Modern Economy, 2013, 4, 600-604
http://dx.doi.org/10.4236/me.2013.49065 Published Online September 2013 (http://www.scirp.org/journal/me)
Exploring the Simultaneity in Public
Assistance and Abortion
Hal W. Snarr
Westminster College, Economics, Salt Lake City, USA
Received December 27, 2012; revised February 10, 2013; accepted March 10, 2013
Copyright © 2013 Hal W. Snarr. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
This paper studies the effects of time limits on abortion and welfare participation of low-income pregnant single fe-
males who may or may not have other children. In doing this, I explore the presence and nature (if it exists) of simulta-
neity in abortion and welfare participation. The results indicate that time limits, childcare and abortion subsidies, and
public assistance payments are linked to abortion. In addition, the results indicate time limits simultaneously reduce
welfare enrollments and increase abortion among low-income childless single pregnant females, and trigger abortion
and shorter stays on welfare of low-income pregnant mothers. Thus, future empirical work should account for simulta-
neity of abortion and welfare participation.
Keywords: Provision and Effects of Welfare Programs; Marriage; Family Structure; Fertility
1. Introduction
The Centers for Disease Control and Prevention (CDC)
latest Morbidity and Mortality Weekly Report reports a
continued decadal long accelerating decline in the abor-
tion rate to 15.1 per 1000 women aged 15 - 44 years [1],
which is shown in Figure 1. The Report also identifies
several factors driving this trend. The abortion rate was
8.5 for whites, 19.3 for Hispanics and 32.5 for blacks. Of
the women who obtained abortions in 2009, 85 percent
were not married, 72 percent were between 20 and 34
years of age, and 40, 46 and 14 percent had zero, one or
two, or three or more live births. Sixty-four percent of
abortions were obtained between the gestational age of
zero and eight weeks, while 1.3 percent were obtained at
a gestational age of 21 weeks or more. The lowest abor-
tion rate was in Mississippi, the state with the highest
teen birthrate and few abortion providers, while the
highest was in New York, the state with the second most
abortion providers. Other contributing factors cited by
the Report include state laws, the economy, and access to
healthcare and contraception.
A limited number of mostly empirical studies identify
another contributing factor to the decline in abortion in-
cidence [2-5]. The evidence in these studies indicates a
link between public policy and abortion. This is not sur-
prising because the stated goals of the 1996 legislation,
which replaced Aid to Families Dependent Children
(AFDC) with Temporary Assistance for Needy Families
(TANF), is to “end the dependence of needy parents on
government benefits” [6] and “prevent and reduce the
incidence of out-of-wedlock pregnancies” [7]. The U.S.
Congress incentivized states to achieve these goals by
directing the U.S. Department of Health and Human Ser-
vices to award bonuses to states achieving the largest
reductions in out-of-wedlock birth rates with constant or
falling abortion rates [8].
U.S. welfare reform also altered the incentive structure
Figure 1. U.S. Abortion rate per 1000 women aged 15 - 44
years. Source: [1].
C
opyright © 2013 SciRes. ME

H. W. SNARR 601
heads of which low-income households are faced with.
Under the new program, participants are required to work,
are limited to 5 years of assistance, and can lose all or
some assistance money if they fail to work. To date, only
[5] have theoretically modeled the abortion effects of
welfare reform. They examine two specific aspects of
welfare reform: permitting childless pregnant single fe-
males to enroll in TANF [9] and lump-sum TANF diver-
sion payments [10]. Their model implies that lump-sum
diversion TANF payments have lower abortion among
low-income mothers but raise it for women who are
childless and pregnant. The empirical results only sup-
port the first part of that statement.
This paper focuses on the effect of time limits on abor-
tion to explore the simultaneity of abortion and welfare
participation, which may explain why [5] rejected their
second hypothesis: diversion payments and TANF eligi-
bility for low-income women who are childless and
pregnant increase abortion incidence. This issue should
concern researchers because failing to account for it can
bias coefficient estimates. Although scant research ac-
counts for simultaneity in welfare program participation
and out-of-wedlock births [11,12], simultaneity of par-
ticipation and abortion has been overlooked.
2. Model of Pregnancy Termination and
Welfare Enrollment
The link between abortion incidence of childless preg-
nant single females and two TANF provisions is theo-
retically modeled in [5]. It focused on some states per-
mitting childless pregnant single females to enroll in
TANF and using lump-sum payments to divert potential
participants from enrolling in TANF. In this section, I
use that model to study the effects of time limits on preg-
nancy termination and welfare program participation de-
cisions of low-income Pregnant Singles (PS) who may or
may not have other children.
2.1. The Budget Constraint
Several factors affect PS’s budget constraint. She must
decide between pregnancy termination or an out-of-wed-
lock birth in month t = 0. If termination is chosen, A = 1,
otherwise A = 0. PS may have other children. If so, O = 1,
otherwise O = 0. Pregnancy termination costs K in month
0, but birth costs k each month thereafter 

0t until
the child reaches adulthood in period T. Following [5],
public assistance payment P exceeds PS’s subsistence
needs but her earnings


Y do not because her skill
level is too low .

PY
In the first scenario, PS has other children


1O

and is enrolled in welfare in month 0. If PS chooses birth
in month zero, t is the age of her newborn. This allows
her to receive monthly public assistance payment P until
her newborn reaches adulthood at age T. If PS chooses
termination, her youngest reaches adulthood earlier. For
example, if this child is 12 months old at month 0, she
can receive payment P for T – 12 consecutive months.
Given that PS’s planning horizon is longer if she chooses
birth, I differentiate the two planning horizons with
T1and T0 where T0 > T1. More generally, the planning
horizon is denoted TA with the subscript taking on the
values of indicator A. After month TA, PS must return to
work because her youngest child has become an adult.
She earns Y every month after returning to work. Thus,
PS’s budget constraint before welfare reform


0R

is


 
 


1
0
0
0
t
tT
Tt
tT






10
1
1
1, 0
1
t
AP K AP
APA P k
cAO RT
AYA P k
Y

 


 



(1.0)
If time limit τ is the maximum number of months PS
can receive public assistance, and it is less than PS’s
planning horizon


10
TT   , welfare reform (R = 1)
alters the budget constraint above:


 
 



0
0
0
0
t
t
tT
tT

1
1
1, 1
1
t
AP K AP
APA P k
cAO R
AYA Yk
Y










 



(1.1)
In the second scenario, PS does not have other chil-
dren (O = 0) and is working a low wage job. Because she
has no other children, her planning horizon is T0. Choos-
ing termination means PS continues to work and earn Y
per month. Choosing birth, however, means childless PS
stops working and enrolls in public assistance. Hence,
her budget constraint pre-reform (R = 0) is


 
 


0
0
0
t
t
tT




0
1
0, 0 1
t
AY K AY
cAO RAYAPkT
Y


 



(2.0)
but is


 




0
0
0
t
t
tT
tT

0
1
1
0, 1
1
t
AY K AY
AYA P k
cAO R
AYA Yk
Y







 


 



(2.1)
post reform. With regard to time limit τ, because child-
less PS is not enrolled in public assistance in period 0,

H. W. SNARR 602
she can remain on assistance until month τ. PS with chil-
dren, on the other hand, was enrolled in public assistance
in month 0, meaning she must exit public assistance the
month before τ is reached. Thus, 0t

 is used in
Equation (1.1) but 0t

 is used in Equation (2.1)
2.2. Constrained Lifetime Utility
Given the budget constraints above, PS maximizes the
same lifetime utility function that the agent in [5] maxi-
mizes:
0
t
t
t
Uu



 (3)
where


0,1  , and




,
tt
tt
uc AcaAbA   1
.
Equation (3) is adapted from the model in [13] with the
agent’s decisions collapsing to pregnancy termination
or birth

1A
 

0
t
A
a
. Periodic utility function u
exhibiting constant marginal utility of consumption
equaling 1 follows from [14]. If θ and φ are both in in-
terval (0, 1), then

and t b

are asymptotic in t.
These expressions model pregnancy termination remorse
and out-of-wedlock childbearing regret waning over time,
respectively. Substituting the budget constraints into (3)
gives
 

0
,,
t
t
t
V AORcAORAA 





1 (4)
where

01
t
t
a
a 







and

01
t
t
b
b 







The difference in PS’s lifetime utility between choos-
ing pregnancy termination and proceeding with an out-
of-wedlock birth is given by

,1, 0, OR
VVORVOR 
or

,
0
1, 0,
t
ORt t
t
VcORc  



 



OR


(5)
Equation (5) is the gain (or loss) in PS’s lifetime utility
resulting from choosing pregnancy termination over an
out-of-wedlock birth. Its value depends on several factors
like, for example, PS’s disutility of pregnancy termina-
tion (α) relative to her disutility of out-of-wedlock (β),
the value of public assistance payment P relative to what
she can earn in the labor market (Y), the one-time cost of
pregnancy termination (K), the monthly costs of raising
children, the age of her youngest child (TA), the length of
welfare reform’s time limit (τ), whether she has other
children or not, and whether or not welfare reform has
been enacted.
2.3. Welfare Reform’s Effect on Pregnancy
Termination
In this section, the marginal benefits of pregnancy ter-
mination before and after welfare reform is enacted are
compared for PS who has other children to one who does
not. For childless PS, Equation (5) simplifies to

00
11
0,0 11
TT
VKkY
 
 



P

 
 (6)
but when public assistance is limited to τ months Equa-
tion (5) simplifies to

011
0,1 11
T
VKkY

 
 



P

 
 . (7)
Given values of K and k, suppose policy makers
picked P, which happened to make childless PS indiffer-
ent between birth and termination when continued par-
ticipation in public assistance was unlimited. Thus, 0 =
ΔV0,0, which can be expanded as follows:


01
0
1
0,0 1
1
1
01
1
T
T
VKkY
YP





 







P












Replacing the expression in [·] with ΔV0,1, and simpli-
fying yields

01
1
0,1 1
T
VP




Y


,
which is positive because P > Y, and 0 < ρ < 1 and τ < T0
imply 01
1T 


. Thus, imposing a time limit welfare
receipt increases termination incidence among low-in-
come childless pregnant singles, and simultaneously in-
hibits their enrollment in public assistance.
For PS mother, Equation (7) simplifies to

00 1
11 1
1,0 11
TT T
VKkY
 
 
 

P

 
 (8)
but when public assistance is limited to τ months Equa-
tion (5) simplifies to
01
1,1 1
T
VK

 


k
. (9)
Because ΔV0,0 can be expanded as follows


00 1
1
11 1
0,0
1
11
1
TT T
T
VKk Y
YP
 
 


 

P



 









H. W. SNARR 603
And ΔV0,0 = 0, the expression in [·] is simply ΔV1,0.
Making the switch and simplifying yields

11
1,01
T
VP




 
Y
which is positive because P > Y, and 0 < ρ < 1 and 0 < T1
imply . Thus, prior to the imposition of a time
limit, a childless PS who is indifferent between termina-
tion and out-of-wedlock birth chooses termination if she
was already the mother of other children.
11
1T



Similarly, because ΔV0,0 can be written as

00
11
0,0 11
TT
VKkY
 
 



  



P
And ΔV0,0 = 0, the expression in [·] is simply ΔV1,1.
Making the switch and simplifying yields

01
1,1 1
T
VP




 
Y
which is positive because P > Y, and 0 < ρ < 1 and 0 < T0
imply . Because T1 < T0,
01
1T



0
11
1T T



or
0 11
1T
T
 



or
1,0 1,1
VV
Thus, limiting the length of time a PS can remain on
public assistance makes pregnancy termination more
likely for those with other children.
Interestingly enough, the model indicates that preg-
nancy termination is a more difficult decision for child-
less PS who is faced with public assistance time limits
than it is for PS mothers not faced with time limits. Ex-
panding ΔV1,0 as follows illustrates this
 
11
1
1,0 11
T
VPY

 





 



1
PY
 
Because the quantity in [·] is , rearranging the
above result gives
0,1
V

1
0,11,01
VV PY





 

Therefore, if low-skilled childless PS females are in-
different between pregnancy termination and out-of-
wedlock birth before time limits are posed, the following
holds:
0,00,1 1,01,1
0VVVV.
Thus, the gain to pregnancy termination is greatest for
a PS female who has other children and is faced with
time limits on public assistance. This is followed in de-
clining order by a PS who has other children and is enti-
tled to public assistance payments over her lifespan, a
childless PS who is faced with time limits, and a child-
less PS who is entitled to continuous public assistance.
2.4. Other Policy Effects
Comparative static analysis is used to examine how other
policies like childcare and abortion subsidies and the
value of public assistance payments affect pregnancy ter-
minations of both types of PS before and after welfare
reform. Because ΔVO,R can be expressed in terms of ΔV1,1
for all O and R, all are rewritten as follows.

01
0,01,1 1
T
VV P



Y

 
,

1
0,11,11
VV PY






 
,
and

0 11
1
1,0 1,11
T
T
VV PY





 
.
Doing the above simplifies the analysis greatly.
The devoutness or religiosity of PS affects pregnancy
termination [15] via regret parameter α. If religion is
more important in period 2 than it is in period 1, PS in
the more religious period will be more reluctant to
choose pregnancy termination

21
. If the differ-
ence in α2 and α1 is large enough such that the gain to PS
mothers faced with time limits is negative

aa


1,1 0V

,
the gains are negative for all others:
0,00,11,01,1 0VVVV

 (10)
Thus, policies that are designed to humanize the fetus
reduce abortion incidence. The intuitive nature of this
result lends credence to the model, and the policy impli-
cations that follow.
Policy makers wishing to reduce terminations among
low-income PS mothers can affect it via changes to
childcare and abortion costs:
01
1,1 1,1
and 1
1
T
VV
kK



 



 
Because 1,1 Vk


is positive due to 0 < ρ < 1 and
T0 > 0, subsidizing childcare (reducing k) reduces the
gains to abortion. The partial derivative on the left indi-
cates that raising the cost of abortion via reducing abor-
tion subsidies or restricting its access (physically or le-
gally) reduces the gains associated with it [16]. If either
action is such that the gain to a PS mother who is faced
with time limits is negative

, property (10)
holds.

1,1 0V
Policy makers can affect reductions in pregnancy ter-
minations by raising public assistance payment P be-
cause the following partial derivatives are all negative:
01
0,0
1
T
V
P



 


,

H. W. SNARR 604
1
0,1
1
V
P





 


,
and
0 11
1
1,0
1
T
T
V
P




 


.
If the increase in public assistance payment P is large
enough to make the gain to abortion for a PS mother who
is faced with time limits negative , property
(10) holds. This makes sense given that raising payment
P reduces the cost of raising children.

1,1 0V

3. Conclusions
The results in this paper indicate a behavioral response to
time limits may simultaneously reduce welfare program
enrollment and increase abortion incidence among low-
income childless single pregnant females. With respect to
low-income pregnant single mothers, time limits trigger
abortion and shorter stays on welfare. Both of these re-
sults suggest that future empirical work should account
for simultaneity of abortion incidence and welfare par-
ticipation.
This paper also informs policy. The results indicate
that time limits, childcare and abortion subsidies, and
public assistance payments are linked to abortion inci-
dence. Welfare reform in general could be driving much
of the decadal decline in the abortion rate. The results
also help to support the CDC’s claim that factors such as
abortion access, state laws, the economy, and access to
healthcare and contraception contribute to the reduction
in abortion incidence.
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