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The E¤ects of the 1978 Pregnancy Discrimination Acton Female Labor Supply
Sankar Mukhopadhyay1 2
1Department of Economics, University of Nevada Reno, Email: [email protected] would like to thank Jere Behrman, Elliot Parker, Frank Schor�de, Petra Todd, Jeanne Wendel,
and two anonymous referees for many helpful comments. Finally I would like to extend specialgratitude towards Ken Wolpin for his advice and help throughout the project. Any remainingerrors are my responsibility.
Abstract
This paper analyzes the e¤ects of the 1978 Pregnancy Discrimination Act (PDA) on the
labor force participation rates of married women. This paper develops and structurally
estimates a dynamic model of labor force participation. Model simulations show that the
PDA increased the labor force participation rate of pregnant women by 8.2 percentage points,
of women with less than one year old child by 3.4 percentage points, and of women with older
children (between one and six years old) by 1.5 percentage points. Counterfactual policy
simulations show that the provision of unpaid leave will increase the labor force participation
rate of women with older children by an additional 3.7 percentage points.
1 Introduction
Maternity leave policies vary widely across countries. In general, they are more generous
in Europe compared to the United States. Many countries in Europe and some states in
the United States are considering more generous maternity leave policies. For example
California initiated paid leaves of up to six weeks in 2004. These policy changes may have
substantial impact on the labor force participation rate of women (Klerman and Leibowitz
1997; Waldfogel 1998; Baker and Milligan, 2008). This paper explores the impact of one
such important policy change that a¤ected the ability of women to remain in the workforce
during the period surrounding childbirth.
In 1978, Congress passed the Pregnancy Discrimination Act (PDA), which amended Title
VII of the Civil Rights Act of 1964. Although the PDA did not mandate any statutory leave
amount, it required employers to treat a pregnancy like a temporary disability. Among other
things, employers were required to allow pregnant women to work as long as they were able
to perform their tasks or to provide them with modi�ed tasks. The employers were also
required to hold the jobs open for the same length of time they would for any other sick or
disabled employee.
This paper evaluates the e¤ect of the PDA by developing and structurally estimating a
dynamic model of women�s labor force participation. The structural approach allows us to
evaluate alternative forms of maternity leave and bene�t legislation found in other countries
using the estimated dynamic model.
This paper contributes to the literature that documents and analyzes the rapid rise in
the labor force participation rate among women in the United States. The labor force
participation rate of married women has increased substantially over the past four decades
with a particularly striking increase among women with very young children. As Table
(1) shows, between 1960 and 2000, the labor force participation rates for married women
increased from 30.5% to 61.6%, while the rate for married women with children under the
age of six increased from 18.6% to 61.8%. The participation rate for women with a child
1
under the age of one increased from about 31% in 1975 to about 55% by 2000.1 Table (2)
shows even more dramatic increase in participation rates for women ages 16-44 during the
period surrounding the �rst birth over the period 1960 to 1995.2 The �rst column shows
the percentage of women who had ever worked six or more months continuously at any time
prior to the �rst birth. Over that period, the participation rate prior to the �rst birth went
up by six percentage points. In contrast, participation six months (one year) after the birth
rose by 35 (37) percentage points with most of the changes occurring between 1971-75 to
1981-85.
There are many explanations proposed in the literature to explain the overall increase in
the participation of married women. They include increasing real wages for women (Smith
and Ward, 1985), increasing divorce rates (Johnson and Skinner, 1986), increasing returns to
experience (Blau and Kahn, 1997), a decreasing gender wage gap (O�Neill and Polachek,1993;
Jones, Manuelli, and McGrattan, 2003), delayed marriage and childbearing (Goldin and
Katz, 2002), a shift in employment toward sectors that are skill and female intensive (Mur-
phy and Welch, 1991), and the introduction of labor-saving devices in home production
(Greenwood, Seshadri and Yorukoglu, 2002). Lee and Wolpin (2009) evaluate several ex-
planations for increased labor force participation of women. They report that supply side
factors, primarily changes in the value of home time and changes in fertility, explain most
of the increase in the labor force participation among women.
However, none of the explanations above can account for the much larger increase in labor
force participation among women with young children. Leibowitz and Klerman (1995) argue
that changes in demographic characteristics and earnings can explain part of the increase
in the participation of married women with children. Olivetti (2001) argues that there has
been an increase in wage return to work experience for women, which makes withdrawal
from the labor force in the period surrounding childbirth more costly. Attanasio, Low, and
Sanchez-Marcos (2004) evaluate several other possible explanations including a reduction in
1U.S. Bureau of Labor Statistics, Bulletin 23072Current Population Report, Smith et.al., 2001
2
child care cost, and increased uncertainty about husband�s earning.
This paper argues that the literature has largely overlooked the e¤ects of the PDA on the
labor force participation rate of women. Gruber (1994) provided the only other analysis of the
PDA. His primary focus was only on health insurance and whether employers ware passing
on the increased cost of health insurance to the employees. He considered all married women
between the ages of 20 and 40 as the treatment group and used data two years before and
after the PDA to estimate the e¤ects. He did not �nd any signi�cant impact on employment
in probit estimation. One reason behind such result might be that the immediate impact of
the PDA was not on such a broad group. Its immediate impact might be only on pregnant
women and women with very young children. This paper evaluates the e¤ect of the PDA by
developing and structurally estimating a dynamic model of women�s labor force participation.
The behavioral model treats the 1978 PDA as an unexpected permanent change because this
act reversed a string of U.S. Supreme Court decisions on this issue. It incorporates the short
run impact of the PDA through a reduction in the utility cost of supplying labor during the
period surrounding childbirth. The behavioral model also postulates that law had a long-run
e¤ect (i.e., on women with older children) because remaining attached to a job in the period
surrounding childbirth meant that women did not have to search for a new job to re-enter
the labor market. Also, any work experience accumulated during the period implied higher
future wages and participation.
The behavioral model builds on previous dynamic models of labor force participation that
incorporate human capital accumulation (Weiss,1972; Heckman, 1976; Weiss and Gronau,
1981; Eckstein andWolpin, 1989). The basic feature of these models is that current participa-
tion a¤ects future wages through increased work experience and, thus, future participation.
In the model employed women are assumed to get a new wage o¤er every period. Upon
receiving an o¤er, women decide whether to accept or to reject the wage o¤er. If she ac-
cepts, she is employed at that wage. If she rejects, she is not employed for that period.
Not-employed women who want to work in the next period incur a cost to �nd a new job.
The PDA is modeled as an unanticipated permanent shock to the cost of supplying
3
labor. The behavioral model also makes explicit the mechanisms through which the PDA
potentially a¤ects labor force participation. Before the PDA, a woman who did not work
on a regular basis in the period surrounding childbirth had no guarantee of being rehired
after childbirth. Given a relatively high utility cost of supplying labor during the period
surrounding childbirth, working regularly is a less attractive option. If a woman stopped
working and was not rehired, she would have to incur the search costs associated with �nding
a new job. After the PDA, the provision of performing a modi�ed task as well as the option of
taking a leave and then returning to the previous job, in e¤ect, lowered the cost of keeping a
job, and made women more likely to remain attached to a job during the period surrounding
childbirth. Remaining attached to a job also meant higher work experience and thus higher
participation in the future; so, even though the PDA only lowered the cost of supplying labor
in the period surrounding childbirth, it not only increased participation during the period
surrounding childbirth, but also increased overall participation later.
The empirical analysis is based on data from the young women�s cohort of the National
Longitudinal Survey, who were between the ages of 14 and 24 in 1968. This data set is
particularly useful to identify the e¤ects of the PDA because the working and reproductive
lives of these women span the period before and after the legislation. The model is estimated
using simulated maximum likelihood. The �t of the model is assessed using within sample
�t criteria as well as out of sample validation. The model captures well the changing pattern
of labor force participation within sample. The NLSY 79 women were used for out of sample
validation of the model. The model accurately predicts the labor force participation rates
for NLSY 79 cohort women.
The estimated model was used to assess how the introduction of the PDA in�uenced
labor market participation. By simulating decisions over the life-cycle with and without
the PDA, one can directly evaluate the cumulative e¤ects of the PDA on pregnant women,
women with very young children (less than one year old) and women with relatively older
children (one to six years old). Simulations show that the PDA increased the labor force
participation rate of pregnant women by 8.2 percentage points, women with less than one
4
year old child by 3.3 percentage points, women with older children (between one and six
years old) by 1.5 percentage points.
The estimated behavioral model allows us to evaluate alternative forms of maternity
leave and bene�t legislation found in other countries. There is wide variation in maternity
bene�ts legislation across countries both in terms of maternity leave and in terms of monetary
bene�ts. Simulations based on the estimated model show that the provision of unpaid
maternity leave (up to a year after childbirth) with a guarantee that they can get back
their job reduces participation immediately around childbirth. Such a policy, for example,
would reduce the labor force participation rate by about 18 percentage points in the quarter
following a childbirth. This result is consistent with Baker and Milligan (2008) who report
that relatively long maternity leave entitlements (i.e., more than a quarter) lead to mothers
spending more time at home immediately after childbirth. However, we also �nd that unpaid
leave increases participation of women with children between one and six years old by an
additional 3.7 percentage points. Thus provision of unpaid maternity leave increases long
term labor force participation rates of women with children. Baker and Milligan (2008) do
not study the longer term impact of maternity leave policies. Provision of monetary bene�t
(in addition to the unpaid leave) has an even larger negative impact on participation during
the paid leave period. Again, this negative e¤ect is temporary as labor force participation
rates go back up once the leave period is exhausted.
2 The Law
Starting in the early 1970�s a large number of pregnancy discrimination cases were brought
before the judiciary. A majority of women in these cases held traditional women�s jobs.
Teachers, nurses, factory workers, �ight attendants, secretaries, and sales personnel com-
posed the bulk of the plainti¤s (Edwards, 1996). The cases can be divided into �ve ma-
jor categories: forced leave, discharge, seniority/rehire, bene�ts, and hire/promotion. In
Geduldig v. Aiello (1974) the Supreme Court ruled that the denial of bene�ts from work
resulting from normal pregnancy did not violate the equal protection clause of the US Con-
5
stitution. Again, in GE Co v. Gilbert (1976) the Supreme Court ruled that excluding
pregnancy from the list of compensable disabilities did not violate Title VII. Some of the
opinions expressed by the judges provide insights into the prevailing beliefs and inadequacy
of the existing laws in the early 1970�s. For example, Judge Haynsworth said,
"No man-made law excludes males from those experiences, and no such laws or regulations
can relieve females from all the burdens which naturally accompany the joys and blessings
of motherhood.... How can the state deal with pregnancy and maternity in terms of equality
with paternity. It cannot, of-course� (Cohen v. Chester�eld County School Board, 1972).
The Pregnancy Discrimination Act 1978 reversed the General Electric Co. v. Gilbert
(1976) Supreme Court decision. Congress enacted the PDA as an amendment to the Civil
Rights Act, 1964. Some primary features of this act are as follows. An employer may not
single out pregnancy-related conditions for special procedures to determine an employee�s
ability to work. If an employee is temporarily unable to perform her job due to pregnancy, the
employer must treat her the same as any other temporarily disabled employee; for example,
by providing modi�ed tasks, alternative assignments, disability leave or leave without pay.
Pregnant employees must be permitted to work as long as they are able to perform their
jobs. If an employee has been absent from work as a result of a pregnancy-related condition
and recovers, her employer may not require her to remain on leave until the baby�s birth.
An employer may not have a rule that prohibits an employee from returning to work for
a predetermined length of time after childbirth. Employers must hold open a job for a
pregnancy-related absence for the same length of time a job is held open for employees on
sick or disability leave.
3 Model
This section presents a dynamic stochastic model of female labor force participation. The
model is restricted to married women. Each woman has a decision horizon that starts at
the age of marriage and ends at age 60. At each age, a woman chooses whether to work
(W ) or not work (NW ) : A birth may occur at any period during the fertile period which is
6
assumed to end at age 40. It is assumed that fertility follows a given exogenous process to be
estimated from the data. At each age the objective of the wife is to maximize the expected
present value of remaining lifetime utility. A period is a quarter.
To allow for the possibility of unobservables a¤ecting fertility and labor force participation
rates, unobserved heterogeneity was incorporated in the form of discrete unobserved types
(e.g., Heckman and Singer, 1984). Let �k be an indicator variable that equals 1 if the
individual is of type k; where k 2 f1; 2; 3g: The probability of being a particular type
depends on education and age of marriage. These variables constitute the initial conditions
in the model. The current period alternative speci�c utility function (U iak) associated with
a person of age a and type k are:
UWak = Ca + �1Ca + (�2Ka�1 + �3K2a�1) +
3Xk=1
�k�k(1 + �6kna + �7kn2a)+ (1)
3Xk=1
�k�k� 0j1 (PDA = 0) 1(Sa = jj1 � j � 7) + 1j1 (PDA = 1) 1(Sa = jj1 � j � 7)
�+
3Xk=1
�k�k(�8 (na + 1) + �9(na + 1)2) (1� pa�1)] + (�4a+ �5a2)na
UNWak = Ca (2)
Ca is the goods consumption at age a. �1 captures whether work a¤ects utility from
consumption. If �1 < 0 then working reduces utility from consumption, while �2 and �3
capture how experience (Ka) a¤ects utility. Note that the utility is not separable across
periods as long as either �2 6= 0 or �3 6= 0: The assumption of non-existence of capital
market is restrictive in general, however if the period utility function is linear and additive
in consumption (i.e. if �2 = 0) then it becomes a problem of wealth maximization modi�ed
by the psychic value of the children (Eckstein and Wolpin 1989).
The parameter �k is the utility cost of supplying labor or value of leisure for women who
do not have any children and are not yet pregnant. It may vary according to unobserved
type (denoted by the k subscript). na represents the number of children in the household. na
7
can take values between zero and three. Value of leisure depends on the number of children
(�6k and �7k captures these changes). The model assumes that the changes in the value of
leisure due to the presence of children is proportional to the baseline value of leisure �k:
The presence of very young children (less than one year old) or being pregnant further
a¤ects the value of leisure. Sa represents pregnancy quarter or age of the youngest child.
Sa = 0 represents women who do not have any children and are not yet pregnant. Then from
equation 1 the value of leisure when Sa = 0 is �k: Sa = 1 represents the �rst trimester of
pregnancy, Sa = 2 represents the second trimester of pregnancy, Sa = 3 represents the third
trimester of pregnancy, Sa = 4 represents a child being born at age a; Sa = 5 represents
child�s age is two quarters, Sa = 6 represents child�s age is three quarters, Sa = 7 represents
child�s age is four quarters (one year old), and Sa = 8 represents child�s age is more than
one year old. Child�s age after one year3. 1 (PDA = 0) is an indicator function which takes
the value one when the PDA is not in e¤ect (before 1978). 0j�k is additional disutility of
supplying labor when Sa = j before the 1978 Pregnancy Discrimination Act (PDA) was
enacted. The e¤ect of the PDA is captured by changes in the utility cost of supplying labor
in the period surrounding childbirth. This approach is implemented because the law did not
specify any statutory leave amount, hence the bene�ts available to a woman depended on
the policy of her employer, a data which is not available. In fact in the NLS data it is not
possible to distinguish whether somebody was actually working or was with a job but on
temporary leave except on the survey week. So when estimating the model, a woman who is
with a job is regarded as employed and the e¤ect of the PDA is captured by estimating the
di¤erences in utility cost of supplying labor during the period surrounding childbirth. 1j�k
is additional disutility of supplying labor when Sa = j for the post PDA period.
Thus from equation (1) the value of leisure for a woman of type k who is in the �rst
trimester of �rst pregnancy (i.e. she does not have any children yet) in the pre-PDA period
is (1 + 01)�k: Similarly value of leisure for a woman who is in the �rst trimester of third preg-
3The model already has mother�s quarterly age and mother�s quarterly experience in the state space.Adding children�s age to the state space would be computationally very burdensome.
8
nancy (i.e. she already has two children) in the pre-PDA period is (1 + 2�6 + 4�7 + 01)�k:
Changes in the value of leisure due to pregnancy and/or children is assumed to be pro-
portional to the baseline value of leisure. This approach allows us to keep the number of
parameters manageable without assuming that these costs are same across types.
It is assumed that women who were unemployed in the previous period but are working
in the current period incur a search cost to �nd a new job. This cost is ex-post in the
sense that only the women who were not employed in period t� 1 but employed in period t
incur the cost. This cost is a quadratic function of number of children. These costs are also
proportional to the baseline disutility from work (�k). Thus from equation (1) the search
cost incurred by women who are type k and who do not have any children yet is (�8+�9)�k;
and the cost for an woman with one child is (2�8 + 4�9)�k: The disutility from work can
vary by age (�4 and �5 captures these changes). Lee and Wolpin (2009) allow disutility to
vary with calendar time. In their model they have multiple cohorts but since the model
essentially has one cohort this would capture any change in the cost of child-rearing, change
in home productivity and social "norms" over time4.
Arrival of a child is assumed to be an exogenous stochastic process, which depends on the
characteristics of the woman such as age, age squared, and also on the number of children
already present. In each period that a woman is not pregnant there is a probability that
she will become pregnant next period and once she is pregnant she progresses in pregnancy
deterministically and becomes not pregnant after childbirth. This process continues for the
whole fertile period (till yearly age 40 or quarterly age 160). The probability of getting
pregnant for a woman of type k at age a is:
Pak (Sa+1 = 1jSa = 0 :or: Sa � 4) =exp(
P3k=1 �k�1k + �2a+ �3a
2 + �3na + �4n2a)
1 + exp(P3
k=1 �k�1k + �2a+ �3a2 + �3na + �4n2a)
(3)
Pregnancy results in a childbirth in the following way5
4We thank Frank Schor�de for pointing this out.5We do not consider abortions or miscarriages becuase data on such events are not available. Such events
may not be very important in this context because we restrict our sample to married white women who aremore than 18 years old. Also most of the abortions/miscarriages are resolved in the �rst trimester.
9
P (Sa+1 = jjSa = j � 1) = 1 for j = 2; ::; 7
The household budget constraint is given by
yha + ywa pa = Ca (4)
where yha is husband�s earning and ywa is the earning of the wife.
The wife�s earnings are endogenous and stochastic. Education does not a¤ect wage
explicitly but the e¤ect of education will be captured by the constant in the wage equation
which is allowed to vary across unobserved types which in turn depend on education. Since
the model starts after the agents have already �nished their education (i.e., education is an
initial condition that does not vary for any given individual), this is a parsimonious way
of modeling the impact of education. This will be discussed further later in the estimation
section. Wages depend on experience in a quadratic way, and also depend on age. This allows
us to capture calendar time e¤ects because the model essentially has one cohort. Wages also
depends on lagged employment. This would capture skill depreciation due to not working
in the previous period. The wage function is
ln ywak =3Xk=1
�k�1k + �2Ka�1 + �3K2a�1 + �4a+ �5a
2 + �6pa�1 + "wa ; (5)
where Ka�1 is total experience at age a and "wa has zero mean and �nite variance and
serially uncorrelated. Work experience evolves according to
Ka = Ka�1 + pa (6)
Another important factor is husband�s income, which is stochastic. The model assumes
that wife can forecast the deterministic part of her husband�s future earnings, based on the
observable characteristics of the wife. This assumption re�ects the hypothesis that women
with similar observable characteristics tend to marry similar husbands (Van der Klaauw,
1996). Another reason for this assumption is that adding the husband�s characteristic into
10
the decision problem would magnify the state space exponentially making it much more
computationally burdensome.
yhak =
3Xk=1
�k�1k + �2a+ �3a2 + "ha (7)
The two wage shocks�"wa ; "
ha
�are assumed to be jointly normal, N (0;
P) ; and serially
uncorrelated.
The maximized present discounted value of lifetime utility at age a; the value function,
is given by
V ((a); a) = maxpa2f0;1g
EfAX�=a
���aU ja j(a)g;
where U ja is the maximum of the alternatives available to the individual at age t: A is the
terminal age of the model, assumed to be age 60 (240 quarters). The expectation is taken
over the distribution of wage shocks.
4 Model Solution and Estimation
The solution to the optimization problem is a set of decision rules that relate the optimal
choice at any age a; from among the feasible set of alternatives, to elements of the state
space: Recasting the problem in a dynamic programming framework, the value function can
be written as the maximum over alternative-speci�c value functions, V j((a); a); i.e., the
expected discounted value of alternative j 2 f0; 1g that satis�es the Bellman equation:
V ((a); a) = maxj2f0;1g
[V j((a); a)]
V j((a); a) = U j(a;(a)) + �E(V ((a+ 1); a+ 1jpa = j;(a)) for a < A;
= U j(A;(A)) for a = A:
The solution of the optimization problem is not analytic, so the model is solved numeri-
cally. The solution consists of values of E(V ((a+ 1); a+ 1jpa;(a)) for all j and elements
of (a): This function is called the Emax. The solution method is by backwards recursion,
beginning with the last period, A. The multivariate integrations necessary to calculate the
11
expected value of the maximum of the alternative-speci�c value functions at each state point
are performed by Monte Carlo integration over the shocks.6 The state space is manage-
able, so the Emax function is evaluated at every possible state point without having to use
interpolation methods.
In solving the model it is assumed that the PDA was an unexpected and permanent
shock. In the numerical solution this is implemented in the following way: for a woman who
got married before 1978, (year of the PDA) for the period before 1978 her value functions
were calculated as if the pre-law regime will last forever. But for the after 1978 period, her
value functions were calculated with the changed set of parameters assuming the new regime
will last for-ever.
The solution to the optimization problem serves as an input in estimating the structural
parameters of the model given the data. The choices a woman make and associated state
variables as well as accepted wages for the women who chose to work in a particular period are
observed in the data. The model assumes that each woman is solving the decision problem
described above. The probability of a woman making a particular choice at a particular age
is computed which is just the probability that the value function associated with that choice
is the maximum of all choice speci�c value functions at that period. Let Oia represent the
outcomes (work choices, observed wages) of individual i and age a: Also, let Ii denote the
set of initial conditions for that individual (age at marriage, education). The contribution
to the likelihood of individual i is given by:
Li (�) =
KXk=1
Pr (OiA0 ; OiA0+1; ::::::; Oia; �k = 1; Ii) Pr (�k = 1jIi) (8)
where Pr(�k = 1jIi) denotes the type probability which depends on initial conditions. The
unobserved type is assumed to be known to the individual but not to the econometrician;
the outside summation integrates over the type probabilities. The likelihood can be written
as the product over the age-speci�c choice probabilities:
6We use 50 draws for the numerical integrations and 1000 simulations to calculate the likelihood.
12
Li =
KXk=1
�Aa=A0 Pr(OiajOia�1; :::; Oia0 ; �k = 1; Ii) Pr(�k = 1jIi): (9)
To illustrate the calculation of the likelihood, suppose that the j th alternative chosen by
individual i is to work, so that the wage is observed at age a. The probability of observing
that choice and wage outcome conditional on the state space (which includes Oia�1; :::; Oia0 ;
I and type) is:
Pr(OiajOia�1; :::; Oia0 ; �k = 1; Ii) = Pr(pa = 1; ywa ; yha j(a); �k = 1; Ii)
= Pr(pa = 1jywa ; yha ;(a); Ii)fw(ywa j(a); �k = 1; Ii)fh(yha j(a); �k = 1; Ii)
where fw(ywa j(a); �k = 1; Ii) is the wife�s wage density and fh(yha j(a); �k = 1; Ii) is hus-
band�s wage density.
The overall likelihood for i = 1::N individuals is the product over the individual likeli-
hoods:
L = �Ni=1Li:
The presence of wage outliers greatly in�uences the parameter estimates. To account for
this it is assumed, not unreasonably, wages are measured with error. In particular:
ln ywak =3Xk=1
�k�1k + �2Ka�1 + �3K2a�1 + �4a+ �5a
2 +3Xk=1
�k�6kpa�1 + "wa + u
wa (10)
where uwa ~N (0; �2u) with no serial correlation and uncorrelated with "
wa and "
ha for all a.
The parameter �2u will be estimated along with the other structural parameters.
It is assumed that type depends on age at marriage and education (the initial conditions,
denoted Ii) in the following way.
P (type = kjIi) =exp(I 0i�)
1 + exp(I 0i�)
There is a degree of arbitrariness in the choice of parameters that is allowed to vary
across unobserved types. The trade-o¤ here is again �exibility versus number of parameters.
13
�(disutility of labor), �1(constant in the wife�s wage function), �1 (constant in the husband�s
wage function), and �1 (constant in the probability of child arrival process) are allowed to
vary across unobserved types. To achieve parsimony without giving up �exibility other cost
parameters associated with labor supply (for example extra cost of labor when pregnant
or the search cost) are measured as a fraction of � (disutility of labor). Hence they also
(implicitly) vary across types.
To estimate the probabilities, Pr(OitjOit�1; :::; Oit0 ;�k = 1) in a way that improves the
empirical performance of the estimator, the kernel smoothed frequency simulator proposed
by McFadden (1989) is used. For each set of error term draws, the kernel of the integral is
expfVi(a)�max(V j(a))
�g
�Jl=1 expfV l(a)�max(V j(a))
�g;
times the density of the observed wages. Here, V i(a) is the value function associated with
the choice that person i made at age a, max(V j(a)) is the value function associated with
the maximal choice, and � is a smoothing parameter. The value of � is set at �ve, which
provided su¢ cient smoothing given the magnitudes of the value functions.
The model parameters enter the likelihood through the choice probabilities that are
computed from the solution of the dynamic programming problem. Subsets of parameters
also enter through the wage o¤er function. The maximization of the likelihood function
iterates between solving the dynamic program and calculating the likelihood.7
4.1 Identi�cation
The wage parameters are identi�ed from data on participation and wages. The logarithmic
form of the wage function is not necessary for identi�cation. Identi�cation of the parameters
pertaining to the change in value of leisure surrounding the childbirth comes from the dif-
ferences in the participation behavior of women in di¤erent phases of life (Sa): In the data
7Standard errors are computed using a scoring method that calculates an outer product approximation tothe hessian with numerical �rst derivatives. See Keane and Wolpin (1994) for a discussion of the propertiesof this estimation procedure.
14
women with di¤erent values of Sa are observed both before and after the 1978 PDA. For ex-
ample di¤erence in participation behavior between women with Sa = 0 (women who do not
have children and not yet pregnant) and Sa = 1 (women in the �rst quarter of pregnancy)
before the 1978 PDA allows us identify 01. Note that the model assumes that the parameter
01 (as well as other �s) does not depend on the number of children. Thus 01 can also be
identi�ed from the di¤erence in participation behavior between women with Sa = 8 (women
with more than one year old child) and Sa = 1 before the 1978 PDA. Similarly di¤erence in
participation behavior between women with Sa = 0 and Sa = 1 (or di¤erence in participation
behavior between women with Sa = 8 and Sa = 1) after the 1978 PDA allows us identify
11: All other �s are identi�ed by the same argument. One implicit assumption needed to
identify �s is that there is no independent time e¤ect. Model speci�cation allows quite a
bit of �exibility including allowing for unobserved types that depend on initial state and age
e¤ects (which can be thought of as proxy for time since there is only one cohort). Note that
even though the PDA is modeled as an unexpected and permanent shock to the agents in
the model, women solving the dynamic problem (in the post-PDA period) are aware of the
fact that the PDA is in e¤ect. So the PDA can have an e¤ect even on women who do not
have any children and are not yet pregnant.
5 Data and Descriptive Statistics
The data used in estimation are from the young women�s cohort of the National Longitudinal
Survey, 1968-91. The original sample consists of 5159 women who were between the ages of
14 and 24 in 1968, when the �rst survey was conducted. These women were interviewed 16
times between 1968 and 1991. The sample used in the estimation consists of white women
whose spouses were always present during the sample period. For the women who later got
divorced, their data was truncated three years before the reported divorce. For example, if
a woman got married in 1973 and then reported being divorced in 1988, then her data from
1973 to 1985 was used in the estimation. The sample is further restricted to consider women
for whom at least two consecutive years (or eight consecutive quarters) of data are available.
15
For each woman, data is used on (i) her age, age at marriage, and schooling; (ii) her entire
work history; (iii) her entire child-birth history; (iv) her wages on the periods she worked;
and (v) her husband�s wage.
NLS interviews were conducted in one-year or two year intervals and once after three
years. In the model a period is de�ned as one quarter. There are two primary reasons
behind estimating the model at a quarterly frequency. First, there is a lot of variation in
the quarterly employment rate of women in the period surrounding a birth and one of the
goals of this paper is to capture this quarterly variation in employment rates. Second, the
estimated model is used to evaluate the impact of more generous maternity bene�t policies.
Most of these policies provide women with one or two quarters of paid leave and up to six
quarters of unpaid leave. Hence, to evaluate such policies, the model needs to be estimated
on quarterly data.
A quarterly data set was constructed from the NLS data set for all the relevant state
variables like employment history and birth history. For all the interviews except for the
interviews in 1975 and 1977, questions were asked about their work history since the last
time they were interviewed as well as about the starting and termination dates of various jobs
they held. Therefore, it is possible to construct a quarterly work history using the relevant
questions. For the interview years 1975 and 1977, though, questions were asked only for a
period of 12 months preceding the interview date. However using the data on weeks worked
in the 12 months preceding the interview it is possible to construct a reasonably accurate
employment history. Also for the employment history prior to the �rst interview in 1968
questions about their date of entry into the labor market and about any intermediate exits
allow us to construct a reasonably accurate employment history.
A woman is assumed to be employed in a quarter if she worked in all three months of a
particular quarter. This de�nition implies that most women who worked only a few weeks
in a quarter are classi�ed as unemployed. Part-time work is not explicitly modeled at the
quarterly level because it is not possible to �gure out how many hours an individual worked
in any particular quarter from the data. While it is possible to �gure out hours worked at
16
the yearly frequency (with some assumptions) it is not possible at the quarterly frequency.
However it is important to note that even though part-time work in terms of hours worked
per quarter is not explicitly modeled here, this model does allow for part time work in the
sense that an agent can work zero, one, two, three, or four quarters in any year. Since almost
all models in this literature have been estimated on a yearly frequency, it can be argued that
this model is allowing for part-time work based on quarters worked. While not having the
data on hours worked per quarter is somewhat restrictive, this structure is more �exible than
the structures that have been used previously.
The quarterly wages were constructed by dividing the yearly wage by the number of
quarters worked. Even then wage information is not available for all work periods. If wage
for a work period is not available then wage is integrated out to calculate the likelihood.
Table (3) presents summary statistics of the variables used in the estimation process.
Figures in parentheses are standard deviations. The sample consists of 49,327 observations
from 863 women. A total of 1388 births are observed during the sample period, or about
1.6 births per woman. Average age during the sample period is about 31 years and average
experience is about 8 years (32 quarters). Mean age of marriage for the women in the sample
is just under 23. 4.9% of the women do not have a high school degree, 43.7% are high school
graduates, 21.8% have some college education, and 29.6% have a college degree. The overall
labor force participation rate during the sample period is 55.0%. Average wage of wives
during the sample period was $3199 per quarter (in 1982 dollars). Average wage of the
husbands during the sample period was $5793 per quarter.
6 Results
Values of the parameters along with their standard errors are presented in table (4). There
are no restrictions on any of the parameters. All the parameter estimates have the expected
sign. However note that some of them are not comparable to earlier studies in this literature
because most studies in this area use yearly data as opposed to quarterly data that is being
used in this paper. In particular estimates suggest that participation decreases utility(
17
�1 < 0). There is substantial heterogeneity across types. Type 3 has the highest valuation
from staying home and type 1 the lowest. This disutility is higher when children are present
at home.
Estimates also show that there is an additional disutility around the time of childbirth
( 0j ; 1j < 0; j = 1; 7); except for
11. Estimates also show that the PDA made it easier for
women to work during ( 0j < 1j ; j = 1; 3). For example before PDA, a woman working
in her third quarter of pregnancy had to incur 19% more utility cost compared to a non-
pregnant woman. After the PDA, a woman in her second quarter of pregnancy incurs only
2% more utility cost. The size of the decline in the �rst two quarters of pregnancy are less
but still substantial. However there was no reduction in utility cost in the post-childbirth
period. The estimates also suggest that there is a substantial cost of �nding a new job and
the search cost increases in the presence of children. Estimates suggest that search cost for
women who do not have any children yet is equivalent to the disutility of working for 1.3
months. This cost is higher for women with children. For example the search cost for women
with two children is equivalent to the disutility of working for 2.1 (=3*1.33-9*0.212) months.
This shows that it is harder for women to come back to the labor market after they have a
child.
Estimates show that type 3 has the highest wage intercept and type 1 has the lowest.
Type 1 has the lowest constant in the children arrival process (they have the least number of
children) and type 2 has the highest. We also �nd positive association between wife�s wage
and husband�s wage. Husband�s wage constant is also highest for type 3 and lowest for type
2. Discount factor is set at 0.95.
6.1 Simulations
This section presents the evidence of within sample �t of the model. Each person�s behavior
is simulated 4000 times (i.e. for 4000 sets of draws of the model shocks) and the results
we report below are the averages from those simulations. Before presenting the evidence
on model �t we should note that there is considerable heterogeneity in the behavior across
18
types. Table (5) shows that in our sample 25.5% of women are type 1, 45.6% are type 2
and 28.9% are type 3. Type 2 women have the highest overall labor force participation rate
followed by type 3 and then type1. Type one women have most kids (1.8 on average) followed
by type 3 and type 2 women have least number of kids.
6.1.1 Internal Validation: Within-Sample Fit
Figure (1) compares the predicted employment rates to the actual employment rates by
women�s ages. As seen in �gure (1), in the actual life cycle pro�le labor force participation
of married women �rst increases with age then it becomes �at and �nally starts increasing
again. This is most likely due to the fact that most women have children in their mid 20�s
and early 30�s (quarterly age from about 90 to 130). Therefore, many women drop out of the
market for childbirth. Once they reach mid-thirties, more women come back to the market,
and that explains the increasing participation rate after they reach mid-30�s. Simulated data
from the model replicates this pattern.
To formally assess how well the model �ts the data we use Pearson�s chi-square goodness-
of-�t test:
nP
p2f0;1g
hf(p)� bf (p)i2bf (p)
where f (1) denotes the empirical frequency for the employed, bf (1) denotes the frequencypredicted by the estimated model, and n is the number of observations. Table A1 (in the
appendix) presents the results of the goodness-of-�t test. We cannot reject the model at
conventional signi�cance levels in 97 out of 108 quarters.
The simulated model accurately replicates the persistency observed in the data. The
probability of being employed in period t + 1; if a woman is employed in period t is 94.7%
(96.2%) in the actual data (simulation). The probability of being not employed in period
t+1; if a woman is not employed in period t is 97.7% (96.7%) in the actual data (simulation).
The simulated data was able to replicate the large di¤erence in participation between
pre-law and post-law periods that we observe in the actual data during the period surround-
19
ing childbirth. Table (6) presents the actual and the simulated participation rates for the
pre-PDA and post-PDA periods. As in the actual data, the di¤erences in the labor force
participation rates during the period surrounding childbirth are greater than the di¤erences
in the participation rate of women without any children. The simulations under-predict
the labor force participation rate for women who do not have any children and are not yet
pregnant. The average participation rate for women who do not have any children and are
not yet pregnant increased from 74.1% in the pre-law period to 82.9% in the post law period
(70.0% to 80.2% in the simulations). Participation rate for women in the �rst quarter of
pregnancy increased from 34.4% to 49.5% (40.3% to 49.9% in the simulations), in the second
quarter of pregnancy increased from 28.8% to 48.1% (31.2% to 46.4% in the simulations),
and in the third quarter of pregnancy increased from 26.2% to 43.3% (26.2% to 44.1% in the
simulations). The model also replicates the labor force participation rate after childbirth.
For example participation for women who have a one year (four quarters) old child increased
from 27.5% (27.2%) to 38.5% (39.8%) in the data (simulation). The higher participation
precipitated by the reduction in the utility cost of supplying labor in the period surrounding
childbirth leads to higher participation in women with older children. The last row of the
Table (6) shows that model accurately replicates the di¤erences in the participation rates for
women with children between one to six years old. For women in this group participation
rates increased from 33.3% (33.9%) to 48.1% (48.2%) in the data (simulation). A goodness-
of-�t test cannot reject the model at 5% level of signi�cance except for women who do not
have any children and are not yet pregnant and for women in the �rst quarter of pregnancy
in the pre-law period.
Table(7) presents at the earning �ts by age group. The log quarterly earning is relatively
�at in the data and the simulations replicates that pattern. In the simulations age and
experience e¤ects cause the earnings to rise with age but the skill depreciation due to breaks
in employment keeps the earnings pro�le �at.
20
6.1.2 Out of sample validation
The women of National Longitudinal Survey, 1979 cohort (NLSY79) was used for out of
sample validation. These women were 14-22 years old in 1979. These individuals were
interviewed annually through 1994 and afterward on a biennial basis. Again we consider
white, married women of this cohort. The NLSY79 data has information on their education,
age at marriage, and their work experience at the time of marriage. Their pro�les were
simulated using the initial conditions. Since these women got married and had children
only in the post-PDA period, (the PDA was passed in 1978), their pro�les are simulated
with the post-PDA parameters. We use data on the 1979 cohort women till 1993 which
implies that the age of the respondents in this sample is comparable to the age of 1968
cohort during the pre-PDA period. Again each person�s behavior is simulated 4000 times
(i.e. for 4000 sets of draws of the model shocks) and the results we report below are the
averages from those simulations. Table (8) shows their actual participation rates and the
simulated participation rates as predicted by the model. The estimated model replicates the
labor supply behavior for the 1979 cohort women even though their information was not
used in the estimation process. The average participation rate for women who do not have a
child is 77.2% (77.0%) in the data (simulation). However during pregnancy and right after
childbirth the model predicts somewhat lower participation rate compared to the data. The
average participation rate for women in the �rst quarter of their pregnancy is 60.1% (53.8%)
in the data (simulation) and labor force participation rate for women with a one quarter
old child is 52.0% (40.1%) in the actual data (simulation). The simulated model however is
close to the data three quarters after childbirth (38.1% as compared to 42.4% in the actual
data). For women who have a child between the ages of one and six, the model predicts a
participation rate of 47.4% as opposed to 50.4% in the data.
6.2 Impact of the 1978 PDA
To �nd out the e¤ect of the PDA the estimated model was simulated assuming that PDA was
never enacted. In practice the model was simulated using the pre-PDA parameters. Table
21
(9) shows the results. The �rst column shows the simulated average participation rates of
the 1968 cohort only for post 1978 period, assuming that PDA was not enacted. The second
column shows the simulated average participation rates of the 1968 cohort (again only for
post 1978 period), but now assuming that the PDA was enacted.
Since the only di¤erence is the change in law, this change in participation rate is purely
due to the e¤ect of the PDA. It generates large di¤erences in participation not only in the
period surrounding birth, but also in the increased participation of women with children
between the ages of one and six years. The impact of the PDA is relatively small for women
who do not have any children. For this group the PDA increased participation rate by 0.7
percentage points (from 79.5% to 80.2%), whereas the impact on pregnant women is large
(from 6.5 percentage points in the �rst quarter of pregnancy to 8.9 percentage points in the
third quarter of pregnancy). The impact of the PDA on women with very young children
is also substantial. It ranges from 5.2 percentage points for women with one quarter old
child to 1.8 percentage points for women with one year old child. The impact of the law on
women with older children is also substantial. For women with children between the ages of
one and six years participation increased by 1.5 percentage points as a result of the PDA.
Table (10) shows that the PDA increased the labor force participation rate during �rst
pregnancy by 10.6% but it increased labor force participation rate during pregnancy by 7.1%
for women who already have at least one child. We �nd a similar pattern in the year following
a childbirth too. Here the increase was 4.1% following the birth of the �rst child and 3.0%
following the birth of subsequent children.
Table (11) shows that the impact of the PDA was not uniform across unobserved types.
The impact during pregnancy, in absolute terms, was higher for type 2 compared to type
1 and type 3. However, in proportional terms, the impact on type 3 was bigger than the
impact on type 2. The absolute (and proportional) impact of the PDA on women with
older children (between one and six years old) was highest for type 3 (2.0 percentage points)
followed by type 2 (1.3 percentage points) and type 1 (0.8 percentage points).
22
6.2.1 Comparison with Di¤erence in Di¤erence analysis
An alternative way to estimate the impact of the 1978 PDA is di¤erence-in-di¤erence analy-
sis. Women who do not have a child and are not yet pregnant serve as a control group for
pregnant women and for women with children. The underlying assumption is that women
who are pregnant and women with children would be a¤ected by the PDA, while women
who do not have a child and are not pregnant yet would not. Table (6) shows that the par-
ticipation rate for the control group went up by 8.8% where as the participation of women
in the third quarter of pregnancy went up by 16.1%, which implies that the PDA increased
the participation of women in the third quarter of their pregnancy by 7.3%. The increase in
participation three quarters after a childbirth is 11.5% which implies that the PDA increased
the participation of women three quarters after childbirth by 2.7%. Di¤erence-in-di¤erence
estimates also suggests that the PDA led to a 5.9% increase in participation for women whose
youngest child is between one and six years old.
However these aggregate comparisons ignore the fact that 58% of pre-PDA births are �rst
births, but only 27% of the births in the post-PDA period are �rst births. It is important
because the labor force participation rate is lower for women who already have children. To
control for number of children as well as di¤erences in education, age, and experience we
estimated a di¤erence in di¤erence regression. In regression we also control for year e¤ects
and allow for individual �xed e¤ects.
It is important to note that if women who do not have children and are not yet pregnant
(in the post PDA period) increase their labor force participation knowing that the PDA is
already in place (which is allowed in the dynamic model) then they are not a valid con-
trol group. In this case di¤erence-in-di¤erence would be biased. We nonetheless present
the di¤erence-in-di¤erence regression estimates in table A2 (in the appendix) for compar-
ison purposes. The estimated impacts of the PDA in the period surrounding a childbirth
from di¤erence-in-di¤erence regression are not too di¤erent from the estimates implied by
the structural model though they are somewhat smaller than the impacts implied by the
structural model. We should also note that the di¤erence-in-di¤erence analysis assumes
23
experience is exogenous while it is endogenous in the structural model. Also, di¤erence-in-
di¤erence analysis condition on fertility. Although fertility is not a choice in the structural
model either, it depends on unobserved types which in turn depend on education and age at
marriage.
7 Policy Analysis
We observe a lot of variation in the maternity (parental) leave as well as monetary maternity
bene�t policies around the world. This section addresses the question of what the impact
would be on the labor force participation rate of women with young children if any of those
policies were adopted in the United States.
7.1 Unpaid leave
Column (2) of table (12) shows the employment impact of unpaid maternity leave in addition
to the e¤ects of PDA. In the model this implies that if a woman was working in the quarter
she got pregnant then she can take a leave of up to four quarters after childbirth and does not
have to incur a search cost to get back into the workforce. Having the option of taking leave
and going back to work without incurring the search cost decreases participation around
childbirth. Note that if an agent is on leave we consider that as non-participation. Labor
force participation rate in the third quarter of pregnancy falls from 44.0% to 27.2% and labor
force participation rate two quarters after childbirth falls from about 37.2% to almost 20.4%
as new mothers take advantage of the leave availability. Thus the job-back gurantee pushes
the labor force participation rates around childbirth even lower than what they would have
been without the 1978 PDA. But labor force participation rate four quarters after childbirth
increases from 39.7% to 50.6%. This sudden spike in participation after four quarters is
coming from the fact that beyond this point, women have to incur a search cost to �nd a
new job. The option of going back to old job substantially increases long term participation.
For example for women who have a child between one and six years old employment increases
by additional 3.7 percentage points (from 48.2% to 51.9%) over and above the post-PDA
24
employment rate. Thus the long term impact of job-back guarantee is substantially bigger
than the impact of the PDA (3.7 percentage points versus 1.5 percentage points). In this
model we cannot implement longer-term unpaid leave policies because model tracks quarterly
age of the child up to four quarters.
Note that even with unpaid leave women face some long term costs of taking time o¤.
Speci�cally in the context of our model they experience a lower wage because of skill de-
preciation (�6 < 0), and also because of lost experience (in addition to the foregone wages
during the quarters they don�t work). Some countries mandate that women be given their
pre-pregnancy wage when they come back to work after childbirth. In the model previous
earning is not in the state space, this policy is implemented by assuming that the non-random
component (which is a function of state variables) remains unchanged. In other words we
simulate the model assuming that women who take time o¤ in the period surrounding a
childbirth do not face a reduction in wage due to skill depreciation (in addition to the un-
paid leave policy outlined above). The results are presented in column (3) of table (12).
This additional bene�t further reduces the labor force participation rate during pregnancy
but the higher wage (compared to the PDA or a simple unpaid leave policy) at the end of
leave period increases labor force participation of women with children between one and six
years old. The size of the increase is rather modest (0.3 percentage points).
7.2 Paid leave
Many countries provide paid maternity leave, although the rate of payment as well as the
amount of time for which women are eligible for paid maternity leave varies. Also, di¤erent
countries have di¤erent eligibility criteria to determine who is eligible for paid leave and
who is not. For example in Canada all women are eligible for up to 30 weeks of payment
(at the rate of 55%) irrespective of their employment status, while in France women are
eligible to receive full payment for 16 weeks. Since in the model previous earning is not in
the state space, this policy is implemented by assuming that they are paid according to the
earnings function. This paid leave is in addition to the unpaid leave and no skill depreciation
25
considered above. This policy further reduces participation compared to the unpaid leave
policy. Since women get paid even if they do not work and they don�t have to incur the
search cost to �nd a new job, thus only cost they incur is lost work experience. In simulations
the bene�ts from not working dominates the costs further reducing the participation during
the bene�t period. Column(4) of table (12) presents the simulation results when women, in
addition to the simple unpaid leave also get paid at the rate of 100% of earnings function
for the quarter immediately following the childbirth. The labor force participation rate goes
down from 21.2% to 3.3% during the bene�t period. In the second quarter labor force
participation goes back up to 19.9% (as the paid bene�ts are not available anymore). There
is no long term impact on employment, as characterized by participation rate of women who
have a child between the ages of one and six years. Column(5) of table (12) presents the
simulation results when women, in addition to the unpaid leave also get paid at the rate of
55% of earnings function for two quarter immediately following the childbirth. The labor
force participation rate goes down from 21.2% to 5.0% during the �rst quarter and 19.9% to
5.1% during the second quarter. In the third quarter labor force participation goes back up
to 25.7% (as the paid bene�ts are not available anymore). Again, the long term impact on
employment, as characterized by participation rate of women who have a child between the
ages of one and six years is very small (52.1% vs. 52.0% without paid bene�ts). Our policy
analysis thus show that the most e¤ective way of increasing labor force participation is the
provision of unpaid leave with the job-back guarantee.
Table (13) shows that the impact of di¤erent maternity leave and bene�t policies is
di¤erent for unobserved types. Panel A presents the impact of di¤erent policies on type 1,
panel B presents the results for type 2 and panel C presents the results for type 3 women.
Type 3 women seem to be most responsive to policy changes followed by type 2 and type 1
women. In particular provision of unpaid leave increases the labor force participation rate
of type 1 women with a child between one and six years old by about 2.6 percentage points
(from 20.9% to 23.5%). The same policy increases the labor force participation rate of type
2 women with a child between one and six years old by about 3.6 percentage points (from
26
81.5% to 85.1%), and of type 3 women with a child between one and six years old by 6.2
percentage points (from 22.2% to 28.4%).
8 Conclusion
This paper studies the Impact of Pregnancy Discrimination Act of 1978 on the labor force
participation of married women by developing and structurally estimating a dynamic model
of women�s labor force participation. We use the estimated model to evaluate how the PDA
a¤ected the labor supply of married women. Simulating labor supply choices over the life-
cycle with pre and post PDA estimated model parameters permits a direct assessment of the
e¤ects of the PDA.
We �nd that the utility cost of supplying labor while pregnant declined substantially in
the post PDA period. Simulation results indicate that the PDA had a substantial impact
on the participation rates of pregnant women and women with young children. In particular
we �nd that the PDA increased the labor force participation rate of pregnant women by 8.2
percentage points, women with less than one year old child by 3.4 percentage points, women
with older children (between one and six years old) by 1.5 percentage points.
We also use the estimated model to evaluate alternative forms of maternity leave and
bene�t policies. We �nd that the provision of unpaid maternity leave with a guarantee that
women can get back their job reduces participation immediately around childbirth. Such a
policy would reduce the labor force participation rate by about 18 percentage points in the
quarter following a childbirth but it increases participation of women with children between
one and six years old by almost 3.7 percentage points. Thus provision of unpaid maternity
leave increases long term labor force participation rates of women with children. Provision
of monetary bene�t (in addition to the unpaid leave) has an even larger negative impact on
participation during the paid leave period. Again, these negative e¤ects are temporary as
labor force participation rates go back up once the leave period is exhausted.
27
9 Appendix
9.1 Solution Method
The solution to the optimization problem is a set of decision rules that relate the optimal
choice at any age a; from among the feasible set of alternatives, to elements of the state
space: Recasting the problem in a dynamic programming framework, the value function can
be written as the maximum over alternative-speci�c value functions, V j((a); a); i.e., the
expected discounted value of alternative j 2 f0; 1g that satis�es the Bellman equation
V ((a); a) = maxj2f0;1g
[V j((a); a)]
V j((a); a) = U j((a); a) + �E(V ((a+ 1); a+ 1jpa = j;(a)) for a < A;
= U j((A); A) for a = A:
The expectation is taken with respect to "wt+1; "ht+1 thus it is a two dimensional integral.
At any age a < A; the problem is to �nd alternative j that maximizes V ((a); a): To solve
that problem we need to know the continuation value at all possible state vectors. The
solution consists of values of E(V ((a + 1); a + 1jpa;(a)) for all j and elements of (a):
We refer to this function as the Emax. The solution method is by backwards recursion,
beginning with the last period, A.
EMAX ((a+ 1)) =R
"wa+1
R"ha+1
V�(a+ 1); "wa+1; "
ha+1
�dF�"wa+1; "
ha+1
�So, all that is left is how to evaluate these Emax function . The multivariate integrations
necessary to calculate the expected value of the maximum of the alternative-speci�c value
functions at each state point are performed by Monte Carlo integration over the shocks.
The state space is manageable, so that we evaluate the value of the Emax function at
every possible state point without having to use interpolation methods. In the numerical
implementation we draw a number ( say N) of shocks from the joint distribution of shocks�"wa+1;n; "
ha+1;n
�Nn=1
; calculate the the value function at each of these shocks, then take the
28
arithmetic mean over the N draws.
EMAX ((a+ 1)) � 1
NV n�(a+ 1); "wa+1; "
ha+1
�EMAX (:) is unbiased and is consistent as N becomes large (by the Law of Large Num-
bers).
9.2 Appendix Tables
29
Table A1: Actual and Simulated Labor Force Participation Rate: By Quarterly age
Age Simulation Actual Age Simulation Actual Age Simulation Actual73 0.149 0.333 109 0.461* 0.502 145 0.606 0.60374 0.182 0.429 110 0.477 0.504 146 0.612 0.61475 0.143 0.333 111 0.477 0.512 147 0.618 0.62876 0.188 0.320 112 0.470 0.506 148 0.619 0.62777 0.326 0.405 113 0.481 0.494 149 0.623 0.63378 0.396 0.442 114 0.493 0.495 150 0.622 0.63179 0.342 0.367 115 0.502 0.478 151 0.619 0.63980 0.337 0.349 116 0.510 0.498 152 0.614* 0.64881 0.335 0.388 117 0.510 0.509 153 0.614* 0.66182 0.353 0.402 118 0.500 0.504 154 0.619* 0.67283 0.367 0.386 119 0.495 0.502 155 0.623* 0.68384 0.400 0.433 120 0.489 0.505 156 0.620* 0.68885 0.401 0.437 121 0.495 0.500 157 0.624* 0.68386 0.426 0.459 122 0.493 0.490 158 0.620* 0.68387 0.436 0.440 123 0.490 0.487 159 0.621 0.66488 0.463 0.460 124 0.487 0.483 160 0.624* 0.69389 0.498 0.489 125 0.484 0.490 161 0.630 0.67990 0.512 0.476 126 0.468 0.487 162 0.630 0.67991 0.515 0.488 127 0.458 0.487 163 0.633 0.67992 0.526 0.504 128 0.465 0.483 164 0.640 0.69893 0.520 0.519 129 0.474 0.484 165 0.649 0.69894 0.503 0.515 130 0.484 0.492 166 0.657 0.69695 0.508 0.539 131 0.486 0.500 167 0.666 0.70096 0.513 0.539 132 0.491 0.510 168 0.676 0.70897 0.507 0.534 133 0.504 0.524 169 0.684 0.73298 0.503 0.513 134 0.523 0.539 170 0.688 0.74199 0.513 0.506 135 0.539 0.525 171 0.694 0.709
100 0.522 0.506 136 0.554* 0.509 172 0.708 0.696101 0.528 0.509 137 0.561* 0.517 173 0.723 0.701102 0.504 0.507 138 0.572* 0.523 174 0.736 0.689103 0.489 0.518 139 0.579 0.552 175 0.744 0.704104 0.473* 0.515 140 0.589 0.567 176 0.748 0.705105 0.452* 0.504 141 0.597 0.580 177 0.747 0.690106 0.440* 0.509 142 0.597 0.587 178 0.748 0.702107 0.440* 0.492 143 0.603 0.599 179 0.744 0.681108 0.449* 0.498 144 0.605 0.587 180 0.745 0.695
Note1.* : indicates that actual mean is statistically different from simulated mean at 5%2. 84.3)1,05.0(2 =χ
30
Table A2: DifferenceinDifference Regression Estimates
Without individual fixed effects With individual fixed effectsEstimate (s.e) Estimate (s.e)
Quarters before birth
Three 0.075 (0.016) 0.077 (0.018)
Two 0.059 (0.015) 0.064 (0.017)
One 0.006 (0.018) 0.018 (0.020)
Quarters after birth
One 0.011 (0.015) 0.011 (0.017)
Two 0.008 (0.013) 0.010 (0.015)
Three 0.035 (0.011) 0.028 (0.014)
Four 0.012 (0.013) 0.005 (0.016)
524 0.029 (0.006) 0.024 (0.011)
Note: Regressions include control for age, age squared, experience, experience squared,year dummies, number of children, education, age at marriage, and lagged employmentstatus
31
10 References
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34
Table 1: Labor force participation rates of women in last four decadesYear Single Married Married with less than
Women Women six year old one year old1960 44.1 30.5 18.6 -
1970 53.0 40.8 30.3 -
1975 57.0 44.4 36.7 31.0
1980 61.5 50.1 45.1 38.0
1985 65.2 54.2 53.4 48.8
1990 66.4 58.2 58.9 52.8
2000 68.1 61.6 61.8 55.2
35
Table 2: Participation rates of 25-44 year old women around �rst birthYear No children Six months after Six year After
childbirth childbirth1966-70 66.4 18.3 23.9
71-75 68.9 21.9 27.9
76-80 73.1 32.2 38.8
81-85 73.4 48.3 56.3
86-90 75.5 52.3 60.8
91-95 73.8 52.9 60.1
Table 3: Summary statistics
Variable Mean/Percent
Age(in years) 31.3
Age at marriage(in years) 22.7
Experience(in quarters) 32.1
Wife�s quarterly wage 3199
Husband�s quarterly wage 5793
Less than High School 4.9
High School degree 43.7
Some college 21.8
College degree 29.6
Labor Force Participaion rate 0.550
Person-quarter observations 49,327
36
Table 4: Parameter estimates (standard errors in parenthesis)
parameter value (s.e) parameter value (s.e)Utility parameters wife�s wage parameters�1(type = 1) -375.8 (23.2) �1(type = 1) 6.2788(0.026)�1(type = 2) -1629.1 (37.9) �1(type = 2) 7.4537(0.079)�1(type = 3) -2755.7 (134.8) �1(type = 3) 7.8837(0.023)�1 -0.0621 (0.0029) �2 0.005267(0.00033)�2 -1.1583 (0.2983) �3 0.0000578(4.78E-06)�3 0.01001(0.0045) �4 0.001328 (0.00016)�4 1.048 (0.6655) �5 -0.00000329 (2.65E-06)�5 0.00547 (0.00786) �6(type = 1) -0.788(0.484)�6(type = 1) 0.0096 (0.098) �6(type = 1) -0.107(0.062)�6(type = 1) 0.1103 (0.0137) �6(type = 1) -0.671(0.339)�6(type = 1) 0.0814 (0.0087) Husband�s wage parameters�7(type = 1) -0.0055 (0.0315) �1(type = 1) 8.003(0.101)�7(type = 1) -0.0241 (0.0032) �1(type = 2) 7.871(0.160)�7(type = 1) 0.0173 (0.0030) �1(type = 3) 8.285(0.357)�8 1.331 (0.065) �2 0.01281(0.00085)�9 -0.212 (0.026) �3 -0.0000452(0.000011)Extra cost of labor supply parameters(Before the PDA) (After the PDA) 01 0.079 (0.096) 11 -0.017 (1.279) 02 0.168 (1.599) 12 0.056 (1.641) 03 0.192 (1.488) 13 0.019 (1.892) 04 0.069 (1.305) 14 0.135 (1.633) 05 0.142 (0.998) 15 0.239 (1.161) 06 0.003 (1.069) 16 0.009 (0.948) 07 0.005 (1.053) 17 0.004 (0.684)Children arrival process Variance parameters�1(type = 1) -3.360 (2.097) �w" 0.5772(0.0339)�1(type = 2) -3.545 (1.740) �h" 0.4510 (0.0651)�1(type = 3) -3.405 (1.094) cov
�"wa ; "
ha
�-0.0001 (0.1502)
�2 0.0449 (0.0103) �wu 0.4430 (0.3315)�3 -0.000784 (0.00051)�4 0.0174 (2.030)
-0.111 (0.676)Type probability parameters Type probability parameters� 11 -0.208 (11.13) � 21 -0.218 (14.42)� 12 0.755 (13.31) � 22 0.0093 (15.57)� 13 -0.137 (13.25) � 23 0.079 (4.41)� 14 0.003 (1.04) � 24 0.0096 (1.24)ln L=-21492.3
37
Table 5: Predicted Selected Characteristics by Unobserved type
Type 1 Type 2 Type 3Labor force participation rateNo Children yet and not pregnant 44.3 86.8 84.4
During pregnancy 20.6 58.2 20.5
With less than one year old child 16.0 52.1 16.9
With one and six year old child 21.1 78.2 21.0
Number of births per woman 1.82 1.61 1.77
Proportion 25.5 45.6 28.9
38
Table 6: Model �t for pre and post law participation rates before, around, and after childbirth
Data SimulationBefore After Di¤erence Before After Di¤erence1978 1978 1978 1978
No Children 74.1 82.9 12.5 70.1* 80.2* 12.1
Quarters before birthThree 34.4 49.9 15.4 40.3* 49.9 14.1
Two 28.8 48.1 18.7 31.2 46.4 17.5
One 26.2 43.3 16.6 28.9 44.1 14.8
Quarters after birthOne 24.5 36.7 12.0 26.4 39.4 13.8
Two 25.3 34.6 9.1 25.0 37.3 12.2
Three 26.2 37.7 11.5 26.2 38.5 11.7
Four 27.5 38.5 10.8 27.2 39.8 11.5
5-24 33.3 48.1 14.8 33.9 48.2 13.8
Note1.* indicates that actual mean is statistically di¤erent from simulated mean at 5%2. �2 (0:05; 1) = 3:84
Table 7: Actual and Simulated (log) earningsAge Data Simulation20-24 7.74 7.81
25-29 7.88 7.87
30-34 7.86 7.88
35-39 7.87 7.87
40-44 7.92 7.89
39
Table 8: Out of sample model �t for pre and post law participation rates before, around,and after childbirth for 1979 NLSY cohort
Actual Data SimulationNo Children and not pregnant 77.2 77.0
Quarters before birthThree 60.1 53.8
Two 58.9 49.7
One 56.0 46.4
Quarters after birthOne 52.0 40.1
Two 48.4 36.9
Three 42.4 38.1
Four 36.9 39.1
5-24 50.4 47.4
40
Table 9: Impact of the 1978 PDA on participation rates
After 1978No PDA PDA
No Children and not pregnant 79.5 80.2
Quarters before birthThree 43.4 49.9
Two 37.1 46.4
One 35.2 44.1
Quarters after birthOne 34.2 39.4
Two 34.1 37.3
Three 35.7 38.5
Four 37.0 39.8
5-24 46.7 48.2
Table 10: Impact of the 1978 PDA on participation rates: by birth order
After 1978PDA no PDA
First pregnancy 67.8 57.2
Subsequent pregnancies 36.9 29.8
All pregnancies 46.6 38.4
Year following the birth of �rst child 54.5 50.4
Year following the birth of subsequent child 30.7 27.7
Year following the birth of a child 38.7 35.3
41
Table 11: Impact of the 1978 PDA on participation rates: by unobserved type
Type 1 Type 2 Type 3PDA No PDA PDA No PDA PDA No PDA
No children and not pregnant 39.3 38.1 89.9 89.3 95.1 94.5
During Pregnancy 20.1 16.5 73.2 61.5 33.4 26.6
With less than one year old child 16.0 14.5 62.5 59.2 23.9 20.5
With between one and six year old 20.9 20.1 81.5 80.2 22.2 20.2
Table 12: Simulated participation rates for alternative maternity leave policies
PDA plus PDA plus Unpaid leave Unpaid leaveBaseline Unpaid leave Unpaid leave one quarter two quarters(PDA) & no wage red paid leave paid leave
No Children 80.2 80.2 80.2 80.2 80.2
Quarters before birthThree 49.9 50.7 50.7 50.7 50.7
Two 46.3 29.3 22.7 22.7 22.7
One 44.0 27.2 25.2 25.2 25.2
Quarters after birthOne 39.3 21.4 21.2 3.3 5.0
Two 37.2 20.4 19.9 19.9 5.1
Three 38.5 28.8 25.7 25.7 25.7
Four 39.7 50.6 51.9 51.9 51.9
5-24 48.2 51.9 52.2 52.2 52.1
42
Table 13: Simulated participation rates for alternative maternity leave policies: by unob-served type
PDA plus Unpaid leave Unpaid leaveBaseline upto one one quarter two quarters(PDA) year leave paid leave paid leave
Type 1
No Children and not pregnant 39.3 39.3 39.3 39.3
During pregnancy 20.1 14.8 14.8 14.8
Youngest child less than one year 16.0 15.7 13.8 12.2
Youngest child less between one and six 20.9 23.5 23.5 23.4
Type 2
No Children and not pregnant 89.9 89.9 89.9 89.9
During pregnancy 73.2 50.0 50.0 50.0
Youngest child less than one 62.5 46.5 39.8 34.7
Youngest child less between one and six 81.5 85.1 85.1 85.1
Type 3
No Children and not pregnant 95.1 95.1 95.1 95.1
During pregnancy 33.4 23.7 23.7 23.7
Youngest child less than one 23.9 19.1 16.0 13.7
Youngest child less between one and six 22.2 28.4 28.4 28.3
43
0.2
.4.6
.8Fr
actio
n W
orki
ng
70 80 90 100 110 120 130 140 150 160 170Quarterly Age
Actual LFP rate Simulated LFP rate
By Quarterly Age Figure 1: Actual and Simulated Labor Force Participation Rate
44
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