The Effects of Single Mothers’ Welfare Use and Labor Force Participation Decisions on Children’s Cognitive Development Hau Chyi WISE, Xiamen University

Orgul Demet Ozturk∗ University of South Carolina

April 2, 2009

Abstract In this paper we examine the effects of single mothers’ welfare use and employment decisions on children’s short-run cognitive development, measured by their pre-school standardized math test scores. We control for three potential channels through which a mother’s decisions affect her child’s outcomes: direct monetary benefits, parental time invested on the child and nonpecuniary benefits from in-kind transfer programs such as Medicaid. We allow mothers’ decisions to have varying effects on attainment by the children’s innate ability. We employ an instrumental variables approach as well as state fixed effect to address the endogenous nature of welfare and labor market participation decisions. Our estimates suggest that an additional quarter on welfare during childhood results in a 1.4 percentage point increase in test scores for the average child. Furthermore, even though the affects on the average child are positive, welfare use and employment of the mother during childhood are detrimental to math skill accumulation if the child has higher than median innate ability. That is, children who were born to mothers with more years of schooling and higher AFQT scores are negatively affected by their mother’s work and welfare use.

Keywords: childhood cognitive ability, mother’s work, welfare JEL CODES: I3, J13, J22

∗ We thank Meta Brown for her guidance and encouragement. We are grateful for valuable suggestions from John Karl Scholz and John Kennan. We would also like to thank Bruce Hansen, Jim Walker, Binzhen Wu, and all participants of the 2008 North America Stata User Meeting, the 20th annual European Association of Labour Economists Conference, the 14th International Conference on Panel Data, the International Symposium on Contemporary Labor Economics, and the seminar participants at Academia Sinica and University of Wisconsin-Madison Public Economics workshops. All errors are our own.

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Introduction

In this paper, we study the effects of low-skilled single mothers’ welfare use and employment choices on their children’s early cognitive development. The welfare program we consider is the Aid to Families with Dependent Children (AFDC). Before 1996, AFDC was the largest welfare program in the U.S.1 In addition to offering cash benefits, participating in the AFDC program often assured eligibility for other programs such as Head Start, food stamps and Medicaid.2 For example, before the expansion of Medicaid in 1986, applying for AFDC was the primary means of getting health insurance for poor children. Participation in AFDC can thus be used as a proxy for welfare use in general. Early cognitive development is found to be a strong predictor of long run achievements. High early test scores are strongly correlated with educational attainment, low crime involvement, high salaries and low probability of teenage fertility (see reviews by Duncan and Brooks-Gunn(1997), Haveman and Wolfe(1995), Currie and Thomas(1999), and Bernal and Keane, 2005). Thus, it is highly crucial to understand whether welfare policies can potentially affect cognitive outcomes of the children. Particularly, since parental time and financial resources are most likely components of early “nurturing,” any public policy that will affect parents’ incentives and the costs of these inputs should be carefully evaluated. Our research contributes to the literature on the determinants of children’s attainments on three fronts. First, effects of a mother’s decisions in our attainment production function are allowed to interact with the child’s (observed) innate ability. This allows us to obtain distributions for the effects of work and welfare by children’s innate ability, in addition to a single coefficient that measures only the effect at the mean level. To our knowledge, our paper is one of the few that allows this flexibility. Second, our analysis differs from many others by modeling the child’s attainment as a function of 1 In

1996, the Personal Responsibility and Work Opportunity Reconciliation Act of 1996 (PRWORA) ended AFDC, replacing it with the new, Temporary Aid for Needy Families (TANF) program. TANF differs from AFDC by introducing a time limit on welfare benefits and gives U.S. states more flexibility in developing their own programs. 2 See Table D-1, Citro and Michael (1995) for a survey of transfer programs with AFDC as prerequisite. Keane and Moffitt (1998) state that 89% of AFDC recipients also received food stamps and Medicaid, and another 42% had a fourth benefit, mostly housing subsidies.

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the mother’s cumulative inputs. A child’s attainment, observed at age six, is determined by the cumulative welfare use and work experiences of the first twenty quarters after birth. This relatively long history not only enables us to identify the effects using a much richer variation in mothers’ decisions, but also allows us to investigate the implication of different “intensity” levels of work and welfare use. Third, we model multiple channels through which a mother’s decisions can affect child’s math score: direct monetary benefits, parental time invested on the child and non-pecuniary benefits from in-kind transfer programs. The estimates hence provide a deeper understanding of the workings of the welfare program. Most studies on the relationship between welfare participation and early cognitive achievements focus either on the determinants of children’s attainments or on the consequences of growing up in poor families. In both areas, researchers use samples of all children they can obtain in the surveys and use an Ordinary Least Squares (OLS) method for estimation. They generally find significantly negative relationships between welfare recipiency and children’s attainments of all sorts. As pointed out before by, for example, Currie (1998), Duncan, Magnuson and Ludwig (2004) and Dahl and Lochner (2005), these negative relationships do not necessarily indicate causal connections due to improper comparison groups or unobserved heterogeneity issue. In this paper we focus only on the attainments of children born to single mothers with twelve or fewer years of schooling. This group of low-skilled mothers are most likely to satisfy the financial eligibility for welfare.3 As a result, rather than comparing to children from economically stable two-parents families that are not qualified for welfare, we measure effects of welfare by the difference in attainments between welfare recipients and eligible non-participants. Moreover, we employ an instrumental variables (IV) approach to control for potential endogeneity issues that may simultaneously affect mothers’ decisions and children’s attainments.4 IV approach is commonly used to address the unobserved heterogeneity issue. For example, both Currie (1995) and Hill and O’Neill (1994) use the variation in the “guarantee” benefit level, i.e., the AFDC monetary benefit for a single mother with two kids and no income, to identify the effects of mothers’ welfare decisions on children’s short-run test scores. The instruments we propose, similar to those of Hill 3 We can theoretically define our sample using the exact financial eligibility of welfare based on each individual’s information. However, a sample based on financial eligibility creates a potential selection problem, as earning is an outcome of the endogenous work decision. 4 We also incorporate state fixed effects to control for unobserved long term state factors.

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and O’Neill (1994), are predicted quarters of welfare use and work.5 Due to the length of our data, we are able to include annual benefit rules in construction of our instrument. These parameters, including the effective tax rates on earnings and non-labor income and the increases in benefit level due to having additional children, capture the annual variation in the economic incentives of the welfare program. They provide richer exogenous variation that affect participants’ behaviors than the widely adopted guaranteed level that captures only the generosity of the welfare program.6 In particular, observations on mothers who, all else equal, reside in states with different effective welfare tax rates on earning help us separate the effects of work from welfare use. Another possible way of evaluating determinants of children’s attainments is to use sibling comparisons under a fixed-effect framework. By assuming members in a family face the same unobserved characteristics, Currie and Thomas (1995) and Garces, Currie and Duncan (1995) use sibling comparisons to investigate the effects of Head Start on participants’ short- and long-run outcomes. Dahl and Lochner (2005) investigate the effect of family income on children’s test scores and use a fixed effect instrumental variables (FEIV) estimator, which combines sibling comparisons and instrumental variables approaches to control both individual and family related unobserved heterogeneity. One important restriction of the sibling comparison is that it requires many observed siblings in the sample to make viable comparisons. It also disregards all observations of one-child families in the estimation. Due to the fact that we do not have enough siblings in our sample, we do not incorporate the sibling comparison approach in our analysis. In all of the above studies, the variable in interest is specified linearly in the outcome regression. After applying the IV approach, Hill and O’Neill (1994) find that welfare use is still negatively associated with children’s test scores while Currie (1998) finds that the negative correlation no longer exists. Furthermore, Hill and O’Neill (1994) find that work has a significant negative effect on test scores. However, the comparison group (children who have no childhood welfare experiences) is comprised of children who were potentially ineligible for welfare. Currie and Thomas (1995) find that Head Start has different effects (from insignificant to positive) on test scores based on a child’s ethnic background, and Garces, Duncan and Currie (2002) find that it has a positive effect on a child’s long-run outcomes, such as reducing crime rate. Using FEIV estimates, Dahl and Lochner (2005) 5 Hill

and O’Neill (1994) use a family average sample. Their welfare measure is the average proportion of welfare exposure since the first child was born. 6 See Moffitt (2002) and Keane and Wolpin (2002) for reviews on various IVs adopted in the welfare literature.

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find that work has no significant effect on a child’s short-run test scores, but they do not include welfare in their investigation. In sum, average effects of mothers’ decisions are still inconclusive. Bernal (2008) discusses the importance of allowing the marginal effect of a mother’s decisions to vary with the child’s (observed) innate ability. She studies the effects of mothers’ child care and work decisions on their children’s test scores. She finds that the marginal effects of a mother’s choices are decreasing with innate ability of the child. That is, although the effects on a child with the mean innate ability may be small and positive, there are significantly larger positive impacts for the low end of the innate ability distribution and large negative effects for the high end. We follow a similar setup to construct our attainment production function. Our estimates suggest that allowing mothers to have more time taking care of their children through substituting work for welfare is one of the most important source of the benefits of the welfare program. First, estimates suggest that the negative associations between childhood welfare use and test scores mostly disappear, even in a model that is not controlling for the unobserved heterogeneity, upon choosing the proper comparison group to measure the effect of welfare use. IV estimates suggest that the effect of non-pecuniary benefits from in-kind transfer programs that correlate with participation in the AFDC program on test scores of children with mean (or median) innate ability is close to zero. Combining the effect of welfare from the above channel and from an increase in monetary benefits from welfare participation into the welfare coefficient does not change the magnitude nor the statistical significance of estimates on the average child by much. However, the effect of welfare use on the average child becomes statistically significant and large in magnitude when we include the effect from the increase in parental time saved through substitution of work for welfare. In this case, a quarter more of welfare use is associated with a 1.4 percent increase in the average child’s standardized math test score. Effects of mothers’ work decisions also exhibit a similar pattern. Marginal effects of work for a child with mean level of the innate ability is a 0.8 percent increase in test scores. Finally, we find that mothers’ decisions exhibit diminishing marginal productivity in the observed innate ability of a child. In other words, children with low observed innate abilities benefit from childhood welfare use, but children with high innate abilities are likely to suffer in their math test scores if their mothers participate in welfare or work more during childhood.

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The structure of the paper is as follows. The next section proposes an economic model of a child’s attainment production. Section 3 discusses econometric estimation of this model and identification of parameters and the details of the IV approach. Section 4 describes the data. Section 5 reports the estimation results, and section 6 offers a discussion of the results and concludes with directions for future research.

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Economic Model

In our model, a mother makes welfare and work participation decisions quarterly. She cares about her consumption of leisure and a composite good, and her child’s ability. She observes her child’s innate ability and produces the current potential attainment by contributing time (choosing how much to work) and money (choosing how much to work and whether to use welfare). When childhood is over (at the end of age 5), we observe a test score which proxies the ability accumulated as a function of cumulative welfare use and employment history. This setup follows the tradition of human capital formulation proposed by Ben-Porath (1967) where cumulative investment determines human capital, not the current time and money input as it is in most research on this subject.7 The log of child’s attainment AT is produced according to (1): ln AT = ln A0 + γ1 WT + γ2 ln A0 WT + γ3 ET + γ4 ln A0 ET (1) + γ5 ln YT + γ6 T + ui ,

where A0 is the innate ability, ET is the cumulative work experience, WT is the number of quarters on welfare, Y is cumulative income and T is the age of child (in quarters) when we observe their first test score 8 . Although the PIAT math test is given to each child biannually from age five on, some of the first observed test scores are from later ages. Initial ability, ln A0 , is a linear function of time-invariant characteristics like gender, race, AFQT score, education and age of mother at birth as shown in equation (2). We do not use the actual 7A

different modeling strategy is based on the timing of investment (Todd and Wolpin, 2003). The empirical results of a such model (which is not presented in this version) show that none of the coefficients are significant. These results are available upon request. P20 P20 8E = T t=1 ht . ht = 0 if no work at quarter t, 1 otherwise. WT = t=1 ωt , ωt = 0 if mother is not on welfare at P20 quarter t, 1 otherwise. YT = t=1 {YtO +ht YtL +ωt .Bt } represents available financial resources, which are determined by other income (Y O ), labor earnings (Y L , if work) and welfare benefits (Bt if on welfare)

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age but an indicator for teenage mothers (ageless18) to capture the increased possibility of health problems for children born to young mothers.

ln A0 = γ7 Gender + γ8 Black + γ9 Hispanic (2) + γ10 Ageless18 + γ11 ln AF QT + γ12 Edu We assume that income from different sources have the same effect on ability. Currie (1998) suggests that the effect of AFDC income is just like other income sources. Finally, ui is the unobserved portion of a child’s ability. Marginal effects of mother’s work and welfare choices on ability are: ∂ ln At = γ1 + γ2 ln A0 , and ∂Wt ∂ ln At = γ3 + γ4 ln A0 , ∂Et respectively. This setup allows the effects of mothers’ decisions to vary with observed initial abilities. It is useful to discuss channels through which a mother’s welfare and work decisions affect her child’s attainment and what are captured by the coefficients of WT and ET in (1). The welfare has three possible ways to affect potential attainment of a child. First, any income effect is captured by the coefficient of Y. Second, a mother may choose to substitute welfare for work so that she can have more time invested on her child. However, this effect will be captured by a decrease in maternal employment, ET . Finally, the coefficient of welfare will be capturing the contributions of the non-pecuniary benefits of being on welfare. Many means-tested transfers programs are linked with AFDC, such as the early childhood education program, HeadStart, housing subsidies and perhaps most importantly, the health insurance program, Medicaid. Since we do not separately control for participation in different programs that are linked with the AFDC (according to Currie, 1998, it is almost impossible to do so), the benefits from these programs on a child’s attainment will be captured by the coefficient of the welfare experience, WT . The employment decision of the mother has two possible ways to affect ability. The first effect comes through the increase in labor income and is captured by the coefficient of YT . The second

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source of impact for work on ability is through the time spent with the child. We can think of two possible directions for this effect. On the one hand, work picks up the effects of the unobserved lost time for a mother to educate her child, and may thus be detrimental to a child’s attainment. On the other hand, children’s attainments can improve when working mothers exhibit a good role model for them to follow. Also, mothers who work more may be able to take care of their children more intensely and efficiently. As a result, we may observe a positive relationship between child’s attainment and mother’s work choice. Unless we are willing to make more structural assumptions on how a mother takes care of her child, both effects will be captured by the coefficient of ET in equation (1). It becomes an empirical question to see which of these effects dominate.

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Econometric Issues

Define the mother of child i’s history of decisions as (Wi , Ei ) ≡ di , and let Xi be the rest of the child’s observed characteristics. The basic econometric model of ability determination is Ai = f(Xi , di ) + ui ,

(3)

where ui is the residual. Using nationally representative data sets, such as the NLSY or PSID surveys, previous studies have generally estimated different versions of equation (3) by OLS models. However, it is very likely that certain characteristics unobserved by econometricians can simultaneously affect both a mother’s work and welfare use choices and the child’s attainments. If this is the case, we have a typical problem of endogenous regressors and OLS estimators are inconsistent. To be able to identify the unbiased effects of a mother’s decisions on her child’s attainment, as described in Section 2, we need to isolate the potential effects of unobserved factors on the child’s attainment. We address the issue by instrumenting for WT and ET in equation (1). There are two fundamental requirements for our instruments to be valid. First, they have to be correlated with single mother’s decisions for which they are used as instruments. Second, they have to be uncorrelated with (or mean-independent of) the unobserved component (u) of a child’s attainment (AT ). The instruments we propose are similar to that of Hill and O’Neill(1994), which are the predicted quarters of welfare use and work. In the following section we describe the construction of our instruments.

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3.1

Instruments

Suppose every quarter a mother chooses whether to use welfare or not (ωt = 0 or 1) and whether to work or not (ht = 0, 1). Let Cjt represent a single mother’s jth alternative concerning work and welfare participation in the tth quarter. This  0    1 Cjt =  2    3

two-dimensional choice problem can be written as if if if if

(ht (ht (ht (ht

= 0, = 1, = 0, = 1,

ωt ωt ωt ωt

= 0) = 0) = 1) = 1).

We set Cjt = 0 as the baseline decision. We define the value of choosing alternative j as Vjt . That is:  V0t    V 1t  V 2t    V3t

=0 = β10 Zt + u1t = β20 Zt + u2t = β30 Zt + u3t .

(4)



 u1t Assuming u = u2t  follows a multivariate normal distribution, we can estimate this model using a u3t multinomial probit model. The explanatory variables (Zt ) are: (i) mothers’ characteristics, including age, age squared, race, number of years of education, number of children, other income (in 2000 dollars) and (ii) excluded explanatory variables, including all state AFDC benefit rule parameters. The estimation results are given in Section A.1. We use the joint probabilities

20 X

c t = 0, ωt = 0) Pr(h

t=1 20 X

c t = 1, ωt = 0)] Pr(h

t=1 20 X

c t = 0, ω = 1) Pr(h

t=1

as IVs.9 The benefit of doing so is that joint probabilities correspond to the simultaneous nature of the welfare use and work decision making process. From Chyi (2008), we do know mothers make 9 To

avoid a perfect multicollinearity between constant terms and IVs in the first stage OLS estimations for WT P c and ET , we arbitrarily exclude 20 t=1 Pr(ht = 1, ω = 1). Second stage results do not vary widely with the exclusion of alternative joint probabilities.

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sophisticated simultaneous decisions. As a result, the variation in joint probabilities will help us better identify mothers’ decisions. Given that we have more instruments than endogenous decisions, Section A.2 provides an overidentification test as well as other tests for instrument validity. These estimated joint probabilities we use can be categorized as generated instruments. The consistency of the effects of WT and ET in the context of endogenous regressors and generated instruments follows standard requirements of the validity of an IV approach (Chapter Six, Wooldridge, 2001). Also, the asymptotic distribution of the second stage estimator is not affected by the fact that the IVs are generated under weak conditions. Furthermore, given that we have relatively large samples for constructing the instruments, as well as estimating a child’s attainment production function, small sample problem is not concern. In Section A.2, we discuss the validity of instruments using various econometric tests. Below we discuss the economic rationale for the identification.10

3.2

Identification

There are several sources of variation in the data that enable us to identify the effects of a mother’s decisions. First, our sample includes children who were born to a group of low-skilled, single mothers. Children who have not received welfare (the comparison group) in our sample were equally likely to be eligible for welfare and faced similar socioeconomic disadvantages as the treatment group. As a result, a comparison in attainments between children who received welfare benefits during childhood and those who were eligible but have not will provide us a way to measure the effect of welfare (controlling for unobserved characteristics that may be correlated with welfare use). On the other hand, almost all previous studies on children’s attainments include samples of children from two-parents, economically stable families. Second, because a mother’s decisions are measured by accumulated quarters during childhood of a child, we compare not only attainments between children who have experienced one decision and those who have not, but also attainments between those who have different levels of exposure to 10 Another

widely adopted empirical strategy to control for possible correlation between endogenous regressors and unobserved heterogeneity is to control for mother’s fixed effect. However, identification of such a fixed-effect model relies on comparisons between siblings. Estimates include fixed estimates (not reported in this paper) reveal similar yet insignificant results. We suspect that too few multiple child families in our sample make fixed-effect estimates not viable. The average number of observed children in our sample is only at 1.55 (see Table 1). Conditional on having more than one child, the average number of observed children is at 2.8, but the sample size reduces by more than 20%.

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their mothers’ decisions. For example, the effect of welfare use is identified not only by comparing children who have never been on welfare and those with welfare experience during childhood, but by variation in attainments between children with different quarterly welfare experiences. With the existence of possible endogenous regressors, we also need to consider the consistency of our estimators. We follow Keane and Wolpin’s (2002) strategy and use the exogenous variation from economic incentives implied by the state benefit structures in Zt . Since AFDC is a state-administered program, participants’ statutory benefits are exogenously determined by state governments (under the guidance of the federal government). These benefits do affect mothers’ likelihoods of participating in welfare or work, and it is reasonable to assume they are uncorrelated with children’s attainments. As the AFDC benefit structure implies different economic incentives for mothers’ behaviors, it is natural to use parameters of the benefit rule, rather than particular levels of benefit, to provide identification.11 In this research, we use the annual estimates of the parameters of the State AFDC rules from Ziliak (2007). The parametrization of the the annual State benefit rule can be written as: 1kid 2kids 2kids 3kids Bist =b0s G1kid × Dist + b2st G3kids × Dist ist × Dist + b1s Gist ist 4+kids O L + b3st G4+kids × Dist + b4st Yist + b5st Yist , ist

where Bist is the monetary level of annual benefit of individual i who lives in state s in year t. G1kid , G2kids , G3kids and G4+kids represent the guarantee levels of benefit for a family with one, two, three and more than three children, respectively. D1kid , D2kids , D3kids and D4+kids are indicators to denote families with one, two, three and more than three children, respectively. Y O refers to a family’s unearned income (family income excluding AFDC and Food Stamps benefits and labor income). Y L is a single mother’s labor income. These parameters capture different economic incentives implied by the AFDC benefit structures that will help us to identify a mother’s different decisions. In particular, b1s to b3s account for the guarantee levels of benefits a family can expect when there is no other financial resource. The higher they are, the more likely a mother will be on welfare. On the other hand, b4s and b5s represent the 11 As

the structure in determining a participant’s AFDC monetary benefit level (the so-called benefit rule) is a complicated nonlinear function depending on at least family structure, size, income, and parents’ work decisions. There is a wide range of candidates to choose from. For example, many previous studies choose guaranteed statutory benefits for a single mother who has two eligible children with no income, to serve for the identification purpose (see a survey of instruments used in these studies by Moffitt, 2002).

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effective tax on unearned and earned income, respectively. In particular, a higher b5s implies a higher effective AFDC tax rate on work and induces less work from a mother. Recent studies reveal growing concern about the existence of unobserved state factors that may simultaneously affect mothers’ decisions and children’s attainments. For example, a state with a more generous benefit rule is also more likely to have a better system of assisting poor families in raising their children. One benefit of using annual variation of state benefit rule is that we will be able to control for the state fixed effects in equation (1).

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Data

We focus on children born to single mothers with at most twelve years of schooling and who have been single for at least one year during their children’s childhood.12 The reason for avoiding use of all single mothers who are financially eligible for welfare is that financial eligibility is, to some extent, the result of a mother’s decisions. Therefore, it creates a more serious sample selection problem. Also, state waiver programs granted by the federal government have allowed states much greater flexibility in designing their own benefit rules since as early as 1992; we exclude children who have experienced waiver programs during their childhoods by using the exact date of the enactment of the state waiver programs. Another reason to focus only on children who were born before state waiver programs and welfare reform is due to the design of the NLSY 1979. Mothers followed by the NLSY 1979 were between 14 to 21 years old in 1979. As a result, most of them were passed their prime ages of child bearing by the time of welfare reform. Including children who were born to older mothers creates further complication. Table 1 summarizes variables used in this research. Sample means of variables are weighted using customized children’s weight provided by the NLSY. We convert all annual monetary variables into real, year 2000 dollars using the non-durable Personal Consumption Expenditure Deflator. We have 36, 660 sample quarters from 1, 833 children who were born to 1, 183 single mothers.13 The upper panel lists mean patterns of mothers’ decisions during the first twenty quarters since the children’s birth. Defined as having reported positive welfare income for more than one month in a quarter, the 12 An alternative way to construct the sample is to require mothers to have always been single during this period. The estimation results are similar, but this requirement significantly reduces the sample size (by about 60%) and the significance of the estimation. 13 In other words, the average observed number of children for a mother in our sample is 1.55.

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childhood welfare participation rate of this group of children is 42%. In terms of employment, 42% of this group of low-skilled single mothers have worked part-time (defined as having worked between 125-375 hours per quarter) during their children’s childhood, while 31% of them have worked fulltime. In other words, the labor force participation rate is roughly 73%. Next panel lists children’s characteristics. First, the sample of children is comprised by an equal percentage between male and female. Among them, 31% are black. The average PIAT standardized math score is 97.4, which is lower than the mean test score of the 1968 norm population (100). This indicates the disadvantage of growing up poor. In terms of mothers’ characteristics on the right side of the table, the mean age at birth is 23.4 years old. This is younger than the average age (27 years old) that NLSY mothers gave birth to their children. The mean sample mother receives 10.9 years of education and has about 2 children. Also, those who have worked received a mean annual labor income of $9,917 (in 2000 dollars) and have other income (family income other than welfare and labor income) of $16,374. Table 2 further distinguishes a mother’s welfare use and work decisions according to her child’s age. The table begins from two years before a child’s birth. Comparing pre- and after-birth welfare use, we note that low-skilled, single mothers have increased welfare use by a minimum of 10 percentage points due to giving birth to a new child, from 31% a year before to 41% in the first year after the child’s birth. The mean welfare participation rate remains fairly stable for the first five years after a child’s birth. In terms of labor force participation, only that of the first year seems to have been affected by childbearing. In fact, mothers’ mean hours of work (conditional on work, in the last column of Table 2)increase significantly after their children turn one year old. Table 3 tabulates means and standard deviations of PIAT math standardized scores in different quartiles of variables used in the estimation. For example, the mean of the first quartile of the sample mother’s welfare use is zero (never been on welfare between child’s ages one to five), while the mean of the forth quartile of welfare use is 19.5 quarters. The mean PIAT test score for children whose childhood welfare use is in the first and the forth quartiles are 100 and 93.6, respectively. Combining a similar pattern observed in the work variable, simple correlations of mothers’ decisions and test scores indicate that less welfare use and more work during a child’s childhood is associated with higher test scores. The quartiles of PIAT math score itself indicate that more than 50% of the children who were raised by low-skilled, single mothers have test scores below the 1968 population mean (100),14 as the mean test score of the third quartile is only 102.8. 14 It

is well known that the cohort mean scores improve over time. As a result, this group of children from disad-

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In terms of mothers’ characteristics, the first set of variables includes the hourly wage rate, labor income and other income. To measure general financial wellbeing during childhood, these are average values over twenty quarters.15 In general, a child’s test score is positively correlated with the available financial resources during childhood. The next set of mothers’ characteristics includes AFQT percentile score, education level (the last reported education level) and her age at the time of the child’s birth. Given our sampling strategy, all mothers in our sample received at most twelve years of schooling. We group them into reporting less than twelve and exactly twelve years of schooling and summarized test scores of children of the mothers in these groups accordingly. There is a significant positive correlation between mothers’ AFQT percentile scores as well as education levels and their children’s test scores. In terms of age at birth, children with older mothers tend to have lower scores. However, as it will be seen later in the table, this correlation might be explained by the fact that older mothers also tend to have more children, and this reduces average resources to be invested on each of her child. The next category is children’s characteristics, including race, gender and number of siblings. Even though all sample children grew up in disadvantaged backgrounds, Black and Hispanic children have lower test scores than their non-Black, non-Hispanic counterparts. On average, females perform better than males. Finally, we separate the number of siblings into zero, one, two, three and more than three. The sample exhibits a negative correlation between the PIAT math test score and number of siblings a child has. For example, a child who has no sibling is associated with a mean test score of 100.5, but the mean score for a child with more than three siblings is just 91.7.

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Empirical Results

Coefficient estimates for different specifications of a child’s attainment production function are listed in the upper panel of Table 4. Dependent variables in all specifications are the natural logarithm of a child’s first observed PIAT math standardized test score. The effects are hence measured in terms of the percentage change of the test score. To better illustrate the dependence between the effects of a mother’s decisions and her child’s observed innate ability (ln A0 ), the bottom panel of Table 4 vantaged families perform even lower relative to the children from average families. 15 We use the Personal Consumption Expenditure Deflator for non-durable goods (PCED Non-Durable) to convert nominal monetary terms into 2000 dollars. Other income is defined as annual family income less labor and welfare (AFDC plus food stamp) income.

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lists the estimated marginal effects of childhood welfare use at different positions of the estimated innate ability distribution, including 1% (a child who has almost the lowest level of observed innate ability), 25%, 50%, 75%, 99% (the highest observed innate ability) and mean levels. We list five different specifications in Table 4. The first specification is the estimation of equation (1) without controlling for the possible effects of unobserved characteristics. Specifications two to five employ an IV approach to address the issue of endogenous mother’s decisions. See discussions in Appendix A.1 for the construction of instruments and in Appendix A.2 for first-stage results as well as tests of the validity of the instruments. We include different explanatory variables in the specifications to investigate the effects of welfare through different channels. Based on the discussion in Section 2, the coefficient of the welfare use variable in equation (1) captures mainly the nonpecuniary benefit from means-tested transfers programs that are associated with the welfare program (upon controlling for a mother’s work experience and accumulated family income during the child’s childhood). Specification two estimates this version and is hence our baseline model. The third specification excludes the accumulated family income variable. The coefficients of the welfare use variable therefore also incorporate the effect of cash benefits on a child’s attainment from increased family income. In specification four, we exclude a mother’s work experience from the child attainment production function. As a result, the coefficient on W measures the overall effect from welfare monetary benefit and time saved from substituting welfare for work. The last specification presents an overall measure of the effect of welfare use through three channels by excluding both work and family income from the attainment production function. As discussed in Section 2, a mother may use welfare more or work less due to unobserved reasons that can impede a child’s attainment. As a result, we expect the estimates of welfare to be biased downwards in the first specification. Using a Durbin-Wu-Hausman test shown in Table A-3, we conclude that this estimation is indeed inconsistent with the IV estimation. We include it to compare the improvements from implementing an IV approach. The first column of Table 4 shows that the child’s attainment in this context is significantly associated with the background characteristics, such as log accumulated family income (measured in thousand dollars), mother’s log AFQT percentile score, gender, race and years of education a mother has, in the same directions as sample patterns shown in Table 3.

14

Also, none of the coefficients of the mother’s decisions in the first specification appear to be correlated to her child’s attainment. Note that the sample includes only children who are mostly likely to be eligible for welfare. The insignificant results are already different than the negative correlation found in studies reviewed in Haveman and Wolfe (1995) using samples that include children who were ineligible for welfare. Furthermore, the estimated marginal effect of welfare is negative, small and does not seem to vary across children with different observed initial abilities. We turn to the IV estimation results below.

5.1

Observed Innate Ability

First we discuss the observed innate ability estimates. A set of a child’s time-invariant characteristics is used to capture the observed part of the test scores that are not affected by variation in a mother’s decisions during the child’s childhood. We term it observed innate ability, which includes the mother’s log AFQT percentile score, her education level measured by number of years of schooling, whether she gave birth when she was eighteen years old or younger, gender of the child and whether the child is black or Hispanic (hence non-black, non-Hispanic children are the comparison group). Except for the log AFQT percentile score and the number of years of education, these observed innate ability measures are all dichotomous variables and capture the mean differences between various demographic groups. As a result, it can be expected that within a specific demographic group, most of the variation in the observed innate ability resulted from the mother’s log AFQT percentile score and her number of years of education. Table 4 shows that the innate ability estimates from specifications two to five are similar. According to our estimates, children who are female have higher observed initial abilities than their male counterparts. Compared to a non-black non-Hispanic child, Hispanic children are associated with higher initial abilities, but the difference between blacks and non-black, non-Hispanics is not statistically significant. Children who were born to young mothers (who were eighteen years or younger at birth) are associated with higher observed initial abilities according to our estimates. Finally, children born to mothers who have higher AFQT percentile scores and more years of education are also associated with higher initial abilities. The most important difference between specification one and models that account for endogeneity regressors is that that black and Hispanic children are no longer associated with lower performances than non-black non-Hispanic children. Moreover,

15

Hispanic children even appear to have better performances. In our specification, two coefficients are related to the effects of mothers’ decisions. For example, quarters of childhood welfare use affect a child’s log test score through the primary effect (γ1 ) and the interaction term between welfare experience and the observed innate ability (γ2 ). Specifications two to five all exhibit a statistically significant estimates of γ2 , which indicate that the effect of mothers’ quarterly welfare use decision indeed varies with children with different initial abilities. Furthermore, since γ2 is negative, the effect of welfare use exhibits diminishing marginal productivity in the observed innate ability. For example, baseline model suggests that conditional on W (E), a 1% increase in innate ability is associated with with a 4.8% (5.4%) decrease in test scores. Given that both γ1 and γ3 are positive, welfare use and employment are more beneficial to a child with lower innate ability than a child with a higher one. We will discuss this in more detail below.

5.2

Effects of Mothers’ Decisions

For the marginal effects of mothers’ welfare use decisions, we focus on the bottom panel of Table 4. Specification two in Table 4 is the baseline model, which controls three different channels of welfare effects separately with the coefficient on welfare capturing non-pecuniary benefits from inkind transfer programs. The estimates show that the marginal effect of welfare use is higher at the mean level of the innate ability than it is at the median. Given the negative correlation between the effect and innate ability, this fact implies that the distribution of innate ability is left-skewed. However, both welfare effects at mean or median levels are close to zero. As a result, services provided by in-kind transfers programs for children with observed initial abilities in the middle of the distribution are not expected to have a significant effect on their test scores. Since γ2 is negative, an additional quarter of welfare use is beneficial to the test scores of children with lower than median initial abilities. As most of the variation in the observed initial abilities come from those in mothers’ log AFQT scores and education levels, we can expect that within each specific demographic group, children who were born to mothers with lower (than median level of) AFQT scores and fewer numbers of years of education benefit more than those with higher ones. On the other hand, specification two shows that for children with higher than median initial abilities, an additional quarter on welfare may be detrimental to their test scores. The fact that even after controlling for the unobserved factors using an IV approach, welfare use is still negatively 16

associated with the outcomes of some of the participating children seems disconcerting and requires us to provide a plausible explanation. Recall that welfare use in specification two accounts mainly for the effect from nonpecuniary means-tested transfers programs, in particular, health insurance for poor families (Medicaid) or Head Start.16 One thing that we do not control in the estimation is the quality of services provided by these programs. It has been noted in the literature, for example, that the quality of child care has non-homogeneous effects on attainments of children with different initial abilities (Bernal, 2008). Our finding seems to further suggest that effect of these programs on children’s attainments also depends on program qualities. However, we do recognize that without a further investigation, we cannot conclude a causal relationship. Specifications three to five in Table 4 indicate that the marginal effect of welfare use is larger when we combine different channels into welfare coefficients. Specification three excludes accumulated family income in the attainment production function. As a result, its effect is going to be absorbed by variables that are correlated with it. For example, the coefficients of welfare use now include the benefit from an increase in cash benefit through participating in the welfare program. Also, the coefficients of work variable will incorporate the effect from an increase in labor income through employment. In specification three, the marginal effect of welfare use becomes the combination of that derived from specification two and the effect through an increase in financial resources due to welfare participation. As we can see from column three in Table 4, although an increase in family income does significantly attribute to a child’s test score (as γ5 in specification two is significantly positive), marginal effects of welfare use in specification three do not significantly alter when we include the effect from welfare cash benefit. The effect of welfare use for a child at the median innate ability level changes from slightly negative to exactly zero. The same effect at the mean level also increases slightly. Since cash benefit is not sizable,17 this result is not too surprising. Similarly, when work is excluded in the attainment production function (but family financial resources are controlled), the marginal effect of welfare use incorporates both the effect of nonpecuniary means-tested transfers programs and that of the time saved from substituting work for 16 Children

living under the federal poverty line or in a family that receives AFDC (after 1996, TANF) are eligible for Head Start. Unlike AFDC, Head Start is not an entitlement due to its limited budget. In 1994-1995, only 38% of all eligible children between 3 to 5 years old were served. Hofferth (1994) indicates that among eligible ones, children in two-parent families are more likely to participate in the program. Also, the mother’s work status does not appear to be correlated with Head Start enrollment. 17 Average annual cash benefit across US states from 1970-1996 is only $5,768. See Table 5.13 of ”Aid to Families with Dependent Children: The Baseline” by the Office of the Assistant Secretary for Planning and Evaluation and Office of Human Services Policy

17

welfare. Specification four indicates that welfare provides even stronger benefits. Combining these two effects, both the marginal effects at the mean or median levels of initial abilities are about a one percentage point increase in the test score. Our estimates suggest that allowing mothers to have more time taking care of their children through substituting work for welfare is one of the important source of the benefits of the welfare program. Finally, specification five combines the effects of all three channels of welfare use into the coefficients of welfare experience variable. The last column of Table 4 shows that only the marginal effects of welfare for those children who have initial abilities at the top quartile remain negative. The mean welfare effect estimated in specification five is 1.4 percentage points. It implies that, after combining all channels of welfare effects, welfare improves most of the participating children’s attainments. Figure 1 lists the total effects of welfare and work on a child’s test score based on the estimates of the baseline model. Total effects depend on how many quarters of welfare use or work a child experiences. In Figure 1(a), we calculate the total effects according to the median quarters of welfare use (fourteen quarters) and work (nine quarters) exhibited by the sample children. The dashed lines represent the 99% confidence intervals. As we can see, total effects for most participating children are between two log points to negative one point. Furthermore, the effect of work also exhibits a similar pattern of decreasing marginal productivity with the initial abilities. Table 1(a) shows that for children with higher initial abilities, mothers’ work during their childhoods are detrimental.

6

Conclusion

This research investigates the relationship between a single mother’s welfare use decision on her child’s short-run test scores at age six. After controlling for the effects of welfare cash benefits and substituting work for welfare by including accumulated family income and the mother’s work experience since her child’s birth, respectively, our welfare use variable captures mainly the benefits from nonpecuniary means-tested transfers programs that are linked with the welfare program, such as the health insurance program for poor families, Medicaid. We further control for the possible endogeneity of the mother’s welfare use and work decisions by an instrumental variables approach. The effect of welfare use is identified not only by a comparison between children with and without childhood welfare experiences, but also by comparing children who have different exposure to the 18

welfare program during the first twenty quarters since their birth. Also, by including the parameters of the AFDC benefit determination rule for each U.S. state in which sample parents reside, we include variation in mothers’ economic incentives that arise from the U.S. state benefit structures in constructing our instrumental variables. This variation further enables us to disentangle the effects of a mother’s decisions on her child’s attainment. We use the first observed Peabody Individual Achievement Test standardized math scores from Children of the NLSY 1979 as a measure of attainment. The IV estimates imply that the marginal effect of childhood quarterly welfare use exhibits a diminishing marginal productivity in the observed innate ability of the child. As a result, the lower the innate ability of a child, the more the welfare is beneficial to his test score. We find that on the mean level, welfare use does not appear to affect a child’s test score. However, it has a significantly positive effect on children who have lower than median innate ability level.

19

7

Tables and Graphs Table 1: Sample Descriptives - Means and Standard Deviations Mother’s Decisions Welfare participation Quarterly Work Participation Part-Time (125-375 hours) Full-Time (>= 375 hours) Hours of Work† Children’s Characteristics Female Male Black Other Race Birth Weight PIAT Standardized Math Score Age Taking Test (Months) Children-Quarters Children Mothers

0.42 (0.49)

Mother’s Characteristics Age at Birth Years of Education

0.42 (0.49) 0.31 (0.46) 425 (196)

0.50 0.50 0.31 0.69 114 (22) 97.4 (13.3) 76.6 (14.9)

Number of children Annual Labor Income∗∗ † Annual Other Income∗∗ AFQT

23.4 (3.5) 10.9 (1.4) 1.9 (1.1) 9,917 (9,052) 16,374 (51,321) 25.7 (20.2)

36,660 1,833 1,183

*

Population weighted to reflect 1979 national population of low-skilled, single mothers ** In 2000 dollars deflated by PCED nondurables † Conditional on work

20

Table 2: Mother’s Welfare Use and Employment by Child’s Age Child’s Age -2 -1 1 2 3 4 5 †

Welfare Use

Part-Time (125-375 Hours)

Full-Time (>= 375 Hours)

Hours of Work†

0.25 (.43) 0.31 (.46) 0.41 (.49) 0.42 (.49) 0.43 (.50) 0.43 (.49) 0.42 (.49)

0.50 (.50) 0.40 (.49) 0.32 (.47) 0.40 (.49) 0.43 (.50) 0.45 (.50) 0.48 (.50)

0.37 (.48) 0.28 (.45) 0.22 (.42) 0.29 (.45) 0.32 (.47) 0.35 (.48) 0.37 (.48)

393 (194) 385 (194) 390 (197) 411 (188) 426 (193) 439 (200) 448 (194)

Conditional on work Table 3: Detailed Descriptive Statistics

Quartile

1st

Mother’s Quarterly Decisions Welfare Use 0 Mean Standard Scores 100.0 (Standard Deviation) (13.5) Work 0.24 94.0 (13.4) PIAT Math Test Score 80.2 (6.4) Age Taking Test 63.2 (months) 95.6 (15.4) Mother Characteristics Real Hourly Wages† 0.8 97.1 (13.4) Average Labor Income† 413 95.3 (12.9) Average Other Income 3934 96.5 (13.4) AFQT Score 4.8 92.3 (12.5) Eduction < 12 0.47 95.3 (13.2) Age at Birth 21.5 98.0 Continue to next page 21

2nd

3rd

4th

3.4 99.1 (12.5) 4.3 97.1 (13.3) 94.2 (2.9) 71.0 97.5 (13.0)

12.7 96.2 (13.2) 11.4 99.0 (13.1) 102.8 (2.2) 78.4 98.1 (11.8)

19.5 93.6 (13.0) 18.4 99.7 (12.7) 114.3 (6.8) 97.5 98.6 (12.4)

2.6 97.3 (12.7) 2,495 98.6 (13.4) 8,710 95.6 (13.5) 15.1 96.6 (13.3) = 12 0.53 99.1 (13.2) 24.5 97.5

4.9 100.4 (13.2) 6,676 99.3 (12.4) 14,777 98.4 (12.5) 29.2 99.1 (13.6)

10.8 99.8 (12.7) 17,190 100.1 (12.8) 38,465 99.0 (13.6) 55.4 101.9 (11.9)

26.9 97.0

30.9 96.9

Continue from last page Quartile

1st

(12.8) Children Characteristics Race Black 0.31 93.4 (13.3) Gender Male .50 96.7 (13.6) Number of Siblings 1 0 100.5 (13.1) †

2nd

3rd

4th

(12.9)

(13.2)

(14.4)

Hispanic 0.09 94.3 (12.5) Female .50 98.1 (13.1) 2 1 101.7 (12.5)

Other 0.59 100.0 (12.9)

Conditional on work.

22

3 2 97.6 (13.4)

4 3 95.1 (12.9)

>3 91.7 (12.6)

Table 4: Results for NLSY Test Scores Specification

1 OLS Model Observed Innate Ability Gender 0.013 (γ7 ) (0.008) Black -0.044*** (γ8 ) (0.016) Hispanics -0.035** (γ9 ) (0.014) Age 18D 0.014 (γ10 ) (0.018) ln AFQT 0.020*** (γ11 ) (0.007) Education 0.008** (γ12 ) (0.004) Mother’s Decision W 0.000 (γ1 ) (0.002) ln A0 × W -0.009 (γ2 ) (0.013) E 0.001 (γ3 ) (0.003) ln A0 × E 0.000 (γ4 ) (0.018) ln Income† 0.003*** (γ5 ) (0.001) Age Taking Test 0.001*** (γ6 ) (0.000)

2 Baseline Model

3 No Income

4 No Work

5 No Work, Income

0.431*** (0.057) 0.123 (0.097) 0.368** (0.156) 0.596*** (0.101) 0.083** (0.041) 0.290*** (0.024)

0.443*** (0.058) 0.102 (0.098) 0.357** (0.158) 0.605*** (0.100) 0.089** (0.042) 0.292*** (0.025)

0.289*** (0.030) -0.003 (0.046) 0.210*** (0.063) 0.609*** (0.073) 0.097*** (0.025) 0.278*** (0.014)

0.294*** (0.030) -0.004 (0.046) 0.214*** (0.064) 0.616*** (0.073) 0.104*** (0.025) 0.280*** (0.014)

0.199*** (0.006) -0.048*** (0.001) 0.225*** (0.011) -0.054*** (0.002) 0.010*** (0.003) 0.005*** (0.001)

0.202*** (0.005) -0.048*** (0.001) 0.224*** (0.011) -0.053*** (0.002)

0.213*** (0.006) -0.054*** (0.001)

0.215*** (0.006) -0.054*** (0.001)

0.004*** (0.001)

0.010*** (0.003) 0.008*** (0.001)

0.008*** (0.001)

-0.039 -0.015 0.000 0.021 0.078 0.005

-0.028 -0.006 0.009 0.031 0.092 0.014

-0.028 -0.006 0.009 0.031 0.093 0.014

1,833

1,833

Marginal Effects of Welfare = γ1 + γ2 ln A0 99% -0.0017 -0.039 75% -0.0013 -0.015 50% -0.0010 -0.001 25% -0.0008 0.021 1% -0.0001 0.077 Mean -0.0010 0.004 Marginal Effects of Employment = γ3 + γ4 ln A0 99% -0.0027 -0.041 75% -0.0019 -0.015 50% -0.0013 0.002 25% -0.0008 0.026 1% 0.0004 0.087 Mean -0.0013 0.007 Sample Size

2,243

1,833

-0.040 -0.014 0.003 0.026 0.088 0.008 1,833

·

Specifications 2 to 5 also include state fixed-effects. Measured in thousand real dollars (in year 2000 price). *** : significant at 1% significance level. ∗∗ : significant at 5% significance level. ∗ : significant at 10% significance level. †

23

Figure 1: Total Effects of Median Welfare Use and Work on Children’s Test Scores

—– : Predicted Effects - - - : 99% confidence interval ln(Test Score) 3 2.5 2 1.5 1 0.5 Initial Ability 0 0.7

1.2

1.7

2.2

2.7

3.2

3.7

4.2

4.7

5.2

-0.5 -1 -1.5 (a) Total Effects of Median Welfare Use (14 quarters)

ln(Test Scores) 2.5

2

1.5

1

0.5

Initial Abilities 0

0.7

1.7

2.7

3.7

-0.5

-1 (b) Total Effects of Median Work (9 quarters)

24

4.7

8

References

Baum, C., M. Schaffer and S. Stillman “Enhanced Routines for Instrumental Variables/GMM Estimation and Testing.” Stata Journal, 7(4) (2007), pp. 465–506. Ben-Porath, Y. “The Production of Human Capital and the Life-Cycle of Earnings.” Journal of Political Economy, 75(4), (August 1967), pp. 252-265. Bernal, R., 2008. ”The Effect Of Maternal Employment And Child Care On Children’S Cognitive Development,” International Economic Review, vol. 49(4), pages 1173-1209, November. Bernal, R. and M. Keane, 2007, ”Child Care Choices and Children’s Cognitive Achievement: The Case of Single Mothers,” manuscript, Universidad de los Andes, UTS and Arizona State University. Chyi, H. “The 1993 EITC Expansion and Low-Skilled Single Mothers Welfare Use Decision,” manuscript, 2008. Citro, C. and R. Michael, Measuring Poverty: A New Approach, Washington DC: National Academy Press, 1995. Currie, J. Welfare and the Well-Being of Children: Fundamentals of Pure and Applied Economics 59. Switzerland: Hardwood Academic Publishers, 1995. — “The Effect of Welfare on Child Outcomes.” Welfare, the Family, and Reproductive Behavior. Washington, DC: National Academy Press, 1998. Currie, J. and D. Thomas “Does Head Start Make a Difference?” American Economic Review 85(3), (June 1995) pp. 341–64. — “Early Test Scores, Socioeconomic Status and Future Outcomes.” Working Paper 6943, National Bureau of Economic Research, Cambridge, MA, 1999. Dahl, G, and Lochner, L. “The Impact of Family Income on Child Achievement.” Working Paper 11270, National Bureau of Economic Research, Cambridge, MA, February 2005. Duncan G., and Brooks-Gunn J. “Consequences of Growing Up Poor.” Russell Sage Foundation, New York. 1997. Duncan G., Magnuson K., and Ludwig, J. “The Endogeneity Problem in Developmental Studies.” Research in Human Development I (1&2), (2004), pp. 59-80. Garces E., Duncan, T., and Currie, J. “Longer Run Effects of Head Start.” American Economic Review 92(4), (September 2002), pp. 999-1012. Haveman, R. and Wolfe, B. “The Determinants of Children’s Attainments.” Journal of Economic Literature, 33 (December 1995), pp. 1829–78. Hill, M., and O’Neill, J., “Family Endowments and the Achievement of Young Children with Special Reference to the Underclass” Journal of Human Resources 29(4), 1994, pp. 1064–1100. Keane, M. and Moffitt, R. “A Structural Model of Multiple Welfare Program Participation and Labor Supply.” International Economic Review 39(3) (August 1998), pp. 553–89. Keane, M. and Wolpin, K. “Estimating Welfare Effects Consistent With Forward-Looking Behavior: Part I: Lessons From A Simulation Exercise.” Journal of Human Resources 37(3) (2002), pp. 570–99. — “Estimating Welfare Effects Consistent With Forward-Looking Behavior: Part II: Empirical Results.” Journal of Human Resources 37(3), (2002), pp. 600–22.

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Moffitt, R.“The Temporary Assistance for Needy Families Program” Means-Tested Transfers in the U.S., 2002, http://www.nber.org/books/means-tested/. Office of the Assistant Secretary for Planning and Evaluation and Office of Human Services Policy ”Aid to Families with Dependent Children: The Baseline”, June 1998, A technical report Staiger D. and James H. Stock, 1997. “Instrumental Variables Regression with Weak Instruments,” Econometrica, Econometric Society, vol. 65(3), pages 557-586, May. Todd, P. and Wolpin, K. (2000), “On the Specification and Estimation of the Production Function for Cognitive Achievement,” The Economic Journal 113, (February 2003), pp. F3-F33. Wooldridge, J. “Econometric Analysis of Cross Section and Panel Data”, 2001, Cambridge, MA: MIT Press. Ziliak, James P. 2007. ”Making Work Pay: Changes in Effective Tax Rates and Guarantees in U.S. Transfer Programs, 1983-2002,” Journal of Human Resources, 42(3): 619-642.

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Appendices

A.1

Mothers’ Working and Welfare Participation Decisions

As described in Section 3, our IV approach falls into the category of generated instruments described in Chapter six of Wooldridge (2001). Our proposed instruments are predicted quarters of a mother’s welfare use and work during the first twenty quarters since her child’s birth. We assume in each quarter a mother can choose between whether to use welfare and to work described by equation (4). This quarterly decision model used to construct the instruments is estimated jointly using a multinomial probit model. The result is shown in Table A-1. Section A.2 discusses first stage results and the validity of instruments using various econometric tests.

A.2

First-Stage Results and Validity of Instruments

Table A-2 lists the first-stage estimation results of the baseline model (Specification two in Table 4). The first-stage estimation of an IV approach is a linear projection of both W and E onto the included exogenous variables in main equation (Equation 1) as well as the instrumental variables. They do not necessarily have behavioral implications. Note that an over-identification test requires us to have more IVs than endogenous explanatory variables. As a result, rather than using marginal probabilities of welfare use and work (which implies an exact identification), we use joint probabilities of two decisions as instruments which have four alternatives for a mother to choose. To avoid a perfect multicollinearity between the constant term and predicted four alternatives (which sums up to twenty) in the first stage estimation, we include only the sum of twenty quarters of three alternatives. Table A-2 shows that all of our proposed IVs are strongly correlated with the mother’s decisions. Table A-3 lists the results of the validity of IVs. Baum, Shaffer and Stillman (2007) discuss that under heteroscedasticity of error and weak identification (to be discussed below), a continuously updated estimator is more stable than a standard two-stage estimator. As a result, we report test statistics under both estimation methods. There are two requirements for the validity of an IV approach. First, the instrumental variables (including both included regressors and the excluded regressors) have to be uncorrelated with the main equation error term (ui ), and second, they should be correlated with endogenous regressors, in our case, a mother’s quarters of welfare use and work during her child’s childhood. There are several existing tests for both requirements in the econometric literature which are incorporated by the -ivreg2- package in Stata.

27

The first test in Table A-3 tests if an IV approach is indeed necessary. That is, if a a mother’s decisions during her child’s childhood are indeed correlated with the unobserved determinants of the child’s attainment. If the instruments are indeed uncorrelated (or weakly correlated) with the endogenous regressors, it can indeed increase the bias (Baum, Shaffer and Stillman (2007)). It essentially compares the OLS and IV estimation to see if they are different by a Durbin-Wu-Hausman test. As the results indicate, an IV approach is indeed necessary. Next, we provide an overidentification test to test if instruments are indeed uncorrelated with the unobserved determinants (ui ) in Equation 1. We report here a version of Sagan-Hansen test. Given that we allow for the error term ui to be heteroscedastic and correlated within a family, the test statistic is Hansen J, which is distributed as χ2 under the null hypothesis that the instruments are indeed orthogonal to the errors (see Baum, Shaffer and Stillman (2007) for a detailed discussion). The failure to reject the null hypothesis of our IVs indicates that our instruments satisfy the first requirement of an IV approach. The second requirement of IVs, that they have to be correlated with the mother’s decisions, come in two varieties. First, we need to see if the rank condition is satisfied. The result of the underidentification test indicates a strong rejection of the hypothesis that our model is unidentified. Second, even if the rank condition is satisfied, if the correlations between the excluded regressors (instruments) and the mothers’ decisions are weak, the result may perform poorly (see the same reference above). To this end, we use a weak identification test that employs the Kleibergen-Paap Wald F statistic, which is valid when we allow ui to be correlated within each family. An exact rejection rule for weak identification is not yet established, but according to Staiger and Stock (1997), a test statistic of over fifteen is considered as relatively immune to the weak identification problem. Based on the above discussion, we conclude that current tests available in the econometric literatures do not suggest that our proposed IVs violate the requirements of a valid IV approach.

28

Table A-1: Marginal Effects of Mother’s Decisions - Multinomial Probability Model Welfare = Work =

No No

No Yes

Yes No

Yes Yes

Mother’s Age Age Squared Other Income Black

-0.01 (0.01) 0.0002 (0.0002) 0.0001 (0.0001) -0.08*** (0.01) -0.03** (0.02) -0.02*** (0.004) -0.001***

0.001 (0.01) 0.0001 (0.0002) 0.0001 (0.0001) -0.01 (0.02) 0.04* (0.02) 0.03*** (0.01) 0.003*** (0.0004) -0.04*** (0.01) -0.33*** (0.01) 0.27*** (0.01)

0.02* (0.01) -0.001*** (0.0003) -0.0002 (0.0002) 0.07*** (0.02) 0.02 (0.02) -0.02*** (0.01) -0.003*** (0.001) 0.04*** (0.01) 0.62*** (0.01) -0.19*** (0.01)

-0.02** (0.01) 0.0003** (0.0001) 0.000002 (0.00003) 0.02 (0.01) -0.02** (0.01) 0.005 (0.003) 0.001** (0.0003) 0.003 (0.003) 0.14*** (0.01) 0.08*** (0.01)

-0.002** (0.001) 0.001** (0.0004)

0.001 (0.0004) 0.00002 (0.0002)

-0.00004 (0.0007) 0.0006 (0.001) -0.0001 (0.001)

0.0003 (0.0004) -0.0009 (0.001) 0.0006 (0.000)

Hispanic Mother’s Education AFQT

Number of -0.009*** Kids (0.01) Lagged -0.43*** Welfare (0.01) Lagged -0.17*** Work (0.01) AFDC Effective Taxes on Labor 0.001* 0.0001 Income (0.001) (0.001) Other -0.001* -0.0003 Income (0.0003) (0.0003) Guarantee Level Two -0.001 0.0003 Kids (0.0004) (0.0005) Three 0.0002 0.0001 Kids (0.001) (0.001) Four and 0.0001 -0.0006 More (0.001) (0.001) ·

Marginal effects of explanatory variables are evaluated at the mean level *** : significant at 1% significance level. ∗∗ : significant at 5% significance level. ∗ : significant at 10% significance level.

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Table A-2: First Stage Results for NLSY Test Scores AFQT Gender Black Hispanics Age 18D Family Income Education Age Taking Test Instruments P20 c t=1 Pr(ht = 0, ωt = 0) P20 c t=1 Pr(ht = 1, ωt = 0) P20 c t=1 Pr(ht = 0, ωt = 1) Constant

W -0.704*** (0.195) -0.196 (0.249) 1.156*** (0.403) 0.275 (0.455) -1.563** (0.630) 0.103** (0.047) -0.416*** (0.115) -0.025** (0.011)

E 0.369** (0.153) 0.057 (0.217) 0.939*** (0.321) 0.065 (0.368) -0.633 (0.483) 0.006 (0.038) 0.399*** (0.086) -0.010 (0.007)

-0.698*** (0.036) 0.517*** (0.038) 2.024*** (0.328) 17.069*** (1.411)

0.829*** (0.030) -0.527*** (0.034) 1.548*** (0.311) 0.994 (1.135)

: significant at 1% significance level. ∗∗ : significant at 5% significance level. ∗ : significant at 10% significance level.

***

Table A-3: Tests for Correlation Between Mothers’ Decisions and Instruments GMM2S

CUE

86.953 .0000

86.953 .0000

4.166 .1245

3.569 .1679

104.374 .0000

104.374 .0000

32.048

32.048

Endogeneity Test H0 : OLS estimator is consistent with IV estimator p-value

Overidentification test H0 : Instruments are orthogonal to errors p-value

Underidentification Test H0 : Model is unidentified

p-value

Weak Identification test H0 : Instruments are weak

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