Child Care Subsidies and the Work. E ort of Single Mothers

Child Care Subsidies and the Work E ort of Single Mothers Julio Guzman jguzman@uchicago.edu August, 2007 [PRELIMINARY DRAFT, COMMENTS WELCOME] Abstract Child care subsidies were an important part of the 1996 welfare reform in the U.S. However, there is little evidence whether they have in fact contributed to increase employment and self-su ciency among low-income families. This paper examines the e ects of these subsidies on the work e ort of single mothers, the main target group for welfare reform. I specify a bivariate probit model estimated by maximum likelihood approach, where the subsidy indicator S acts as one of the binary dependent variables and also as an endogenous explanatory variable of the employment equation. The amount of pre-determined child care funding (Mandatory Funds) in each state is used as an exclusion restriction (variable that a ects the subsidy receipt but not employment 1

directly). I also extend this model to allow for selection on unobservables by estimating probit models with sample selection. The evidence presented is based on data collected in 1999 and 2002 from the National Survey of America s Families (NSAF). Results from the bivariate probit model indicate that on average, among mothers whose youngest child is 5 or younger, receiving a subsidy increases the probability of being employed by 31 percent. I nd no signi cant e ect among mothers whose youngest child is older. The estimates from the probit models with sample selection rea rm this pattern. These estimates are larger than the marginal e ect estimated from the single employment probit equation (14 percent, evaluated at the covariates means). This is consistent with the negative correlation between the unobservables resulting from the bivariate probit estimation. Further analysis is needed to determine the sources of this selection, however, it might indicate that the least employable mothers are singled out for subsidies by administrators of the subsidy system. 1 Introduction The 1996 welfare reform in the U.S. (PRWORA, 1996) changed the welfare system into one that requires work in exchange for time-limited assistance 1. For that purpose, the reform included, among other components, a substantial redesign and increase in work-related child care subsidies. It consolidated four di erent child care subsidy programs for low-income families into a single block grant, the Child Care and Development Fund (CCDF). The new welfare law also allowed states to transfer up to 30 percent of their Temporary Assistance 1 See a summary of the PRWORA at http://www.acf.dhhs.gov/programs/cse/new/prwora.htm. 2

for Needy Families (TANF) funds into the CCDF and to use TANF block grants for "direct" child care. During 1999-2004 the state and federal spending in CCDF has increased more than TANF expenditures in real terms, and more than the Earned Income Tax Credit, which is another competing instruments in encouraging low-income parents to seek employment. Thus, these subsidies have become of one of the main policy instruments for helping welfare recipients move into the workforce and for keeping other low-income families from becoming welfare dependent. There is little evidence, however, on whether these child care subsidies have in fact contributed to an increase in employment and self-su ciency among low-income families (Blank, 2002; Grogger and Karoly, 2005). Also, there is very little evidence of the e ect of child care subsidies on child development outcomes (Blau, 2000). It is relevant to know these e ects because child care subsidies are one of several competing policy instruments available to achieve these goals. Moreover, if there is a trade-o between the policy goals of increasing economic independence and improving child outcomes, then a subsidy designed speci cally to achieve one of these goals will usually be relatively ine ective at accomplishing the other goal (Blau, 2000). It might be the case, therefore, that work-related child care subsidies are stuck in the middle, neither su ciently increasing the work incentives and economic independence of the targeted group, nor improving child outcomes. This study focuses on one of these questions, namely the e ects of these subsidies on the work e ort of single mothers, the main target group for welfare reform. The evidence of the e ects of actual subsidy receipt on the behavior of mothers of young children is limited, mainly because of lack of data on child care subsidies and because of 3

problems in dealing with selection issues. The existing evidence on the e ects of child care subsidies on female employment is almost entirely limited to the pre-1996 period (e.g., Berger and Black, 1992; Meyers, Heintze and Wolf, 2002; Gelbach, 2002). These results might not be useful to predict the employment responses to current work-related subsidies because of the substantial changes that have been made to the child care system through welfare reform (Blau and Tekin, 2003). Other evidence concerning the e ects of child care subsidies on work incentives has been provided from studies that infer the impact of child care subsidies indirectly by estimating the price e ects (elasticity) of child care on employment. These studies might also not be useful in making inferences about the e ects of child care subsidies on employment if there are substantial costs to collecting a subsidy (e.g., psychic costs ("stigma"), time costs to applying or being on a waiting list, etc.). In fact, CCDF child care subsidies are a capped entitlement, with no obligation to serve all eligible families. As a result, nearly half of all states have placed eligible families on waiting lists or just have imposed a freeze in their intake. The presence of rationing i.e., when not all eligible mothers who demand a child care subsidy receive one - suggests that the costs of take-up for the CCDF subsidies are likely substantial. This prevents us from using child care price elasticity as a guide for estimating the e ect of CCDF subsidies on employment. As result, instead of focusing on child care price elasticity, this paper provides evidence on the e ects of the actual child care subsidy receipt on the probability of being employed and other outcomes. An additional problem arises in the presence of rationing in the child care subsidies. If program administrators select mothers on the basis of characteristics that are not observed 4

by the investigators, then the selection into the program is driven, therefore, by both the mother s choice to demand the subsidy and the agency s decision to award it. This means we cannot sign the direction of the selection bias a priory. In this case, estimates from a single probit employment equation using people on waiting lists as a control group for those accepted into the subsidy programs might be inconsistent. The core questions this paper aims to answer are: (1) What are the e ects of work-related child care subsidies on the employment probabilities of single mothers? (2) Which groups of mothers bene t most from these subsidies in terms of employment? (3) How do these subsidies a ect child care arrangements used by single mothers? To answer these questions, this paper speci es a bivariate probit model estimated by maximum likelihood approach (ML), where the subsidy indicator S acts as one of the binary dependent variables and also as an endogenous explanatory variable of the employment equation. As an exclusion restriction, I use the variation across states in the amount of predetermined child care funding (Mandatory Funds), scaled by the number of children living with a single mother head of household in each state. The Mandatory Funds are assumed to a ect the probability of being rationed out of the subsidy, but not the probability of being employed, conditional on subsidy status 2. Single probit estimates are also presented. The choice of treatment (i.e., subsidy receipt) is modeled as a combined decision of mothers demanding a subsidy based on utility maximization process and of program admin- 2 Pre-determined child care funding at the state level corresponds to established mandatory funds. Mandatory funds provide a guaranteed level of federal child care funding to states, for which no state matching funds are required. Each state receives a xed amount each year, equal to the funding it received under the AFDC child care programs in either FY 1994, FY 1995, or the average of FY 1992-1994, whichever is highest. 5

istrators o ering a subsidy based on some maximization (or cost-minimization) rule. The analysis uses household survey data from the post-prwora era coming from the 1999 and 2002 rounds (repeated cross-sections) of the National Survey of America s Families (NSAF), conducted by the Urban Institute. The NSAF sample includes a large number of current and former welfare recipients and other low income families. Also, a potential advantage of using individual level data (instead of state level data) is the possibility to interact state policy variables with demographics characteristics of each individual in my sample, which I do in this paper. The entire NSAF sample of the 1999 and 2002 rounds includes 42,360 and 39,798 households, respectively. Using both 1999 and 2002, I select a subsample of 8945 unmarried mothers with at least one child under age 13. This paper focuses on single mothers because they are the main target group for welfare reform. Also, most of the studies that estimate the e ect of actual subsidy receipt on employment focus on single mothers and therefore, it is easier to compare the results with the previous literature. Preliminary results from the bivariate probit model indicate that, among the whole sample of single mothers with at least one child under 13 years old, receiving a subsidy increases the probability of being employed by 21 percent (evaluated at the covariates means). This estimate is larger than the marginal e ect estimated from the single employment probit equation (11 percent, evaluated at the covariates means). This is consistent with the negative correlation between the unobservables resulting from the bivariate probit estimation. When splitting the sample by the age of the youngest child, I found a larger e ect of subsidy receipt among mothers whose youngest child is 0-5 years old (31 percent, evaluated at covariates means) than among mothers whose youngest child is 6-12 years old (7 percent, evaluated at 6

covariates means). This paper is organized in the following way. Section 2 describes the CCDF subsidies. Section 3 reviews the previous literature on the e ects of child care subsidies on employment. Section 4 develops a conceptual model which serves as the basis for the econometric speci cation shown in Section 5. Section 6 discusses the data from the NSAF used in this paper and shows descriptive statistics of the main variables used in the estimations. Section 7 shows the empirical results. Section 8 concludes. 2 Child Care Subsidy Programs Before welfare reform, there were four major child care subsidy program with di erent goals, rules, and target populations (Blau, 2003). PRWORA consolidated the four programs into a single child care block grant program called the Child Care and Development Fund (CCDF). As a result, this block grant has become the most important source of funding for workrelated child care subsidies. The main goal of the consolidated program is to assist lowincome families, families receiving welfare, and those transitioning o welfare in obtaining child care so they can work or attend training/education. States have substantial exibility in designing their CCDF program, including the income eligibility limit, reimbursement rates to providers (the subsidy rate), co-payments by families and work requirements (see Figure 1 and 2). States can use CCDF funds to assist families with income up to 85 percent of state median income, but are free to use a lower incomeeligibility criterion. Only nine states currently set income eligibility at the maximum allowed 7

by law, 85 percent of state median income. Seven states set the income eligibility limit at less than 50 percent of median income. States are permitted to waive fees (co-payments) for families with income below the poverty line, and there is substantial variation across states in use of this provision. Fees are determined in many di erent ways, including at rates, percent of cost, percent of income, and combinations of these. States are required to have sliding scale fee structures, with fees that rise with family income. Federal guidelines for implementation of the CCDF law require that the subsidy rate be set at the 75th percentile of the price distribution from a recent local market rate survey. Some evidence suggests that in practice many states use out-of-date market rate surveys or set the subsidy rate lower than the 75th percentile of the price distribution (Adams, Schulman, and Ebb, 1998, p. 23). The average subsidy rate for a 4 year-old assisting to a center care is between $400-450/month. Parents must be employed, in training, or in school, although some exceptions are permitted (see Figure 1). States authorize payments for 6 or 12 months, after which there is a recerti cation process. Child care providers quality is regulated by states. CCDF subsidies can be used only in arrangements that satisfy state licensing standards or are legally exempt from such standards. Priority for CCDF funds is supposed to be given to families with very low incomes and children with special needs. Speci cally, states must use at least 70 percent of their mandatory and matching funds 3 to serve families on welfare, families in work activities who are moving o welfare, and families at risk of going on welfare. The CCDF 3 Federal CCDF funds are provided to the states in three streams: discretionary, mandatory, and matching. Discretionary and mandatory funds are distributed according to rules similar to those of the old programs, primarily based on the number of children and state income. These two streams do not require state matching funds. To receive funds from the matching stream, a state must maintain its expenditure of state funds for child care programs at speci ed previous levels ( maintenance-of-e ort spending) and spend additional state funds above those levels. (U.S. General Accounting O ce, 1998, p. 5). 8

also requires that a portion of the funds be used to assist working poor families who are not currently, recently, or likely future welfare recipients. As part of the general increase in exibility provided by PRWORA, states are permitted to transfer up to 30 percent of their TANF block grant funds to the CCDF to be used for child care, and can also use TANF funds directly for child care services without transferring the funds to CCDF. There has been a substantial increase in CCDF funding, however, not enough to meet increasing demand for subsidies. CCDF subsidies are a capped entitlement, with no obligation to serve all eligible families. As a result, nearly half of all states have placed eligible families on waiting lists or just have imposed a freeze in their intake. This indicates the presence of rationing i.e., when not all eligible people who demand a child care subsidy receive one. However, there is no systematic information on the degree of rationing among di erent states 4. States determine (explicitly or implicitly) the degree of rationing they are willing to tolerate by adjusting the "generosity" of the subsidy and/or varying the state funds allocated to this program. For example, states might reduce the income eligibility limit well enough to guarantee the subsidy receipt for all eligible applicants. Also, states trade-o generosity in eligibility for additional generosity in bene ts (Herbst, 2006). They ration bene ts to families with speci c characteristics (Herbst, 2006, Schulman et al., 2001). Rationing mechanisms appear to di er across states in ways that are not captured by program rules and policies (Blau and Tekin, 2003). Overall, this indicates states choose their preferred combination 4 It is estimated that the CCDF served only 12-15 percent of eligible children in 1999 (Administration for Children and Families, 1999, 2000). However we do not know how many of these eligible children were in families that demanded the subsidy and were rationed out and how many just did not apply for it. 9

of child care policy variables -including the degree of rationing they are willing to tolerategiven the federal rules and the endogenous and exogenous budget constraints. 3 Previous Literature There are three broad types of studies that provide evidence on the e ect of child care subsidies on employment in the U.S. 5 : (1) evaluation of actual child care subsidy programs, (2) welfare demonstration projects that include a child care component, and (3) studies on the e ects of the price of child care. This paper falls into the rst category. The three main di culties encountered in research on this issue are nding appropriate control groups, accounting for the wide prevalence of unpaid child care arrangements, and identi cation of the e ect of the price of child care (Blau, 2000). Under the rst type of study, three papers have been published that estimate the impact of actual child care subsidies on employment in the U.S. using data from pre-welfare reform period (Berger and Black,1992; Gelbach, 2002; Meyers, Heintze and Wolf, 2002) and one study that uses data from post-welfare reform (Blau and Tekin, 2003). Berger and Black (1992) evaluate the employment impact on single mothers of two Kentucky child care programs. They compare employment of single mothers who received a subsidy with employment of single mothers who were on the waiting list for a subsidy. They estimate a single probit equation for employment of the pooled sample of both groups (recipients and mothers on waiting list), with a binary indicator of subsidy receipt. Since they argue that 5 See an extensive survey in Blau (2000). 10

the waiting list group is a valid control group for dealing with selection bias, they estimate the probit equation considering subsidy receipt as an exogenous regressor. Evaluated at the means of other variables ( X), their results indicate a 12 percent increase in the probability of employment due to the subsidies. The authors recognize that waiting list group could not be a valid control group and therefore, they provide additional evidence to deal with that issue 6. If program administrators select mothers on the basis of characteristics that are not observed by the investigators, then the estimates from their single probit employment equation are not consistent, even when using the waiting list mothers as the control group. In that case, the subsidy receipt regressor is correlated with the unobservable characteristics that a ect employment status. Under those conditions, a valid approach would be to estimate a bivariate probit model of the joint probability of employment and subsidy receipt, as done in this article. Meyers, Heintze and Wolf (2002) use data from a sample of 903 low-income single mothers of California in four counties during 1992-1995 to analyze the impact of subsidy receipt on labor market activity (employment or job preparation activity). The speci cation of the labor market activity equation used is of the form A = 0 S + X 0 0 + u 0, where A is the latent index for the observed discrete indicator of labor market activity (A), S is the actual subsidy receipt and X 0 an array of covariates. They replace S with the predicted probability of subsidy receipt, ^S, estimated from a rst stage probit and thus, they estimate 6 They develop a second evaluation strategy using additional information from a sample of single mothers from the Current Population Survey (CPS). They decompose what they call full e ects of subsidies into sign-up, waiting list, creaming and subsidy e ects. Thus, the estimated impact of subsidies on employment from this approach varies from 8.4 percent to 25.3 percent, depending on whether these other e ects are considered part of the impact of the subsidies on employment. 11

A = 1 ^S + X1 1 + u 1. In other words, they use the predicted subsidy probability from the rst stage probit model as a regressor in the second stage labor market activity probit 7. The coe cient of this predicted probability in the employment probit is positive and signi cantly di erent from zero. At the sample mean of the other regressors, the authors show, through a simulation, that as the probability of subsidy receipt moves from 0.0 to 0.5, the employment probability increases from 0.210 to 0.727. This two-step procedure, however, does not produce consistent estimators for this model. The implicit non-linearity in the probit model with S acting as a binary endogenous regressor rules out the possibility of using simple two-step procedures (Maddala, 1983, p.123; Wooldridge, 2002, p.478). Although the rst stage gives consistent estimates of the coe cients of the subsidy receipt, the nonlinear nature of the indicator A causes this inconsistency. A correct approach under the assumptions of this model is to use full information maximum likelihood approach, like the bivariate model estimated in this paper 8. Gelbach (2002) estimates the impact on employment of the implicit child care subsidy provided by free public kindergarten for ve year old children, using data of the 1980 Census 7 They initially estimated the rst stage probit of subsidy receipt as a probit with selection on the utilization of child care services. They claimed that the model is censored because the subsidy receipt S is only observed when mothers use child care services. However, the subsidy receipt S is actually observed for the whole sample, being equal to zero when mothers do not use child care services. It is true that S = 1 only if child care services are used, but it does not imply the presence of sample selection for estimating a probit of the subsidy receipt for the whole sample of mothers. Hence, it is not clear what motivates this initial approach. However, they nally estimate the predicted probability of subsidy receipt from a standard probit model, since they found no evidence of selectivity in the subsidy equation. 8 Another possibility is to assume that the underlying model of the employment equation generating the data includes the probability of subsidy receipt, ^S, and not the actual subsidy receipt, S. This is actually the model speci ed by the authors in a previous version of their paper (Meyers et al., 1999). This speci cation, however, implicitly assumes that mothers must choose their employment status before knowing whether they will have a subsidy available. This point is raised by Blau (2000) when commenting the speci cation used by Meyers et al. (1999). However, including the probability of receiving the subsidy might be a correct approach, given the characteristics of the eligibility rules governing the child care subsidies, which requires applicants to be working or in work-related activities when the subsidy is o ered. 12

on single mothers. He uses variation in the quarter of birth of children as an instrument for being enrolled in kindergarten at age 5. He nds that there is a signi cant impact on labor supply (6-24 percent) of providing free public schooling for the ve-year-old among single women whose youngest child is ve. However, it is unclear that these ndings can be extrapolated to mothers having younger children. It also unclear whether the results from a universal subsidy, like free public kindergarten, are representative of the mean-tested child care subsidies analyzed here (Blau, 2000). As pointed out by Blau and Tekin (2003), the evidence of the pre-reform period might not be informative of the e ects of current CCDF subsidies on the employment. Those results might not be useful to predict the employment responses to current work-related subsidies because of the substantial changes that have been made to the child care system through welfare reform. These authors use data from the 1999 round (post-reform) of the National Survey of America s Families (the same survey that we use) to analyze the determinants of receipt of a child care subsidy and the e ects of subsidy receipt on employment, school attendance, job search, and welfare participation. They use OLS estimates, that treat subsidy receipt as exogenous, and 2SLS estimates, that treat subsidy receipt as endogenous. The 2SLS approach is based on a linear probability model for the outcome and the subsidy equations and a common treatment e ect assumption. They use county dummies as identifying instruments. They assume that the county dummies are good proxies of factors that determine how subsidies are rationed at the county level. Their OLS estimates show an e ect of subsidy receipt of 13 percentage points on employment. The 2SLS estimates show an e ect of 32 percentage points. However, even the authors present evidence that is 13

inconsistent with the assumption that county dummies are valid instruments. In fact, even controlling for county-level demographic and labor market characteristics, it is likely that county dummies should not be excluded from the employment equation. The second type of study provides evidence on the e ect of child care subsidies on employment consists of welfare demonstration programs that were conducted prior to the PRWORA. They use randomized assignment methods to evaluate the impact of those interventions. It is di cult, however, to determine how much of the e ect is due to child care subsidy receipt per se, since in each case child care was only one of several components of the bene ts and services provided to help low income families to achieve economic independence 9. The third type of study infers the impact of subsidies indirectly by estimating price e ects of child care. Some reviews of this literature can be found in Anderson and Levine (2000) and Blau (2000). Initially, studies examined indirect measures of child care costs (Heckman, 1974) and indirect measures of women s total work-related costs (Cogan, 1980). Evidence from these investigations suggested that costs of work have a signi cant e ect on labor force participation. More recent studies have estimated the e ect of the price of purchased child care on the employment outcomes of mothers (e.g., Blau and Robins, 1988; Connelly, 1992; Ribar, 1992 and 1995, Kimmel, 1998, Anderson and Levine, 2000). There is signi cant dispersion in the estimated price elasticities reported. Blau (2000) shows that the price elasticities reported from several studies vary from 0.06 to -1.26. Several explanations for the variation in results have been advanced (e.g., quality heterogeneity (Blau and Hagy, 1998), speci cation and estimation issues (Blau, 2000), misspeci cation (Averett at al., 1997))). 9 See Blau (2000) and Blau and Tekin (2005) for a comprehensive list of those projects. 14

Inferences about the e ects of the CCDF subsidies drawn from this type of study might not be useful if there are substantial costs to collecting a subsidy (Blau and Tekin, 2003). This is the case when there are psychic costs ("stigma", or time costs to applying or being on a waiting list. In fact, the presence of rationing in the CCDF subsidies -i.e., not all eligible mothers who demand a child care subsidy receive one - suggests that the costs of take-up for the CCDF subsidies are likely substantial. This prevents us from using child care price elasticity as a guide for estimating the e ect of CCDF subsidies on employment. 4 Conceptual Model I develop a simple static one-period model of behavior as a basis for the econometric speci - cation. A single mother has preferences over a composite market good, X, leisure, T l, and the quality of care extended to her child, Q, (assume one child per mother for simplicity). This static framework implicitly treats parents prior family formation (the decision of whether to stay single), family structure (whether to live with grandparents or other relatives), fertility, education and savings behavior as exogenous variables. Let these preferences be represented by a strictly concave utility function, increasing in all its arguments U = U(X; T l ; Q; u ) (1) where u represents the parameters of the utility function. The quality of care Q is assumed to depend on the number of hours of formal child care used, F, the number of hours of informal child care used, I, the number of hours of maternal care, T m, and their 15

respective productivities represented by the vector q = ( F; I ; M ) Q = Q(F; I; T m ; q ) (2) Assume that the child requires continuous care by an adult. The mother s time can be divided among leisure (say, other household production activities), T l, work T h and maternal care T m. During her leisure and work hours she can receive child care from a relative (namely informal care I) or purchase formal child care in the market (F ). The mother is assumed to maximize U(X; T l ; Q(F; I; T m )) with respect to the choice of optimal quantities of X, T l, Q, F, I, T m, subject to the following constraints: Budget constraint : X + PF F + P I I = W T h + N (3) Quality prod. function : Q = Q(F; I; T m ) (4) Mother s time : T l + T m + T h = 1 (5) Child s time : F + I + T m = 1 (6) Non-labor income, N, is assumed to be predetermined 10. The price of an hour of informal child care, P I, might include both direct costs and the monetary representation of indirect costs. Assuming that the child requires continuous care by an adult implies that the child s time constraint is binding at the optimum. The mother s time constraint is likely binding 10 This is a strong assumption, since we could argue that N should include welfare transfers, at least for some fraction of the relevant population (single mothers). Indeed, welfare transfers are likely to be decreasing with earnings, and hence, with number of hours worked, T h, one of the choice variables of the model. This will create non-linearities in the budget constraint, which is not fundamental for the exposition but is relevant for the choice of number of hours worked. 16

as well (which is guaranteed if the marginal utility of T l is always positive). Therefore F + I = T l + T h always, which means that every hour the mother chooses not to take care of her child must be o set with an hour of informal or formal care. This implicitly assumes, a priori, a minimum amount of child care quality consumed. On the other hand, unlike the majority of previous studies, non-maternal child care (F + I) is allow to be positive if the mother decides not to work (T h = 0): This case is possible if the optimal solution involves T h = 0 and T l > 0 (positive "pure leisure", or other non-market activities not related to maternal care) 11. The mother can receive a subsidized price of formal care P S F = P M F (1 ) + c < P M F if her income is below some threshold E and if she works a minimum amount of hours (say T h > 0, for simplicity). For simplicity, the subsidy rate is assumed to be independent from the level of income 12. The parameter c is the monetary representation of the xed cost of demanding the subsidy, like the bureaucracy cost associated with the application process. 11 Like this paper, previous studies usually assume that the child is supervised by an adult at all times (e.g., Blau and Robins, 1988; Michaelopolous et al, 1992, Blau and Tekin, 2003). As mentioned, this implicitly assumes a minimum amount of consumption of child-care quality. For example, Heckman (1974) argues that the fact that children only rarely go unsupervised when a mother works is a statement about consumer preferences and not one about the need to consume a minimum amount of child-care quality. On the other hand, this assumption simpli es the analysis and is not restrictive in this paper for the following reasons. This assumption would be restrictive if (1) we did not distinguish between leisure (T l ) and home production of child care (T m ) and if (2) we also assumed that all of the mother s non market time (1 T h ) is spent caring for her child at home. In this case ~ T l = T l + T m, so ~ T l + T h = 1 and then F + I + ~ T l = 1, which implies F + I = T h. This would imply treating non-maternal child care as purely work-related expenses. If the mother decides not to work, then T h = 0 and no non-maternal care will be used (F + I = 0). This is assumed, for example, by Blau and Tekin (2003). We do not observe that in the data, since nearly forty percent of single mothers that are not in the labor force use some form of non-maternal care, either formal or informal. In the model, I do not assume either (1) or (2). Hence, even though I assume a minimum amount of consumption of child care quality, the model still allows us to observe positive demand for non-maternal care, even if the mother decides not to work. 12 CCDF subsidies have a sliding fee structure, with fees increasing with family income. Assuming just one common subsidy rate simpli es the analysis, since the budget constraint has just one kink in this case (at the income eligibility limit). 17

If the mother chooses not to receive the subsidy, then P F = P M F (child care market price). Therefore, P F = P M F (1 S) + cs, where S = 1 if the mother chooses to receive the subsidy and S = 0 if not. From the maximization problem, a system of equations for F; I; T h ; T m may be solved as functions of the exogenous parameters of the model W; N; E ; P I and P F, that is conditioned on the endogenous subsidy receipt S, such that P F = P M F (1 S)+cS. I denote the optimal number of hours worked under the subsidy program rules by T 1 h and the optimal number of hours worked with S = 0 as T 1 h then T 1 h = T 1 h(w; N; E ; P I ; P M F (1 ) + c; u ; q ) (7) T 0 h = T 0 h(w; N; P I ; P M F ; u ; q ) (8) The decision to work a positive number of hours (T h > 0) can be characterized by a latent index function Y such that Y = max S fv H;S 1 (PF M (1 S) + cs; P I ; W; N; E ; u ; q )g V H 0 (P M F ; P I ; N; u ; q ) = f h (P M F ; ; c; S; E ; P I ; W; N; u ; q ) (9) Y = 1 if Y > 0 Y = 0 otherwise (10) Note that the income eligibility limit E directly appears in the latent propensity to be employed (and not only through its e ect on S). This is because the income eligibility limit a ects the maximum amount of earnings that can be made under the subsidy rules and 18

hence, the attractiveness of being employed (Blau and Tekin, 2003). Note also that if the mother chooses to use no informal child care when employed, then V H;S 1 does not depend on P I, and if she chooses to use no formal (or informal) child care when employed, then V H 0 does not depend on P M F (P I): Assume there is no rationing in the subsidy receipt. Hence, if the mother decides to apply for the subsidy, she will get one for sure 13. As a result, the mother chooses to receive the subsidy (and hence to become eligible) if the indirect utility with the restriction W T h + N E and with the subsidized price P F = P M F (1 ) + c is greater than the indirect utility without this restriction and with the unsubsidized price P F = P M F. In other words, the mother has to trade o the xed cost c and the restriction in the maximum income with receiving a subsidized price of formal care. Let S d represent an index function for the net utility of receiving the subsidy, such that the mother demands the subsidy if S d 0. Let V S 1 represent the best attainable utility if the mother chooses to receive the subsidy and V S 0 the best attainable utility if she chooses not to receive the subsidy. Let the vector (X 1 ; T 1 l ; Q1 ) represent the optimal solution if the mother chooses to receive the subsidy (S = 1) and hence to become eligible, and (X 0 ; T 0 l ; Q0 ) if not (S = 0). Recall that the optimal number of hours worked when choosing the subsidy is denoted by T 1 h and the optimal number of hours worked when choosing not to receive the subsidy is denoted by Th 0. Then, the quasi-reduced form of the propensity to demand a subsidy, S d, expressed as a function of hours worked 13 This assumption is relaxed in the econometric speci cation presented below. 19

Th 1 and T h 0 is given by S d = U S 1 (X 1 ; T 1 l ; Q 1 ) U S 0 (X 0 ; T 0 l ; Q 0 ) = V S 1 (P M F (1 ) + c; P I ; W T 1 h( E ) + N; u ; q ) V0 S (PF M ; P I ; W Th 0 + N; u ; q (11) ) S = 1 if S d > 0 and S = 0 otherwise where I emphasize the relationship between S d and hours of work T h, by implicitly keeping the dependence on F and I 14. Equation (11) indicates that the propensity to demand a subsidy depends, on the one hand, on the net utility gains (or losses) of changing the number of hours worked from Th 0 to T h 1 S, given by V1 (:; W Th 1) V 0 S (:; W Th 0 ): This change in the utility is likely positive if the mother s optimal number of hours worked with the subsidy is greater than without the subsidy, such that W T 0 h < W T h 1. This change in the utility is likely negative if, to become eligible, the mother has to reduce the optimal number of hours worked from Th 0 to T h 1, such that W T h 1 < E < W Th 0. But this is just one margin of adjustment. Of course, the mother could be willing to trade o some optimality in the number of hours worked in exchange for better composition of the other variables a ecting her utility (say e.g., better child care arrangements as a consequence of the subsidy). Thus, the propensity to demand a subsidy also depends on the market price of formal child care P M F, the parameters of the subsidy program t, the xed cost to applying to the program c, 14 The obvious alternative is to formulate the problem as a multinomial choice speci cation with j=1...j alternatives. That is, work, not-work, formal, informal, and subsidy receipt. I do not express the problem in that way to emphasize the margin of adjustment in terms of employment, but I do consider implicitly the heterogeneity in child care arrangements as a determinant in the choice to demand the subsidy and the extensive and intensive choice to work. 20

nonwage income N, the taste for consumption, leisure and child care quality, represented by the vector u, and the productivities of formal, informal and maternal care, represented by the vector q. The income eligibility rules E a ects the demand for the subsidy trough the e ect on the number of hours worked under the program rules (Th 1 ). Note, for example, that if the mother chooses to use no informal child care when S = 1, then V S 1 does not depend on P I, and if she chooses to use no formal child care when S = 0, then V S 0 does not depend on P M F : Substituting (7) and (8) into the quasi-reduced form given by (11), we nd the full reduce form of the propensity to demand the subsidy, S d S d = V S 1 (P M F ; ; c; E ; P I ; W; N; u ; q ) V S 0 (P M F ; P I ; W; N; u ; q ) (12) = f d (P M F ; ; c; E ; P I ; W; N; u ; q ) (13) S = 1 if S d > 0 and S = 0 otherwise As a result, the latent index functions of Y given by (9) and the latent propensity to demand the subsidy, S d given by (12) are the basic equations to formulate the econometric model. We need to incorporate into the model the presence of rationing in the subsidy receipt, since not all mothers who demand a subsidy receive one. Note the joint nature of the decision to work and to demand a subsidy. This is re ected in the reduced form equations S d and Y, since both equations depend on the same variables. The presence of rationing, however, make it possible to come up with potential exclusion restrictions to estimate the e ect of the subsidy receipt on employment outcomes. This is explained in the next section. 21

5 Econometric Model The econometric model is based on a latent-index framework inspired in the conceptual model presented in the previous section, but introducing several modi cations. First, we need to include the presence of rationing into the model. Given the existence of rationing in the CCDF subsidies, the latent propensity to receive a subsidy is determined by both the mother s choice to demand the subsidy and the agency s decision to award it. See the Appendix 1 for the derivation of this latent propensity using the characterization of the mother s choice and the agency s decision problem. Second, exogenous determinants ( ) of wages W, market prices of formal care PF M, and prices of informal care P I are substituted into the model, and hence, a fully reduced form speci cation is estimated 15. The basic econometric speci cation is based on the reduced form relationship between the subsidy indicator S (the treatment) and the probability of working a positive number of hours, Pr(Y 0), (the outcome). This implies estimating the propensity to receive the subsidy and an employment outcome equation. Let Y ij be an indicator variable that takes the value 1 if the mother i living in state j works and 0, if not. As a result, the econometric model is based on the following equations. 15 Alternatively, I could have estimated wages and prices of care using selection methods to account for the non observability of wages and care expenditures, since wages are not observed for mothers who do not work, and non-maternal care expenditures are only observed for mothers who work and who utilize formal care. This is because the NSAF reports expenditures on child care at the family level only, and only for mothers who work. Hence, the selection methods would involve a double selection correction in the case of care expenditures. However, wage e ect on employment is not the focus of this paper. Also, this paper is aimed at estimating the e ect of actual subsidy receipt on employment outcomes, and not child care price elasticities on employment. As mentioned before, inferences about the e ects of the CCDF subsidies drawn from price elasticities might not be useful if there are substantial costs to collecting a subsidy, which is likely the case when there is rationing. 22

The latent propensity to receive the subsidy is 16 S ij = y ij 1 + T F j 2 + ij (14) S ij = 1 if S ij > 0, S ij = 0 otherwise And the employment outcome equation is Y ij = y ij + S ij + U ij (15) Y ij = Y ij if Y ij > 0; Y ij = 0 otherwise where is the (common treatment) e ect parameter (the parameter of main interest). This parameter depends on both preference parameters and the parameters of the mechanism used by agencies to assign the subsidies. And y ij = [X ij; Z j ] are the observed demographic and state characteristics, common to both the latent propensity to receive the subsidy and the employment equations. X ij includes observed demographic characteristics of the mother i living in state j (including interactions between demographic characteristics of the mother i and state j welfare policies). Z j includes observed characteristics of state j (including income eligibility limit in state j, parameters of the CCDF subsidy program in state j, and state j welfare policies). Tj F : amount of pre-determined child care funding, scaled by the number of children 16 Equation (14) is a reduced form speci cation of the joint probability of demanding and receiving a subsidy. It does not distinguish demand e ects (mother s decision to apply for a subsidy) and supply e ects (the agency s decision to award a subsidy) of y ij and Tj F, just the net e ects on subsidy. 23

living with a householder single mother in state j ( ij ; U ij ) : unobserved demographic and state characteristics, that might be correlated (because of the endogeneity of the subsidy receipt) Basically, the model speci ed by (14) and (15) states three reasons why we might observe Y and S to be correlated: 1) a direct relation due to the in uence from S on Y through the parameter, 2) because of correlation among the observable variables (the 0 s), and 3) because of correlation among the unobservable variables (; U). If and U are correlated, S is correlated with U. In this case, the treatment (receiving a subsidy) is endogenous to the decision to work. The Appendix 1 explains in detail the underlying assumptions used to construct these equations. In consequence, the empirical analysis consists of estimating a selection equation for the latent propensity of receiving a subsidy and an employment outcome equation (common for the treated and non-treated state). Both equations are discrete. Note that since and U are assumed to be correlated, S is correlated with U. In other words, the treatment (receiving a subsidy) is assumed to be endogenous to the decision to work. Following Heckman (1978), one can impose a system of equations for the joint determination of the endogenous regressor (subsidy receipt) and the outcome variable (employment status), and then impose joint normality assumptions on the error terms to develop the maximum likelihood estimator for the resulting model. This implies specifying a bivariate probit model estimated by ML where S acts as one of the binary dependent variables and also as an endogenous explanatory variable of (15). Formally, the model is identi ed without an exclusion restriction, although semiparametric identi cation requires such an excluded 24

variable (Altonji, Elder, Taber, 2005). If the coe cient of correlation among the unobservables of both equation ; U is di erent from zero ( 6= 0), then S and U are correlated, and probit estimates of Equation (15) are inconsistent. The e ect of S is the primary interest. In this model, the average e ect of S on Y (for a given value of covariates y ) is ( y ij + ) ( y ij )17. This model, with two binary dependent variables that are correlated, where one of them is also an explanatory variable of the other, is sometimes called a recursive simultaneous-equation model (see e.g. Maddala (1983), p.123). Because S and Y are observed as dichotomous variables, we need to impose the conditions V ar() = 1 and V ar(u) = 1. The model is estimated by full information maximum likelihood approach. The endogenous nature of S on equation (15) can be ignored in formulating the log-likelihood. I use the variation across states in the amount of pre-determined child care funding (Mandatory Funds) as an exclusion restriction (i.e., a variable that a ects S but not Y directly). I scaled these funds by the number of children living with a single mother head of household in each state. The Mandatory Funds are assumed to a ect the degree of rationing at the state level and hence the propensity to receive a subsidy, but not the probability of being employed, conditional on subsidy status 18. To be a valid instrument, this variable must be uncorrelated with the unobservable determinants of employment of single mothers, U. 17 See Vytlacil and Yildiz (2005) for further discussion about this type of models under non parametric assumptions. 18 Pre-determined child care funding at the state level corresponds to established mandatory funds. Mandatory funds provide a guaranteed level of federal child care funding to states, for which no state matching funds are required. Each state receives a xed amount each year, equal to the funding it received under the AFDC child care programs in either FY 1994, FY 1995, or the average of FY 1992-1994, whichever is highest. See Besharov and Higney (2006) and Meyer and Rosenbaum (2000). 25

Because varies across states, T F j may be correlated with unmeasured state-level variables that a ect current employment decisions of single mothers. In particular, state waivers implemented before 1996 may have a ected AFDC child care expenditures in 1992-1995 (a ecting Mandatory Funds) and may a ect current employment decisions of single mothers as well. This would preclude the use of T F j as an exclusion restriction. As a result, I use a set of state welfare policy variables constructed by Bernal and Keane (2006) to control for di erences in welfare regulation across states that might in uence both Mandatory Funds and employment decisions. These welfare policy variables can be interacted with demographic characteristics at the individual level, as explained in the next section. 6 Data I use repeated cross-section survey data from the 1999 and 2002 rounds of the National Survey of America s Families (NSAF), conducted by the Urban Institute. This data corresponds to post-prwora era (after the welfare reform). The NSAF was designed to analyze the consequences of transferring the responsibility for social programs from the federal government to the states. The survey was conducted by telephone on a sample derived primarily from random-digit dialing 19. Residents of 13 states 20 were over-sampled in order to allow within-state analysis and low-income households (below 200 percent of the federal poverty level) were over-sampled as well. The entire NSAF sample of the 1999 and 2002 rounds 19 Cellular telephones distributed by the survey organization were used to conduct interviews with households without a telephone. 20 Alabama, California, Colorado, Florida, Massachusetts, Michigan, Minnesota, Mississipi, New Jersey, New York, Texas, Washington and Wisconsin. 26

includes 42,360 and 39,798 households, respectively. Using both 1999 and 2002, I select a subsample of 8945 unmarried mothers with at least one child under age 13 (from now on, 0-12y sample). This is the eligibility age limit for CCDF child care subsidies and the most common age limit used in other studies (e.g. Blau and Robins (1988), Kimmel (1998), Anderson and Levine (2000), Blau and Tekin (2003)). For the estimations, I split the selected sample in two groups according to the age of the youngest child of each mother: 0-5 year olds (4632 mothers) and 6-12 year olds (4313 mothers). Child care subsidy receipt is coded in the following manner. The mother is asked whether she receives any government assistance in paying for child care. I code a mother as receiving a child care subsidy if a welfare, income maintenance, social service, family service, or child care resource and referral agency helped her pay for child care either in the month prior to the survey or in the past 12 months. According to this classi cation, 15 percent of single mothers whose youngest child is 0-12 years old report receiving a child care subsidy (23 percent among 0-5 year olds, 7 percent among 6-12 year olds, see Figures 3-5). According to the Administration for Children and Families (1999, 2000), 12-15 percent of eligible families received a CCDF subsidy in 1998-99. I (roughly) estimate eligibility for each household in the selected sample (according to the assumptions shown in the Appendix 2). Based on that estimation, 22.5 percent of eligible single mothers received a subsidy. This overrepresentation of single mothers among bene ciaries is in line with overrepresentation of single mothers among low-income families. Figures 3-5 show employment variables by subsidy receipt category and age of the youngest child. Employment status is measured by whether the mother has worked a posi- 27