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Discussion

Papers

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Responses of Female Labor Supply and Fertility

to the Demographic Cycle

“,

Evangelos M. Falaris

University of Delaware

H. Eli<abeth Peters

University of Colorado

.

December 1989

~s project was funded by the U.S. Department of Labor, Bureau of Labor Statistics under grant. numkr E-9-J- : 

8-W 1. me research has dso ken supported, in part, by gran~, fmm the University of Delaware Reseamh

Foundation and from the University of Colorado Council on Research and CRative WO~. Opifions stated in ,

tis paper do not nemsstiy represent me official position or ~ficy of the U.S. Depanment of Labr.
Objectives: We establish and

(or baby boom and baby bust ),

.

,,

Executive Summary

measure the relation between the demographic cycle

the timing

timing of their return to work folloving

.

of U.S. vomens, first births and the

tbe first birth.

Methodology : We propose a model according to which women alter the timing of

the first birth and the return to work following that birth in order to mitigate

any adverse effects of the demographic cycle on their wage profiles. The

demographic cycle confronts women with different vage profilee depending on when

they enter the labor market. Consequently, women would have an incentive to

alter the timing of fertility and return to work so as to face a more

advantageous wage profile than would othdrwiae be the case. We test the

predictions of our model using data from three cohorts of the National

Longitudinal Surveys of Labor Harket Experience. The data include information

for women born during clifferent phases of the demographic cycle: 1918-37, 1942-

53, 1957-64. We estimate hazard rate models which permit us to utilize

information on women who have not had a first birth or have not returned to work

a by the latest observation p,eriod slow with information on yomen who have

experienced these events du=ing the observation period. We also control for

.

unobserved clifferences among women which may influence the timing of their first”

●

birth and return to work. We measure the effect of

means of two relative birth cohort size variables.

background characteristics and schooling. We treat

variable.

the demographic cycle by

We also control for family

schooling as a choice
Findings: We find that women who were born during the upswing of the

demographic cycle would have an incentive to have their first birth earlier and

to return to work more quickly (holding schooling constant) than would

were born during the downswing of. the demographic cycle. The findings

the predictions of our economic model.

women who

confirm

Implications: Our findings indicate that women alter the timing of the first

birth and the return to work following that birth in order to mitigate any

adverse effects of the demographic cycle on their wage profiles.
Introduction

Huch of the variation in female life-cycle labor supply across different

mhorts of U. S. women born during the twentieth century has been due to change5

in the age at which a woman has her first birth and in the length of time went

.

not working following childbearing. Two contrasting schools have emerged to

explain the relationship between the changes in fertility and female labor fOrCe

participation aver time: ““”””the mChicago* school (e.g: Butz and Ward, 1979)

focuses primarily on changes in the value of a woman ,s time (i.e. female wage

rates ) and the Easterlin school (Easterlin, 1968 ) focuses on changes in rel~ive

income due to the demographic cycle (i.e. the baby boom and baby bust). In this

paper we utilize idea= from both schools, and we address empirically the issue

of how important the demographic cycle is in explaining the variation in women ,s

ages at first birth and in the duration of time not working following the first

birth. The literature suggests that individuals born in different phases of the

demographic cycle face different potential wage profiles due to exogenous s~fts

in the potential supply of labor. Thus the demographic cycle is the direct

cause of exogenous wage changes which, in turn, alter the labor force

participation and fertility decisions of women.

* Host of the empirical. work done by other researchers has focused on the

consequences of the demographic cycle (and, in particular, the impact of the

baby boom ) for labor market wtcomes--bot h wages and unemployment. That

research has, for the most part, ignored behavioral responses to the Constraints

imposed by the demographic cycle. We suggest that some individuals may be able

to avoid or partially offset any adverse consequences of being born into a large

cohort by altering the characteristics with which they enter the labor markx or

by altering the timing of entry. For example, changes in educational

attainment, life-cycle labor force participation, and for women, the timing of
marriage and fertility

constraints imposed by

2

might be optimal responses

the demographic cycle.

1

to the labor market

,.,.

w In this paper we propose a theoretical model in which women alter the timing

of their first birth and duration of time not working following that. birth in

order to mitigate any adverse effects of the demographic cycle on their wage

profiles. The model utilizes the idea that the demographic cycle confronts

women with different wage profiles depending on when they enter the labor

market. The model predicts that (holding schooling constant) women born during

the upswing of the demographic cycle have an incentive to begin childbearing

earlier and return to work more quickl~ following child, birth than would iwaen

who are born during the downswing- of the demographic cycle. We test the.

predictions of this model and our empirical findings confin the predictions of s.

the economic model.

We estimate hazard rate models of having a

subsequent to that birth. We model the timing

of exogenous family background variables, race,

first birth and returning to work:

of these two events. a- functions

predicted: education, and; ,

measure5 of the size of the mother, s birth cohort; This technique allows. us to 

include observations that are right -censored (i.e. women who have not yet

experienced either a first birth or labor market reetiry ).

We use data from

three cohorts of the National Longitudinal,~Surveys .ofiLabor Market Ex~rience

(Kature Women. Young Women, and Youth 1. ~~~Theserdata contain informatim about :-..

the age at:iirst bifih and the duration between that birth and labor n~rket

reentry for individual women born in various phases.of the demographic ~cle:

1918-37, 1942-53, and 1957-64. We construct- measures. of the detigraphtc wcle

using information from U.S. Vital Statistics.
3

Cohort Size and Demographic Behavior

The connection between the demographic cycle and the timing of the first

birth and labor market reentry following the first birth can be described very

briefly as follows. An increase or decrease in the number of births in a given

.

year will Ehift (in the same direction) the supply curve of labor 18-20 years

later. As long as women with different amounts of labor market experience are

not perfect substitutes for one another, this shift will alter the potential

wage profile facing a woman in that cohort and will alter the relative

attractiveness of home versus market work. The number of potential competitors

in surrounding birth cohorts will also affect the benefits of choosing to enter

the labor market at an earlier or later time. For example, a woman born during

the upswing of the demographic cycle who delays entry into the labor market will

compete with the larger cohort that was born a few years later, but earXier

entry will mean that she will be in the labor market with the smaller cohort

that was born a few years before. The opposite is true for vomen born during

the downswing of a demographic cycle.

There is a consensus in the empirical literature that the present value of

life-cycle wages is smaller for workers competing in large cohorts (see Welch,

1979; Freeman, 1979; Berger, 1985; Hurphy, Plant, and Welch, 1988; and Falaris

and Peters, 1989a). 2’3 Therefore if women do not alter their timing of labor

force participation in response to the demographic cycle, women born closer to

the peak of the cycle would face worse labor market prospects than women born

further from the peak. For example, look at chart 1, vhich gives the

distribution of births over time in the U.S. Women vho are born during

earlier part of upswing of the baby boom cycle (e.g., in 1946) would be

the

faced
4

..

with more favorable labor market prospects than those born during the later part

of the upswing of that cycle (e.g., ‘in 1954). Conversely, for women horn during

the dovnsving of the demographic ~de. cohorts born earlier (e.g., in 1960) ~ .

would face verse labor market prospects than cohorts born later (e.g., in 1968).

A woman may be able to choose a more favorable Iatiormarket cohort and alter

the present value of her lifetime wage stream through two channels: 1 ) the

timing of her first birth and 2) the timing of labor market reentry following

the first birth. Thus women born during the upsving of the demographic cycle

will want to move away from the peak of the cycle and will have an’incentive to

try and join an earlier cohort by speeding UP the tim1n9 Of their first birth

.

and the timing of labor market reentry following that birth. Women born during

the downswing of the demographic cycle will want to move away from the peak of

the cycle by joining a later cohort and thus slowing down the timing of their

first birth and labor market reentry following that birth.4

If there were no : .. ~~

crest= to changing cohort= then thi8 kind of behavior would lead to PerfeCt ,

arbitrage: women would change cohorts until there was no further return to that

activity, and the size of labor market cohorts onr time would be equalized. We

will assume that there are adjustment costs to changing labor market cohorts

which increase with the size of the adjustment, and that there is unobserved

heterogeneity in these adjustment. casts, across

will thus focus on marginal changes. and these

arbitrage may not occur.

different women.

assumptions imply

The analysis , ,.:. .. 

that perfect- ~, ~

In this section we

behavioral responses to

the issues discussed in

present a simple partial equitibr.im model of these

the demographic. cycle. The model abstracts from some. of

the more complex birtb timing models in the economic

literature to focus directly on the possible effects of the demographic
5

cycle discussed above. FirEt, assume that all women will have one child and

that a woman receives utility from lifetime wealth, Z. and from her enjoyment

from the child, K. Utility derived from the child is, in turn, a function of

the mother, s age at childbirth, b, and the length of time the mother spends at

.

home after the child is born, s. Lifetime wealth also depends in a specific way

on s and b, and this will be described later. If we assume for simplicity that

lifetime utility (U) is separable in Z and K then

(1) U = Z(s,b) + K(s, b).

Assume also that child related utility with respect to the timing of child

birth is a function that increases over some range as the age of childbirth

increases and then’begins to decrease ~see figure Z] . This assumption can be

justified if there are costs to having a child too early. For example,

biological and social losses in utility may be higher for teenage mothers than,

for vomen who give birth in their 20,s. Eventually, however, cost= of child

bearing (and the probability of giving birth to a child ,vith serious birth

defects ) may begin to rise as a woman approaches the limits of her “biological

clock. “ Child related utility is also assumed to-rise at a decreasing rate with

the length of time ‘spent at ‘home after’childbirth (see figure 1 ).. This

assumption relates to the idea that mothers receive some benefit from spending

time at home with the child and watching the child grow. Mother, s time is also

. an important input into the production of child quality, especially when the

child is very young.

Choices about s and b also enter indirectly into the utility function

through their effect on wages and lifetime wealth. In this model a women can

receive two types of wages: unskilled and career wages. Unskilled wages (v(t))

are solely a function of the labor market conditions in the current
6

period, t. Because unskilled workers vith different levels of experience are

perfect substitutes for one another, wages depend on the total supply of

unskilled workers in the population and are independent of the size of the ; .?.

unskilled worker, s cohort. Wages in *career m jobs are modeled as a ‘functtin of & ..

years of experience of the worker, E, and the labor market cohort to’ which an

individual belongs, C:

(2) w = w(E, C) where &/~E>O

Note that C represents the date of the cohort along a time line rather than

the size of

demographic

peak of the

born during

that cohort. For individuals born during the upswing of the

cycle, a small increase in C implies joining a cohort closer to the

cycle with lower vage prospects, i.m-, blat < 0. For individuals

.

the downswing of the demographic cycle, a small increase in C

implies’ joining a cohort further away from the peek of the cycle with more

favorable wage prospects’, i.e. , h/at > 0.

To illustrate how individuals may be able to choose their l=bor market .,

cohort we first characterize three distinct types of workers: 1 ) continuous . .

workers; 2 ) traditional mothers; and 3 ) caree~ interrupters. COnt inuous

workers enter the labor market at age m (which is assumed to be exogenous and

6

invariant across’ individuals in different birth cohorts) and work continuously :..

until retirement at age R. The life cycle labor force pattern8 of ma. men and :

of permanently childless women are examples of this type of worker. The labor :

market cohort for these workers is defined as i+m, the date, at...wh~ch a

continuous worker who is born in year. i :enters the labor force. $By ,assumption

continuous workers do not alter their life cycle labor supply in respame to

the demographic cycle.
7

The life cycle labor supply of traditional mothers is divided into three

segments: 1) she works full time prior to the birth of the child (age m to age

b) ; 2) she works zero hours for some period of s years following that birth;

and 3 ) after she returns to the labor force (at age b+s) she works full time

.

until retirement. It is often argued that prior to childbearing women have a

disincentive to invest in on-the-job training, because specific human capital

depreciates during the period of time spent out of the labor force after the

birth of a child. In the extreme, this picture of the “traditional” mother

implies that prior to childbearing she would receive an unskilled or spot market

vag,e, W(t ) and would wait ‘until after the childbearing period to begin a cara.r. -

Her labor market cohort is defined as the date at which she begins a career,

i.b.s, her date of birth plus the age at vhich she returns to work after having

a child. Compared to a continuous worker ehe delays her relevant labor market

cohort by b.s-m years. Thus at any date, t

the same labor market cohort (i.e. have the

continuous worker born in cohort i+b.s-m.

2 i+b.e she is assumed to compete in

same level of experience) as a

Career interrupters are defined as delayed cfiildbearers who first begin ●

labor market career at age m prior to having a child. then drop out of the labor

market for a period of time to have the child, and finally resume their careers

at age b+s. This type of labor force pattern has become more common, in recent

years. Note that at the limit career ‘interrupter become cant inuous workers

when s approaches zero. The wage profile for these women is broken into two

parts --pre and post childbearing -- and each part is determined by a different

labor market cohort. If we make the extreme assumption that there is no

depreciation of human capital during the period of time spent out of the labr
a

..

force, then career interrupters will have the same incentive to invest in onthe-job training, the same rate of return to experience, and the :same early wage

profiles as continuous workers who are born in their cohort., When the career

iriterrupter born in cohort i reenters the labor force at date i+b.s with b-m

years of experience, she has the same level of experience as a continuous worker

who was born in cohort i+s, and she is a member of labor market cohort i.s+m.

Thus all individuals who at any date t have the equal amounts of experience in a

career job are defined to be member= of the same labor market cohort.

Lifetime wealth for the ‘traditional’ life-cycle labor supply pattern where

the true career begins after cb’ildbirth can be written as fdlaws:

i +b _,, , i+b:s i+R

(3) Z =j [v(t) + w(t)ldt +~[v(t)dt +~[v(t) + w(i+b+s, t-i-b-s}]dt ~ ..

i+m i+b i+b+ S

where V (t) represents non-wage income, i+b is the date of childbirth, i.b.s.is .-.-

the date at.which the woman returns to work following childbirth, i.R is the .

date of retirement, and m is the age the woman begins market work (note that. m.

must be less than or equal to b, the age of,chil&irth). Labor supply is equal

to 1 during period of work and O otherwise. For simplicity, the interest rate

is assumed to be zero. In the first term in equation (2) the income a woman ,-

receives prior to childbearing is equal to non-wage income plus earnin9S. fro=’ an

unskilled job. In the second term her.income is just equal to non-wage income, . ;.: 

because she is not working during that:period. During the third :segment of:her 

lifescycle a woman begins a career in which her wage.depends on experience

her labor market cohort. Because her prior labor market experience was .in

unskilled job, we assume that the relevant career experience (the second

argument in the career wage function) ie zero when she begins a career at

and” k ?.

an.
9

date

wage

i+b+s. Similarly, the relevant” cOhOrt (the first ar9ument in the career

function) is the date at vhich she begins her career.

Substituting (3) into the utility function specified in (1 ) we maximize

utility with respect the two choice variables s and b and obtain the following

.

first order conditions:

L+R

(4) w(i+b+s, O) + ~ (b/~E - &/~c)dt = &/~s and

i+b+s

(a) (c) (d)

i+R

(5) w(i+b+s, O) - w(i+b) +’j (&/~E - b/~c)dt = ~k/~b.

i+b+s

(a) (b) (c) (d)

Equation (4 ) gives the conditions for the optimal choice of s. Term (a) is the

opportunity cost of lost career wages from increasing s by one unit. Term (c )

is the cost due to lost experience from increasing s by one unit. The

experience cost is summed over the entire remaining working lifetime of the

woman. Term (d) is the cohort slippage effect of increasing s by one unit.

This term is also summed over the entire remainin~ lifetihe of the woman. As

described above, this term will be negative or positive depending, on whether the

voman is born on the upswing or the do.vnswing of the demographic cYcle. At the

optimum the net marginal cost in’terms of lost lifetime wealth (the left hand

side of equation 4) is equal to the marginal child related benefits from an

increase in 6.

Figure 1 shows the tangency condition implied by equation (4 ) and can be

used to illustrate the effect of the demographic cycle on the optimal choice of

s. For, individuals born on the upswing of the demographic cycle the cohort

slippage effect ie negative (*/~c < 0) which leads to an increase in the wealth
10

related marginal cost of more s. For these individuals the tangency will occur

at a steeper part of the marginal benefit cur,ve and produce an optimal .= at a

point like Su. ,For individuals born. on the downswing of the demographic; VCle

the cohort slippage effect is positive, the marginal wealth cost is lower, and

‘d is greater than Su.

The choice of the timing of child birth can be analyzed in a similar way,

In equation (5 ) the marginal effect of b on wealth contains terms which capture

the experience cost (c) and cohort slippage effect (d) discussed above. The

remaining terms represent the difference between the unskilled wage a woman

would receive just prior to childbirth and the beginning career wage she would ‘

receive after reentering the labor market. This net marginal cost (benefit ) in

terms of wealth is set equal to the marginal child related benefit (cost) from

increasing b. As before the cohort slippage effect for wome; born during the

upswing of the demographic cycle is negative, increasing marginal wealth cost=

(or reducing marginal benefits). The tangency condition vould lead to a choice

of b euch as b~ in figure 2. h positive cohort slippage effect for womem born

during the downswing of the demographic cycle would reduce marginal wealth

costs and lead to a choice of birth timing such as bd where b~ > bu. ,.

Lifetime wealth for a career interrupter can be written as follows:

i+b i+b+s i+R

(6) Z -~ [v(t) + w(i+m, t-i-rn))ldt +j[v(t)dt +~ [v(t) + w(i+m+s, t-i-s-m} ldti

i+m i+b i+b+s

As desmibed above, the career v=ge path for these women is

parts and.each part is governed by z different labor wrket

Substituting (6) into the utility ‘function specified in (1)

.

broken into ::tva,

cohort. ,

and maximizing

utility with re8pect to s, we find that the first o,rdercondition for the
11

optimal choice of s is identical to equation (4). Career

the upswing of the demographic cycle have an incentive to

their labor market reentry following childbirth and women

interrupters born on

speed up the timing of

born during the

downswing of the cycle have the opposite incentives regarding s. Interestingly,

we observe that the birth timing decision, b, does not enter as a determinant of

the cohort argument in the wage function. Therefore the demographic cycle will

have no effect an the timing of childbirth for women who can be characterized

career interrupters.

The analysis presented above implies that choices about the timing of

reentry to the labor market can be used by all types of women to alter their

as

labor market cohort, but that the effect of the timing of childbearing on labor

market cohort depende, in part, on how we treat pre-childbearing labor market *’

experience. We have described two extreme cases. For the traditional mother

none of the pre-childbearing market experience counts, and upon reentry she 1s

considered to be the same as a brand new entrant. The longer she delays

childbearing and the beginning of her career, the greater is the cohort slippage

effect. For the career interrupter all the pre-chtidbearing experience count=,

and when she reenters the market she competes with a group of individuals who

. have the same labor market experience that she had when she first left the

market. Thus the delay in her career and the cohort slippage effect is solely a

., function of the length of time she spends out of the labor force after

childbearing. In general many vomen are likely to be some combination Of 0~

two extreme cases. Some years of effective experience may be lost due to

depreciation of specific human capital while out of ,the labor force. Upon

reentry this woman will be competing with a group of individuals who have

slightly less experience than she had reached just before dropping out of the

labor force. If the extent of this depreciation is a positive function of the
12

amount of her pre-childbearing experience, then birth timing decisions may to

some extent be able to affect the choice of labor market cohort for career

interrupters.

To summarize the empirical implications of the model, we predict that women:..

born during the upswing of the demographic cycle vi11 have their births earlier

.

and will return to work more quickly. Women born during the downswing uf the

demographic cycle will delay their first birth and their labor market reentry.

We also expect the response of the timing of labor market reentry to the

demographic cycle to be larger than the response of birth timing.

7

The delayed childbearing of the baby boom generation might, on the surface,

seem to contradict the hypotheses proposed above. Baby boom women, however, are

~ ..

also getting more schooling (Falaris and Peters, 1989e, b) which tends to :be

associated with later childbearing. This educational effect could partially or ... .

totally offset any tendency towards earlier childbearing associated with the

woman, s position in the demographic cycle. Our theoretical model takes

schooling decisions and the age of labor market entry as exogenous. In our

empirical work ve utilize results from our previo~s paper to account far the

endogeneity of schooling choices, and we disentangle the marainal effect .&

cohort size on age at first birth (i.e. conditional on predicted education) from

tbe t= effect which includes the offsetting schooling and:cohort wage ;

effects.

In the econometric specif ication of age,ak first birth and :,timing”of labor, ..

market reentry we control for the effect. of exogenous ifamil~ background :

characteristics, education, and relative cohurt size. : In other liter.atur.e

several kinds of measures have been used to -pture.: the effects Of the.

demographic cycie: 1 ) number of individuals born in a given year (own birth
13

cohort ); 2 ) an indicator of the part of the demographic cycle during which an

individual is born, e.g., the beginning, peak, or end of the cycle (relative

cohort size ); 3) number of labor force participants in a given year (labor

market cohort ). In the empirical work we use the second measure for two

.

reasons. First, this measure can be regarded as exogenous from the point of

view of the individual. In contrast, measures of labor market cohort used by

Welch (1979), Berger (1985), and Freeman (1979) are, in our specification,

choice variables. Relative cohort size is also more appropriate than absolute

cohort size in a model that focuses on the timing of fertility and labor market

reentry. It is the number of individuals born just prior and after one, s own

cohort that determines how easily a woman can alter the labor market

OPPOrtunlties she faces by changing the timing of demographic behavior such as

first birth. We represent relative cohort size by two variables, past and

future cohort size.

preceding (past) and

(7) Past= (I/S)

These are defined as the ratios of own cohort size to

subsequent (future ) cohorts, each averaged over five years:

5 coh 5 cohi 1

E ---------; Future= (US) E

---------

j=l coh i-j j=l cohi.j

For individuals born during the upswing of the demographic cycle,

greater than one and Future is less than one.

individuals wbo are born during the dowriswing

Household production theory predicts that

Past is

The opposite is true for

of the demographic cycle.

non-wage income (e.g. hu5band ,s

income or other family income) should affect the value of home time, and, as a

consequence, age at first birth and the timing of labor market reentry. We da

not control for income for the following reasons. First, income varies over

time, and Heckman and Singer (1984a) state that hazard rate estimates are
14

sensitive to the specification of the discretization of time-varying covariates.

Secondly, whether or not to marry and who to marry are choice variables, and

these choices may also be influenced by the constraints imposed ,by the

demographic cycle. Inclusion of these endogenous variables will produce

inconsistent estimates of the age at first birth and t+ming of labor market

reentry. Eodeling these marriage choices explicitly is beyond the scope of this

paper. In our specification, the effect of these marital choices will thus be

captured indirectly through family background variables and cohort size which,

in part, determine marital choices.

.

Data and EmQirical Estimation

We estimate the model for the timing of..the first birth using observations

on 10, 386 u. s. women born from 1918-1964. The observations are drawn from three

cohorts. of, the National Longitudinal Surveys of Labor Market Experiena..(Hature

Women, Young Women, and Youth). These cohorts are nationally representative

samples of women born during the downewing of the demographic cycle OL the , ....

1930 ,s, the upswing of the demographic cycle of the mid 1940,s-1957 (the baby

boom ), and the downswing of the demographic cycle following its peak in 1957

(see Chart l).”-”70 percent of the women in the sample have had a first bitih

before the end of the observation period (although only 55:percent of the women 

in the youth cohort had a first birth, so for that sample the right censoring is

more severe ). We estimate a hazard model to study the effect of the demographic ; 

cycle. on the interval from age 12 to a woman, s age at her first birth :(the first

birth interval ). If we assume that the first birth interval~ T, ha~:the

extended generalized gamma distribution. then the log of the :first birth

interval can be written as Y = log (T) = 8X + aW, where X is a matrix of
15

regressors, fiis a vector of parameters (including a constant), u is a scale

parameter, and W is a random variable which has the extended generalized gamma

distribution (Lawless, 1962, p. 240). The density function of W (note that

W = (Y- BX/a) is

~-2

(8) ‘(w’ “)=~~fiy ‘a-z) exp(=-z(aw-exp(aw))

-m<”<e

r is the complete gamma function and u the gamma shape parameter. This

distribution nests the gamma, lognormal, Weibull, and exponential distributions

as special cases. We ,can test this more general distribution against the

special cases by imposing restrictions on the parameters a and u testing them

statistically. To use both censored and uncensored observations (i.e. women who

have not had a first birth by the most recent observation period, but who are

“likely to have a birth sometime in the future) we s?ecify the following loglikelihood function:

(9) iogL(S, u, a) = Z (logfi(w, a) - logu) + Z (log(l-Fi(w, a)))

iCB iGc

where f (.) is the density function, 1-F(. ) is the survivor function (the

complement of the CDF of W), B denotes completed or uncensored first birth

.

intervals, and C denotes censored first birth intervals.

Using maximum likelihood methods we estimate the parameters a, B, and a,

and we test the restrictions on a and a. Likelihood ratio tests indicate that

the more general extended generalized gamma model is the correct model. Tables

1 and 2 report summary statistics, definitions of the variables an~ years of

last observation for each data set. Estimates of the model for the first birth

interval, conditional on schooling, are reported in Table 3.
16

The regressors i;clude exogenous individual family background

characteristics, two relative cohort size variables and predicted” education. In

this model education is an endagenous variable which is affected by relative

cohort size (see Falaris and Peters, 1989a,b, for a justification of this

treatment ), so we replace that variable by its predicted value to obtain; .

consistent parameter estimates. Predicted education is obtained by using the

coefficient estimates of the ed.”cation eq”atian for women which is reported in

Appendix Table 1 (this is similar to the education equation reported in Falaris

and Peters, 1989a, except that here we include Mature Womei’s data as well as

data for younger women ). The identifying restriction is that her parents,

.

educational attainments are assumed to affect a woman ,s educational attainment

s

but not her first birth interval (except indirectly through education). In

Appendix Table 2 we report estimates of a model for the first birth interval.

which contains only exogenous regressors and thus requires no exclusionary

identifying restrictions.

In our previous paper we found that a woman vould increase hef educational ~

attainment in response to a baby boom. Our resu~ts indicated that cohort size

affects educational choices by altering the relative rate of return to education

.,

for ~ndividuals born during different phases of the demographic cycle. In 

contrast, in the theoretical model presented above, cohort size operates on

fertility primarily through its effect on the timing of fertility. We

hypothesize in the present study that, conditional on education, a woman born . .. ‘.:

during the.upswing of the demographic cyc~ would shorten the first birth” ,,.

interval. It is unclear what sign the relative cohort size coefficients should K, ,.

have in the reduced form, since they capture two opposing influences.. The :first ..

birth model which is conditional an schooii”g allows us to test tbe ex~ence of

a Pure demographic cycle effect on the timing of the first birth.
17

The main results in Table 3 are that an increase in a woman,s education

increases the first birth interval (see Bloom, 1982, for similar results), and

that both future and past relative cohort size significantly affect the first

birth interval. In particular, being born during the upswing of the demographic

*

cycle (Past > 1 and Future < 1) has the marginal effect of shortening the first

birth interval. Conversely, for individuals born during the downswing of the

demographic cycle (Past c 1 and Future D 1 ) the first birth interval is longer.

These results are consistent with the hypothesis that one of the ways in which

women attempt to mitigate the adverse effects of.a baby boom on their wages is

through the timing of fertility. In Appendix Table 2, the relative cohort size

coefficients have the same signs as the structural ones but are smaller in

absolute value and only one is significant. This result is not surprising since

the relative cohort variables capture two opposing influences.

According to the estimates in Table 3, a vhite woman

longer first birth interval than a nonwhite woman. This

with other evidence on the relationship between race” and

is predicted to have

result is consistent

age of childbearing

(see, e.g., Bloom, 1982). The results also indicate a negative relationship

between the number of siblings a woman has and the length of her first birth

interval. Thinsresult could be due to a correlation in family size across

generations. If women with a large number of siblings also have tastes for a

larger family, they will begin their childbearing at an earlier age. We S1s0

estimated a similar model which included a trend variable. Its coefficient

was not significant at the ten percent level, so the trend was omitted.

Table 4

measured in

distinguish

reports estimates of the return to work model. The time interval

months from the first birth until the return to work. We do not

between being out of the labor force and being unemployed but treat

a

is

them as a common state (not working). We use data an the 6,321 women who have
18

had a first birth and for whom it is possible to calculate the return to work

interval. The proportions of women who have.returned to work by the end of the

observation per,iod are 67%, 78X, and 80% for the mature women, young women and

youth, respectively. The mature women were asked a retrospective question on

the timing of their return to work following their first birth at the beginning

8’”” of the survey. For the young women and youth subeamples we use employment

history information to calculate the return to work intervals. 9

In all three

surveys some women report that they never etopped working after their first

birth (most of these vome” probably were on a brief maternity leave and returned

to work for the same employer). We assign a value of one month to these

intervals so we can calculate their natural logarithm. We estimate positive and

negative coefficients for Future and Past relative cohort size variables,

respectively. This indicates that women born on the

cycle tend to shorten their return to work intervals

downswing of the demographic cycle do the opposite.

upswing of the demographic

while women born during the

Our estimates confirm the

predictions of the model in the previous section. White women and women ~a

grew up in ,urban areas tend to return to work later than other women (these may

reflect income effects ), and there is a strong negative trend (implying shorter ~: .. 

return to work intervals). We find no significant effect of’predicted

education.

In Appendix Table 3 we report estimates.:of a rekurn to work model which

contains only exogenous regressors and thus: nee& no -dusionan,y identifying : .

restrictions of the sort required for the model which is: conditional ‘on:

.

schooling. The estimate= are generally highly similar to those in Table. 4. The

coefficient estimates for Future and Past Relative Cohort Size are tiithin one ::

standard error of the corresponding estimates in the two’tables.
19

Heteroqeneitv

Two observationally identical women may have different first birth (return

to work) intervais because they differ in ways which are not observed by the

investigator (unobserved heterogeneity). Neglecting such unobserved

.

heterogeneity may result in biased coefficient estimates of the statistical”

models such as ours even if the heterogeneity is uncorrelated with the

included regressors of the models (Heckman and Singer, 1984a). Some previous

studies (e.g. Lancaster, 1979; Even, 1987 ) have modeled heterogeneity as

foliowing some parametric distribution such as gamma or beta logistic whose

parameters can be estimated from the data. Heckman and Singer (1984a, 1984b )

have argued that the results in these studies are highly sensitive to the

distributional assumptions about heterogeneity and have proposed a method of

controlling for heterogeneity which imposes very weak distributional

assumptions. Their method, minimizes the impact of distributional assumptions

on the estimates of the model.

We implement the method of Heckman and Singer as follows. We assume that

the first birth interval (return to work intervall- is Y ❑ log(T) ❑ ei + flX + aW,

(8 does not include a constant term) where ei is a parameter (constant term)

drawn from a discrete distribution with points of support 91, 82,.... ex and

. associated probabilities P~, P2, ..., PK (the Pi sum to one). In other” words

the probability is Pi that- an individual drawn from the population at random

will have a constant term 8..

1

Controlling for heterogeneity, the likelihood function becomes

(10) logL(. ) = Z (log($ Pjfij (.)) - logs) * Z (log($ Pj(l-Fij (.))))

iEB iEC
20

.

where j indexes the points of support of 8. We treat as an empirical matter how

mahy points of support e will be specified. as having by estimating models .in

...

whic~ we increase the number of points of support until there

increase in the value of the log-likelihood. Thus we spec>fy

first birth interval with three points of support for e and a

return to work with four points of support. The estimates of

is no si~ificant

a model for the

model for the

these models are

,

10 reported in Tables 5 and.6 . For both models the value of the log-likelihood

is much higher than in the corresponding models without het~rogeneity in Tables

. .

3 and 4. ‘A This indicates the presence of significant unobserved. heterogeneity.

.

The estimatee of the slope coefficients, however, do not differ very much ii the

specification with and without heterogeneity. The estimates of the coefficients

of future and pa=t relative cohort size are within one =tandard error OS each

other in the models which allow for heterogeneity and.those

the first birth and return to work models.

It is instructive to look at some predictions obtained

of this model which allows for heterogeneity. The weighted

that do not for both

using the parameters

survivor function,

$ Pj (l-F(t) ), gives the predicted proportion of vomen who have not had a first

birth by age t. This statistic is the simplest vay to illustrate the impact of : = 

cohort sizs an fertility decisions. We can compare the weighted survivm 

function c~culated using our estimated coefficients for observationslly 

identical. amen born @uring different phases :of thw’demographic cycle. For. a

woman with sample mean characteristics who was born: in,1951 (during the .upsvi~

of the demographic cycle) the value of the survivor- function at age 24.3 is

0.499. This means that we predict that 49.9 percent of ‘these women have not had

a first birth by the age of 24.3 (this age i= chosen because it is the mean age

at first birth in the sample). For a woman vlth mean characteristics born in
1964 (during the downswing of the demographic

survivor function of O. 535. Fewer vomen born

demographic cycle have not had a birth by the

cycle ) the predicted value of the

during the upswing of the

age of 24.3 (i.e. the first birth

interval is shorter) relative to women born during the downswing of the

demographic cycle. These survivor functions are depicted in Chart 2. Chart 3

presents survivor functions for the return to work following the first birth for

women with sample mean characteristics born in 1951 and in 1964, respectively.

In evaluating these survivor functions we abstract from trend effects by setting

the trend equal to its sample mean. The results are similar to those obtained

for the first birth interval. At 3.s years since first birth the value of the

survivor function is O.510 for women born in 1951. For women born in 1964 the

predicted value of the survivor function is O.556. Thus we predict a shorter

return to work interval for women born during the upswing of the demographic

cycle than for women born during the downswing of the demographic cycle.

Conclusion

In this

of the first

mitiga”te any

paper we propose a model according t- vhich “women ~lter the timing

birth and the return to work following that birth in.order to

adverse effectq of the demographic cycle on their wage profiles.

We predict that women who were born during the upswing of the demographic cycle

would have an incentive to have their first birth earlier and to return to work

more quickly (holding ‘schooling constant) than would women who were born durfig

the downsving of the demographic cycle. Our empirical evidence confirms these

predictions.
The behavioral responses to the demographic cycle described in this paper

have implications for the dramatic “changes that have occurred over the past few

decades in the Labor force participation rates Of mothers with young children.

Some of the increase in these ra”tes during. &he later 1960s and 1970s.,can.be

explained by the incentives to return. to work more quickly for vomen who wme

born during the upswing of the demographic cycle. Our results indicate,

however, that the increase in participation rates during the 1980s might well

have been even larger if women born during the downswing of the demographic

cycle did not have incentives to delay their return to work following

childbearing.

.
Endnotes

1. In previous research (Falaris and Peters, 1989a,b) we focus on

educational choices--both the timing and level of educational attainment. In

that research we find that both men and women alter their schooling in response

to the demographic cycle. In addition, we find that the increase in schooling

in response to the baby boom mitigates the adverse direct effect of cohort Size

on wages. The magnitude of the educational response and the extent of

mitigation due to this response, hovever, is much larger for men than for

women. The puzzle posed by this last result of our previous research is the

etarting point for this paper. Why is the effect smaller for women than for

men ? We suggest that women have additional behavioral responses to the

demographic cycle that are less available for men. In particular, patterns of

labor force participation are more variable for women than for men; women can

alter their life-cycle labor supply through changing their number of children,

the timing of childbearing, and the timing of reentry to the labor market

following the birth of a child.

2. There is still, however, some debate over the size of the cohort penalty

over the life cycle. Berger (1984, 19a5 ) argues that wage profiles are also

flatter for workers in large cohorts. Thus the cohort penalty increases over

the life cycle. Hurphy, Plant, and Welch (19aa ) make the opposite argument.

3. Because most of the evidence on cohort 5ize and wages is for men, there is

as yet no clear consensus about the effect of the demographic cycle on female

wages. Freeman (1979) finds no effect of cohort size for women. Using more

recent data, however, Falaris and Peters (19a9a ) do find a significant

effect of cohort size on women, s wages.

4. This basic timing argument was first proposed by Wachter and Wascher

(19a4). They apply the argument to decisions about schooling. In our previous

work (Falaris and Peters, 19a9a,b) we find evidence that individuals do alter

schooling choices in response to the demographic sycle, “but that the timing of

schooling is not the primary response.

5. See, for example, Razin (19aO) and Newman and HcCulloch (19a4). We ignore

issues of consumption smoothing, spacing of births, and the interaction of

timing with the demand for numbers of children.

6. In our empirical work we relax this assumption by treating schooling as .

endogenous.

7. ‘Some women vill have more than one birth. The general implications of our

economic model may hold in these cases also. Data on spacing of subsequent

births and female life cycle labor supply, however, are not available over a

long period of time. Therefore, we do not deal with these issues.

a. However, 99% of all first births to these vomen who are in our fertility

sample had taken place by the beginning of the survey so the amount of

information lost by ignoring return to work intervals for births occurring after

1967 is quite small.

9. For the young women we can do this only for the period 196a-1983.
10. We do not” report standard errors for the model in Table 5 because of

numerical difficulties in their estimation. The standard errors in Tables 5 and

6 are evaluated numerically because of the great complexity of the analytical , ...

derivatives. In these cases it is possible that the numerically evaluated .

hessian may be singular at the function optimum making it impossible to obtzin

estimates of the standard errors of the parameters. This occurs for the model

in Table 5 but not for the model in Table 6. We attempted to estimate the model

in Table 5 using a variety of alternative optimization computer programs: the

function minimization routines of LIKDEP; a variety of algorithms of G90PT;

the hessian approximation subroutines in both the IHSL and NAG libraries. In

all cases the estimated hessian was singular. In any case, the (pofnt )

estimates of the slope coefficients in Table 5 do not differ very much from

those in Table 3.

11. A likelihood ratio test is not applicable in this case because it would

involve testing ‘a restriction on the boundary of the parameter space.
Table 1. Heans and Standard Deviations of the Variablesa

Variable Hean Standard Deviation

Time to First Birthb 147.342 77.341

White 0.763 0.425

Father, e.Education 10.044 4.053

Mother, 5 Education 10.360 3.308

Predicted Education 12.494 1.360

Urban 0.743 0.437

Siblings 3.689 2.682

Future Relative Cohort Size 1.019 0.072

Past Relative, Cohort Size 1.021 0.075

Time to Return to Workc 43.063 55.408

‘The summary statistics of all the variables other than Time to Return to

Work are based on the sample used for the estimation of the model for the

first birth interval.

b

Time in months from

have not had a fir=t

the last observation

statistics.

‘Time in months from

have not returned to

the last observation

statistics.

age 12 to the time of the first birth. For women who

birth by the end of the observation period the time of

IB included in the calculation of these summary

the first birth to the return to work. For women who

work by the end of the obsematlon period the time of

is included in the calculation of these dummary
Table 2. Variable Definitions and Years of Last Observation for Each

Data Set.

A. Variable Definitions

White 1 if white and O otherwise

Urban 1 if a woman lived in an

urban area at age 14 (Young

Women, Youth ) or age 15

(Hature Women ) and O otherwise

Father, s Education, in single years

Mother, s Education

Predicted Education prediction obtained using

each individual, s

characteristics and the

parameters of the education

equation for women reported

in Appendix Table 1

Future Relative Cohort Size defined in the text

Past Relative Cohort Size defined in the text

Prewar

Postwar

Trend

B. Years of Last

Hature Women

Young Women

Youth

1 if born before 1945, 0 otherwise,- .’

1 if born in or after 1945, 0 otherwise (

time elapsed between 1900 and a womm’s

year of birth

Observation

First Birth Return to Work

19e2 1967

1985 1983

1987 1987

Note: these dates are upper bounds for the,data sets. Some individual women

dropped out of the survey at earlier dates which are known.
(t-statistic) (20.061)

White O.215**

(14.835)

Predicted Education o.105**

(19.552)

Urban 0.002

(0.126)

Sibling8 -0.004.

(-1.690)

Future Relative 0.308..

Cohort Size (3.3531

Pact Relative -o. 158*

Cohort Size (-1.803)

Scale Parameter (u) 0. 5a5~.

(115.9al )

Gamma Shape Parameter (u) -o. 513**

(-23.006)

Log-Likelihood -86aa.232

Sample Size 10, 3a6

● ● Significantly different fram zero at the 5 percent level

● Significantly different from zero at the 10 percent level

.
Table 4. Haximum Lik~lihood Estimate= of the Extended Generalized Gamma Hodel

for the Return to Work Interval Following the First Birth, Conditional

on Schooling.

Constant

(t-statistic)

White

Predicted Education

Urban

Siblings

Future Relative

Cohort Size

.

Past Relative

Cohort Size

Trend

Scale Parameter (u)

Gamma Shape Parameter (a)

Log-1ikelihood

Sample Size .-..

5.303**

(7.906)

‘o.338**

(6.310)

-0.002

(-0.101)

o.151**

(2.911)

0.014

(1.s09)

. 0.82s..

(2.09s)

-o.aaa..

(-2.399)

-o.04a..

(-20.745)

1.670**

(65.03a)

o. 223*.

(3.794) -

-1073s.147

6,321

.:-

.● Sign ificsntly clifferent from zero at the S percent level

. Significantly different from zero at the 10 percent level.
Table 5. Haximum Likelihood Estimates of the Extended Generalized Gamm”a K6dei

for the First Birth Interval, Conditional on Schooling, with

Heterogene&ty.

Predicted Education

Urban

Siblings

Future Relative

Cohort Size

Past Relative

Cohort Size

01

e2

‘3

‘1

‘2

Scale Parameter (a )

Gamma Shape Parameter

Log-Likelihood

Sample Size

o. 10s

0.009

-0.004

0.337

-o.la8

3.098

2.S77

3..295

0.24S

0.013

0.s7a

(ai -0.711

-a632.S67

10,”386
Table 6. Haximum Likelihood Estimate8 of the Extended Generalized Gamma Model

for the Return to Work Interval Folloving the First Birth, Conditional

on Schooling, with Heterogeneity. ,

White 0.220.. Pi

.,. 

0. 106**

(t-statistic)

Predicted Education

Urban

Siblings

Future Relative

Cohort Size

Past Relative

Cohort Size

Trend

‘2

e3

(5.297)

-0.003

(O.162)

o. 105**

(2:808 )

0.008

(1.116)

0.470.

(1.661)

-0.764**

(-3.163)

-0. 039..

(19.909)

7.370**

(14.343)

6.130*.

(13.283)

4.430**

(9. 751 )

2.500..

(s. 558 )

-10548.24

6,321

(3.113)

P2 o. 405*9

( 14. 878)

‘3 o.”325*-

(27.167)

Scale Parameter (a) O.621**

(38.055)

Gamma Shape O.160.

Parameter (a) (1.753)

Log-Likelihood

Sample Size

.....

● ● Significantly different from zero at the 5 percent level ,:

. Significantly different from zero at the 10 percent level
.

.

Appendix Tsble 1. Ordinary Least Squares Estimates of the Education Equation.

Dependent variable: years of schooling completed.

COnst ant 8.057**

(t-statistic) (13.580)

Father, s Education o.144**

(17.788)

mother, s Education 0.211..

(21.959)

White . Prewara 0.370. ●

(3. 997)

White ● Po@tvarb -o.394* ●

(-5.145)

Siblings -o. 095**

(-10.255)

Urban ● Prewar o. 445**

(5. 473)

Urban * Postwar 0.019

(0.264)

Future Relative -0.621.

Cohort Size (-1.699)

Past Relative 0.891**

Cohort Size (2.433) -

Poetwar 1.249**

(9.599)

~z 0.302

N 8,253

aThe variable Prewar takes the value 1 if a voman was born before 1945, 0

otherwise.

b

The variable Postwar takes the value 1 if a

otherwise.

.. Significantly different from zero at the

● Significantly different from zero at the

woman was born in or after i945, O

5 percent level.

10 percent level.
Appendix Table 2. Maximum Likelihood Estimates of the Extended

Generalized Gamma Hodel for the First Birth Interval,

not Conditional on Schooling.

Constant 4.176..

(t-stati6tic)

White

Father, s Education

Mother’s Education

Urban

Siblings

Future Relative

Cohort Size

Past Relative

Cohort Size

Postwara

Scale Parameter (c )

Gamma Shape Parameter

Log-Likelihood

Sample Size

(25.623)

o. 191**

(12.988)

0.018..

(8. 796)

.0. 020**

(8. 113)

0.018

(1.348)

“ -0.014**

(-s.938)

-

0.240**

(2.549)

-O.0S6

(-0.604)

0.032**

(2.189 )

o. sas+~

(115.740) -

(a) -o. S05**

(-22.77a)

-8688. 03s

10,386 

- . . .. 

al if a woman was horn in 194S or later, O otherwise.

.* Significantly different from zero at the

● Significantly different from zero at the

5 percent level:

10 percent ,level . ,.
.

.

Appendix Table 3. Kaximum Likelihood Estimates of the Extended

Generalized Gamma Hodel for the Return to Work Hodel,

not Conditional on Schooling.

Constant

(t-statistic)

White

Father ,s Education

Bother’s Education

Urban

Siblings

Future Relative

Cohort Size

Past Relative

Cohort Size

Postwar

Trend

Scale Parameter (a)

Gamma Shape Parameter

Log-Likelihood

Sample Size

(a)

5.701**

(7.982)

o.338**

(6.251)

0.016..

(2.07s )

-0.030..

(3.322)

o.1s1..

(2.943)

0.011

(1.1931

0.796**

(2.002)

-1.044..

(-2.348)

0.110

(0.668)

-o.0s1 ● *

(9.780) -

1.666..

(64.489)

0.232**

(3.921 )

.-10729.363

6.321

.● Significantly clifferent from zero at the S percent level

● Significantly different from zero at the 10 percent level
./’

Jpswing

I

(6w/3c < o) I

I

I !

1“ I

1,1

I

●

s

u ‘d

s

K

/

Figure 1. Child Related Util ity of Time at Home

and the Optimal CWice of s.

,.

..

,..

I

I

I

I

I

I

I

I

!.

—b

bu bd

Figure 2. Child Related Util ity of Birth Timing

and the Optimal Choice of b.

..:

.,

...
s

,

.

. .

$.

-..

.

. .

-.

.
I]roportion of

Chart 2

Women with no First Birth

1

,0.9

,0.8

0,7

0:6

0,5

0.4

Q,3

0,2

0.1

0 L~------

12 16 20 24 28 32 36 40

— Born itl 1(1!)

-- Bo rri itl 1!.~(,

!.

‘,,

Age ,,, !

1,I!!ote: ‘rIlk proport~~n,s’laregevall!at~(ll)oldjn~back~rotlndcllaracteriaticsconstant (a; the “s~mple rneari~)
m

●

.

I ,i, l, 1, ,1,, !, !,!
.

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— -- . .

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