2.618 0.8q91947 5.209 3.593 2.473 0.8941948 4.91 3.497 2.301 0.8241949 5.470 3.583 2.314 0.813190 5.C59 3.438 2.200 0.7821951 4.J53 3.373 2.169 0.7851$2 5.C15 3.362 2.155 0.7561953 4.920 3.317 2.108 0.7551954 4.€23 3.510 2.113 0.7511955 5.116 3.480 2.103 0.7181956 5.436 3.516 2.085 0.7441957 5.394 3.54 2.126 0.7221958 5.343 3.478 2.014 0.6991959 5.124 3.527 2.078 0.706196C 4.E12 3.465 2.050 0.6911961 4.799 3.336 2.017 0.6821962 4.560 3.140 1.894 0.6671963 4.228 2.869 1.783 0.6261964 3.(63 2.563 1.654 0.5941965 3.101 2.126 1.454 0.5271966 2.448 1.824 1.187 0.467

*

—10-

TABLE A-2

Age Coefficients From Component Decomposition Analysis

n.a. = not applicable

* = by assumption.

o

0

0

Age First Births Second Births Third Births Fourth Births

18 —59.810 —47.666 —51.294 n.a.19 —54.489 —43.633 —46.989 n.a.20 —49.382 —39.667 .. —42.729

•

n.a.

21 —44.323 —35.710 —38.454 n.a.22 —39.295 —31.743 —34.195 —33.65223 —34.293 —27.754 —29.898 —29.40924 —29.332 . —23.774 —25.636 —25.19625 —24.402 —19.799 —21.388 —21.029

26 —19.480 —15.843 —17.125 —16.83827 —14.608 —11.863 —12.859 —12.65428 — 9.718 — 7.880 — 8.551 — 8.41429 — 4.875 — 3.951 — 4.295 — 4.23230 0.000* 0.000* 0.000* 0.000*

31 4.775 3.871 4.203 4.13932 9.620 7.801 8.501 9.39733 14.400 11.660 12.723 12.58134 • 19.232 15.541 16.967 16.78435 24.045 19.409 21.198 20.976

36 28.812 23.220 25.391 25.14237 33.578 27.039 29.575 29.29338 38.342 30.857 33.766 33.45239 43.010 34 573 37.853 37.507

—11-

TABLF A—3CU.NT yr crrrrc TENTS FPfl1 i)MP:JNENT UECO4POSI T ICN NALY3LS

YEAR192019211.9221923192 4192 S

I 92 6

1. 927

I 92 81 92 9

1 930

19311932193319:34

193519361 93.7

19381939I 940194113421 343

19441 9451945194719481940195)195 1195?195319541955195619571958195919601961[96219631964[9651966

FIPST 8LTHSI 9 9 • /432

• 493189.34818'4. 307179.3551 74.3071.69.270l4 • 262159.219154.176149.212144 • 176139.135134.073129.149124.209119.243114. 300109.367104.30599 • 43594.553N.A.N.A.N.A.N.A.'1 • A.N.A.60.0315/4 • 99249.95145.02040.04535. 04330.0712 5.0632 0. 070

15.08810. 0535.0260.000

— • 03 3—10.087—15.120—20.061—25.106—30.119

SECOND 8LTHS162.468158.457154.353150.293146.223142.098137.983133.877129. 74112 S, 617

121.556117. 437113.323103.195105. 167101.08797. 02 592 • 97 1

88.95184.88980.87776.854N.A.N.A.N. 4.N.A.N. A.N.A.48.70444.62740.56736.54632. 51428.46724.42720. 36 3

16. 31312.2588.1654.0810.000

—4.081—8. 198

—12.292—16.397—20.548—24.684

THIRD URT.HS FOURTh LRTHS176.214 N.A.171.376 .A.167.300 N.4.162.098 N.A.158.479 N.A.154.050 152.004149.602 147.651145.165 143.323140.131 138.920136.242 134.519131.842 130.197127.385 125.806122.956 121.447118.50! LI7.C6o114.131 112.747109./06 108.367105.286 103.988100.885 99.3496499 95.29992.082 90.92087.736 86.59783.341 82.213N.A. N.4.N.4. N.4.N.A. N.A.N.A. N.A.N.A. N.A.N.A.52.710 51.95248.314 47.2543.907 43.29039.538 39.00035.183 34.70330.791 30.37826.420 26.06622.024 21.72517.637 17.39113.247 13.0648.819 8.6984.415 4.3520.030 C.000

—4.41.8 —4.366—8.868 —8.770

—13.326 —13.169—17.779 —17.570—22.306 —22.C47—26.827 —26.531

—12—

TABLE 4—4ifc T (tE FICT[!rS F'cr COMPONENT DECI1MPOS IT I)N 4NALVS Li

') I

i')3

LI)!

I')'))

1)104 1111

I'U2

1)1419151)161117

• 1918L.)E)192)

19?211231-24192

192719281q291939tt3 I

1')32

10341)3i-

1)3')I

194 1

19"21443I114194')

I qST rTpTHS— [54.c'97— 14). 743—144.761— 139. 7')—134. 740— 129.703—124 • 701.—119. 728—114.74?— 109. 764—104. 78—99. 772—94.771—8° • e08—84.—79 • 876— 74.904—69.939—64.91.9—59 • 838—54.853—49.921—44.9.31—39.922—34.957—30 • 001—25 •006—20.01.!—1 4. 985—9 • 98 1

—4. 9°?0.00)5.018 /

10.061.15.06520.10125. 12830.1.4435. 15240. 16°45. 17150. 16355. 13260.10365.07970.04514.977

SECOND 8IRTrIS—126.207—122 • 19 3—118.139—114. 073— 109.c85—105.91?— 101.830—97.752—93.676—69.595—85.492—81.412—77.353—73.265—69.209—65. 147—61.072—57.017—52.918—48.83144. 78•7—40.764—36. 702—32.626—28. 5.6—24.522—20.458—16.395—12.295—8. 188—4.0850.0004.0328.185

1.2. 248

16. 3 35

20. 41524.49328.51832.55936.72240.73444.83448.86252. 89956.91560.949

THIRD 3ITHS—136.445—132.088—127. 710—123.320—118. 914—114.538—110.1.34—105.131—101.321

—95.920—92.480—88.068—83.67679. 242—74.833—70.428—66. 02 1—6 1. 6 10

—51.203—52.824—48.429—44.026—39. 638—35.230—30.909—25. 500—22.036—11.681—13. 259—8.841—4. 41.3

0.0004.4038.817

13. 22 8

11.65322.0642 6. 479

30.37235.27339.68544.07748.45052.8295 7. 249

61.o1266. 04 1

FCUNTH 8IRTHS— 13'.. 480—1.30.200—125.390—121.548—117. 193—112.853— lOd.. 4t5—104. 175—99.829—95. 144—91.076—86.720—82.375—78. C28—13.682—69. 3.38

—64.968—60.660—56.334—52.052—47.707—43.365—39.043—34. 72—30. 3t5—6.033—21.695—17. .35—13. 030

—8.686_/4. 3440. coo4 • 3533. 704

13. C4517.39521.74726.C9530.41534.74639.06843.365(47.695N.A.'.4.'.4.V.A.

0

o

0

FOOTNOTES

1. The general fertility rate is defined as the ratio of the number

of births to the number of women 15—44, multiplied by 1,000,

2. The data in Graph 1 are from Vital Statistics of the United States:

1968, Volume 1, Natality,

3, The increases in fertility from 1968 to 1969 and from 1969 to 1970

show up not only in the crude birth rate, but in the general fertility

rate as well. The following pattern of recent fertility variations

has been drawn from various issues of the Monthly Vital Statistics

Report, a publication of the U.S, Department of Health, Education

and Welfare,

Year Crude Birth Rate General Fertility Rate

1967 17,8 87,8

1968 17,5 84,8

1969 17,8 86,5

1970 18,2 87,6

1971 17,3 82,3

1972 15,6 73,4

Source; U. S. Department of Health, Education and Welfare, PublicHealth Service, Health Records Administration, Monthl'Vital Statistics Report.

Issues: Vol. 16, No. 13, July 26, 1968; Vol, 17, No, 13, August 15,1969; Vol. 20, No. 13, August 30, 1972; Vol, 21, No, 13,June 27, 1973; Vol. 22, No. 7, Supplement, October 2, 1973,

It is possible that more disaggregated fertility measures such as

age— and parity—specific birth probabilities do not show the 1969

and 1970 increases.

4, See the March/April 1973 Supplement to the Journal of Political

Economy,partlcularly Willis (1973),

—2—

Footnotes (continued)

5. By "native" white women, we mean women born in the United States,

6. Data for the years 1920 through 1949 appear in Wheipton (1954),

Table E. Data for 1950 can be found in Table C,

7. See Wheipton and Campbell (1960), Although birth probabilities were

not published in that report, it laid the foundation for the birth

probabilities which were subsequently published in various issues

of Vital Statistics of the United States.

8. Our estimates are created with a methodology wiich differs from the

original Whelpton procedures in a large number of relatively unimpor-

tant ways. For example, our estimates explicitly take twinning into

account, whereas the Wheipton birth probabilities do not, However,

there is one quite important difference in our methods. We have taken

into consideration the fact that women who have had a child are not

inmediatej.y at risk of bearing another child, The Wheipton methodology

makes no distinction ebtween women who have had births within the

previous year and those who have not, See Sanderson (1974) Appendix A

for a more comprehensive discussion of the methodology used in creating

the current estimates as well as the methodologies used by others.

9. We have not re—estimated birth probabilities for cohorts born in

the nineteenth century. There are a number of difficulty technical

problems involved in doing this which seem to make this data con-

siderably less reliable than the data for twentieth century birth

cohorts. Our estimates stop in 1966 because this is the latest date

Footnotes (continued)

9. (cont'd.)

for which birth data on native white women are published in the

needed detail, Age— and parity—specific birth data for all white

women have, at this writing, been published only through 1968,

Thus even adjusting the white data as best we could would only

give us two extra years of data.

10, For example, see Keyfitz (1971).

11. The birth probabilities presented in this paper have been computed

on the assumption that, neglecting twinning,, a woman mast wait at

least a year between births, While twelve months may be slightly

longer than the average period of gestation and pst—partum aiumenorhia,

using that figure iads in our computations without doing much violence

to reality.

12, Throughout this paper, wesha11 use the phrase 'baby boom peak! to

refer to the highest birth probability in a series during the period

1950 to 1966.

13. These birth probability series are time series of age- and parity—

specific birth probabilities. Thus the 30 first order birth pro-

bability series referred to in Table 1 are for women from age 15 to

age 44. We assume, following Wheipton, that 15 year old women do

not have second births (except for twins) and therefore there are

only 29 series for second births, It is these minimum age assumptions

which cause the number of series to decrease as the birth order in-

creases.

—4-..

Footnotes (continued) . 014. By coherent set of birth probabilities we simply mean a set of

birth probability series with adjacent ages. Thus the birth

probability series of women 20, 21, and 22 would be coherent, in

this sense, but not those of women 31, 35, and 39,

15. The third order birth probability peak for 40 to 44 year old women

occurred in 1954, 1955, and 1956, but the fall from. 1956 to 1957

is so small that for practical purposes 1957 may also be considered

a peak year.- -

16. This article can be found in Easterlin (1968), Chapter 3,

17, Briefly, this hypothesis suggests that adolescents' tastes and

hence ultimately their adult fertility are affected by their

parents standard of living.

18, Above, we have defined m as that cohort which is of age j in year

• • k • Since m and n must differ, it will never be possible to

observe women of cohort n at age j in year k ,

19. See Coale and Zelnik (1963), page 22,

o

REFERENCES

Becker, Cary S., "A Theory of the Allocation of Time," Economic Journal,

75 (September 1965), 493—517.-

Coale, Ansley J. and Melvin Zelnik, New Estimates of Fertility and

Population in the United States, Princeton, Princeton University

Press, 1963.

Easterlin, Richard A., Population, Labor Force and Long Swings in Economic

Growth: The American Experience, General Series 86, New York,

National Bureau of Economic Research, 1968.

Keyfitz, Nathan, "How Birth Control Affects Births," Social Biology, 18,

No. 2 (June 197.1), 109—21.

Michael, Robert T., "Education and the Derived Demand for Children,"

Journal of Political Economy, Vol. 81, No. 2, Part II, March/April

1973, S128—S164.

Sanderson, Warren C., Toward an Economc Understanding of the Fertility

of American Women in the Twentieth Century, Ph.D. dissertation,

Stanford University, pending, 1974.

United Sts Department of Health, Education and Welfare, Public Health

Service, Vital Statistics of the United States, various years,

Washington, D. C., U.S. Government Printing Office.

Wheipton, Pascal K., Cohort Fertility, Princeton, Princeton University

Press, 1954.

Whelpton, Pascal K., and Arthur A. Campbell,"Fertility Tables for Birth

Cohort.s of American Women," Vital Statistics — Special Reports,

Vol. 51, No. 1, January 1960, National Office of Vital Statistics,

Public Health Service, Washington, D. C.