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A STRUCTURAL APPROACH TO
ASSESSING RETENTION POLICIES IN
PUBLIC SCHOOLS
Celia P. Vera∗
Universidad de Piura
December 2018
Abstract.- One out of five entering public school teachers leave the field
within the first four years. Despite that the presence of a newborn child is the
single most important determinant of exits of female teachers, retention policy
recommendations rely on models that take children as predetermined. This
article formulates and estimates a structural dynamic model that explicitly
addresses the interdependence between fertility and labor force participation
choices. The model with unobserved heterogeneity in preferences for children
fits the data and produces reasonable forecasts of labor force attachment to
the teaching sector. Structural estimates of the model are used to predict
the effects that wage increases and reductions in the cost of childcare would
have on female teachers’ employment and fertility choices. The estimates un-
pack important features of the interdependence of fertility and labor supply
and contradict previous studies that did not consider the endogeneity between
these two choices.
JEL Classification: J13, J44, J45, C61.
∗Contact information: Universidad de Piura, Calle M´artir Jos´e Olaya 162, Lima 18,
Per´u; Phone (+511) 2139600 Ext.2109; Email celia.vera@udep.pe.
1
1 INTRODUCTION
One particular issue that has pervaded policy discussions for decades is the difficulty that
US school districts experience in retaining teachers. One out of five entering public school
teachers leave teaching within the first four years, citing “personal life factors” as the main
reason why they voluntarily leave the job (Goldring et al. 2014; Gray and Taie 2015). While
there have been several areas of growth in the literature, one aspect that deserves particular
attention is the role of family circumstances, such as maternity and marriage, in explaining
teacher mobility patterns. The significance of these factors is consistent with the facts that
women make up a dominant portion of total employment in elementary and secondary schools
(76% in 2015, NCES 2016) and that female teachers carry smaller wage penalties for labor
force interruptions than women in other occupations (Flyer and Rosen 1997; G¨orlich and
Grip 2009; Polachek 1981).
One key question for investigation is, therefore, to what extent fertility is related to
teacher mobility patterns and what role it plays at key points over the course of teachers’ ca-
reers, i.e, attrition and potential return after a spell out of teaching. Another important
question concerns the effects of retention policies on labor force attachment to the teaching
sector. Answering these questions is relevant given the growing emphasis that school districts
are placing on facilitating work and family life balance for young teachers, as well as the lack
of empirical evidence on the effects of these efforts on retention.1Addressing these issues
requires an understanding of the dynamics of female teachers’ choices, how unobserved fertil-
ity preferences affect the sorting into different career paths, and how intermittency patterns,
work decisions, and fertility choices interact with each other.
This paper targets these questions by constructing and estimating a structural dynamic
model that explicitly addresses the interdependence between fertility and labor force partici-
pation choices. The proposed model builds on the early works by Stinebrickner (2001a, 2001b)
by allowing the certified teacher to choose a labor activity from among a set of teaching, non-
teaching, and leisure options. This paper, however, differs in the modeling approach toward
fertility. While Stinebrickner (2001a, 2001b) assumes fertility is exogenous or stochastic, I
construct a dynamic setting that endogenizes fertility. Hence, this model integrates occupa-
tional and fertility choices into a female teacher’s life cycle plan, where women with different
taste toward childbearing opt for different occupations so as to balance their career path with
family formation choices. With this framework, I generate predicted life-cycle trajectories
for employment status, wages, and fertility that match the observed ones. The behavioral
parameters of the model are recovered through the Method of Simulated Moments (MSM)
1Despite the fact that many school districts have begun to offer child care benefits, to my knowledge, no
prior studies have provided empirical evidence regarding their effects on retention.
2
using data from the National Longitudinal Study of the High School Class of 1972 (NLS-72)
and are used to simulate the effects that potential wage changes and reductions in the cost
of childcare would have on female teachers’ employment and fertility decisions.
The joint nature of fertility and female labor supply decisions has long been recognized
and discussed.2However, none of this literature pertains to teachers.3The issue of teachers
and mobility takes on particular importance for two reasons. First, teaching has a relatively
high turnover rate compared to other occupations (Harris and Adams 2007; Ingersoll 2001,
2002). The higher mobility observed among teachers remains when exits are associated with
childbirth (Stinebrickner 2002). Second, schools that experience high mobility appear to
have lower student achievement (Kane and Staiger 2008; Levy et al. 2012; Rivkin et al.
2005; Ronfeldt et al. 2013).4
The negative effect of childbearing on teacher employment has been described in both
duration models (Flyer and Rosen 1997; Frijters et al. 2004; Scafidi et al. 2006; Stinebrickner
1998, 2002) and dynamic frameworks (Stinebrickner 2001a, 2001b). However, while these
studies are an important step forward, they assume that the presence of children is exogenous
(with the exception of Stinebrickner 2001b, who models births stochastically), and thus have
substantial limitations. First, they may overestimate the effect of children on attrition.5
Second, they disregard the potential effects that policy initiatives may have on fertility. To
the extent that fertility and employment are jointly determined, ignoring a channel through
which policies may affect employment inevitably leads to inaccurate policy recommendations.
The structural model enables this article to disentangle and thus understand the true
impact that labor and fertility decisions have on each other along teachers’ career paths.
Estimates indicate that gains of career interruptions due to childbirth vary between 83%
and 98% of the teaching wage if departure occurs within five years after certification, and
that reentry penalties for nonworking women with children lie between one and two times
the teaching wage.
The results of this article are in stark contrast with the work by Stinebrickner (2001b),
whose estimates indicate that childcare subsidies would not be a cost effective policy when
2Early papers, which apply a reduced-form approach, include Cain and Dooley (1976), Hotz and Miller
(1988), Moffitt (1984), and Schultz (1990). More recent papers, which use dynamic life-cycle models, include
Adda et al. (2017), Francesconi (2002), Gayle and Miller (2012), Keane and Wolpin (2010), and Sheran
(2007).
3There is a trend in the literature toward estimating structural models for the specific population of
teachers. For instance, van der Klaauw (2012) and Ni and Podgursky (2016) use this approach to evaluate
subjective expectations and pension systems, respectively.
4In schools with high rates of attrition, students may be more likely to have inexperienced teachers who,
on average, are less effective (Kane et al. 2008; Rivkin et al. 2005; Rockoff 2004).
5This would occur if, for instance, job unhappiness makes individuals more likely to leave work to have
children. The overestimation arises because a model in which children are treated as predetermined could
not take into account that individuals with more children would be, on average, more likely to leave work
(than individuals with fewer children), even if they had the same number of children.
3
dealing with retention problems, given the large negative effect that children have on the
utility of teachers. By allowing fertility and labor supply to be jointly determined, on the
other hand, this study’s estimates indicate that giving teaching-employed women subsidies to
offset childcare costs would reduce fertility-related career interruptions, and thus contribute
to increasing retention.
The presented policy simulations also illustrate how different fertility responses to ex-
ogenous changes in women’s environments yield increases in retention. Wage increases have
a negative effect on fertility, and thus decrease exits related to childbirth. Reductions in
the cost of childcare, on the other hand, increase fertility and are shown to be effective in
increasing job attachment to the teaching sector among beginner teachers as more teaching
jobs and births are simultaneously chosen at early periods.
Previous research has established a strong and positive relationship between teacher pay
and the length of time that teachers remain in their first teaching job.6Relatively few
studies, however, have examined which factors affect teachers’ decisions to return to the
profession. Most of the work done on this topic has been limited to descriptive or analytical
single-state studies, which used administrative data that contained no information about the
labor force status of individuals after they left teaching, or about family formation variables
(Beaudin 1993; DeAngelis and Presley 2007; Kirby et al. 1991; Murnane et al. 1988; Plecki
et al. 2006). Only a few studies used longitudinal data containing family variables to explore
the reentry decision (Grissom 2012; Stinebrickner 2002). None of these studies, however,
established an empirical link between family-oriented policies and the potential decision to
reenter the profession.7
The remainder of this article is set out as follows. Section 2 outlines the model. Section 3
introduces the data and describes the salient characteristics of the sample. The estimation
methodology is presented in Section 4. The estimation results and the model fit are discussed
in Section 5. The policy simulations are presented in Section 6, and Section 7 concludes.
2 THE DYNAMIC MODEL
Each female teacher has a finite decision horizon beginning at age (A0), the age she is the
year after certification, and exogenously ending Tyears later. At each age t, she chooses
6See Murnane and Olsen (1989, 1990), Gritz and Theobald (1996), Stinebrickner (1998), Dolton and van
der Klaauw (1999), Boyd et al. (2005), and Li (2009) for an examination of the issue in reduced-form models
and Stinebrickner (2001a, 2001b) for an overview of teacher attrition in a dynamic setting.
7Grissom (2012) finds that former female teachers are less likely to reenter with young children at home,
suggesting that childcare assistance policies would increase reentry of former teachers. Frijters et al. (2004)
and Scafidi et al. (2006) also mention a day care subsidy for women with young children as a policy alternative,
but rely on Stinebrickner’s (2001b) results to conclude that this may not be a cost-effective policy.
4
whether she works in a teaching job or not, whether she works in a nonteaching job or not,
and whether she has a child or not. A birth may occur in any period during the fertile stage,
which exogenously ends at age 40. Therefore, a female teacher faces six mutually exclusive
alternatives denoted by j:j= 1 if teaching and no birth; j= 2 if teaching and birth; j= 3
if nonteaching and no birth; j= 4 if nonteaching and birth; j= 5 if nonworking and no
birth; and j= 6 if nonworking and birth. Let djt = 1 if alternative jis chosen at time tand
djt = 0 otherwise. All alternatives are mutually exclusive, implying Σ6
j=1djt = 1.At any age
t, the objective of a particular female teacher is to maximize the expected present value of
remaining lifetime utility,
Et"A0+T
X
t=A0
δt−A0Ut(ct, et, nt, kt, Kt)#,(1)
with respect to et, nt,and ktfor ages t=A0,...,40 and with respect to etand ntfor ages
t= 41, . . . , A0+T. The variables are defined as follows: ctis the level of goods consumption
at t;etis a dichotomous variable equal to unity if the female teacher works in a teaching
job and equal to zero otherwise; ntis a dichotomous variable equal to unity if the female
teacher works in a nonteaching job and equal to zero otherwise; kt= 1 indicates a birth at
tand kt= 0 indicates no birth; Ktrepresents the total number of children at age t;δ [0,1]
is the subjective discount factor; and Etis the expectations operator.8
Per period utility at any age t,Ut, is assumed to have the following form:
Ut=ct+a1tet+a2tnt+bt+g1tet+g2tnt.(2)
The disutilities of working in teaching and in nonteaching without children (a1tand a2t,
respectively), the direct utility obtained from having children (bt), and the difference in the
disutilities of teaching and of nonteaching when having children instead of being childless
(g1tand g2t, respectively) are further parameterized as functions of age and the stock of
children as follows:
alt =αl1+αl2t+αl3t2, l = 1,2 (3)
bt=β1Kt+β2Ktt+β3Ktt2+β4K2
t+β5K2
tt+β6K2
tt2(4)
glt =γl1Kt+γl2Ktt+γl3Ktt2+γl4K2
t+γl5K2
tt+γl6K2
tt2, l = 1,2 (5)
Thus, the utility in equation 2 is decreasing in etand nt, reflecting disutility of working
in teaching (α11 <0) and in nonteaching (α21 <0). Labor market decisions interact with
age through α12, α13 , α22,and α23 . The parameters βcapture the effects that children have
on utility. I expect that a larger number of children provides a higher instantaneous utility
8To limit the size of the state space, the maximum number of children allowed in the model is three.
Consequently, giving birth during the fertile stage is an option provided the individual has fewer than three
children at the beginning of the decision period.
5
(β1+β2t+β3t2>0) at a decreasing rate (β4+β5t+β6t2<0). The effect that children have on
utility through their interactions with current participation is represented in the parameters
γ. The disutility of working in both sectors when children are present is expected to be
greater than the disutility of working while being childless. That is, I expect g1tand g2t<0.
This in turn implies that the marginal utility of children in the nonmarket alternative is
expected to be greater than the gains of children in both teaching and nonteaching sectors.
I incorporate persistent unobserved individual differences in preferences for children fol-
lowing an approach similar to that proposed by Heckman and Singer (1984). Specifically,
unobserved heterogeneity arises in the utility function through β1, allowing women to differ
in their direct utility of children, bt. The distribution of the time-invariant heterogeneity
component, β1, is specified to be discrete joint multinomial. Accordingly, I distinguish be-
tween J‘types’ of individuals where each type j,j= 1, . . . , J, is characterized by a different
value of β1. The population proportions of each type are given by pj=P r(β1=β1j),
j= 1, . . . , J. In the specification of the model I allow for two types of individuals, who differ
in the values of β1according to their preferences toward childbearing.9The proportions of
women with low and high preferences for children are defined as P r(β1=β11) = p1and
P r(β1=β12) = 1 −p1, respectively.
The proposed model generates two different sources of children gains that depend on the
number of children and the women’s age.10 The first one, “children premia,” is relevant to
understanding quitting behavior. It measures the gains that a teaching-employed woman
receives if she keeps her current teaching job and gives birth, as well as the gains she receives
if she leaves teaching and bears a child.11 My results are expected to be consistent with
previous literature that has found that attrition is positively related to childbirth. Thus, I
expect the gain of dropping entirely out of the workforce to give birth to be greater than
the gain of keeping a current teaching job and giving birth. Although the sign of the utility
flows of switching to nonteaching associated with childbirth cannot be predetermined, it is
expected that if positive, the gains of dropping out of the workforce entirely will be greater
than the gains of switching to the nonteaching sector to give birth.
The second source of children gains, “occupation premia,” measures the nonpecuniary
gains of employment alternatives conditional on having children, and gives insight into two
9See van der Klaauw (1996, 2012) for a similar specification of the unobserved heterogeneity distribution.
10Children gains are based on contemporaneous utility rather than discounted expected lifetime utility.
Thus, they only capture the gains (or losses) incurred in a particular period and do not account for future
choices.
11Let q1t, q2t,and q3tbe the contemporaneous utility independent of consumption, Ut−ct, when
et= 1, nt= 1 and (et= 0 and nt= 0), respectively. The gains of giving birth while employed in
a teaching job have been calculated as q1t(Kt+ 1) −q1t(Kt) and the gains of switching to nonteach-
ing and of leaving the workforce altogether to give birth have been calculated subtracting q1t(Kt) from
q2t(Kt+ 1) and q3t(Kt+ 1), respectively. These premia are evaluated for Kt= 0,1,2.
6
points.12 First, it reflects how children affect the disutility of working. The disutility of
teaching and nonteaching are expected to be greater with more children. Second, when eval-
uated at late periods, it measures the gains and losses of a reentry into teaching associated
with prior fertility behavior. For instance, the gains of teaching relative to nonteaching re-
flect the rewards that an average former teacher with children and enrolled in a nonteaching
job receives if she returns to teaching. The gains of teaching relative to the nonmarket alter-
native, on the other hand, provide information about the rewards incurred by a nonworking
former teacher with children if she returns to teaching.13
The choice decision in each period as described in equation 1 is made subject to the
woman’s budget constraint, which is assumed to be satisfied period by period, and is given
by: w1tet+w2tnt=ct+f1et+f2nt+f3Kt,(6)
where w1tand w2tdenote the female teacher’s wage earnings in teaching and nonteaching,
respectively; f1and f2represent the corresponding fixed costs of work, and f3is the goods
cost per child.
The female teacher’s current earnings depend on the initial wage draw and age t. They
are given by:14
wlt =ωlexp (zl1t+zl2t2), l = 1,2,(7)
where ω1and ω2are drawn from truncated lognormal wage offer distributions
F1(x) : ln x ∼N(µ1, σ2
1|ln ω1, ln ω1) and F2(x) : ln x ∼N(µ2, σ2
2|ln ω2, ln ω2), respec-
tively. That is, when employed, the individual experiences wage growth as a function of age,
which captures the accumulation of human capital over time.15
The assumption that the female teacher does not carry over any debt incurred during one
period to the next period is extreme. However, given that the instantaneous utility function
in equation 2 is linear and additive in consumption, the above optimization problem becomes
a lifetime wealth maximization problem modified by the psychic value of children and work
(Eckstein and Wolpin 1989; Francesconi 2002).
12Let q1t, q2t,and q3tbe the contemporaneous utility independent of consumption, Ut−ct,
when et= 1, nt= 1 and (et= 0 and nt= 0), respectively. The gains of teaching rela-
tive to nonteaching and to out of the workforce have been calculated as q1t(Kt)−q2t(Kt) and
q1t(Kt)−q3t(Kt), respectively. The benefit of nonteaching relative to out of the workforce has been calculated
as q2t(Kt)−q3t(Kt) . These premia are evaluated for Kt= 1,2,3.
13Considering that most individuals start their working career with a teaching job (74% in the data)
and that the average first teaching spell is 3.3 years, these premia, although not conditioned on a previous
career interruption, provide an idea of gains and losses of returning to teaching associated with prior fertility
behavior.
14CPI is used to deflate nominal wage values into 1986 dollar values.
15Modeling wage as functions of experience would have been preferable, but would also increase the
computation burden to solve and estimate the model. Rendon (2007) and Rendon and Quella-Isla (2015)
also assume age-specific wages in structural models of job search.
7
The set of available employment options in a given year depends on the person’s employ-
ment status in the previous year. If in t−1 the individual is employed as a teacher, in tshe
can continue working in her previously held job, accept a new nonteaching job offer drawn
from the known wage offer distribution F2(.),(x2∈(ω2, ω2),0< ω2< ω2<∞), or choose
the nonmarket alternative.16 Likewise, if in t−1 the person is employed in a nonteaching
job, in tshe can continue working in her previously held job, accept a new teaching job offer
drawn from the known wage offer distribution F1(.)(x1∈(ω1, ω1),0< ω1< ω1<∞), or
choose the nonmarket alternative. If in t−1 the person is out of the workforce, in tshe
receives a teaching job offer with probability ρand a nonteaching job offer with probability
1−ρ. Both job offers are drawn from the known wage offer distributions F1(.) and F2(.),
respectively. The person also has the option of staying out of the workforce.
Contraception is assumed to be perfect during the fertile stage and births are timed
without error. The total number of children at age t,Kt, is a time-varying predetermined
state variable that evolves as Kt=Kt−1+kt. At the time of each period’s work decision the
woman knows the value of her current occupation’s base wage (ωl) for l= 1,2, the distribu-
tion of the wage offer from the alternative occupation, and the wage structure in equation 7,
but does not know the future realizations of the wages in the alternative occupation.
The decisions made at age tdepend on the fertility and employment histories up to that
point in time. This history defines the state at which a female teacher starts a new period.
The state space is denoted as Ωt= (Kt−1, A0, jt−1, ω1I(et−1= 1), ω2I(nt−1= 1)).
Let the value function Vt(Ωt) be the maximal expected present value of lifetime utility
as in equation 1 given the woman’s state Ωt. The value function can be written as the
maximum over alternative-specific value functions, that is,
Vt(Ωt) = max[V1t(Ωt), . . . , V6t(Ωt)], t =A0,...,40,
and
Vt(Ωt) = max[V1t(Ωt), V3t(Ωt), V5t(Ωt)], t = 41, . . . , A0+T,
where Vjt(.) is the value function if the female teacher chooses alternative j. Each of
these alternative-specific value functions obey the Bellman equation (Bellman, 1957):
Vjt(Ωt) = Ujt (Ωt) + δEtVt+1 (Ωt+1|Ωt, djt = 1), t < A0+T
Vj,A0+T(ΩA0+T) = Uj,A0+T(ΩA0+T),(8)
with j= 1,...,6 for t=A0,...,40 and j= 1,3,5 for t= 41, A0+T. The expectation in
equation 8 is taken with respect to the realization of the stochastic earnings conditional on
Ωtand djt = 1. Appendix A describes in detail the numerical solution of the model.
16Given that during the sample period of the data few teachers were laid off, I do not find it restrictive
to assume that all individuals currently teaching will always have the option to remain in teaching.
8
3 DATA
The data come from the NLS-72. This survey collected longitudinal data on the post-
secondary educational activities of 22,652 high school seniors who graduated in 1972 and
included five additional follow-up surveys through 1986. For each person, the survey contains
detailed information on the timing of employment spells and birth events. The analysis in this
study will be restricted to the subsample of 405 female teachers who became certified to teach
at some point between 1975 and 1985 and that had teaching experience after certification.
While the final 1986 follow-up survey was limited to only a subset of the original NLS-72
participants, the sample design oversampled teachers and potential teachers by including
all those who had previously reported having completed teaching training. Therefore, the
NLS-72 surveys combined provide a valuable source for the study of mobility patterns of
a cohort of teachers.17 A valid concern regarding my results is that the data represent
preferences of teachers of several generations past. However, studies that used more current
data illustrate that family circumstances remain important determinants of teacher mobility
(Scafidi et al. 2006 with data from the 90s and Grissom 2012 with the NLSY-79, which
contains information on workers throughout the 1980s and 1990s and into the 2000s).18
In any given year, a woman is defined to be working if she is employed for more than 20
hours per week at any time between the first of November of the previous year and end of
October of the current year.19 A woman’s wage earnings are defined as her weekly wage rate
times 52 weeks.20 She is defined to give birth in a given year if a birth occurs between the first
of November of the previous year and end of October of the current year. For non-interview
years, the employment and fertility histories were obtained using retrospective questions
from the last follow-up survey. Table 1 reports descriptive statistics for the sample. The
first observation year is the year following certification, and the last sample year is 1986. For
the resulting unbalanced panel, the average sample member is observed for 10 years, resulting
in 4,455 “person-years.”21 The majority of individuals in the sample do not have children
17The 1993-03 Baccalaureate and Beyond Longitudinal Study is a more current survey specific to teach-
ers. However, this survey does not track fertility choices. Considering the important role fertility plays in
explaining teacher mobility patterns, the NLS-72 is the survey that best fits the objectives of this study.
18One exception is the work by Gilpin (2011) with data of the Teacher Follow Up Survey for school years
2000-2001 and 2004-2005. He found that the majority of former teachers, regardless of teaching experience,
remain working outside of teaching, in contrast to exiting the labor force entirely.
19In teaching labor markets, it is uncommon for working terminations to occur in the middle of a school
year. Also, the “out of the workforce” designation includes individuals who are working fewer than 20 hours
a week. The same approach is taken by Stinebrickner (2002).
20For some years, wages were reported other than weekly. In these cases, weekly wages were calculated
by dividing annual salary by 52 weeks, monthly salary by 4.6 weeks, or multiplying hourly wages by the
number of hours worked per week.
21Since this article focuses on career choices after certification, and most individuals spent four years after
high school in training courses to be certified, the final data set contains between one and eleven years of
information for every individual. Most individuals are observed for ten or fewer years; only those who spent
9
when they initially become certified to teach. The average female teacher is 27 years old, has
two children, and earns $303 per week in a teaching job and $296 per week in a nonteaching
job. Nonteaching earnings are more dispersed than teaching earnings, reflecting the fixed
structure of wages in the teaching sector. The lower part of table 1 further shows that of the
4,455 person-years, 53% are spent in teaching without giving birth, 5% in teaching giving
birth, 13% working in nonteaching without giving birth, 1% in nonteaching giving birth,
12% not working and not giving birth, and 3% not working and giving birth.
TABLE 1
Descriptive Statistics
Mean Std. Dev No. of obs.
Sample of 405 individuals
Years in sample 9.54 1.60 405
Age in 1st period 22.07 1.77 405
Percent with at least one child (in t= 0) 7.90 - 405
Percent with at least one child (in 1986) 72.35 - 405
Number of children (in t= 0)a0.10 0.37 405
Number of children (in 1986)a1.06 0.67 405
Sample of 4,455 person-year observations
Age 27 3.62 4,455
Number of childrenb1.55 0.66 1,358
Teaching Wage c302.54 99.59 2,565
Nonteaching wage c295.54 143.56 638
Teaching and no birth 60.97 - 4,455
Teaching and birth 5.41 - 4,455
Nonteaching and no birth 15.27 - 4,455
Nonteaching and birth 1.24 - 4,455
Nonwork and no birth 13.43 - 4,455
Nonwork and birth 3.67 - 4,455
aComputed for all individuals observed in t.
bComputed on person-years observations with positive number of children only.
cComputed on person-years observations with positive sector-specific earnings.
Figure 1 illustrates how the employment participation rates of female teachers changes
over time after certification and provides some descriptive insight into the extent of and rea-
son for teacher attrition. During years of decline in teaching participation, the participation
rate in nonteaching occupations remains largely unchanged, suggesting that a large increase
in the proportion of women who are out of the workforce plays a more important role in the
declining teaching participation rate.
three years in college are observed for eleven years.
10
0
.2
.4
.6
.8
1 3 5 7 9 11
Number of years after certification
Teaching Nonteaching
Out of the workforce
FIGURE 1
Actual Participation Rates
Table 2 shows the evolution of employment rates and employment transitions, as well
as wages 2, 4, 6, 8, and 10 years after certification. Employment distributions correspond
to the participation rates shown in Figure 1. Increasing birth rates complement the trends
observed in the employment distributions and support the view of thinking of attrition as
a fertility-related event. Moreover, the fact that birth rates increase in mid-career years
while departures from teaching to the nonmarket alternative decrease suggests that births
are likely to occur within one or two years after dropping out of teaching.
Other employment transitions give some insight into reentry behavior. Higher transition
rates into teaching in early years reflect the fact that some individuals do not work as
teachers right after certification,22 and also suggest that reentry into teaching after a career
interruption is not very likely to occur. The large share of women who keep their nonteaching
job from the previous period, as well as the large proportion of nonworking women who
remain out of the workforce the following period, suggest that once individuals leave teaching,
they are less likely to return.23
22Recall that transitions into teaching can represent both a first entry into teaching or a reentry after a
spell out of teaching. In the data, 26% of individuals do not start their careers employed as teachers.
23Caution should be taken when interpreting reentry behavior in the data. The average teacher is 32
years old in her last year observed. Neither her fertility cycle nor her potential years to return have ended.
An analysis of attrition and reentry patterns indicates that 38% of all exiting teachers who are observed five
or more years after leaving the workforce return at some point within this period. The percentage of the
11
TABLE 2
Employment, Fertility and Wages by number of years since certification
Years after certification
Variable Year 2 Year 4 Year 6 Year 8 Year 10
Employment Distributions
Teaching 76.87 70.56 64.10 58.51 56.91
Non Teaching 17.66 13.96 16.41 17.55 14.80
Out of the workforce 5.47 15.48 19.49 23.94 28.29
Employment Transitions
From teaching
To teaching 87.16 84.28 89.92 93.72 91.71
To nonteaching 7.43 5.35 3.10 2.24 1.10
Out of the workforce 5.41 10.37 6.98 4.04 7.18
From nonteaching
To teaching 45.78 26.92 10.61 5.88 2.00
To nonteaching 51.81 67.31 81.82 79.41 84.00
Out of the workforce 2.41 5.77 7.58 14.71 14.00
From out of the workforce
To teaching 56.52 27.91 16.67 8.24 8.22
To nonteaching 26.09 9.30 3.03 8.24 1.37
Out of the workforce 17.39 62.79 80.30 83.53 90.41
Birth Rate 3.48 8.63 15.90 16.49 5.59
Mean wage in teaching 15,180 14,615 14,223 18,218 17,711
Mean wage in non teaching 13,402 14,461 14,501 18,071 18,993
Mean wage 14,848 14,590 14,279 18,184 17,976
Wage Distribution
w <11,856 20.79 30.93 38.22 11.19 11.47
11,856=< w <15,444 35.79 36.04 24.84 17.48 17.89
15,444=< w <18,876 25.00 16.82 16.88 24.83 29.36
w >=18,876 18.42 16.22 20.06 46.50 41.28
NOTE.- Employment transitions consider flows from period t−1 to period t.
4 ESTIMATION
The estimation strategy is designed to recover the behavioral parameters of the theoretical
model. I use the starting point of each individual in the data as the starting point of
subset of women who leave the workforce after giving birth is 30%. It seems possible, then, that an increase
in the return rates would occur after year 6 when the teacher feels comfortable with childcare or when the
child becomes old enough to attend school. Unfortunately, whether this occurs or not, cannot be examined
with these data.
12
individuals in my simulated sample, which is composed of 20 “copies” of every individual in
the data. Overall, I simulate 89,100 career and fertility paths.24
Consider a woman who, one year after becoming certified to teach, begins her working
career at age A0. Given her state space, Ωt, the woman draws a random shock from F1(.)
or F2(.), calculates the six current utilities and the alternative-specific value functions, and
chooses the alternative that yields the highest value. The state space is then updated ac-
cording to the alternative chosen, and the process is repeated. Exact numerical solution is
carried out by backward induction (value function iterations). Agents solve the dynamic
problem with a finite horizon T= 40.25
The solution to the optimization problem serves as the input into estimating the struc-
tural parameters of the model given data on choices and earnings. From the alternative-
specific value functions, all structural parameters can be estimated, except that the utility
parameters β11, β12 , β4, and γl1, γl4, αl1, for l= 1,2, cannot be distinguished from the bud-
get parameters fdue to data limitations. The identifying restriction is then f1=f2=f3= 0.
This implies that αl1for l= 1,2 should be interpreted as the gross costs of work (normalized
to dollars), while the βand γparameters measure the value of children net of the goods cost
of children.26
The model is estimated using the MSM (see Pakes and Pollard 1989, and Duffie and
Singleton 1993). Based on an initial set of parameters, I solve the dynamic program-
ming problem and then simulate paths of employment and fertility. The simulated data
provide a panel dataset used to construct moments that can be matched to moments ob-
tained from the observed data. Using a quadratic loss function that measures the dis-
tance between the observed and simulated moments, the parameters of the model are
then chosen such that the simulated moments are as close as possible to the observed mo-
ments. The parameters to be estimated are φ={β11, β12 , β2, β3, β4, β5, β6, ρ, p1,Θ}where
Θ = {αl1, αl2, αl3, γl1, γl2, γl3, γl4, γl5, γl6, µl, σl, zl1, zl2,}for l= 1,2.
The moments used in this estimation are the cell-by-cell probability masses for the fol-
lowing distributions:
1. employment status (3 moments ×11 years),
2. wage levels (4 moments ×11 years),
3. children statuses (4 moments ×11 years),
24That is, the starting point of individual iin the data is used as the starting point of individuals
i, . . . , 20 ×(i−1) + jin the simulated sample, where j= 1, . . . 20.
25That is, the model ends 40 years after the woman is certified. For instance, a woman who starts her
working career at age of A0= 25, makes employment and fertility decisions during the first 15 years of her
working career (until she is 40), but only employment decisions for the remaining 25 years.
26As long as the budget parameters are linear in et,ntand Kt(as in equation 6), they are not distin-
guishable from their respective psychic values in the utility function, α11 and α21.
13
4. employment transitions from teaching (3 moments ×10 years),
5. employment transitions from nonteaching (3 moments ×10 years),
6. employment transitions from the nonmarket alternative (3 moments ×10 years),
7. fertility transitions for childless women (2 moments ×10 years),
8. fertility transitions for women with one child (2 moments ×10 years),
9. fertility transitions for women with two children (2 moments ×10 years),
10. attrition rates (11 moments ×10 years),
11. return rates from nonteaching (2 moments ×10 years),
12. return rates from out of the workforce (2 moments ×10 years).
Thus, there are 421 moments to estimate 35 parameters. The MSM procedure relates a
parameter set to a weighted measure of distance between sample and simulated moments:
S(φ) = ∆m0W−1∆m,
where ∆mis the distance between each sample and simulated moment and Wis a
weighted matrix. In this study, Wis an identity matrix and each moment is weighted the
same. The estimated behavioral parameters are thus φ∗= argmin S(φ). The function is
minimized using Powell’s method (Powell 1964), which requires function evaluations, not
derivatives.
5 RESULTS
5.1 Parameter Estimates
Table 3 presents the estimates and asymptotic standard errors of the structural parameters
assuming a discount factor, δ, of .95. Teaching jobs present a lower mean and standard
deviation of the log-wage offer distribution than nonteaching jobs. These parameters imply
an estimated mean yearly wage offer for teaching jobs of $10,043 and of $10,574 for non-
teaching jobs. The wage growth parameters show that wages grow at a declining rate for
both teaching and nonteaching occupations.
14
TABLE 3
Parameters Estimates and asymptotic standard errors
Parameter φEstimate SE
Teaching Pecuniary Utility
Mean of log wage dbn: µ19.163 0.675∗
St. dev. of log wage dbn: σ10.319 0.071∗
Wage growth (linear): z11 0.004 0.000∗
Wage growth (quadratic): z12 -0.001 1.191
Nonteaching Pecuniary Utility
Mean of log wage dbn: µ29.123 1.499∗
St. dev. of log wage dbn: σ20.535 0.294∗
Wage growth (linear): z21 0.038 0.000∗
Wage growth (quadratic): z22 -0.006 0.000∗
Teaching Non-pecuniary
Constant: α11 -7,690.61 2,252.91∗
Year: α12 -2.101 0.334∗
Year ×Year: α13 7.957 0.931∗
Number of children: γ11 113.451 29.951∗
Number of children growth (linear): γ12 3.268 0.671∗
Number of children growth (quadratic): γ13 -54.738 4.795∗
Number of children2:γ14 -65.655 3.833∗
Number of children2growth (linear): γ15 -47.755 3.228∗
Number of children2growth (quadratic): γ16 -8.829 2.078∗
Nonteaching Non-pecuniary
Constant: α21 -15,518.58 4,103.4∗
Year: α22 41.285 3.393∗
Year ×Year: α23 11.176 0.747∗
Number of children: γ21 206.818 5.704∗
Number of children growth (linear): γ22 37.544 9.703∗
Number of children growth (quadratic): γ23 -61.655 9.116∗
Number of children2:γ24 -13.221 0.708∗
Number of children2growth (linear): γ25 -35.355 5.652∗
Number of children2growth (quadratic): γ26 19.743 4.714∗
Children
Number of children growth (linear): β22.098 0.099∗
Number of children growth (quadratic): β367.169 18.317∗
Number of children2:β4-14.164 1.394∗
Number of children2growth (linear): β51.332 0.096∗
Number of children2growth (quadratic): β6-21.863 1.908∗
Unobserved heterogeneity
Number of children: β11 155.634 25.332∗
Number of children: β12 198.096 16.398∗
Type proportion
Prob type 1: p10.363 0.513∗
Labor Market
Prob offer if out workforce: ρ0.601 0.024∗
NOTE: * denotes an asymptotic tratio greater than two.
15
The nonpecuniary parameter estimates seem to be consistent with others available in the
literature. For example, participation decreases utility (α11 and α21 <0 ), particularly in
nonteaching employment. Francesconi’s (2002) and Eckstein and Wolpin’s (1989) estimates
also indicate a disutility of working for a sample of married women observed between 1968
and 1991, and between 1967 and 1982, respectively.27 Using NLSY data, Sheran (2007) also
finds that the utility of women decreases with a full time job.
As expected, estimates show that marginal utilities are positive and diminishing in chil-
dren (β11, β12, β2, β3>0 and β4+β5t+β6t2<0∀t), vary across types substantially, and
are always greater in the nonmarket alternative.28 For instance, the monetary (utility) value
of the first child in the nonmarket alternative for a woman at age 23 is estimated to be
$560 for women with low taste for children (LF) and $602 for women with high taste for
children (HF). A second child would decrease these gains at the same age to $146 and $188
for women with low and high preferences toward children, respectively. The corresponding
gains of the first child in the nonteaching sector for LF and HF women are, respectively,
$382 and $425. The gains in the same sector of a second child are $85 and $128 for LF and
HF women, respectively. The “penalty” of the first child in teaching at the same age is $98
for LF women and $56 for HF women. A second child increases these penalties for LF and
HF women to, respectively, $1,089 and $1,046.
My results further reveal that children decrease the utility gains from working and are
consistent with most studies of female labor supply (Francesconi 2002; Sheran 2007; van
der Klaauw 1996) and with those analyzing the labor market of teachers (Adda et al. 2017;
Stinebrickner 2001a).29 Particularly, the first child increases the penalties for teaching and
nonteaching-employed women of age 24 by $1,147 and $468, respectively. A second child
would increase the corresponding penalty for teaching workers to $1,943 and decrease it for
nonteaching workers to $146.
To illustrate the implications of these estimates on teachers’ career mobility patterns,
I discuss below estimates of the two premia defined in Section 2. They are calculated by
averaging the utility flows over individuals and are presented in terms of the average teaching
wage in order to facilitate economic interpretation.
27Notice, however, that results are not directly comparable. This is because I estimate parameters for a
sample of teachers and because I do not control for marital status. To the extent that the studies mentioned
use data on women and jointly model labor supply and fertility decisions, they provide a simple check on
the plausibility of my results.
28Francesconi (2002) and Kenneth (1984) found a similar result.
29Note, however, that Adda et al. (2017) classify occupations into three groups (routine, abstract, and
manual) according to the tasks involved in each occupation. Because of the interaction with students,
teaching is classified as an abstract occupation. The authors find that abstract jobs are less desirable
when children are present. However, one must interpret this result with caution since primary and high
school teachers are grouped together with university professors, and therefore conclusions made for abstract
occupations are not representative of the single occupation of interest in this article.
16
Table 4 displays the “children premia,” utility flows of employment transitions from the
teaching sector associated with childbirth. The first rows of the three blocks (rows 1, 4, and
7 in the table) measure the gains of starting and enlarging families in teaching. An average
teacher does not have nonpecuniary incentives to bear children and keep her current teaching
job. The corresponding loss, if the first birth occurs within five years after certification, does
not exceed 10% of the teaching wage, but becomes more important in later periods.30 Instead,
an average teacher finds it rewarding to drop out of the workforce to give birth, regardless of
her current number of children. The gains of a first birth within five years after certification
in the nonlabor market alternative (relative to teaching) lie between 83% and 98% of the
average teaching wage.
TABLE 4
Children Premia
(In terms of average teaching wage)
Number of years after certification
1 2 3 4 5 6 7 8 9 10 11 12
First Child
T -0.01 -0.03 -0.05 -0.08 -0.10 -0.14 -0.17 -0.21 -0.26 -0.30 -0.35 -0.40
NT -0.72 -0.71 -0.70 -0.69 -0.67 -0.66 -0.65 -0.64 -0.62 -0.61 -0.59 -0.57
OWF 0.83 0.85 0.89 0.93 0.98 1.05 1.12 1.20 1.29 1.37 1.47 1.56
Second Child
T -0.13 -0.20 -0.29 -0.39 -0.51 -0.65 -0.80 -0.98 -1.17 -1.35 -1.56 -1.77
NT -0.69 -0.67 -0.65 -0.62 -0.59 -0.55 -0.51 -0.46 -0.41 -0.36 -0.30 -0.24
OWF 0.86 0.90 0.96 1.03 1.11 1.21 1.32 1.45 1.59 1.71 1.87 2.02
Third Child
T -0.26 -0.38 -0.53 -0.71 -0.92 -1.16 -1.43 -1.74 -2.08 -2.39 -2.78 -3.14
NT -0.58 -0.51 -0.41 -0.30 -0.17 -0.02 0.15 0.35 0.57 0.78 1.02 1.27
OWF 0.96 1.04 1.15 1.27 1.42 1.59 1.78 2.00 2.24 2.46 2.72 2.97
NOTE: T = Teaching; NT = Nonteaching; OWF = Out of the workforce.
The “occupation premia,” the key measure in understanding reentry patterns associated
with the presence of children, are presented in table 5. Provided a positive stock of chil-
dren, former teachers employed in nonteaching jobs receive nonpecuniary gains upon reentry
into teaching, whereas nonworking former teachers face penalties if they reenter teaching.
For instance, the penalties associated with reentering teaching in period 8 for an average
nonworking former teacher with one child are equivalent to 1.41 times the teaching wage.
A reentry into teaching from the nonteaching sector in the same period and with the same
number of children, on the other hand, yields gains equivalent to 42% of the average teaching
wage.
30If the first birth occurs in period 12, the loss is equivalent to 40% of the teaching wage.
17
TABLE 5
Occupation Premia
(In terms of average teaching wage)
Number of years after certification
1 2 3 4 5 6 7 8 9 10 11 12
T-NT
1 child 0.70 0.68 0.65 0.61 0.57 0.53 0.48 0.42 0.36 0.30 0.23 0.15
2 children 0.56 0.47 0.36 0.23 0.08 -0.09 -0.29 -0.51 -0.76 -1.03 -1.33 -1.66
3 children 0.33 0.13 -0.11 -0.40 -0.74 -1.14 -1.58 -2.09 -2.65 -3.28 -3.97 -4.74
T-OWF
1 child -0.84 -0.89 -0.94 -1.01 -1.09 -1.18 -1.29 -1.41 -1.55 -1.70 -1.87 -2.06
2 children -0.99 -1.11 -1.25 -1.42 -1.62 -1.86 -2.12 -2.42 -2.76 -3.14 -3.55 -4.01
3 children -1.21 -1.42 -1.67 -1.98 -2.34 -2.74 -3.21 -3.73 -4.32 -4.97 -5.70 -6.49
NT-OWF
1 children -1.55 -1.56 -1.59 -1.62 -1.66 -1.71 -1.77 -1.84 -1.91 -2.00 -2.10 -2.21
2 children -1.55 -1.58 -1.61 -1.65 -1.70 -1.76 -1.83 -1.91 -2.01 -2.11 -2.22 -2.35
3 children -1.54 -1.55 -1.56 -1.57 -1.59 -1.61 -1.63 -1.65 -1.67 -1.70 -1.72 -1.75
NOTE.- T-NT = Teaching relative to nonteaching; T-OWF= Teaching relative to out of the workforce;
NT-OWF = Nonteaching relative to out of the workforce.
My estimates are consistent with those found by Stinebrickner (2001a, 2001b) regarding
the role of children in explaining teachers’ quitting decisions: as families are created or
enlarged, female teachers become less likely to be employed in teaching jobs and become
more likely to drop out of the workforce altogether. The introduction of endogenous fertility
in this model, however, opens up a new channel through which policies can affect retention
outcomes. By allowing labor supply and fertility choices to be jointly determined, this
study’s estimates thus lead to different policy recommendations, as will be elaborated upon
in Section 6. My estimates also allow us to understand how each choice affects the other not
only within the early stages of a teacher’s career, but also after a career interruption. Findings
reveal that in late periods, after families have been created, the nonmarket alternative offers
large nonpecuniary rewards in comparison to teaching, thus resulting in important penalties
if nonworking teachers return to the profession. This outcome, combined with the gains of
dropping out of the workforce due to childbirth, suggests that policy initiatives targeted to
fertility choices will also generate changes in teachers’ retention.
Key results of the interdependence of fertility behavior and labor force attachment to
the teaching sector are depicted in table 6. Using births within two years after exit as
a measure of fertility-related career interruptions, table 6 shows that teacher attrition is
mostly a fertility-related event, especially for teachers exiting to the nonmarket option.
Among leaving teachers, 66% give birth within two years after exit, and this percentage
accounts for 81% and 50% among exiting teachers to the nonmarket alternative and the
nonteaching sector, respectively. Furthermore, exiting teachers who leave for nonteaching
and who drop out of the workforce differ in fertility behavior during their first teaching spell.
Among exiting teachers who leave the workforce entirely, 18% accumulate children during
18
TABLE 6
Teacher Career Paths: Employment and Fertility
Overall Left to NT Left OWF
First Teaching Spell
Percent with children at exit timea13.5 7.54 18.25
Percent Returnb1.29 17.22 3.27
Percent birth within 2 years after exit 66.17 50.41 80.61
Percent Returnb10.71 5.58 13.65
Percent no birth within 2 years after exit 33.83 49.59 19.39
Percent Returnb56.43 54.95 59.90
Career Interruption
Percent birth during career break 33.15 15.48 54.66
Length career break 2.14 2.44 1.78
Return
Percentc23.71 29.37 19.20
Percent with children at reentry timed36.97 19.90 57.76
aExit time is the last year of the first teaching spell.
bCalculated as a proportion of leaving teachers associated with the previous row.
cCalculated as a proportion of leaving teachers.
dReentry time is the first year a former teacher is observed in a teaching job after a spell out.
their first teaching spell. This percentage accounts for only 8% among exiting teachers who
enroll in a nonteaching job.
Table 6 further illustrates that reentry into teaching is more likely to occur among former
teachers who do not give birth during a spell out of teaching. The percentage of former
teachers who return after a fertility-related career interruption is 11%, whereas 56% of former
teachers who do not give birth within two years after exit return at some point. Since teachers
exiting to the nonteaching sector accumulate fewer children during their careers than those
who exit the workforce entirely, it is not surprising that the former are more likely to return
than the latter (29% vs 19%, respectively). One point discussed in the literature is that after
the child is old enough, the former teacher will return. Given the sample ends when most
individuals are still fertile, it is not possible to account for the effect of children’s age on a
person’s labor supply. However, this information is necessary to solve the value functions of
forward-looking individuals who take into account that their young children will eventually
become older. The estimates in this article are obtained using the assumption that school-age
children have the same effect on nonpecuniary utility as younger children.
5.2 Model Fit
To formally examine the extent to which the model is able to capture changes in the behavior
of women that take place after certification, the parameter estimates in table 3 were used
19
to compute the simulated participation rates that correspond to the descriptive figure 1.
Figure 2 shows that the model very accurately predicts the decreasing teaching participation
rate that is observed over time for women. It also accurately predicts that this decrease
takes place almost exclusively because of an increase in the proportion of women who are
out of the workforce.
0
.2
.4
.6
.8
1 3 5 7 9 11
Number of years after certification
Teaching Nonteaching
Out of the workforce
FIGURE 2
Simulated Participation Rates
As an additional measure of goodness of fit, table 7 presents the actual and predicted
percentages of total person-years spent in each employment alternative, as well as the actual
and predicted percentage of aggregate years in which a birth occurs. The dynamic model
appears to fit the overall choices of the individuals in the sample very well. This is formally
confirmed by chi-square goodness of fit test statistics which, at a 0.05 level of significance,
do not lead to a rejection of the null hypothesis that the employment proportions generated
by the model are the same as the employment proportions observed in the data. The model
also predicts that the actual number of total person-years in which a birth occurs is the
same, at the 0.05 percent level, as the predicted number of total person-years in which a
birth occurs.
20
TABLE 7
Actual and predicted choices
Actual Predicted Chi Square
Percent of total person-years spent: 1.68
Teaching 66.38 65.52 0.44
Nonteaching 16.51 16.63 0.03
Out of the Workforce 17.11 17.85 1.20
Giving Birth 10.33 9.43 3.27
NOTE.- χ2= Σ(np−na)2/np,np= number predicted and na= number actual.
χ(2,0.95) = 5.991; χ(1,0.95) = 3.841.
6 POLICY SIMULATIONS
To illustrate how relaxing the assumption of exogeneous fertility leads to different policy
recommendations, I perform two simulations. First, as in Stinebrickner (2001b), I raise the
salary of all teachers by 20 percent. This uniform wage increase represents an increase in
the pecuniary benefits of choosing a teaching job and is consistent with the current rigid
wage structure in public schools. Second, I simulate reductions in the cost of childcare by
increasing the utility of working in teaching jobs when children are present.31 Specifically,
I simulate subsidies of $3,000 per year and $4,000 per year by changing the parameter γ11
in table 3 from 113 to 3,113 and 4,113, respectively.32 It is important to mention that the
setting used by Stinebrickner (2001b) did not allow this author to simulate reductions in
the cost of childcare. Consequentely, this author relies on his estimates of an increase in
teaching pay to provide policy recommendations regarding childcare subsidies. This paper,
on the other hand, empirically evaluates childcare policies with grounds on a setting that
has been long recognized ideal while dealing with female labor decisions.
Rather than comparing the effects of these policies, the aim of these exercises is to illus-
trate the interdependence between family changes and employment decisions. In a setting
where individuals simultaneously decide their fertility and labor force status, both policies
have an impact on retention, measured as the percentage of aggregate years spent in teach-
ing, and on fertility, measured as the average number of births per woman. From a policy
point of view, however, we are not interested in teachers’ fertility, and therefore the analysis
below will focus on the main outcome of interest: retention. Changes in fertility will only
be presented as they explain why retention has changed.
31This experiment is not based on what working women actually pay for childcare, since this information
is only available for the last year of the survey. Instead, a childcare subsidy is given to all mothers working
as teachers. This can be interpreted as either a financial payment or some nonpecuniary effort (such as
increased work flexibility or a cost-free assistance during working hours for their children).
32Recall that an increase in γ11 reduces the disutility of working in teaching jobs and increases utility
gains of teaching relative to the nonteaching sector. As Sheran (2007), I assume that the cost of childcare
does not vary with age.
21
According to the US Bureau of the Census (2016), families with employed mothers spent,
on average, $44 per week (approximately $2,200 per year), on childcare in 1986. Therefore,
the changes in the cost of childcare that I simulate represent substantial reductions in the
actual cost of childcare in the United States. Changes in the fiscal treatment of childcare
costs over time allow us to further understand the magnitude of this study’s second proposed
policy. In 1954, a deduction for employment-related care expenses was established. The
deduction became a credit in 1976, and in 1981 the limits were placed at $2,400 per year
for a family with one child and at $4,800 per year for a family with two or more children.
The effects of both policies on the two outcomes are reported in table 8. A 20% raise
in teaching pay increases retention by 17%, a result mainly attributed to a larger decrease
in the aggregate years spent out of the workforce rather than to a decline in the proportion
of years spent in nonteaching (49% and 15%, respectively). Figure 3 illustrates that wage
increases yield employment flows between teaching and out of the workforce throughout the
sample period, and that the impact becomes more pronounced as the number of years since
certification increases. Furthermore, higher teaching earnings decrease the average number
of births by 50%. The negative effect on fertility is in line with previous empirical findings
(Adda et al. 2017; Doepke et al. 2015; Galor and Weil 1996; Hondroyiannis 2010; Siegel
2017).
TABLE 8
Policy Experiments
Benchmark Increase Decrease childcare cost
Wages $3,000/year $4,000/year
Percent of total
person-years spent:
Teaching 65.52 76.85 71.87 75.93
Nonteaching 16.63 14.07 14.86 13.90
Out of the Workforce 17.85 9.07 13.27 10.17
Average number births 0.96 0.48 1.36 1.29
22
0
.2
.4
.6
.8
1
2 4 6 8 10
Number of years after certification
Benchmark Policy One
(a) Teaching Participation Rate
0
.2
.4
.6
.8
1
2 4 6 8 10
Number of years after certification
Benchmark Policy One
(b) Nonteaching participation Rate
0
.2
.4
.6
.8
1
2 4 6 8 10
Number of years after certification
Benchmark Policy One
(c) Share out of the workforce
FIGURE 3
Policy One: A 20% Increase in Teaching Wages
The incorporation of a fertility channel in this article leads to different policy implications
from Stinebrickner’s (2001b) work, in which a framework where births occur stochastically
is used to study teacher attrition patterns. First, the negative impact that wage increases
have on fertility (which was not accounted for by Stinebrickner 2001b) reinforces the positive
impact that wage increases have on employment, and thus leads to a more accurate impact on
retention. Second, Stinebrickner’s (2001b) estimates indicate that a 20% increase in teaching
wages leads to a very large decrease in the proportion of individuals who choose nonteaching
jobs, but has small impacts on the proportion of individuals who are out of the workforce.
He relies on this result to conclude that childcare subsidies (which increase net teaching
wages) would not be a cost-effective way to deal with teacher retention problems. By jointly
modeling fertility and labor supply, however, I find that the increase in retention achieved
with wage increases is mainly explained by a decrease in the proportion of nonworking women
(see figure 3 and table 8). From a policy standpoint this is important because it demonstrates
that only models that explicitly consider the endogeneity of fertility and labor supply are
able to predict changes in fertility-related career interruptions, and thereby account for the
potential benefits of policies targeted toward fertility choices.
23
In order to understand the forces behind the results in table 8, I present in table 9 the
effects of regime changes on several choice probabilities along teachers’ career paths. Wage
increases diminish the percentage of teachers leaving the field by 30% and are more effective
in retaining those who would otherwise exit the workforce entirely than in retaining those
who would enroll in nonteaching jobs. Moreover, the negative effect on fertility is more
concentrated after career interruption and among those who exit to the nonteaching sector.
24
TABLE 9
Policy Experiments: Exit and Return indicators
Overall Left to NT Left to OWF
B Increase Decrease B Increase Decrease B Increase Decrease
childcare cost childcare cost childcare cost
Wages $3,000/year $4,000/year Wages $3,000/year $4,000/year Wages $3,000/year $4,000/year
First Teaching Spell
Left to 55.77 39.11 55.63 48.99 44.32 56.03 43.41 47.30 55.68 43.97 56.59 52.70
Lengh teaching spell 3.72 3.12 4.22 4.18 3.12 2.86 3.21 3.19 4.20 3.45 5.00 5.07
Perc with children at exit timea13.50 13.07 84.64 84.78 7.54 6.20 81.24 82.05 18.25 21.82 87.25 87.23
Returnb1.29 3.88 21.77 25.23 17.22 30.91 37.44 42.73 3.27 5.92 17.35 18.80
Percent birth 2 years after exitb66.17 31.92 37.48 34.70 50.41 20.48 20.24 19.20 80.61 48.65 53.90 53.48
Returnb10.71 10.28 32.90 39.21 5.58 6.46 61.92 66.10 13.65 12.63 22.52 27.51
Percent no birth 2 years after exit 33.83 68.08 62.52 65.30 49.59 79.52 79.76 80.80 19.39 51.35 46.10 46.52
Return 56.43 69.78 40.14 45.94 54.95 68.02 39.12 44.55 59.90 73.77 41.82 48.86
Career Interruption
Perc birth during career break 33.15 10.36 33.01 31.27 15.48 3.95 28.66 26.07 54.66 22.18 38.79 39.47
Length career break 2.14 2.51 2.29 2.28 2.44 2.68 2.62 2.59 1.78 2.20 1.85 1.80
Return
Percentc23.71 46.91 32.47 36.67 29.37 54.25 42.64 47.42 19.20 37.54 24.67 27.02
Perc with children at reentry time d36.97 13.86 100.00 100.00 19.90 7.48 100.00 100.00 57.76 25.62 100.00 100.00
Avg number of children at reentry timed0.37 0.14 1.01 1.04 0.20 0.08 1.00 1.02 0.58 0.26 1.02 1.05
NOTE.- B = Benchmark.
aExit time is the last year of the first teaching spell.
bCalculated as a proportion of leaving teachers associated with the previous row.
cCalculated as a proportion of leaving teachers.
dReturn time is the first year she is observed in a teaching job after a career interruption.
25
It is important to point out the implications of evaluating an increase in wages in a
setting where the interdependence between employment and fertility decisions is taken into
account. Fertility changes concentrated after a career interruption help explain the large
effects on decreasing exits to the nonmarket alternative, and vice versa. Taking these two
effects together, increasing wages reduces fertility-related career interruptions by 52%, which
in turn changes the nature of the attrition problem in public schools. Unlike baseline results,
leaving teachers respond to increasing wages by exiting more to the nonteaching sector than
to the nonmarket alternative, resulting in exits out of teaching no longer associated with
childbirth.
I next examine how changes in attrition patterns affect reentry behavior. Table 9 shows
that higher teaching earnings increase the proportion of returners from 24% to 47% and
that the effect is more pronounced among former teachers with exits not associated with
childbirth. From the analysis of employment and fertility changes above, these results sug-
gest that higher teaching pay increases the attractiveness of the teaching sector as teachers
simultaneously decrease their fertility.
The $3,000 and $4,000 annual reductions in the cost of childcare increase retention by
10% and 16%, respectively. Figure 4 allows for a closer examination of the impact on
yearly work patterns and reveals that the higher proportion of teachers employed in teaching
jobs responds mainly to employment flows from the nonmarket option. The proportion of
individuals employed in the nonteaching sector barely responds to reductions in the cost
of childcare at early and late periods, whereas the share of individuals in the nonmarket
alternative decreases throughout the sample period. Furthermore, reductions in the cost of
childcare increase fertility. Yearly choice patterns reveal that the effect is higher at earlier
periods and more pronounced in the teaching sector. My finding is in line with that of Adda
et al. (2017), who show that women respond to a cash transfer at birth by having their
children earlier.
26
0
.2
.4
.6
.8
1
2 4 6 8 10
Number of years after certification
Benchmark $3,000/year
$4,000/year
(a) Teaching Participation Rate
0
.1
.2
.3
.4
2 4 6 8 10
Number of years after certification
Benchmark $3,000/year
$4,000/year
(b) Nonteaching Participation Rate
0
.2
.4
.6
.8
2 4 6 8 10
Number of years after certification
Benchmark $3,000/year
$4,000/year
(c) Share out of the workforce
FIGURE 4
Policy Two: Reductions in the Cost of Childcare
Table 9 further indicates that reductions in the cost of childcare prolong the first teaching
spell (particularly for those exiting the workforce entirely) and slightly decrease the percent-
age of exiting teachers. This result, combined with increases in fertility concentrated at
early periods, suggests that reductions in the cost of childcare are an important initiative
in increasing job attachment among beginner teachers, particularly among those who would
otherwise have a fertility-related career interruption.
Changes on the children premia provide some insights into this result. Reductions in the
cost of childcare increase the gains derived from children in the teaching sector, and therefore
decrease utility flows associated with leaving teaching due to childbirth. Figure 5 illustrates
the effect of reductions in the cost of childcare on children premia. The gap between the
gains of exiting teaching entirely due to childbirth and those of staying in teaching and giving
birth significantly shrinks. Indeed, Figures 5(b-c) illustrate that in early years, with a $4,000
reduction in the cost of childcare, the differences in gains associated with a second and third
child are close to zero.33 This result explains why starting teachers respond to reductions in
33In order to make figure 5 as readable as possible, changes in utility flows associated with leaving to
nonteaching to give birth are not shown. Since baseline simulations produced negative values (see rows 2, 4,
27
the cost of childcare by, on average, staying longer in teaching while simultaneously having
more children.
-.5
0
.5
1
1.5
2
2 4 6 8 10 12 14
Number of years after certification
Benchmark T $3,000/year T
$4,000/year T Benchmark OWF
(a) 1st Child Premium
-4
-2
0
2
4
2 4 6 8 10 12 14
Number of years after certification
Benchmark T $4,000/year T
Benchmark OWF $4,000/year OWF
(b) 2nd Child Premium
-4
-2
0
2
4
2 4 6 8 10 12 14
Number of years after certification
Benchmark T $4,000/year T
Benchmark OWF $4,000/year OWF
(c) 3rd Child Premium
FIGURE 5
Children Premia. Benchmark and reductions in the cost of childcare.
Table 9 allows further examination of how reductions in the cost of childcare, by si-
multaneously increasing fertility and the duration of the first teaching spell, affect reentry
propensities. On the one hand, increases in fertility lead to increases in reentry rates. On
the other hand, longer first teaching spells, which decrease the number of years in which a
return to teaching could be observed, undermine propensities for reentry. The fact that the
group that exhibits the greatest change in the first teaching spell, those who drop out of the
workforce entirely, also exhibits the smallest increase in reentry rates illustrates this point.
However, this smaller reentry effect that reductions in the cost of childcare have on the group
with longer first teaching spells does not mean that this policy is ineffective in promoting
reentry into teaching. Forecasts of the model beyond the actual data, which allow for an
analysis of return propensities over a longer time period, is a field for further research.
and 6 in table 4) and reductions in the cost of childcare increase these penalties further, they do not play
any role in explaining quitting behavior associated with fertility changes.
28
Changes in the occupation premia, shown in figure 6, provide further insight into reentry
behavior. Reductions in the cost of childcare increase the gains associated with a return to
teaching from the nonteaching sector and decrease the penalties associated with a return to
teaching from the nonmarket option. Despite the increase in incentives associated with a
return to teaching for nonworking women with children, results suggest that the large non-
pecuniary rewards of the nonmarket alternative, combined with attrition rates concentrated
at later periods, do not favor reentry into teaching.
-.5
0
.5
1
2 4 6 8 10 12 14
Number of years after certification
Benchmark $3,000/year
$4,000/year
(a) T-NT with one child
-3
-2
-1
0
1
2 4 6 8 10 12 14
Number of years after certification
Benchmark $3,000/year
$4,000/year
(b) T- OWF with one child
FIGURE 6
Occupation Premia. Benchmark and reductions in the cost of childcare.
Although the policies are not comparable, this study illustrates the mechanisms through
which different fertility responses lead to increases in retention. On the one hand, increasing
wages yield gains in retention through lower attrition and higher return rates as teachers
simultaneously decrease their fertility. Reductions in the cost of childcare, on the other hand,
increase fertility and the length of the first teaching spell as teachers simultaneously increase
births and choose teaching jobs at early periods.
7 CONCLUSIONS
This article has been concerned with the construction and estimation of a structural dy-
namic model of career and fertility choices that a female teacher makes over her lifetime. In
this model, the individual’s finite-horizon optimization problem constitutes a dynamic pro-
gramming problem that can be solved by backward induction. I estimate the model using
the MSM with data from the NLS-72. Self-selection among the joint employment and fer-
tility choices, based on expected future utility and unobserved heterogeneity in preferences
for children, is shown to be an important element in fitting the data on the fertility and
participation choices of female public school teachers. The proposed model is able to match
accurately the decreasing trend in the teaching participation rate occurring after certification
29
and to predict that this decrease takes place almost exclusively because of an increase in the
proportion of women who are out of the workforce. The model also confirms that the total
person-years spent in each employment alternative as well as the aggregate years in which
a birth occurs are the same, at the 0.05 level, as the employment proportions observed in
the data and the actual number of total person-years in which a birth occurs. The estimates
were used to predict changes in teachers’ patterns of employment and fertility stemming
from a uniform 20% increase in teaching wages and to reductions in the cost of childcare.
Estimates indicate that attrition is a fertility-related event that responds to nonpecuniary
gains lying between 83% and 98% of the average teaching wage if the exit occurs within five
years after certification. Children increase the disutility of working in teaching jobs, and
thus reentry into teaching is more likely to occur among former teachers who do not give
birth after exit. A reentry into teaching for an average former teacher with one child yields
nonpecuniary gains that lie between 15% and 42% of the teaching wage if reentry occurs
from the nonteaching sector, and nonpecuniary penalties that lie between one and two times
the teaching wage if reentry occurs from the nonmarket alternative.
Increasing wages improves retention through lower attrition and higher reentry rates
as teachers simultaneously decrease their fertility. The largest attrition effect is observed
among those who would otherwise drop out of the workforce, resulting in an average exiting
teacher being more likely to leave teaching for the nonteaching sector than for the nonmarket
alternative. Consequently, fertility-related career interruptions decrease by 52%. Former
teachers respond to higher earnings by returning to teach in higher proportions. The positive
effect on return rates is more pronounced among former teachers with exits not associated
with childbirth.
This study’s results shed light on new alternatives in dealing with retention problems.
Unlike studies that take children exogenously or stochastically, this article finds that the
gains in retention derived from wage increases respond to reductions in fertility-related career
interruptions (and thus, in the proportion of nonworking women) rather than to a decline in
the proportion of women employed in nonteaching jobs. This article, therefore, supports the
view that policies that increase net teaching pay (such as childcare subsidies) would have
important effects on retention.
Reductions in the cost of childcare of $3,000 and $4,000 increase retention by 10% and
16%, respectively. Both longer first teaching spells and higher reentry rates yield gains in
retention. Fertility effects concentrated at early periods occur as teachers simultaneously
choose teaching jobs resulting in longer first teaching spells. Large nonpecuniary benefits
of the nonmarket alternative, however, seem to overcome the gains of returning to teach-
ing when children are present, resulting in a greater impact on return rates among former
teachers enrolled in nonteaching jobs rather than nonworking former teachers.
30
ABBREVIATIONS
NLS-72 - National Longitudinal Study of the High School Class of 1972.
MSM - Method of Simulated Moments.
1
APPENDIX
A Model Description
A.1 Dynamic Choice
I now describe in more detail the dynamic choices that individuals make. Section 2 presents
the generic Bellman equation:
Vjt(Ωt) = Ujt(Ωt) + δEtVt+1(Ωt+1 |Ωt, djt = 1), t < A0+T
Vj,A0+T(ΩA0+T) = Uj,A0+T(ΩA0+T),
where jdenotes the joint option of employment and fertility and Ωtdenotes the state space
defined as Ωt= (Kt−1, A0, jt−1, ω1I(et−1= 1), ω2I(nt−1= 1)).
As mentioned in section 2, there are 6 possible alternatives. The value functions of each
of these alternatives are:34
VT,N B (Ωt) = UT,N B
t+δEtVt+1(Ωt+1),(9)
VT,B (Ωt) = UT ,B
t+δEtVt+1(ΩP
t+1),(10)
VNT,N B (Ωt)= UNT,N B
t+δEtVt+1(Ωt+1),(11)
VNT,B (Ωt) = UNT ,B
t+δEtVt+1(ΩP
t+1),(12)
VH,N B (Ωt) = UH,NB
t+δEtVt+1(Ωt+1),(13)
VH,B (Ωt) = UH,B
t+δEtVt+1(ΩP
t+1).(14)
The individual maximizes these conditional value functions in sequence. I denote these
conditional value functions by indexing them with Bfor birth and NB if the woman does
not give birth. I also index them with Tfor teaching, NT for nonteaching and Hfor out of
the workforce. The subscript Pindicates that the woman gives birth in t, so the number of
children in the future state space is increased by one.
At the beginning of a period, women take as given their age, occupation, number of
children, and their labor supply in the previous period. Women then decide to conceive a
child or not. Women next decide how much to consume. Once fertility and consumption
choices have been made, individuals observe shocks to labor supply, which consist of job offer
arrivals. These shocks determine the labor status at the beginning of the next period.
I present below the employment-specific value functions. In all cases, the tilde (˜) in the
34Note that V1t, V2t, V3t, V4t, V5t, V6tin section 2 are referred, respectively, as
VT,N B , V T ,B , V N T,N B , V N T ,B , V H,NB , V H,B , in this section.
2
future state space (˜
ΩP
t+1 or ˜
Ωt+1) describes the future state space when the individual accepts
the job offer from the alternative sector.
A.2 Value of teaching
I start with the value of teaching and conceiving a child. A woman working in a teaching
job receives a job offer from the nonteaching sector. If she accepts it, she switches to the
nonteaching sector. If she rejects it, she can either keep her current job for the next period
or she can drop out of the workforce. The value is written as:
VT,B (Ωt) = UT,B
t+δE1max.
The first term consists of the current utility of consumption, leisure, and children, as de-
scribed in equation 2. The second term is the future flow of utility, defined as:
E1max =Etmax[V T (ΩP
t+1), V N T (˜
ΩP
t+1), V H (ΩP
t+1)].
The woman compares the future utility flows of keeping her current teaching job, accept-
ing the job offer from the nonteaching sector, and dropping out of the workforce, and chooses
the sector that provides the highest utility. The employment decision is made conditional
on having an additional child. That is, the number of children in the future state space is
increased by one.
The value of teaching and not giving birth is defined as:
VT,N B (Ωt) = UT,N B
t+δE2max,
where
E2max =Etmax[V T (Ωt+1), V N T (˜
Ωt+1), V H (Ωt+1))].
Since there is no birth in period t, the individual starts the next period with an updated
state space Ωt+1, where all the state variables but the number of children have been updated.
A.3 Value of nonteaching
When working in the nonteaching sector, a woman receives a job offer from the teaching
sector. If she accepts the job offer, she becomes employed as a teacher. If she rejects it,
she can either keep her current job or drop out of the workforce. The value of being in
nonteaching and giving birth is:
VNT,B (Ωt) = UNT,B
t+δE3max.
The term E3max is defined as:
E3max =Etmax[V T (˜
ΩP
t+1), V N T (ΩP
t+1), V H (ΩP
t+1)].
3
The woman compares the future utility flows of keeping her current nonteaching job,
accepting the job offer from the teaching sector, and dropping out of the workforce, then
chooses the sector with the highest utility. The employment decision is made conditional on
a future state space where the number of children is increased by one.
The value of nonteaching and not giving birth is:
VNT,N B (Ωt) = UNT,N B
t+δE4max,
where the term E4max is defined as:
E4max =Etmax[V T (˜
Ωt+1), V N T (Ωt+1), V H (Ωt+1)].
Since the woman chooses not to give birth in t, the future state space Ωt+1 is updated
but the number of children remains the same.
A.4 Value of being out of the workforce
When a woman is out of the workforce, she receives a job offer from the teaching sector with
probability ρand a job offer from the nonteaching sector with probability 1 −ρ. The value
of being out of work and giving birth is modeled as :
VH,B (Ωt) = UH,B
t+δ[ρE5max + (1 −ρ)E6max],
where
E5max =Etmax[V T (˜
ΩP
t+1), V H (ΩP
t+1)],
and
E6max =Etmax[V N T (˜
ΩP
t+1), V H (ΩP
t+1)].
The woman compares the utility flows of remaining out of the workforce and accepting
the job offer from the corresponding sector. As in VT ,B and VN T ,B , the employment decision
is made conditional on a future state space where the number of children is increased by one.
The value of being out of the workforce and not giving birth is modeled as :
VH,N B (Ωt) = UH,N B
t+δ[ρE7max + (1 −ρ)E8max],
where
E7max =Etmax[V T (˜
Ωt+1), V H (Ωt+1)],
and
E8max =Etmax[V N T (˜
Ωt+1), V H (Ωt+1)].
Since there is no birth occurs in t, all variables but the number of children in the future
state space are updated.
4
A.5 Fertility decision
The decision of whether to give birth or not is taken as:
VT(Ωt) = max[VT,B (Ωt), V T ,N B (Ωt)],
VNT (Ωt) = max[VNT,B (Ωt), V N T ,N B (Ωt)],
VH(Ωt) = max[VH,B (Ωt), V H,N B (Ωt)].
The decision to give birth, noted by ktin section 2, is the arg max of the expressions
above.
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