Manajemen | Fakultas Ekonomi Universitas Maritim Raja Ali Haji 453.full

Childcare Subsidies, Wages, and
Employment of Single Mothers
Erdal Tekin
abstract
This paper develops and estimates a model for the choice of part-time and
full-time employment and the decision to pay for childcare among single
mothers. The results indicate that a lower childcare price and a higher
full-time wage rate both lead to an increase in overall employment and the
use of paid childcare. The part-time wage effects are found to be too small to
have significant behavioral implications. An analysis of cost-effectiveness
indicates that the additional hours of work generated per dollar of
government expenditure is larger for a childcare subsidy than a wage subsidy.

I. Introduction
The Personal Responsibility and Work Opportunity Reconciliation
Act (PRWORA) of 1996, commonly known as welfare reform legislation, marks a
cornerstone in U.S. welfare policy. Among the main goals of the PRWORA are to
increase employment and to reduce welfare dependence among the low-income population. In order to facilitate the transition from welfare to work and help low-income
families maintain economic self-sufficiency, the new law streamlined the childcare
assistance system by consolidating four main childcare subsidy programs into a single block grant, the Child Care Development Fund (CCDF).1 Under the new law,
states are given unprecedented flexibility to design and implement their own childcare assistance programs. Furthermore, states are allowed to transfer up to 30 percent

1. The main reason for streamlining the childcare system was to eliminate the fragmentation and to help
create a ‘‘seamless’’ system that would be easier for families to access and for administrators to manage.
See Blau (2003) for a review of the childcare system under welfare reform.
Erdal Tekin is an assistant professor of economics at the Andrew Young School of Policy Studies at
Georgia State University, a faculty research fellow at NBER, and a research fellow at IZA. The author
thanks David Blau, Naci Mocan, Thomas Mroz, David Ribar, Paula Stephan, and seminar participants
at University of North Carolina at Chapel Hill, Tulane University, Georgia State University, Urban
Institute, Research Triangle Institute (RTI), and the Institute for the Study of Labor (IZA) in Germany for
helpful comments and suggestions. The author is also grateful for research support from the Child Care
Bureau and the UPS Foundation. The data used in this article can be obtained beginning October 2007
through September 2010 from Erdal Tekin, P.O. Box 3992, Atlanta, GA 30302-3992 tekin@gsu.edu
[Submitted August 2005; accepted August 2006]
ISSN 022-166X E-ISSN 1548-8004 Ó 2007 by the Board of Regents of the University of Wisconsin System
T H E JO U R NAL O F H U M A N R E S O U R C E S

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of their Temporary Assistance to Needy Families (TANF) funds into the CCDF and
to directly spend additional TANF funds for childcare assistance. These changes
have placed childcare at the center stage of the welfare reform debate. As a result,
total expenditures on childcare have increased substantially since the passage of
PRWORA. For example, total CCDF expenditures rose by 84 percent, from about
$4.4 billion to about $8.1 billion, between 1997 and 2001. In 2003, total expenditures
from federal and state funds reached around $9.3 billion, which served approximately 1.75 million children on average every month (Besharov and Hihney 2006).
The goal of this paper is to examine the effects of the price of childcare and wages
on the part-time and full-time employment decision, as well as the decision to use
paid childcare among single mothers. Although it is well documented in the literature
that the cost of childcare serves as a deterrent to the employment of mothers, there is
little consensus on the size of the childcare price elasticity of employment. Therefore, it is important to provide new evidence that would help resolve this uncertainty.
The majority of the early studies on this issue focus on married mothers. Although
researchers have recently started to focus on samples of single mothers or have conducted analyses separately for married and single mothers, our knowledge on the

responses of single mothers to the price of childcare is still limited. Given the recent
legislative changes aimed at increasing employment among the low-income population, of whom single mothers are overrepresented, more insights are needed on the
responses of single mothers to wages and the price of childcare.2
There is a relatively large literature on the effect of childcare prices on the employment of mothers. However, most studies use data that predate welfare reform
and other important policy changes of the early and mid-1990s. The empirical analysis in this paper is a step forward because it uses a data set that was collected after
these changes.3 This paper also adds to the literature by incorporating the childcare
subsidy receipt decision into the mother’s choice set along with the employment and
childcare mode decisions. Another contribution of the present paper is that it treats
the market price of childcare differently between subsidy recipients and nonrecipients by implementing an adjustment to the price of childcare by the amount of
the subsidy for those mothers who receive one. This may be important because
the price of childcare faced by subsidy recipients is different from those faced by
nonrecipients, and mothers respond to the childcare price net of subsidy when making their employment decision. Blau and Tekin (forthcoming) and Meyers, Heintze,
and Wolf (2002) examine the effect of actual subsidy receipt on the binary employment decision of mothers, accounting for the endogeneity of subsidy receipt. However, this paper is the first study to incorporate the childcare subsidy receipt into the
choice set of employment and childcare payment decisions.
2. For example, more than 90 percent of TANF cases with an adult recipient were headed by a single
mother in 1998 (U.S. House of Representatives, Committee on Ways and Means, 2000, p. 437). Furthermore, single mothers constitute an increasingly large proportion of all mothers with young children and
they are the main target group for welfare reform. According to Census data, about 18 percent of families
with children were headed by a single mother in 1996, compared with less than 11 percent in 1970.
3. Many states did not start fully implementing the provisions of welfare reform right away. Therefore, the
data set used here cannot be considered from a period when welfare reform was fully in place. However, it

can be considered from the early post-welfare reform environment and after many policy changes of the
early and mid-1990s.

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The majority of the studies in the childcare literature consider the binary employment decision. Exceptions include Powell (1998), Connelly and Kimmel (2003b),
Michalopoulos and Robins (2000) who distinguish between the part-time and fulltime employment decision (similar to this paper), and Michalopoulos, Robins, and
Garfinkel (1992), Powell (1997) and Averett, Peters, and Waldman (1997) who estimate hours of work equations. Distinguishing between part-time and full-time work
may be important as childcare utilization is likely to differ between the two markets
due to different attractiveness and transaction costs (Connelly and Kimmel 2003b).
This paper also allows for the wage rate to be determined separately for part-time and
full-time workers and distinguishes between part-time and full-time wage rates. One
of the main goals of welfare reform is to reduce welfare dependence and increase
employment. Therefore, policies designed to raise the effective wage rate also would
be considered as a tool for this objective in addition or as an alternative to childcare
subsidies. In order to fully understand the effectiveness of different policy options, it
is important to examine the effect of wages on single mothers’ employment decision.
This paper develops and estimates a behavioral model for the choice of part-time
and full-time employment and the decision to pay for childcare among single mothers, using data from the 1997 National Survey of America’s Families (NSAF). A
multinomial choice model for the discrete decisions of employment, childcare payment, and childcare subsidy receipt are estimated jointly with the continuous wage
equations for part-time and full-time employment and the price of childcare.

The results show that both the price of childcare and the wage rate affect the
behavior of single mothers in the ways predicted by economic theory. That is, a decrease in the price of childcare increases employment and the use of paid childcare, and an increase in the full-time wage rate raises both overall employment
and the use of paid childcare. Furthermore, the effect of the part-time wage rate
on employment is found to be much smaller than the effect of the full-time wage rate.
The results also indicate that single mothers who are employed full-time are more
sensitive to the price of childcare than those who are employed part-time. The elasticity of employment with respect to the full-time wage rate is found to be larger than
both the part-time wage elasticity of employment and the childcare price elasticity of
employment. However, the cost-effectiveness, as measured by the additional number
of hours of work generated per dollar of government expenditure, is found to be
larger for a childcare subsidy than a wage subsidy.
The remainder of the paper is organized as follows. Section II provides a literature
review. Section III discusses the theoretical model and the econometric approach.
Section IV describes the data set. Section V reports the empirical results. Section
VI presents the concluding remarks and the policy implications.

II. Literature Review
Results from the previous literature consistently suggest that a higher
price of childcare is associated with lower probabilities that a mother will work and
pay for childcare. Despite a large number of studies, there is still uncertainty about
the size of the elasticity of employment with respect to the price of childcare. The

elasticity estimates vary substantially, from a low of zero (Connelly 1990; Blau

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and Robins 1991; Michalopoulos, Robins, and Garfinkel 1992) to a high of 21.26
(Hotz and Kilburn 1994), with some clustering between 20.3 and 20.4. The studies
differ in data sources, sample compositions, specifications, and estimation methods.
However, sample compositions and data sources alone are unlikely to account for
much of this wide variation because the range of estimates is large even within studies using the same data set and similar sample compositions (Kimmel 1998; Blau
2003). Most of the recent studies recognize that employment and childcare mode
decisions are made simultaneously. Therefore, the econometric models in these studies are estimated in a unified framework.
Studies focusing on samples of single mothers find elasticities of zero (Connelly
1990; Michalopoulos, Robins, and Garfinkel 1992), 20.35 (Kimmel 1995), 20.22
(Kimmel 1998), 20.47 (Anderson and Levine 2000), 20.50 (Han and Waldfogel
2001), between 20.32 and 21.18 for different specifications (Connelly and Kimmel
2003a), and 20.40 for part-time employment and 21.29 for full-time employment
(Connelly and Kimmel 2003b).4 A comparison of elasticities between studies focusing on single mothers and those using samples of married mothers suggests that the

variation is similarly large for these two groups. However, the comparison would be
more meaningful if the analyses were done separately for single and married mothers
using the same data sets. Results from studies estimating models separately for married and single mothers with the same data set suggest that the estimated elasticity of
employment with respect to price of childcare is somewhat more elastic for single
mothers than the married mothers.5
Another useful comparison would be to consider studies that estimate multinomial
choice models similar to the one in the present paper. These studies report elasticities
that fall in the lower end of the range of estimates documented in the literature. They
include 20.34 of Blau and Robins (1988), 20.09 of Ribar (1995), 20.16 of Michalopoulos and Robins (2000), and 20.20 of Blau and Hagy (1998).6 However, the first
three papers use samples of married women only and the last one uses a sample of
both married and single women. Blau and Robins (1988) differ from the current
paper and the other two in that it includes the price of childcare in all the alternatives
available to employed mothers instead of only to those in which a paid childcare arrangement is used. The price of childcare used in Blau and Hagy (1998) is derived
4. Elasticities from studies of married mothers only or both married and single mothers combined include –
0.34 (Blau and Robins 1988), -0.74 (Ribar 1992), -0.20 (Blau and Hagy 1998), -0.92 (Kimmel 1998), -0.20
(Connelly 1992), -0.78 (Averett, Peters, and Waldman 1997), -0.30 (Anderson and Levine 2000), -0.30
(Han and Waldfogel 2001), -1.26 (Hotz and Kilburn 1994), -0.21 for part-time work and -0.71 for full-time
work (Powell 1998), -0.09 for part-time work and -0.75 for full-time work (Connelly and Kimmel 2003b),
0.06 for high income and –0.45 for low-income (Fronstin and Wissoker 1995), and 0.04 (Blau and Robins
1991). Anderson and Levine (2000) and Blau (2003) provide excellent reviews of the literature on the effect

of the price of childcare on employment. See Chaplin et al. (1999) for a review of the literature on the link
between the price of childcare and the demand for childcare.
5. Anderson and Levine (2000), Connelly and Kimmel (2003b), and Han and Waldfogel (2001) find the
elasticity for single mothers to be more elastic than the elasticity for married mothers. One exception is
Kimmel (1998) who finds the opposite.
6. Connelly and Kimmel (2003b) estimate an ordered probit for the employment decisions and a multinomial logit model for the childcare mode decisions. Powell (2002) estimates a mixed logit choice model
and a universal logit model. However, she reports the elasticity of employment with respect to particular
types of childcare settings.

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from a provider survey, while the measure typically used in other studies including
the current paper is based on consumer expenditure. When these authors redid their
analysis using consumer expenditure data, they found a childcare price elasticity of
employment of 20.06. Therefore, it appears that studies using a multinomial choice
framework find small estimates despite using different data sets, although it is risky
to generalize from only four studies (Blau 2003).
Several studies consider the effect of actual subsidy receipt on the employment
decision of mothers. For example, Meyers, Heintze, and Wolf (2002) estimate the
impact of actual subsidy receipt on the employment of welfare recipients using data
from California and find a positive effect on employment. Similarly, Blau and Tekin

(forthcoming) estimate binary models to examine the effects of subsidy receipt on
the outcomes of employment, welfare, unemployment, and schooling among single
mothers, using data from the NSAF. They also find a positive effect of subsidy receipt on employment. However, none of the studies in the literature incorporate
the childcare subsidy decision into the set of employment and childcare payment
decisions.

III. Theoretical Model and Empirical Strategy
The behavioral model developed here is based on a single decisionmaker framework. A single mother is assumed to make a decision among the following discrete choices: (1) whether to work, and conditional on working, whether to
work part-time or full-time; (2) whether to pay for childcare; and (3) whether to receive a childcare subsidy (conditional on paying for childcare). Let I be a categorical
variable, defined by a cross-classification of the discrete alternatives available to each
mother. The mother is assumed to maximize her utility from time at home (L), quality of her children (Q), consumption of market goods (C), unpaid childcare hours
(HNP), and the categorical variable (I). Then the mother’s utility function can be
expressed as
ð1Þ U = UðL; Q; C; HNP ; I; X; y1 Þ;
where X and y1 are the observed and unobserved determinants of preferences, respectively. A mother may derive disutility from receiving a childcare subsidy, using
a paid childcare arrangement, or being employed due to the fixed costs associated
with each of these individual choices or combinations of them.7 For example, there
may be direct disutility from receiving a childcare subsidy as a result of stigma. The
discrete choice indicator (I) is included in the utility function in order to represent
these fixed utility costs (Blau and Hagy 1998). The I can influence utility directly

or indirectly by interacting with other variables in the utility function.
7. There may be indirect costs associated with the use of unpaid services (such as the value of the care
provider’s time in alternative activities) and these costs may influence the mother’s decision as to whether
to utilize paid or unpaid care. Including unpaid childcare hours into the utility function aims to capture
these indirect costs. Specifically, incorporating unpaid childcare hours in the utility function allows for
the possibility that a mother may choose a paid childcare arrangement even when an unpaid alternative with
similar quality is available.

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Table 1
List of Alternatives and Budget Constraint

Alternative

Employment
Status

1
2
3
4
5
6
7

No-work
Part-time
Part-time
Part-time
Full-time
Full-time
Full-time

Childcare
Payment
Status

Childcare
Subsidy
Status

Budget Constraint

—
Yes
No
Yes
Yes
No
Yes

—
Yes
No
No
Yes
No
No

C=N
C + (Ps-Ss)HP=WPTHP + N
C=WPT HNP + N
C + PsHP=WPTHP + N
C + (Ps-Ss)HP=WFTHP + N
C=WFTH + NNP
C + PsHP=WFTHP + N

It is assumed that paid childcare can only be used if a mother is employed.8 This is
necessary because childcare information is available only for employed mothers.
Furthermore, the subsidy recipients and nonrecipients are combined together into
a single alternative for non employed mothers.9 Under these assumptions, the maximum number of discrete alternatives available to each mother is seven. A complete
list of these alternatives is presented in Table 1.
Child quality is determined by a production function with the inputs of unpaid
childcare time (HNP), paid childcare time (HP), the mother’s time at home (L), and
the quality of purchased care (A). Therefore, the child quality production function
can be expressed as
ð2Þ

Q = QðHNP ; HP ; L; A; X; y2 Þ;

where y2 represents the unobserved determinants of child quality. A mother receives
care from paid and unpaid sources during her work hours. Her time during nonwork
hours is divided between leisure and maternal care. It is assumed that hours of maternal care are a fixed proportion of leisure time because of data limitations (Ribar 1992).
Therefore, L includes both leisure and maternal childcare time. Normalizing the total
number of available hours to one, the time constraints facing a mother and her child are
ð3Þ

L + H = L + HNP + HP = 1;

where H is the mother’s number of hours of work while HP and HNP are the paid and
unpaid childcare hours, respectively. The employment choices facing a mother are no
8. Most of the literature makes this assumption for the same reason. It is reasonable to assume that the use
of paid care among nonemployed single mothers is rare since these individuals tend to live in low-income
households and the mother is generally the primary childcare provider.
9. The law requires parents to be employed or attending a job training or educational program to be eligible
for a childcare subsidy. Some of the nonemployed mothers in the sample may be eligible for a childcare
subsidy through training or schooling activities. However, given that the focus of the paper is the employment decision, subsidy recipients and nonrecipients are combined together for nonemployed mothers. Employment is an increasingly common requirement imposed by states and some states require mothers to
engage in work regardless of their participation in a training program.

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work, part-time work, and full-time work. This approach simplifies the labor supply
decision to a multinomial choice problem and avoids the difficulties of dealing with a
nonlinear budget constraint.
As illustrated in Table 1, the complete budget constraint facing the mother
depends on the alternative chosen. It incorporates the cost of childcare, PsHP, if
the mother uses paid care, where Ps is the hourly price of childcare in market s;
the total amount of childcare subsidy, SsHP, if she uses a subsidy (conditional on being eligible for one), where Ss is the subsidy rate per hour in market s; the labor income from part-time employment if she is employed part-time; and the labor income
from full-time employment if she is employed full-time.
The mother maximizes her utility subject to her child quality production function,
budget, and time constraints, along with the appropriate nonnegativity constraints.
The outcome of interest is I, the discrete choice indicator. For a given value of I,
the utility function can be maximized with respect to L, C, HNP, HP, and A, and then
the demand functions can be substituted into the utility and quality production functions. By substituting the quality production function into the utility function, one
can obtain the alternative-specific indirect utility for a given value of I as a function
of all the explanatory variables in the model. Then a linear approximation to the indirect utility function for alternative i yields the following equation
ð4Þ Vi = Xbi + aPi Ps * + aPTi WPT + aFTi WFT + ei ;

i = 1; .:; J

where WFT and WPT are the full-time and part-time wage rates, respectively. The ei is
the alternative specific disturbance, X is a vector of observed determinants of preferences that are invariant to the alternative chosen (for example, age, nonwage income, et cetera), and b’s and a’s are the parameters to be estimated. The a’s are
allowed to differ by employment type and childcare payment status. The price of
childcare used in Equation 4 is the one to which the mother responds behaviorally
and it is adjusted for the amount of childcare subsidy for eligible mothers who
use a subsidy. Specifically, for each of the discrete choices available to a mother, eligibility for a childcare subsidy is determined by a comparison between the household
income and the state income threshold for subsidy eligibility. Income is the sum of
nonwage income and labor income from part-time or full-time employment depending on mother’s type of employment.10 Note that incomes from all three employment
alternatives (no-work, part-time work, and full-time work) are required for each
mother in order to estimate the multinomial choice model and determine eligibility
in each of these employment types. There are three possible scenarios to consider for
a mother. In the first scenario, the mother may be ineligible for a childcare subsidy
regardless of her employment type. Thus, Alternatives 2 and 5 in Table 1 are excluded from the choice set for this particular mother. In the second scenario, a mother
may be eligible for a subsidy only when she is employed part-time. Thus, Alternative
5 is excluded from her choice set. In the third scenario, she may be eligible for a
10. Incomes from cash-assistance programs are excluded since these are disregarded in the household income calculation. Labor income from part-time (full-time) employment for full-time (part-time) working
mothers is calculated by multiplying the predicted part-time (full-time) wage rate by the average number
of part-time (full-time) hours worked per year in the sample. The wage rates used in this calculation are
predicted from the regression models that are corrected for selection into both labor force and part-time/
full-time employment types outside the main empirical model.

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subsidy regardless of her employment type. In this case, all seven alternatives are
available to the mother. Therefore, the total number of alternatives available to a
mother, J, can be five, six, or seven, depending on which of the three scenarios is
relevant. Consequently, the hourly rate of subsidy is subtracted from the hourly price
of childcare for those alternatives in which the mother uses a subsidy. As illustrated
in Table 1, the subtraction of Ss from Ps is implied by the theoretical model.11 Therefore, Ps * is equal to Ps- Ss in Alternatives 2 and 5 and is equal to Ps otherwise. (See
Appendix 1 for a more detailed description of these three scenarios and information
on the implementation.)
The theoretical model implies that a higher price of childcare reduces the utility in
the alternatives in which a mother uses paid childcare but does not affect the utility in
other alternatives (aP2, aP4, aP5, aP7 < 0; aP1 = aP3 = aP6 = 0). Other implications
are that a higher part-time wage increases the utility in alternatives in which a mother
works part-time but does not affect the utility in other alternatives (aPT2, aPT3, aPT4 >
0; aPT1 = aPT5 = aPT6 = aPT7 = 0); a higher full-time wage increases the utility in
alternatives in which a mother works full-time but does not affect the utility in other
alternatives (aFT5, aFT6, aFT7 > 0; aF1 = aF2 = aF3 = aF4 = 0); and a higher childcare
subsidy increases the utility in alternatives in which a childcare subsidy is received
but does not affect the utility in other alternatives (aP2, aP4 < 0; aP1, aP3, aP5, aP6,
aP7 = 0).12
It is optimal for a single mother to choose alternative i if
ð5Þ

Vi . Vj ; "j 6¼ i or
ei 2ej .Xðbj 2bi Þ + Ps *ðaPj 2aPi Þ + WPT ðaPTj 2aPTi Þ + WFT ðaFTj 2aFTi Þ;
"j 6¼ i:

Given the discrete nature of the alternatives, a multinomial logit model is used to
estimate Equations 4 and 5. In addition to the multinomial logit model, there are
auxiliary equations for the part-time and the full-time wage rates, and the price of
childcare that need to be estimated. The estimation of these equations is necessary
for two reasons. First, these variables may be endogenous. Second, it is necessary to
assign a childcare price and two wages to each mother in the sample regardless of
her childcare payment and employment status in order to estimate the multinomial logit
model.
The price of childcare is observed only for mothers who are employed and pay for
childcare and this may be a self-selected sample. Further, the price is not exogenous
because it depends in part on the quality of care purchased. That is, the price of
childcare is in part determined by the quality of purchased care, A, and the specific
characteristics across different markets. In the absence of data on quality attributes of
childcare, the demand for quality of purchased care can be derived as a function of
all the exogenous variables in the model by solving the first order conditions to the
11. The childcare subsidy rate is the hourly rate if the state sets an hourly level. If the subsidy amount is set
daily (weekly), average hourly rate is calculated by dividing the daily (weekly) amount by eight (forty).
12. It can be argued that the price of childcare affects a mother’s behavior by lowering her wage rate. In
this case, the coefficients of the price of childcare and the wage rates should be equal to each other in magnitude, but with opposite sign. The specification in Equation 4 is more general and does not impose this
restriction. See also Blau and Hagy (1998) and Michalopoulos and Robins (2000) for similar specifications.

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optimization problem. This implies that the variation in the quality of childcare is
captured by household variables. The market specific price variation, on the other
hand, can be captured by cross-state variation under the assumption that each state
constitutes a different childcare market. This cross-state variation captures the variation in the price of childcare caused by differences in the market conditions and it is
assumed to be independent of the choices made by the mothers. Under these assumptions, the equation for the market price of childcare can be expressed as a fully reduced form as follows:
ð6Þ Ps = Ds ds + X dP + jP ;
where Ds is a vector of binary indicators for state of residence. The dP’s are the
parameters for X and the ds is a set of state specific intercepts. The jP is the disturbance term. Then the quality-adjusted exogenous price of childcare can be constructed from the fitted values, holding X constant at the sample means.
In order to identify the childcare price coefficient in the multinomial logit model,
aPi, one needs at least one variable that is correlated with the price of childcare
(Equation 6), but uncorrelated with the mother’s preferences. However, the childcare
price function is a reduced form equation and therefore it contains all the exogenous
variables in the model. This implies that the only theoretically valid instrument for
the identification of the childcare price coefficient is the vector of state indicators
in Equation 6. Therefore, the state fixed effects are used to identify the childcare
price coefficient in the multinomial logit model. This implicitly assumes that location
affects the price of childcare through the supply side of the childcare market and that
it does not affect preferences directly. Equation 6 is estimated jointly with the multinomial logit model, allowing jP to be correlated with the ei’s in Equation 4. This
strategy controls for the selection bias due to the possibility that mothers who use
paid childcare constitute a nonrandom sample of the population.
Similarly, measures of the part-time and the full-time wage rates are needed for
each mother in the sample regardless of the mother’s employment status in order
to estimate the multinomial logit model. The equations for the logarithm of the
part-time and the full-time wage rates are specified as follows:
ð7Þ lnWPTj = Ds d1PT + Xj d2PT + jPT ;
ð8Þ lnWFTj = Ds d1FT + Xj d2FT + jFT ;
where Ds and X are as defined before. The d’s are the parameters and the j’s are the
disturbance terms. Similar to the childcare price equation, the state indicators are used
as identifying instruments for the wage coefficients in the multinomial logit model.
Equations 6–8 implicitly assume that location affects preferences only through its
effects on the price of childcare and the wages. The use of state dummies as identifying instruments in either the wage or the childcare price equations would be invalid if
location affects preferences directly. However, there are no other good alternatives that
would be theoretically justifiable. Also, this approach is more general than the previous studies, which usually rely on variation of one or several state-level variables for
identification. In order to control for the labor demand factors that would affect preferences, the state’s unemployment rate for females is included in the multinomial logit

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model. The wage equations for part-time and full-time employment are estimated
jointly with the multinomial logit model, allowing for correlation across the disturbance terms. This approach also accounts for self-selection into part-time and fulltime employment sectors.
The possible correlation across disturbances in the indirect utility functions (the
ei’s) can cause bias to the estimated coefficients. Such a correlation is likely because
alternatives are defined by cross-classifying the discrete outcomes available to a single mother. For example, if a mother has strong preferences for work, these preferences will appear in the error terms of all the choices in which she is employed
(Alternatives 2–7). Similarly, if a mother possesses unobserved preferences for
part-time (or full-time) work, this effect will appear in all the alternatives in which
she is employed part-time (or full-time). Furthermore, mothers who receive childcare
subsidies are a self-selected sample of the population. A mother’s decision about receiving a childcare subsidy is likely to be correlated with her decision on labor supply. For example, if a mother has strong preferences for work, she also may have a
higher motivation to seek a childcare subsidy. Alternatively, the least employable
mothers may be singled out for subsidies by administrators of the subsidy system
(Blau and Tekin forthcoming). However, in a multinomial logit model, the correlation
among the disturbance terms is restricted to zero because of the independence of irrelevant alternatives assumption. A second source of error correlation is between the
discrete outcomes and the continuous wage and childcare price equations. For example, a mother who is strongly motivated to work may also face better wage prospects.
To deal with these correlations in a tractable way, the econometric model uses a
random effects estimator with discrete factor approximations. This method obviates
the need to evaluate multivariate integrals by approximating the distribution of the
heterogeneity with a step function and ‘‘integrates out’’ through a weighted sum of
probabilities (Blau and Hagy 1998; Picone et al. 2003; Mocan and Tekin 2003). Mroz
(1999) shows that this estimator provides more robust estimates compared to methods
imposing a specific distributional assumption.13
To implement this method, the following error structure is imposed on the disturbances of the multinomial logit model and the continuous wage and childcare price
equations:
ð9Þ

ei = ui + ri h;

ð10Þ jP = mP + rP h;
ð11Þ jPT = mPT + rPT h;
ð12Þ jFT = mFT + rFT h;
where the ui, m’s and h are mutually independent disturbances that are assumed to be
independent of X, WPT, WFT, and Ps *. The r’s are called the factor loadings. This
13. In principle, one could estimate the system of equations by imposing a joint distribution, such as joint
normality, for the sources of unobserved heterogeneity. The problem with this approach is that it requires
computing complex multiple integrals. Further, it requires making strong assumptions about the exact distribution of heterogeneity.

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structure places the restriction that all the correlation among the error terms enters
the model through the common factor h that is assumed to have a discrete distribution (Heckman and Singer 1984). In order to account for the missing price of childcare for mothers who do not pay for childcare and for the missing wage rate for
mothers who are not employed, the Gaussian Quadrature is used. As described in
Appendix 2, this is a convenient method to approximate normal integrals accurately
at a low computing cost (Butler and Moffitt 1982).
The multinomial logit model and the equations for the price of childcare and two
wage rates are estimated jointly with full information maximum likelihood, accounting for nonindependence of errors across outcomes. The u’s in Equation 9 are assumed to have mean zero and to be independently extreme-value distributed and
the m’s in Equations 10–12 are assumed to have mean zero and to be independently
normally distributed. The likelihood function and the details of the heterogeneity distribution are discussed in Appendix 2.

IV. Data
The data are drawn from the 1997 National Survey of America’s
Families (NSAF), which was conducted by the Urban Institute. The NSAF is representative of the United Stated civilian, noninstitutionalized population younger than
65. Residents of 13 states and households with income below 200 percent of the federal poverty line are oversampled.14 The full NSAF sample contains 44,461 households. The NSAF is particularly well-suited for the purposes of this study for several
reasons. First, it was specifically designed to collect detailed information on income,
childcare, and participation in various programs, and to provide better data on such
variables than can be obtained from most other surveys. Second, it was conducted
after the enactment of the welfare reform legislation and many other important policy
changes of early and mid-1990s. Third, the NSAF is one of the few national household surveys with information on childcare subsidies.15 Finally, it provides a relatively large sample of single mothers, who are the target group of welfare reform.
The main variables of interest are employment, childcare payment, and childcare
subsidy receipt. In the NSAF, mothers are asked whether they receive any assistance
paying for childcare, including help from a welfare or social services agency, an employer, and a noncustodial parent. Mothers who report receiving assistance from a
welfare or social services agency are coded as receiving a childcare subsidy.16
14. The 13 targeted states were Alabama, California, Colorado, Florida, Massachusetts, Michigan, Minnesota, Mississippi, New Jersey, New York, Texas, Washington, and Wisconsin. These states contain more
than half of the U.S. population and the welfare caseload. There are observations only from 29 states in
the analyses sample and about 90 percent (3,653 individuals) of the sample lives in the oversampled states.
15. To my knowledge, the only other national survey with information on childcare subsidy receipt is the
Kindergarten cohort of the Early Childhood Longitudinal Survey (ECLS-K).
16. It must be noted that the NSAF data may underestimate the actual estimate of childcare subsidy receipt.
As in other survey data, the information is based on self-reports and a mother whose childcare expenses are
fully paid by a welfare agency may consider childcare as simply ‘‘free’’ and report as not receiving subsidy.
Alternatively, a respondent may not realize that she receives a subsidy if she pays part of the childcare bill
and the subsidy program pays the remainder. Another reason for underreporting may be that the respondent
is too embarrassed to report receiving government assistance (Giannarelli, Adelman, and Schmidt. 2003).

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Employment is specified as a trichotomous variable defined at zero hours of work,
part-time work, and full-time work.17 Childcare payment status is a binary variable
equal to one if the mother reported any payment for childcare, and zero otherwise.
The mother’s wage rate is computed as the ratio of her annual earnings to annual
hours of work. In the NSAF, the childcare hours are collected for up to two randomly
chosen children, one between ages 0–5 and the other between ages 6–12. These children are referred to as focal child I and focal child II in the NSAF. Childcare expenditures on the other hand, are collected for all children ages 0–12.18 Therefore, the
hourly childcare expenditure per child can be approximated by dividing the total
childcare expenditures for all children ages 0–12 by the total childcare hours for
all children ages 0–12. The later can be obtained by the sum of childcare hours
for all children ages 0–5 (the product of the childcare hours for focal child I and
the number of children ages 0–5) and childcare hours for all children ages 6–12
(the product of the childcare hours for focal child II and the number of children ages
6–12). However, the NSAF provides information only on the number of children
ages 0–5 and ages 6–17. The number of children ages 6–12 can be obtained perfectly
for those mothers with a focal child II and only one child ages 6–17 because that
child has to be the only one the mother has ages 6–12. There is also no problem
for mothers who do not have a focal child II because in this case the mother has
no children ages 6–12 anyway. For mothers with a focal child II and with at least
two children ages 6–17, I obtained the proportion of the U.S. population between
ages 6 and 12 as a fraction of the total population ages 6 and 17 in 1997 from the
U.S. Census Bureau. Then, this figure is multiplied by the total number of children
ages 6–17 in the NSAF. Note that only 28 percent of the single mothers in the sample
have more than one child between ages 6–12. However, estimation of the models excluding these mothers with multiple children between ages 6 and 12 did not change
the implications of the current results in a significant way.
According to the statute for federal eligibility for a childcare subsidy, ‘‘all eligible
children must be younger than 13 and reside with a family whose income does not
exceed 85 percent of the state median income for a family of the same size and
whose parent(s) are working or attending a job training or educational program or
who receive or need to receive protective services.’’ (U.S. Department of Health
and Human Services 2000). The federal law allows states to set the eligibility criteria
up to 85 percent of State Median Income, but in 1997, only nine states set income
eligibility at the 85 percent level and seven states set it at less than 50 percent level.
Data on state annual median income, income-eligibility rules, and the reimbursement
rates are obtained from the Childcare Bureau’s Report of State Plans of the Child
Care Development Block Grant (U.S. Department of Health and Human Services
2000). Because the sample includes only single mothers with at least a child younger
than 13, every mother meets the first major eligibility criterion. States’ reimbursement rates vary by the age of the child and they are set on hourly, daily, weekly,
17. Mothers with weekly work hours from 1 to 35 are classified as working part-time and those with 35 and
over are classified as working full-time. Similar definitions have previously been used in the childcare
literature (Michalapoulos and Robins 2000).
18. A focal child II can actually be ages 6–17. However, childcare information is collected for children
only up to age 12. Thus, this does not cause an age inconsistency in calculating childcare expenditures.

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Table 2
Frequency Distributions of the Discrete Outcomes

State
1
2
3
4
5
6
7
Total

Employment
Status
No
Part-time
Part-time
Part-time
Full-time
Full-time
Full-time

Childcare
Payment Status

Childcare
Subsidy Status

—
Yes
No
Yes
Yes
No
Yes

—
Yes
No
No
Yes
No
No

Count

Percentage
Total

1,285
86
308
303
208
757
1,082
4,029

31.9
2.1
7.6
7.5
5.2
18.8
26.9
100.0

Source: 1997 National Survey of America’s Families.

or monthly bases. All figures are converted to an hourly base assuming full time care.
Reimbursement rates sometimes vary within states. In these cases, the geographic region that includes the largest city in the state is used.19
The other variables used in the multinomial choice model include the mother’s
age, nonwage income, race, ethnicity, and binary indicators for the mother’s educational attainment, health status, the presence of children by age, and the region of
residence. These variables are included in the model to control for mother’s preferences and her quality of childcare. Nonwage income is the sum of household income
from nonmarket sources, excluding income from means-tested programs. The number of family members age 25 and over who live in the household are included to
control for the availability of free care by a relative to the mother. Finally, the state
unemployment rate for females is included in order to control for labor demand conditions that would affect preferences.
The empirical analysis is performed on a subsample of households headed by a
single mother with at least one child younger than 13. The total sample includes
4,029 households. Table 2 displays the distribution of employment, childcare payment, and childcare subsidy outcomes. About 68 percent of the single mothers in
the sample are employed. The percentage of part-time and full-time working mothers
is about 17 and 51, respectively. About 56 percent of part-time working mothers and
19. Note that it is unavoidable to make certain simplifying assumptions in this process. For example, if the
reimbursement rates are set differently for children at different ages within the 0–5 and 6–12 groups, then
the reimbursement used here is the one that is set for the focal child. For a mother with only one child, the
reimbursement rate is the one that corresponds to the focal child’s age from the State Plans report. If there
are at least two focal children, one aged 0–5 and the other aged 6–12, the average of the hourly reimbursement rates are used. Although, these would introduce some measurement error into the hourly rate of subsidy for a mother with multiple children in different age groups, it is unlikely to be substantial since the
difference between reimbursement rates for children in different age groups is small and in some cases
the same. Income eligibility limit varies by family size with up to five members. Households with more
than five members are assigned the same income eligibility limit as those with five members.

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63 percent of full-time working single mothers pay for childcare. The proportion of
the sample receiving a childcare subsidy is about 12 percent among part-time workers and about 10 percent among full-time workers. Sixty-four percent of working
mothers (1,756 mothers) in the sample are eligible for a childcare subsidy under
the income eligibility rules set by states in 1997. Therefore, about 17 percent (294
mothers) of these eligible receive a childcare subsidy. Note that this number is close
to the figure from a report by the Administration for Children and Families (1999),
which estimates that 12–15 percent of eligible families received a CCDF subsidy in
1998–99. Definitions and the summary statistics are presented in Table 3. Employed
mothers have a higher level of education than nonemployed mothers and full-time
working mothers have a higher level of education than part-time working mothers.
Whites have a higher rate of employment than both blacks and other races. Expectedly, mothers working full-time earn higher wages on average compared to those
working part-time.

V. Results
The results from the estimations of the childcare price and the fulltime and part-time wage equations are presented in Appendix Tables A2 and A3.
While space limitation precludes a detailed discussion of these results in the text,
they are consistent with those usually found in the relevant literature. The results
of the discrete choice model are presented in Table 4.20 The reference category is
alternative 1 in which the single mother does not work, does not pay for childcare,
and does not receive a childcare subsidy. A likelihood ratio test rejected a model with
a single price coefficient against a model that allowed price coefficients to vary by
part-time and full-time employment status. Consistent with the predictions of the
theoretical model, a higher price of childcare reduces the utility in alternatives in
which the mother works and pays for childcare. The coefficient estimates suggest
that a higher price of childcare is a stronger deterrent to full-time employment than
it is to part-time employment. The estimated childcare price coefficients for full-time
and part-time working mothers are 20.192 and 20.093, respectively. The implied
childcare price elasticities with respect to full-time and part-time employment are
20.139 and 20.068, respectively. The finding that the price elasticity with respect
to part-time employment is smaller than that of full-time employment in absolute
value is consistent with other studies that distinguish between part-time and full-time
employment. For example, Powell (1998) estimates the elasticity to be –0.20 for
part-time employment and –0.71 for full-time employment using a sample of married
mothers from Canada; Connelly and Kimmel (2003b) find the elasticities to be
20. The results presented in the paper are taken from a model with four Hermite and four mass points. The
model is estimated with alternative combinations of numbers of heterogeneity and Hermite points. A model
with five Hermite points did not provide a significant improvement in the likelihood function over a model
with four Hermite points nor did it result in an appreciable change in the coefficient estimates. Also, a
model with five mass points did not yield a higher likelihood compared to a model with four mass points.
This model also performed worse in terms of fit obtained by comparing actual and predicted choice probabilities. Models with higher support points failed to converge. Fortran programming language is used in
the estimation along with the optimizer GQOPT to obtain the maximum likelihood estimates.

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20.40 and –1.29 for part-time and for full-time employment, respectively, for a sample of single mothers; and Michalopoulos and Robins (2000) estimate the elasticities
to be 0.159 for part-time and 20.342 for full-time using a sample of two-parent families from Canada and the United States.
The price elasticity with respect to overall employment is calculated to be –0.121.
This figure falls in the lower end of the range of estimates reported in the literature.
However, it is particularly close to those from several studies that are similar to the
current paper in terms of their use of a multinomial choice model in the estimation.
Examples include 20.09 of Ribar (1995) and 20.38 of Blau and Robins (1988) who
estimate a discrete choice model with multinomial logit; 20.156 of Michalopoulos
and Robins (2000) who estimate a multinomial logit distinguishing between full-time
and part-time employment; and 20.20 of Blau and Hagy (1998) who e