WELFARE REFORM AND CHILDREN'S EARLY COGNITIVE DEVELOPMENT

WELFARE REFORM AND CHILDREN’S EARLYCOGNITIVE DEVELOPMENT

HAU CHYI, ORGUL DEMET OZTURK and WEILONG ZHANG∗

In this paper, we use a dynamic structural model to measure the effects of (1) singlemothers’ work and welfare use decisions and (2) welfare reform initiatives on the earlycognitive development of the children of the NLSY79 mothers. We use PIAT-Math scoresas a measure of attainment and show that both the mothers’ work and welfare usebenefit children on average. Our simulation of a policy that combines a time limit withwork requirement reduces the use of welfare and increases employment significantly.These changes in turn significantly increase children’s cognitive attainment. Thisimplies that the welfare reform was not only successful in achieving its stated goals, butwas also beneficial to welfare children’s outcomes. In another policy simulation, weshow that increasing work incentives for welfare population by exempting labor incomefrom welfare tax can be a very successful policy with some additional benefits forchildren’s outcomes. Finally, a counterfactual with an extended maternal leave policysignificantly reduces employment and has negative, though economically insignificant,impact on cognitive outcomes. (JEL I38, J22, J18)

I. INTRODUCTION

In 1996, the Personal Responsibility andWork Opportunity Reconciliation Act(PRWORA) ended Aid for Families with Depen-dent Children (AFDC), replacing it with thenew Temporary Assistance for Needy Families(TANF) program. TANF differs from AFDC byending the “entitlement” period of welfare viaintroduction of a time limit on welfare bene-fits and work requirement for participants. In

∗The authors would like to thank all participants atthe European Society for Population Economics 2007 andSouthern Economic Association 2007 conferences and sem-inars at University of Kentucky; Academia Sinica, Taiwan;CCER, Peiking University, China; University of South Car-olina; Tsinghua University; and WISE, Xiamen University,China. We would like to give special thanks to Jay Zagorsky,who generously provided us the child custom weight pro-gram for children of the NLSY79 mothers.Chyi: Research Scientist, University of Chicago, National

Opinion Research Center and Harris School of PublicPolicy Studies, Chicago, IL 60637. Phone 773-256-6357,Fax 773-276-3795, E-mail [email protected]

Ozturk: University of South Carolina, Economics Depart-ment, Moore School of Business, Columbia, SC 29208.Phone 803-777-4904, Fax 803-777-6876, E-mail [email protected]

Zhang: Ph.D. Candidate, University of Pennsylvania, Depart-ment of Economics, Philadelphia, PA 19104. Phone 215-317-8684, Fax 215-573-2057, E-mail [email protected]

this paper, we analyze the impact of this wel-fare reform on the early cognitive develop-ment of welfare program participants’ childrenusing a multiperiod structural model. We firstestimate the effects of mothers’ work and wel-fare use on children’s ability formation usinga sample of single mothers and their childrenfrom the National Longitudinal Survey of Youth1979 (NLSY79) Cohort. We then simulate dif-ferent policy initiatives of the welfare reformto evaluate how each particular change impactswork and welfare participation behaviors of themothers, and as a result, children’s cognitivedevelopment.

ABBREVIATIONS

AFDC: Aid for Families with Dependent ChildrenAFQT: Armed Forces Qualification TestBW: Birth WeightCRRA: Constant Relative Risk AversionNLSY79: National Longitudinal Survey of Youth 1979

CohortPCED: Personal Consumption Expenditure DeflatorPRWORA: Personal Responsibility and Work Oppor-

tunity Reconciliation ActPSID: Panel Study of Income DynamicsTANF: Temporary Assistance for Needy Families

729Contemporary Economic Policy (ISSN 1465-7287)Vol. 32, No. 4, October 2014, 729–751Online Early publication 11 March 2014

doi:10.1111/coep.12042© 2014 Western Economic Association International

730 CONTEMPORARY ECONOMIC POLICY

Early cognitive development has been foundto be a strong predictor of long-term achieve-ment and other outcomes such as educationalattainment, crime involvement, salaries, and out-of-wedlock pregnancy (see reviews by Currieand Thomas 1995; Duncan and Brooks-Gunn1997; Haveman and Wolfe 1995). Thus, it iscrucial to understand whether, and by how muchwelfare program participation affects children’scognitive outcomes. Moreover, any public pol-icy initiative, such as PRWORA, that affectsparents’ incentives to work or participate inthe welfare program by altering the opportu-nity costs of parental time and financial inputsshould be carefully evaluated. There is an abun-dance of studies on the effects of welfare reformon mothers’ behaviors. However, implicationsof welfare reform on children’s outcomes havenot been studied by many. To our knowledge,other than this paper, there is only one otherstudy, Miller and Zhang (2009), that analyzesthe indirect effects of welfare reform on chil-dren’s cognitive outcomes.

Earlier studies generally find significantlynegative relationships between welfare receiptand various types of child attainment measures.However, these negative relationships may notbe causal due to improper comparison groupsor the unobserved heterogeneity issue that isnot addressed (Currie 1998; Dahl and Lochner2012; Duncan, Magnuson, and Ludwig 2004).Chyi and Ozturk (2013) show that welfare pro-gram participation is not detrimental to earlydevelopment of the children when the analysis isconstrained to families who are most disadvan-taged (and thus likely to be eligible for welfarebenefits) and when unobserved heterogeneity isproperly controlled for. We follow their lead andfocus only on the attainment of children bornto single mothers with 12 or fewer years ofschooling. We model unobserved heterogeneityand use exogenous variations in welfare benefitsacross states and local labor market conditions toalleviate concerns of endogeneity. Moreover, weincorporate the dynamic nature of welfare pro-gram participation and employment decisionsinto our econometric setup. We estimate struc-tural parameters of our model which enable us torun policy simulations with counterfactuals thatimitate the changes brought upon by PRWORA.Thus, we not only provide insight on how wel-fare and employment affect the children’s cogni-tive development, but also document behavioralresponses to the welfare reform and resultingimpact on children’s outcomes.

Our estimates show that on average mother’swork and welfare use both are beneficial forchildren’s cognitive development. In our model,their effects are allowed to vary by chil-dren’s ability endowment and they do; we findthat benefits are highest for children with lowendowment. Moreover, we allow the effectsto vary by mother’s attitudes toward welfarereceipt and work and by her ability to uti-lize resources in child-rearing. We model unob-served heterogeneity in these dimensions andidentify two types of mothers: mothers who arenot likely to use welfare but are very efficient atusing welfare resources if they do (Type I) andmothers who are very likely to use welfare butare not efficient at utilizing welfare resources(Type II). Both an additional year of employ-ment and an additional year of welfare use eachincrease the test scores by about 1% if the childhas median level of ability endowment withoutcontrolling for mother’s type. For children withType I mothers, the welfare participation benefitis higher (1.61% per year for the median ability)and positive regardless of their cognitive abilityendowment. For the ones with Type II mothers,on the other hand, effect of welfare participationis not only lower but it becomes negative if theyhave higher than median cognitive endowment.Effect of mother’s employment is positive forall children even though it becomes economi-cally insignificant as the ability endowment getshigher.

In our simulations, we find that policychanges that reduce welfare use and/or increaseemployment are generally beneficial to earlycognitive development. Specifically, a policythat combines a work requirement and a 2-year welfare time limit significantly increasesthe test score of a child with median abilityendowment by 3.55%. Miller and Zhang (2009)also find positive welfare reform effects forchildren’s cognitive outcomes. They show thatwelfare reform narrows the gap in the mathtest scores of high- and low-income childrenamong 4th to 8th graders. Our findings of pos-itive association between welfare reform andchildren’s early cognitive outcomes complementMiller and Zhang’s by providing estimates of theeffects at an earlier age, prior to schooling.

Following an initiative that is adopted bymany state waiver programs, we also simulate apolicy that exempts labor income from “welfaretax.” Employment increases sharply in this sim-ulation without much change in welfare partic-ipation. Consequently, the simulated test score

CHYI, OZTURK & ZHANG: WELFARE REFORM AND CHILDREN’S OUTCOMES 731

for a median child increases by 0.46%. We alsoanalyze a counterfactual of an extended mater-nity leave policy that has not been implementedbut may be of interest to policy makers. Simu-lation suggests that this policy reduces employ-ment by about 10 percentage points but doesnot change welfare use significantly. This policyeventually decreases log test scores by 0.31% onaverage.

Overall, we see that the most successfulpolicies are the ones that encourage more workthrough tax incentives and time limits. Welfarereform resulted in big reductions in welfare rollswhich potentially increased resources for otheruses such as child care subsidies and afterschoolprograms. Our results indicate that access tothese resources boosts cognitive outcomes.

The structure of the paper is as follows.In the next section we construct our economicmodel and discuss how it works in capturing thepatterns in the data. We give an overview of ourdata in Section III. In Section IV we not onlyreport the parameter estimates, but also analyzeour policy simulations in a subsection, SectionIV.B. Section V will conclude our paper with adiscussion of our results.

II. MODEL

Our dynamic structural model is motivatedby Bernal (2008). We assume that a child’searly attainment is determined by the cumulativewelfare use and employment of the motherduring the first 5 years after child-birth. Amother cares about how much leisure and thecomposite consumption good she has, and theability of her child. In this dynamic setup, everyperiod she chooses how much to work andwhether to use welfare to maximize her expectedutility. Below we discuss the economic rationaleof our model. The solution and the estimationof the model is discussed in detail in AppendixSection A.

A. Child’s Cognitive Attainment

We assume each child is born with a fixedlevel of cognitive ability endowment (A0). Amother is assumed to know this but we, aseconometricians, do not. We approximate thisendowment using time-invariant characteristicssuch as birth weight (BW), race (Black = 1),and gender (girl = 1) of the child, as well asArmed Forces Qualification Test (AFQT) per-centile score and years of education (edu) of

the mother.1 We also consider two age-relateddummy variables: one if the mother is youngerthan 18 (ageless18) and another if she is olderthan 33 (agemore33). These dummy variablescapture the increased possibility of health prob-lems for children born to young mothers andpossible complications of geriatric pregnancythat may lead to lower cognitive ability.2 Cor-relations between these variables and cognitiveability endowment are modeled linearly as fol-lows:

ln A0 = γ6BW + γ7gender + γ8race(1)

+γ9ageless18 + γ10agemore33

+γ11edu + γ12AFQT.

A mother “produces” her child’s currentcognitive achievement (At ) by using monetaryand nonmonetary resources. Even though we donot observe the amount directly spent on thechild, we have the amount of labor income,welfare income, and other income received bythe household in our data. Moreover, we donot observe measures of nonmonetary inputs,including time spent with the child or noncashwelfare benefits such as housing and healthcare. We use work and welfare use decisions asproxy variables to capture the availability andthe amount of these monetary and nonmonetaryinputs. A child’s cognitive ability is correlatedwith these factors and the cognitive abilityendowment as follows:

ln At = ln A0 + γ1 lnYt

Nt

(2)

+γ2Et + γ3Wt + γ4 ln A0Wt

+γ5 ln A0Et .

In this expression, Yt is the income accumulatedsince child-birth and Nt is the number of chil-dren in the household.3 Cumulative work experi-ence is defined as Et = ∑t

k=1 hk where hk = 0,1, or 2 if the mother is not employed, employedpart-time or full-time in year k, respectively.Similarly, cumulative welfare experience is

1. This setup is also used by Bernal (2008), Bernal andKeane (2010, 2011) and Chyi and Ozturk (2013).

2. When mother’s age is included directly, its effect isnot significant. We suspect that the effect may have beenabsorbed by other maternal characteristics such as years ofeducation or pre-birth work experience and welfare use.

3. Yt is the sum of labor earnings, wel-fare benefits (B), and other income (M), that isYt = ∑t

s=1 (hsws + ωsBs + Ms) . We approximate the


Wt = ∑tk=1 ωk , where ωk = 0 if the mother

is not on welfare at year k, 1 otherwise.4 Byadding interactions between the mothers’ deci-sions and the observed cognitive ability endow-ment, we allow for possible differential effectsof the mothers’ decisions. In other words, achild’s cognitive ability endowment can affectthe returns to inputs in the production of currentcognitive ability.

All children in the NLSY79 have takenseveral cognitive achievement tests biannuallyonce they turn six. We use the child’s first PIAT-Math test score (Ot ) as a proxy for the abilityas follows:5

ln Ot = ln At + γ13testage + μ0 + νt(3)

where testage is the child’s age in months, μ0is the mean test score, and νt is the randomdisturbance drawn from a normal distributionwith mean of zero, and a variance of σ2

ν.6

In our model, welfare use can affect the cog-nitive development of a child in three ways.First, welfare program provides income, effectof which is captured by the coefficient of Yt

Nt

in Equation (2). Second, a mother may chooseto substitute welfare for work so that she canspend more time with her child. This effect willbe captured by a decrease in maternal employ-ment, Et . Finally, many means-tested transfer

average income spent on each child by dividing Yt bythe number of children in the household (N ) at year t .We treat children born to the same mother as independentobservations. Bernal (2008) and Bernal and Keane (2010,2011) use a similar treatment. Initially, we allowed incometo interact with ln A0 to capture the potential differentialeffects of income by cognitive ability endowment. Thecoefficient for this interaction was insignificant, thus wedropped it for simplicity.

4. We assume that only the cumulative inputs matter.Bernal (2008) and Bernal and Keane (2010, 2011) have asimilar setup. A different modeling strategy is based on thetiming of investment (Brooks-Gunn, Han, and Waldfogel2002; Todd and Wolpin 2003). In such a model, inputs madeby the mother at each age may have differential effects onthe child’s potential achievement. The empirical results ofsuch a model estimated with our sample (not presented butavailable upon request) indicate that we cannot reject thatall of the age-specific coefficients are the same. We believe,instead of proving that the effects are not sensitive to timing,this just reflects the lack of variation in the data that isneeded to identify such age-specific effects.

5. We choose mathematical attainment because it hasshown to be mostly closely related to a child’s later cognitiveachievement (Claessens, Duncan, and Engel 2009).

6. Although the PIAT-Math tests are given to each childbiannually from age five onwards, some of the first observedtest scores are from later ages. Also, PIAT test scores areknown to have a potential “cohort effect.” Namely, lattercohorts have higher mean test scores than previous cohorts.We deal with this issue by adding the cohort mean, μ0, tothe outcome, Equation (3).

programs are linked with AFDC (and now withTANF), such as the early childhood educationprogram, Head Start, housing subsidies, and theMedicaid health insurance program. As we donot separately control for participation in dif-ferent programs that are linked with AFDC,7

the benefits on a child’s attainment from theseprograms are captured by the coefficient of thewelfare use history, Wt .

Mothers’ employment decisions can affectability through two channels: income and time.Income-related effects will be captured by thecoefficient of cumulative income variable. Thus,the work coefficient itself picks up the time-related effects only. By working, mothers forgotime to educate or care for their children andas a result employment may be detrimental tochildren’s attainment (Baker, Gruber, and Mil-ligan 2008; Blau and Grossberg 1992; Curieand Hotz 2004; Morrill 2011). On the otherhand, children’s attainment can improve when,for instance, working mothers provide a positiverole model. Both sociology and psychology lit-erature commonly argue the role model effectis strong. Also, according to Cascio (2009),compared to the general population of moth-ers, low-income single mothers are more likelyto put their children in kindergarten, perhapsbecause kindergarten is 100% subsidized daycare. Children from disadvantaged families whoare placed in kindergarten may have access toeducational tools in the classroom that are notavailable in the home environment. This mayresult in a positive relationship between a child’sattainment and the mother’s employment. Ouroutcome measures take place before children goto elementary school. So low-income mothers’employment can capture the benefits obtainedfrom subsidized child care.8 Unless we are will-ing to make more structural assumptions on howa mother takes care of her child, these oppos-ing time-related effects will be all captured by

7. It is almost impossible to separately identify theeffects of various programs. For example, before the expan-sion of Medicaid in 1986, applying for AFDC was the pri-mary means of obtaining health insurance for poor children.Before 1992, a mechanical correlation implies that anyonewho participated in the AFDC was automatically eligible forMedicaid, food stamps, school lunch, Head Start, etc. SeeCitro and Michael (1995) for a complete list of all means-tested programs of which the eligibility hinges directly onthe AFDC.

8. As Cascio and Schanzenbach (2007) and Bedard andDhuey (2006) point out, this could lower the age at schoolentry for disadvantaged children, which might be detrimentalbecause younger children tend to perform worse than olderchildren in most school cohorts.


the coefficient of Et in Equation (2). Empiri-cal results will show which effect dominates. InAppendix Section B we give a detailed discus-sion of the identification of these channels in ourdata.

B. Mother’s Utility Function

We assume a mother’s current period util-ity is determined by her consumption of leisureand a composite good and by her child’s cur-rent level of cognitive ability. She chooseshow much to work and whether to use wel-fare or not. She has six possible combinationsof work and welfare use as her alternatives:j = {(ht ,ωt ) : ht = 0, 1, 2; ωt = 0, 1}.9 Themother’s current-period utility of choosing alter-native j is given by:

U(j, εj t ) = α1cλ1j t

λ1+ α2ht(4)

+α3(A

λ2t − 1

λ2) + α4ωt

+α5I (Wt = 0) + α6I (Et = 0)

+α7h1 + εj t .

The utility function has constant relative riskaversion (CRRA) both in terms of compos-ite consumption and the child’s cognitive abil-ity, captured by the parameters λ1 and λ2. Ifλ2 < 1, by CRRA a mother receives dimin-ishing returns to her child’s cognitive achieve-ments and thus has incentive to compensatefor low cognitive ability endowment with moreresources. Both α1 and α3 should be positivesince both composite good consumption andthe child’s current ability should increase themother’s utility. To capture the well-known factthat many low-income mothers do not use wel-fare (even though they are eligible), and that alot of them do not work, we have parameters α2and α4, distastes for work and welfare, respec-tively. We further add α5 and α6, the additionaldisutility incurred when applying for welfare forthe first time and the cost of initiating work,respectively. α7 is added to capture the extracosts of work during the first year after giv-ing birth.10 As our population focuses on poor

9. For example, if j = 1 we have (ht , Iwt ) = (0, 0),

meaning that a mother chooses (no work, no welfare) inperiod t ; j = 2 corresponds to (ht , I

wt ) = (1, 0) (part-time,

no welfare); j = 3 represents (ht , Iwt ) = (2, 0) (full-time, no

welfare),..., etc. dj = 1 indicates that alternative j is chosen.10. This parameter captures the psychological cost of

separation from the child when the child is very young. In

families with little to save, we choose not tomodel saving decisions. As a result, the com-posite consumption good is determined by thecurrent-period income:

cjt = wtht + Bstωt + Mt

in which wt is the offered wage, Bst is theannual welfare income, and Mt is the nonlaborand nonwelfare income. Welfare benefits varyby the state of residence, by the number ofchildren (noC is the number of children, noCSqis the squared number of children) and theamount of labor and other income one has, asfollows:

Bst = b0 + (b2 +∑

s

b3sDst ) · noCt(5)

+(b4 +∑

s

b5sDst ) · noCSqt

+(b6 +∑

s

b7sDst )Mt + (b8

+∑

s

b9sDst )(wtht )

where Dst is the indicator for the state ofresidence at time t (in state s, Dst = 1).

Wage offer, wt, is determined as a functionof labor market experience and other humancapital attributes, as well as local labor marketcharacteristics. Specifically, we have:

ln wt = φ1age + φ2age2 + φ3race(6)

+φ4edu + φ5AFQT + φ6

−δt + φ7Et + φ8(Et × edu)

+φ9pt−1 + φ10ft−1 + L′ctϕ + ξt

where δ is the depreciation rate, Et = ∑t−1−2 hτ

is the mother’s cumulative work experience in2 years prior to giving birth, and ft−1 and pt−1indicate whether a mother has worked full timeor part time immediately before giving birth.Lct is a vector of county-level labor market qual-ity measures, including the county unemploy-ment rate, employment share in services sector,and average wage level, where c is the county inwhich the mother and her child reside at time t .Finally, ξt is the random shock that is assumed

practice, labor force participation in the first year will beslightly overestimated if we do not include α7 in the model.Table A1 shows the big drop in employment in the first yearfollowing child birth.


to be i.i.d. normal. Even though this assump-tion is not crucial in estimations, it simplifiesthe estimation and the simulations.

Unobserved Heterogeneity. In our setup, moth-ers are heterogeneous in terms of their tastesfor work and welfare use. Specifically, α2 andα4 are determined at the time of child-birth asfollows:

α2 = α21edu + α22race + α2α4k = α41edu + α42race + α4k, k = L,H

(7)

where α4k, which we will call welfare stigma, isthe unobserved component of taste for welfareuse. We assume that there are two unobservedtypes: mothers with low welfare stigma, α4L,and mother’s with high welfare stigma, α4H .

Furthermore, we assume that mothers alsodiffer in how efficiently they can use theresources (to which they gain access throughthe welfare program, such as health care andchild care) in rearing their children. In particu-lar, we link γ3, the production function param-eter regarding welfare use in Equation (2), tothe welfare stigma types: γ3H for a high stigmamother (Type I) mother and γ3L for a low stigma(Type II) mother.11 Associated type proportionsare denoted by πH and πL, which are parame-ters to be estimated.12

Note that the marginal effect of a mother’swelfare use on her child’s attainment is:

∂ ln Ot

∂Wt

= γ3 + γ4 ln A0.

By adding unobserved variation to γ3, we allowfor the intercept of the marginal effect of welfareuse to be different. However, we assume thiseffect does not vary by the endowed ability ofthe child.13

11. Although γ3 is linked with α4, we allow the datato tell us whether γ3H > γ3L. That is, we do not imposea mother who has lower welfare stigma (α4L) to be lessefficient at using welfare-related non-cash benefits for herchild.

12. We choose not to link ln A0 with α4. In other words,we assume mothers of different tastes in welfare use can givebirth to children with the same observed ability, so long astheir observed covariates are identical.

13. The unreported result indicates that the empiricaldifference in the slope terms for the two types of mothersis economically and statistically insignificant. Thus, we donot link γ4 to welfare types for simplicity.

III. DATA AND SAMPLE

We construct our mother-child pair sampleusing the following criteria: (1) the child’smother must have always been single for theentirety of the first 5 years after child-birth,14

(2) the child’s mother must have recoverableinformation on work and welfare use for thefirst 5 years of the child’s life, and (3) the childmust have at least one valid PIAT-Math testscore. Given that we do not model initiatives ofwelfare reform at this point, we exclude childrenwho reside in states that implemented any statewaiver programs prior to the welfare reform andchildren who directly experienced the welfarereform.

We have 2,820 observations from 564 chil-dren who were born to 392 mothers. Table 1reports the mean values for the variables weuse. Welfare participation rate in our sampleis 79.4%. Out of 392 mothers, 12.8% of themothers worked part time, whereas 18.6% ofthem worked full time. The sample of chil-dren consists of a nearly equal share of malesand females, and is predominantly Black (74%).The average for PIAT-Math scores is 93.1,which is significantly lower than the popula-tion mean (100).15 This is indicative of the dis-advantages of growing up poor. Average ageis 25.5 at child birth which is younger thanthe NLSY79 average of 27. Sample mothers,on average, have 10.9 years of education andtwo children. Those who have worked receive amean annual labor income of $10,737.16 Table 1indicates that our average mother is at the14th percentile of the AFQT distribution. Oursample mothers tend to live in counties withhigher unemployment rates (the sample averageis 7.9% while the national average is 6.8%),higher shares of service industry (16.5% vs.

14. Single motherhood is measured by not having aspouse or a cohabiting partner. It is well known that marriageis a common way for single mothers to gain economicsupport. For example, O’Neill, Bassi, and Wolf (1987)found that about one-third of single mothers who left thewelfare program from the late 1970s to the mid-1980s didso via marriage. Conversely, dissolution of marriage canlead to economic hardship. Since we do not model marriagedecisions and the potentially complicated joint householdlabor supply decisions, we use only mothers who havealways been single during our study period.

15. PIAT standardized test scores range from 65 to 135with a mean of 100 and a standard deviation of 15 based onthe 1968 national norm sample of children.

16. All monetary variables are adjusted to year $2000by the Personal Consumption Expenditure Deflator fornondurable goods (PCED-nondurable).


TABLE 1Sample Descriptives—Means

Mother’s decisions Mother’s characteristicsWelfare participation 0.794 Age at birth 25.5

(0.404) (4.4)Annual employment Years of education 10.9Part time 0.128 (1.6)(500–1499 h) (0.335) Number of children 2.4Full time 0.186 (1.3)(>= 1500 h) (0.389) Annual labor incomea 10,737.2Hours of work 1605 (9,070.4)(Conditional on work) (626) Annual other incomea 6,063.0

(33,938.9)Child’s characteristics AFQT 14.2Female/male 0.48/0.52 (14.0)Black/others 0.74/0.26 County characteristicsBirth weight (ounces) 110.7 Unemployment rate 7.8

(22.9) (3.2)Age taking test (quarters) 25.3 Service industry 0.16

(4.8) (0.04)PIAT-Math score 93.1 Medium income 23,967.1

(13.4) (6,228.3)Child-years 2,820Children 564Mothers 392

Notes: Standard errors are in parentheses. Population weighted to reflect the 1979 national population of low-skilled singlemothers. aIn 2000 dollars deflated by PCED-nondurable.

15.8%), and lower median income ($23,967 vs.$27,019).

Table 2 looks at the distribution of indi-vidual characteristics and distribution of testscores. Such correlations between these vari-ables and the outcomes indicate variations thathelped us identify the corresponding modelparameters. First, we see that more than 75%of the sample children score below the pop-ulation mean (100), as the mean test scoreof the third quartile is only 93.3. We nextreport the quartiles of the variables, and foreach of these quartiles we report the mean testscore observed. For example, the second quar-tile mean of real hourly wages is $2.60. Forchildren whose mothers’ wages fall into thisquartile, the mean test score is 92.4.17 We seethat both a mother’s AFQT scores and edu-cation are positively correlated with the chil-dren’s test scores and children of older moth-ers tend to have lower scores. Furthermore,we see that Black and Hispanic children have

17. To get a measure of general financial wellbeingwhile children grow up, we take an average of the wageand income measures over the study period.

lower test scores than their non-Black, non-Hispanic counterparts and girls perform bet-ter than boys. There is a negative correlationbetween a child’s PIAT-Math test score andthe number of siblings, capturing the effect ofdefused resources as the household gets larger.Finally, test-taking age and the county labormarket characteristics do not exhibit clear pat-terns of correlation with test scores without fur-ther controls.

IV. RESULTS

In this section, we first discuss the implica-tions of mothers’ decisions on their children’sattainments derived from our estimates. We thenperform policy simulations and discuss theirimplications.

A. Parameter Estimates

Our model fits the data very well, we predictmore than 90% of the work behavior and morethan 95% of the welfare use behavior correctly.Appendix Section C gives further details on themodel fit.


TABLE 2Detailed Descriptive Statistics of Test Scores by Quartiles of Demographic Characteristics

Quartile

First Second Third Fourth

PIAT-Math score 75.60 89.40 98.40 111.02(5.56) (2.67) (2.75) (6.43)

Mother’s characteristicsReal hourly wagesa 1.1 2.6 4.8 10.6Mean standard test scores 94.8 92.4 95.8 96.7(Standard deviation of scores) (13.7) (14.8) (12.5) (12.7)Average labor incomea 181.6 1010.9 3598.1 11,823.2

94.8 97.3 93.2 96.2(13.4) (13.6) (13.2) (12.2)

Average other income 479.0 1919.4 4126.5 19,805.894.0 93.5 93.6 94.8

(14.50) (13.90) (12.90) (12.70)AFQT score 3.0 7.8 14.0 34.9

90.2 92.3 94.1 96.7(13.2) (12.8) (12.5) (14.3)

Education < 12 = 1291.4 94.7

(13.60) (13.30)Age at birth 21.1 25.0 28.4 33.7

93.9 93.5 92.6 92.0(13.20) (13.40) (13.20) (14.00)

Child’s characteristicsRace Black Hispanic Other

73.8 12.9 13.393.6 92.2 97.8

(11.89) (13.59) (13.24)Gender Male Female

92.6 93.6(13.80) (13.03)

Number of siblings 1 2 3 40 1 2 3 > 3

95.7 95.3 93.0 90.7 90.2(13.62) (13.73) (12.53) (13.00) (14.10)

Age taking test 21.2 24.1 26.4 32.1(Quarters) 91.6 94.6 93.3 92.5

(14.70) (12.70) (12.50) (13.50)County characteristicsUnemployment rate 4.7 6.5 8.3 12.3

93.5 93.2 93.0 92.7(14.0) (13.6) (12.8) (13.4)

Service industry 0.09 0.14 0.18 0.2293.9 92.4 92.2 94.0

(13.7) (13.0) (12.5) (14.4)Medium income 15,433.50 21,000.50 25,317.30 31,582.70

92.4 94.1 92.3 93.7(13.4) (14.0) (13.1) (13.1)

Notes: Standard errors are in parentheses. aConditional on work.


Table 3 reports the estimates of the log-wage function, Equation (6). Both part-timework and full-time work and the interactionof each with education are associated withhigher wages. A higher local unemploymentrate is associated with lower wages. A highercounty service employment ratio and medianincome, on the other hand, are associated withhigher wages. According to the estimates, anextra year of work increases wage by only0.7% for our sample mothers. This effectis smaller than the ones estimated by Bernal(2008) (2.8%), Moffitt (1984) (4%), and Blauand Kahn (2004) (4%) using general samplesof female workers. The depreciation rate is0.0107, which means the wage offer in thenext period will be 1% lower if a mother doesnot work in the current period. This is largerthan what is estimated by Bernal (2008) formothers who are married and on average moreeducated. Our estimate of the discount rate isabout 0.9.

Table 4 reports the parameter estimates ofutility function, Equation (4). The utility fromthe composite consumption, α1, is 0.7112. Asλ1 is 0.7275, marginal utility from consumptionis decreasing. A mother receives a significantlypositive utility from her child’s cognitive abil-ity (a highly positive α3). We also find that λ2is 0.52, which indicates that a mother has anincentive to invest more in a child with lowercognitive ability. A mother’s taste for work (α2)is captured by a constant term (α2), years ofeducation, and ethnicity. The estimates suggestthat mothers generally value leisure (α2 is neg-ative). Mothers who have more years of educa-tion tend to dislike work more. Black mothers,on the other hand, receive slightly higher util-ity from work, everything else constant.18 Otherthings equal, mothers who are better educatedand Black are more likely to use welfare. Thereare two very distinct types in terms of welfarestigma (α4H and α4L); high stigma types haveutility cost of −1.0028 as opposed to −0.2188

18. Bernal (2008) finds that compared to mothers ofother racial or ethnic backgrounds, Black mothers receivea larger negative utility from work. However, Bernal alsofinds that Black mothers receive a higher positive utilityfrom using child care. The combined effect of the twodecisions is that Black mothers receive a positive utilityfrom working and using child care simultaneously. Since wedo not model child care use decisions, our work decisionmay have captured the average utility effects from bothemployment and child care use decisions.

TABLE 3Log-Wage Estimates

Variables Coefficient

Time-invariantAge at birth (φ1) 0.0625

(0.0013)

Age squared at birth (φ2) −0.0010(0.0000)

Race(φ3) −0.0041(0.0025)

Education(φ4) 0.0052(0.0020)

AFQT (φ5) 0.0014(0.0003)

Constant (φ6) 0.6124(0.0232)

Depreciation rate (δ) 0.0107(0.0033)

Experience-relatedWork experience (φ7) 0.0065

(0.0013)

Education*experience (φ8) 0.0006(0.0001)

Part-time premium (φ9) 0.1013(0.0096)

Full-time premium (φ10) 0.1713(0.0060)

County characteristics (ϕ)

Unemployment rate (ϕ1) −0.0270(0.0070)

Services industry (ϕ2) 0.0003(0.0026)

Medium income (ϕ3) 0.0026(0.0005)

Note: Standard errors are in parentheses.

for low stigma types. We discuss the implica-tions of welfare types in detail in AppendixSection D.

We see that mothers have a cost of initiatingwelfare (negative α5) that is even higher thanthe disutility of receiving welfare (α4 for bothhigh stigma and low stigma types). This cap-tures the observation that many eligible singlemothers choose not to participate in the welfareprogram. Moreover, both utility parameters forfinding a new job after child-birth and workingin the first year (α6 and α7) are negative. Thisreflects the fact that many mothers chose not towork in the first year after their children’s birth.

Table 5 reports the parameters of the log abil-ity production function, Equation (2). First, wesee that the estimates of the observed cognitiveability endowment, Equation (1), are compara-ble to estimates from the literature (Bernal 2008;


TABLE 4Utility Parameters


λ1 0.7275(0.0085)

Consumption (α1) 0.7112(0.0204)

Taste for work (α2)Disutility from work (α2) −3.8780

(0.1164)

Mother’s education on taste for work (α21) −0.0632(0.0436)

Mother’s race on taste for work (α22) 0.0042(0.0178)

Ability of the child (α3) 4.7047(0.0333)

λ2 0.4120(0.0036)

Taste for welfare (α4)Disutility from welfare type I (α4H ) −1.0028

(0.0149)

Disutility from welfare type II (α4L) −0.2188(0.0766)

Mother’s education on taste for welfare (α41) 0.1574(0.0428)

Mother’s race on taste for welfare (α42) −0.6537(0.0544)

First year using welfare after birth (α5) −4.7570(0.0758)

First job after birth (α6) −0.2926(0.0590)

Work in first year after birth (α7) −0.9359(0.1001)

Discount factor (β) 0.9041(0.1001)


Bernal and Keane 2010, 2011). On average, girlsperform better than boys. A higher birthweight,a higher maternal education, and a higher AFQTscore all imply a higher cognitive ability endow-ment. Having a mother who is younger than 18or older than 33, on the other hand, both lead toa lower cognitive ability endowment. Estimatedlog cognitive ability endowment ranges between0.1092 and 0.4180. Figure 1 draws the marginaleffects of work and welfare use against the dis-tribution of ln A0.19 We see that a mother’swork improves her child’s math test score,

19. The effect of employment on a child’s log testscore is: ∂ ln O

∂E= 0.0104 − 0.0029∗ ln A0. Welfare effects

are: ∂ ln O∂WH

= 0.0607 − 0.1465∗ ln A0 for a child of a Type I

mother and, ∂ ln O∂WL

= 0.0452 − 0.1465∗ ln A0, for a child of

a Type II mother.

TABLE 5Initial and Current Ability Parameters


Initial ability parametersBirth weight (γ6) 0.0428

(0.0003)

Gender (γ7) 0.0110(0.0039)

Race (γ8) −0.0177(0.0010)

Mother too young dummy (γ9) −0.0424(0.0084)

Mother too old dummy (γ10) −0.0202(0.0096)

Education of mother (γ11) 0.0234(0.0012)

AFQT (γ12) 0.0011(0.0003)

Current ability parametersCumulative income (γ1) −0.0043

(0.0011)

Cumulative work experience (γ2) 0.0104(0.0011)

Cumulative years on welfare of Type I (γ3h) 0.0607(0.0015)

Cumulative years on welfare of Type II (γ3l ) 0.0452(0.0006)

Cumulative years on welfare*initial ability (γ4) −0.1465(0.0041)

Cumulative work experience*initial ability (γ5) −0.0029(0.0006)

OutcomeAge (γ13) 0.1491

(0.0029)

Mean test score (μ0) 3.4185(0.0147)


but the effect declines with the child’s cogni-tive ability endowment. The marginal change inattainment resulting from a 1-year increase inwork ranges from 9.23% at the lowest cogni-tive ability endowment to 2.20% at the high-est, with the median effect (marked by middledashed line) at 3.13%. The highest, lowest, andmedian marginal effects translate to 1.01, 0.919,and 0.962 points increases in the standardizedtest scores, respectively.20 Estimates in Table 6shows that 60% of our sample mothers are TypeI. For a Type I mother, the net marginal effectof welfare use on her child ranges from 4.47%to −0.0005%, with a median of 1.61%. Thiseffect is quite substantial, as it translates to a

20. These positive employment effect estimates, how-ever small in magnitude, are significantly different from


1.50 points increase in the mean PIAT-Math testscore. That is, despite higher disutility for themother, children of Type I mothers can poten-tially benefit greatly from welfare use, exceptfor those children with the highest cognitiveability endowment. On the contrary, for abouthalf of the children with Type II mothers, thenet effect of welfare use on the child’s cogni-tive achievement is negative. The net effect ofwelfare use for the children of Type II moth-ers ranges from 2.92% to −1.60% per year,with an economically insignificant effect onthe median child (0.00062%, which is 0.00057points increase in the standardized test score).Recall that the coefficients of welfare capturethe benefits from in-kind transfer programs suchas Medicaid and Head Start. We would expectMedicaid to have universal benefits for all par-ticipants. However, programs such as Head Startmay benefit children with high cognitive abilityendowment less compared to low-ability chil-dren. Having a negative role model, on the otherhand, may hurt the children with high cognitiveability more.

Chyi and Ozturk (2013) estimate a similar buta reduced form attainment production functionusing a correction function approach. In thatstudy, they find that the marginal effects ofan additional year of employment and welfareuse for a child with median level of cognitiveability endowment are at 1.44% (1.34 points)and 0.649% (0.604 points), respectively. Ourestimates are comparable to theirs in directionand magnitude.21

Bernal (2008) and Bernal and Keane (2010, 2011), whofind that a mother’s employment is detrimental to a child’scognitive achievement. Our sample and model differ in cer-tain ways that may explain the differences in findings. First,Bernal (2008) focuses on a population of married mothers,who may have different child-rearing technology and chil-dren of much higher ability endowments. Second, Bernal andKeane (2010, 2011) study the effect of child care focusingon a group of single mothers that also includes potentiallybetter-educated mothers. Finally, as NLSY79 does not pro-vide detailed child care information, they use employmentas a proxy. We find that about 20% of our sample reportedusing child care in the first 3 years but no employment.However, such cases are defined as having worked in Bernaland Keane (2010, 2011). We find that such variations in thedefinition of employment explains a significant part of thevariation between our results. Detailed explanation and com-parisons of estimates by different samples is available uponrequest.

21. Though they have the same sign, these effectsare smaller than ours. Modeling and sampling differencesmay explain the difference in magnitudes. Our dynamicmodel with unobserved heterogeneity is likely capturingmore of the variation. Moreover, Chyi and Ozturk (2013)use “sometimes single mothers” in addition to “always

TABLE 6Type-Related Parameters


Type proportionsType I stigma from benefit use (πh) 0.5989

(0.1097)

Type II stigma from benefit use (πl) 0.4011(...)

Welfare stigmaDisutility from welfare Type I (α4H ) −1.0028

(0.0149)

Disutility from welfare Type II (α4L) 0.2188(0.0766)

Rearing technologyCumulative years on welfare of Type I (γ3h) 0.0607

(0.0015)

Cumulative years on welfare of Type II (γ3l ) 0.0452(0.0006)


B. Policy Analysis

Using the estimated parameters, we simulatethe effects of three policy changes. These policychanges gauge mothers’ behavioral responsesfacing (1) a welfare time limit and work require-ment, (2) a relief of welfare tax on labor income,and (3) a policy that is similar to maternity leave.In each policy exercise, we look at the changesin work and welfare participation and analyzehow achievement measures differ for children ofwomen with different work and welfare choices.

Imposing Time Limit on Welfare and WorkRequirement. According to the new TANF rules,the longest time one can be on welfare withoutworking is 2 years, and the cumulative welfareuse cannot exceed 5 years. We simulate thispolicy by setting benefits to zero if cumulativewelfare use exceeds 2 years and no work is cho-sen.22 Figure 2(a) and (b) documents the behav-ioral responses for an average mother whoseobserved covariates are at the sample mean. Wecan see that welfare choice decreases by about 4percentage points in the first two periods. After

single mothers.” Robustness checks indicate children ofalways single mothers are more responsive to their mother’semployment and welfare use. Chyi and Ozturk (2013) alsoinclude children born after welfare reform in addition to pre-reform sample to utilize policy variations as IVs. NLSY79mothers who gave birth after welfare reform were mucholder, and thus they have more work experience and possiblyhigher wages.

22. Since we only model the first 5 years of a child’slive, it is not possible for us to impose the 5-year time limit.


FIGURE 1Effects of Mothers’ Decisions on Ability Given Cognitive Ability Endowment. (a) Effect of Work

Experience on Ability; (b) Effect of Welfare Experience on Ability

.009

2.0

094

.009

6.0

098

.01

.010

2

da/d

h

.109171 .418044Abilities at birth

0.3043

.02

0.0

2.0

4

.109171 .418044

Abilities at birth

dInA/dW for type I dInA/dW for type II

0.3043

(a)

(b)

that, welfare participation decreases graduallyby about 9 percentage points. Meanwhile, theincrease in work participation is also significant.The employment rate goes up by about 12 per-centage points in the first two periods. In the lastthree periods, this increase reaches more than 30percentage points.

These results indicate that the combination ofa welfare time limit and work requirement has asizable effect on mothers’ behaviors. Accordingto the new welfare rule, a typical mother whocurrently gets all of her income from welfarewill no longer be able to receive a welfare ben-efit after the first 2 years. Thus, she will choose

to work to make up for the lost income, whichexplains the sharp increase in employment rateafter two periods. Note that in our model, onecan find employment so long as one wants to.Since we do not model the job matching dif-ficulty and a mother’s searching intensity, theinsurance aspect of welfare use is not factoredinto our model. As a result, welfare use does notdecline by as much as what we observe in thedata.

Our results are in line with other studieson the effects of welfare reform on mothers’behaviors. Fang and Keane (2004) focus on sin-gle mothers and find that work requirements


FIGURE 2Effect of Time Limit and Work Requirement. (a) Effect of Policy Change on Employment; (b)

Effect of Policy Change on Welfare Use; (c) Effect of Policy Change on Children’s Current Ability

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Mean ability Experiment 1

(a)

(b)

(c)

and welfare time limit explains most of thedecrease in the welfare participation rate and theincrease in the work participation rate, even aftercontrolling for other factors such as the 1993EITC expansion and the economic expansion of1990s. Furthermore, Grogger and Michalopou-los (2003) argue that the effects of welfare time

limits may be largest on mothers who haveyounger children, since they value the insurancepurpose of the welfare program more.

Finally, this policy increases the mean of sim-ulated test scores by 3.55% (or a 3.90 pointsincrease in test score. See Figure 2(c)). Eventhough our model is naive in the sense that we


have not taken into account the difficulty of find-ing a job, we find that at least at the meanlevel for cognitive ability, positive impact ofincreased work outweighs the negative impactof decreased welfare use.

Eliminating Welfare Tax on Labor Income. Inthis experiment, we relax the relationship bet-ween the decisions for welfare use and employ-ment. We simulate this policy by assumingthat work income would not reduce the ben-efit from welfare use (in other words, we setb8 + ∑

s

b9sDs = 0). The resulting increase in

work is about 3.54 percentage points in the firstyear. In the next 3 years employment increaseseven more (by about 9 percentage points), butnot as much in the fifth year (only by 1.77 per-centage points). However, this policy changeonly has a slightly positive effect on welfareuse (see Figures 3(a) and (b)). The increaseof mean log achievement is only about 0.46%(or 0.42 points in standardized test scores. SeeFigure 3(c)), which is far smaller than the effectof a combination of a welfare time limit andwork requirements as proposed in the previousexperiment.

As a result, if the policy goal is to promotework, reducing welfare tax on labor income canbe a valid alternative since it sharply increasesemployment. Furthermore, it does increase theattainment of children whose mothers are onwelfare.

Maternity Leave Policy. In this experiment, weanalyze the impact of a maternity leave policyby setting the wage depreciation rate of the firstyear after child-birth to zero.23

This policy change would have no effect onthose mothers who have not worked before giv-ing birth. Thus, we focus on the proportion ofthe sample who worked before giving birth (only42% of the whole sample). Because the mater-nity leave policy decreases the wage depreci-ation cost of leaving a job, we expect fewermothers to work in the first period after giv-ing birth. This reduction may continue for theremaining periods because fewer benefits arereceived from the working experience. At the

23. In the second year wage equation (ln w2 in Equation(6)), we also set the work premium terms for the second yearafter child-birth (corresponding to φ9 and φ10) equal to thefirst year estimates.

Currently, there is a 4-week unpaid maternal leave in theUnited States. However, there was none before 1993.

same time, we expect these mothers to choosewelfare to make up for the loss of labor income.With this policy change, our simulations showthat the employment rate decreases by about 10percentage points in the first year and 6 per-centage points in the second year. The effect isinsignificant for the later years. The increase inthe welfare use is minuscule in all periods (seeFigure 4(a) and (b)). However, even though theeffect on welfare is very small and effect onwork is insignificant in most periods, this pol-icy reform decrease of mean log achievement isabout 0.31% (or 0.34 points in standardized testscores. See Figure 4(c)).

Our finding of a decrease in labor forceparticipation is in line with the findings ofBaker and Milligan (2008), who find that whenCanada changed its maternity leave policy, thepercentage of mothers who went back to workwithin the first 9 months declined significantly,from 53% to about 33%. Furthermore, Han etal. (2011) find that within 9 months of leavingwork after child birth, about 60% of all womengo back to work. This is especially high amongBlack new mothers who are the majority ofour welfare users. They further indicate thatnoncollege-graduate, young, and single mothersare the ones who are most likely to go back towork within 2 months of giving birth. On theother hand, older, married, and at least college-graduate mothers are the least likely to go backto work quickly, because they are likely tohave savings to draw upon and have access tomaternity leave. As this policy experiment onlyapplies to about 40% of our sample motherswho have been working before child-birth, theaverage effect on the whole population shouldbe smaller.

V. CONCLUSION

Our results reveal significant policy effectsfor a sample of children who are in disadvan-taged households with low-income single moth-ers. We find that in this sample a mother’semployment is beneficial for cognitive devel-opment of the child, especially if the childhas a low cognitive ability endowment. Thisresult is significantly different from the literaturewhich documents negative cognitive achieve-ment responses to a mother’s employment. Thispositive impact may be due to a positive rolemodel effect. Alternatively, it may be capturingthe benefits from subsidized child care instead.


FIGURE 3Effect of Eliminating Welfare Tax. (a) Effect of Policy Change on Employment; (b) Effect of

Policy Change on Welfare Use; (c) Effect of Policy Change on Children’s Current Ability

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In our model the welfare program partici-pation variable captures the effect of benefitsfrom nonmonetary programs that are somewhatlinked to the AFDC, such as subsidized hous-ing, Medicaid, and Head Start. Our results showthat a mother’s welfare use contributes posi-tively to cognitive ability accumulation of herchild as well, especially if she is a high-stigma

user, who rarely uses welfare but when shedoes, she fully utilizes the benefits to nurtureher child. However, for high-ability children theeffects are low, even negative, if the mother is ahigh frequency user who does not utilize welfareresources well.

In our counterfactual simulations, we findthat policy changes that reduce welfare use/


FIGURE 4Effect of Extended Maternity Leave Policy. (a) Effect of Policy Change on Employment; (b)

Effect of Policy Change on Welfare Use; (c) Effect of Policy Change on Children’s Current Ability

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increase employment are generally beneficial toearly cognitive development. Specifically, a pol-icy that combines a work requirement and a2-year welfare time limit increases the test scoreof a child with median ability endowment by

3.55%, a result that is both statistically and eco-nomically significant. This implies that welfarereform was not only successful in achieving itsstated goals, but was also beneficial to welfarechildren’s outcomes. Ours is the first paper to


assess the effects of welfare reform on early cog-nitive development at national level with obser-vational data. However, there are some exper-imental studies that provide evidence for posi-tive changes on early outcomes (primary schoolchildren) in response to local welfare reforminitiatives (Duncan and Chase-Lansdale 2001;Morris, Duncan, and Clark-Kauffman 2005).Our results serve to validate this evidence atthe national level with a representative dataset.Moreover, we complement the only other studythat is directly comparable to ours, Miller andZhang (2009) by estimating the effects on pre-school outcomes. Their positive welfare reformeffects for low-income 4th to 8th graders sug-gests the early positive effects we find persist inthe long run and translate into better scores atschool as well.

In another policy simulation, we show thatincreasing work incentives for the welfare pop-ulation by exempting labor income from “wel-fare tax” can be a very successful policy withsome additional benefits for children’s out-comes. However, we find that a counterfac-tual with an extended maternal leave policydoes not provide positive changes to cognitiveoutcomes. This policy, moreover, significantlyreduces maternal employment with no signifi-cant change in welfare use.

We conclude that if the goal is to reduce wel-fare dependency, policies that increase incen-tives to work such as EITC work better thanmandates alone. These policy changes, alongwith improvements in accessibility and qualityof noncash welfare programs, can significantlyimprove the cognitive outcomes of children withdisadvantaged backgrounds. This is promisingin breaking the intergenerational cycle of wel-fare dependency.

APPENDIX

A. Solution to the Mother’s Optimization Problem and theLikelihood Function

At the beginning of period t , a mother faces the statevector St , determined by her choices up to t . St includeswork experience Et and cumulative welfare usage Wt up tothe current year beginning from 2 years prior to child-birthand evolves as follows:A1

A1. Notice that initial conditions E1 and W1 are prede-termined because they depend only on information before achild’s birth, which is taken as given.

E1 = h−1 + h−2

Et = Et−1 + ht−1

W1 = ω−1 + ω−2

Wt = Wt−1 + ωt−1(A.8)

where ht−1 and ωt−1 are the work and welfare choices inthe previous period, respectively. Given this state, a motherchooses ht and ωt that maximize the expected utility forthe remaining periods, which we will call Vt . Vt is thesum of period-specific utilities from the remaining periods,beginning with period t . Defining current-period alternative-specific utility, u(St , j, εj t ), as the sum of a deterministicpart U

jt and an alternative-specific shock εj t , we have:

u(St , j, εj t ) = u(St , j) + djt εj t = Ujt + djt εj t

where djt is the indicator that alternative j is chosen, and εj t

is assumed to be i.i.d. across time. With St , j and discountrate β, we can write Vt as

Vt ≡ V (St , εj t ) = maxdj t

{V j (St , j) + djt εj t }

where V j (St , j) is given by the recursive formA2

V j (St , j) = Ujt + β

∑S′

Pr(S ′ | S, j)EV (S ′, ε′).

This optimization problem is solved recursively using back-ward induction. In order to make a choice at T − 1, a mothercalculates the expected value of her choice at period T , giventhat her choice at T − 1 is j . That is, at the beginning ofperiod T − 1, the mother sets djT −1 = 1 by calculating

V (ST −1, εT −1) = maxj

{Uj

T −1 + djT −1εjT −1

+βEεV (ST , εT |St−1, djt−1)}.In order to do this, first the mother must calculate

EεV (ST , εT ) = maxdjT

Eε(V1T , V 2

T , V 3T , V 4

T , V 5T , V 6

T |

= ST −1, dT −1)∑

k

Pr(ST , dkT = 1) UkT .

Now, returning to period T − 2, before she can decide whatto do in T − 2 she needs to know the alternative-specificvalue functions for every feasible S

j

T −2, and so forth, untilshe comes back at the current period t .

The individual likelihood function for individual i attime t with type k can be written as

Litk = {I,II∑

k

πk[J∑

j=1

dj Pr(dj

= 1 | St , k)g(Ot | k)I [Ot available]]}f (wt | St )

I [ht >0]

where f (wt | St )I (ht >0) is the probability of receiving a

wage offer at wt if the mother is working, conditionalon the work experience and other state variables. g(Ot |k)I [Ot available] is the probability of observing the test score

A2. Note that in our setup of transition of state variables,Equation (A.8), Pr(S ′ | S, j) is deterministic.


TABLE A1Mother’s Employment and Welfare Use by Child’s Age

Child’s Welfare Part-time Full-time HoursAge Use (500–1499 Hours) (≥ 1500 h) of Worka

−2 0.54 0.16 0.18 1510(0.50) (0.36) (0.39) (628)

−1 0.67 0.15 0.17 1519(0.47) (0.36) (0.37) (657)

1 0.81 0.11 0.12 1463(0.39) (0.31) (0.32) (538)

2 0.79 0.13 0.17 1532(0.41) (0.34) (0.38) (600)

3 0.81 0.12 0.19 1625(0.39) (0.32) (0.39) (633)

4 0.80 0.13 0.22 1692(0.40) (0.34) (0.42) (684)

5 0.76 0.15 0.22 1651(0.43) (0.35) (0.42) (618)

Note: Standard errors are in parentheses.aConditional on work.

Ot when a test is taken by a child with a type k motherat time t . The product of Litk across years gives us theindividual likelihood function. The natural logarithm of theproduct of individual likelihoods gives the log likelihoodfunction.

We estimate our model using the maximum likelihoodmethod. We write V

jt as the value function of choice

j in period t, and we need to solve it before we cancompute Pr(dj = 1 | St , k; θ). Given state variable St andthe alternative-specific error term ε

jt , we know that

V j (St , k, εjt , θ) = u

jt + β

∫ε′

max(V 1, V 2, ..., V J )dF (ε′).

We assume that the preference shocks ε are drawn i.i.d.from the Type I extreme value distribution with a locationparameter of 0 and a scale parameter of 1. This enables usto write the probability of choosing dj , given state St , as

Pr(dj = 1 | St , k) = exp(V j (St ,k,dj ))∑k exp(V k(St ,k,dj ))

.

B. Identification

An important source of identification of differences inmothers’ work and welfare behaviors is the exogenousvariation in the AFDC benefits across states and local labormarket conditions.

The benefit rule for the AFDC program of each state isa nonlinear function of a mother’s income, work decisions,and the number of children she has. Keane and Wolpin(2002) find that empirical results vary widely in the literaturemostly because of the adoption of different benefit-ruleparameters. They argue that the benefit level of a specificyear fails to capture the long-term changes in state AFDCrules, which are more likely to affect mothers’ decisions ina dynamic setting. Instead of using randomly drawn, realbenefit levels, they suggest that researchers should estimatethe long-term state-benefit rules and use the estimatedparameters as instruments.

Following the strategy of Keane and Wolpin (2002),we estimate the AFDC benefit rules for each U.S. state by

pooling all single-mother welfare receipts in the Panel Studyof Income Dynamics (PSID) from 1968 to 1992 and usingdummy variables to identify state benefit parameters. TheAFDC benefit for a mother i who lives in state s is givenby the equation:

Bis = b0 + (b2 +∑

s

b3sDs) · noCi

+(b4 +∑

s

b5sDs) · noCSqi + (b6 +∑

s

b7sDs)Mi

+(b8 +∑

s

b9sDs)(wihi)

where Ds is the indicator of the residence of individual i.Ds = 1 if mother i lives in state s. noCi is the number ofchildren in the household and noCSqi is the square of thisnumber. Mi is the unearned income and wihi is the laborincome of the individual.

The fact that we have a panel of 5 years with infor-mation on mothers’ work and welfare use enables uscompare not only the attainment of children who haveexperienced one decision and those who have experi-enced none, but also those who have been exposed tovarying combinations of welfare and work. We incorpo-rate effective welfare tax on earned income to separatethe effects of welfare use and work in the children’sattainment function. The rationale is that the higher theeffective tax on earned income, the less likely a motherwho has already been on welfare would have chosen towork. However, it is important to note that the separa-tion of the effects of welfare use and work on children’sattainment does not simply hinge on the effective welfaretax.

In our model, identification of the parameters relieson at least three assumptions. First, the structure of themodel is correct. Second, the distributional assumptionsrequired for the estimation (i.e., the likelihood function)are correct. Third, there are some exclusion conditions thataffect only mothers’ decisions but not children’s outcomes.For example, both Bernal (2008) and our study rely on


TABLE A2Marginal Effects of Alternative Models

4 5 6 71 2 3 No No Work No No Welfare

Specification Baseline OLS IV Income No Income Welfare No Income

Marginal effects of employment1% 0.0100 0.0115 0.0158 0.0101 0.0043 0.004125% 0.0097 0.0018 0.0070 0.0097 0.0040 0.003950% 0.0096 0.0004 0.0052 0.0096 0.0039 0.003875% 0.0095 −0.0026 0.0030 0.0096 0.0038 0.003799% 0.0093 −0.0076 −0.0030 0.0094 0.0035 0.0035Mean 0.0096 −0.0002 0.0049 0.0096 0.0039 0.0038Marginal effects of Type I welfare usea

1% 0.0383 −0.0135 0.0124 0.0381 0.031425% 0.0212 −0.0006 0.0009 0.0210 0.014250% 0.0161 −0.0031 −0.0010 0.0158 0.009475% 0.0124 −0.0057 −0.0032 0.0122 0.005899% 0.0035 −0.0119 −0.0084 0.0029 −0.0023Mean 0.0172 −0.0028 −0.0008 0.0169 0.0104Marginal effects of Type II welfare use1% 0.0228 0.0227 0.016325% 0.0057 0.0055 −0.000950% 0.0006 0.0004 −0.005775% −0.0031 −0.0033 −0.009399% −0.0120 −0.0125 −0.0174Mean 0.0017 0.0017 −0.0046

aNote that there are no types in OLS and the IV models. Welfare results under Type I heading are just the overall results.

the county labor market conditions to separate mothers’decisions and children’s attainment. For this to be correct,we need to further assume that the county labor marketconditions only affect the demand for low-income singlemothers. That is, these conditions are not correlated withmothers’ taste for work and welfare use. Additionally,we need to assume that the welfare benefit rules are notcorrelated with uncontrolled factors in children’s cognitiveattainment productive function. For example, we need toassume that states with more generous welfare benefits donot have better subsidized child care. Or, even if they do,the effects will not fundamentally change our results.

Although these assumptions are not directly testable,we estimate several alternative models to evaluate theappropriateness of them. As parameter estimates are notdirectly interpretable, we will focus on discussing thechanges in the marginal effects of mothers’ decisions onchildren’s attainment in Equation (3). Table A2 collectsthese marginal effects of an additional year of each decisionagainst children whose cognitive ability endowment is at 1st,25th, 50th, 75th, and 99th percentiles, as well as the meaneffects.

Specification 1 gives the marginal effects of our base-line model. These are the data we use to draw Figure1. Specifications 2 estimates Equation (3) using the OLS.In this specification mothers’ employment is negativelyassociated with outcomes for at least half of the sam-ple children. Even though the median effect is posi-tive (and small in magnitude), the mean effect is nega-tive. Welfare use appears to be negatively associated withchildren’s test scores, regardless of the endowed ability.Comparing Specifications 1 and 2, it is easy to see that

without controlling for the unobserved heterogeneity andthe excluded exogenous variation, estimates are significantlybiased downwards.

Specification 3 is the IV estimation of Equation (3).Comparing Specification 3 to Specification 2 we see thatthe marginal effect of mothers’ employment is now positivefor all children except the ones with highest endowed ability.Both median and mean effects are also positive. However,they are both about 50% smaller than the structural modelestimates in Specification 1. IV estimates overestimate theeffects of mothers’ employment on children with endowedabilities on both the high and low ends of the distribution.In other words, the IV method seems to overestimate γ5 inEquation (3).

Specifications 4–7 further study the effects of differentchannels through which mothers’ decisions affect theirchildren’s attainment as discussed in Section 2.1.

Specification 4 excludes accumulated family income inthe attainment production function. As a result, the incomeeffect is going to be absorbed by the variables that arecorrelated with it. For example, the coefficient of worknow also captures the effects from an increase in laborearnings. On the other hand, an increase in income throughany welfare program is absorbed by the coefficients ofwelfare. The marginal effects do not change much whenincome is excluded from the model. In fact, Bernal andKeane (2011) also find that even after instrumenting for it,the effect of family income on children’s outcome is smalland insignificant. One explanation for this, as pointed outby Keane and Wolpin (2001), is that once variables suchas mothers’ education and AFDC are taken into account,we essentially control for the permanent part of the income


FIGURE A1

Model Fit of Mothers’ Decisions. (a) Model Fit of Full-Time Work Decision; (b) Model Fit of Part-Time Work Decision;(c) Model Fit of Welfare Decision

0.1

.2.3

.4.5

Par

ticip

atio

n ra

tio

1 2 3 4 5Year

Simulated full-time work Actual ful-ltime work

0.1

.2.3

.4.5

Par

ticip

atio

n ra

tio

1 2 3 4 5Year

Simulated part-time work Actual part-time work

0.1

.2.3

.4.5

.6.7

.8.9

1

Par

ticip

atio

n ra

tio

1 2 3 4 5Year

Simulated welfare choice Actual welfare choice

(a)

(b)

(c)

and remaining variations in transitory income (even whenit is cumulative) do not matter much in the behaviors of aforward-looking agent.

Specification 5 excludes controls for mothers’ employ-ment. Note that work is negatively correlated with welfareuse in the data. When work is excluded in the attainment

production function (but family financial resources are con-trolled for), an increase in welfare use hence incorporatesnot only the effect of nonpecuniary means-tested transferprograms but also time-use related effects (such as subsi-dized child care) and role model effects. As a result, themarginal effects of welfare use in Specification 5 are sizably


FIGURE A2

Participation and Attainment of Different Types. (a) Welfare Use and Work; (b) Children’s Ability

.2.4

.6.8

1 2 3 4 5Year

Work type I Work type IIWelfare type I Welfare type II

.4.6

.81

1.2

1 2 3 4 5Year

Mean ability type I Mean ability type II

(a)

(b)

reduced. Specification 6 excludes welfare use. Similarly, wesee that the negative correlation between welfare use andemployment in the data indicates that the effect of eitherdecision is reduced once we drop the other decision in themodel.

Finally, Specification 7 combines the effects of all threechannels of mothers’ decisions into a single employmentvariable by dropping both income and welfare use variablesin the model. The last column shows that the marginal effectis even lower than it is with Specification 6. ComparingSpecifications 6 and 7 to Specification 1, it illustratesthe importance of separately controlling for the effects ofmothers’ decisions from different economic channels.

C. Model Fit

Figure A1 provides support for how well the model fitsthe data. Overall, we fit the participation rates for welfareand work nicely (Figure A1). We predict more than 90% ofmothers’ full-time and part-time work choices successfully.

Meanwhile, we also predict more than 95% of mothers’welfare behavior. However, our estimation of part-time worksuffers a slight underestimation in the second period anda slight overestimation in the fourth period. At the sametime, our prediction of full-time work is mildly overstated,especially in the last two periods.

D. Understanding Unobserved Heterogeneity

Table 6 reports estimates of all parameters that arerelated to “types” in the model. Figure A1 draws the annualmeans of welfare use and work patterns for mothers ofdifferent types. As can be expected, they have noticeabledifferences in terms of welfare use, as mothers with higherwelfare stigma (Type I mothers) use slightly less welfarefollowing child-birth. On the other hand, there is no sig-nificant difference in employment patterns between motherswho have different levels of welfare stigma. As discussedbefore, we assume the distaste of work in the utility functionto be the same for both types of mothers. The difference in


work patterns is hence initially generated only through vari-ation in income resulting from differences in welfare use. Inlater periods, variation in wages coming through the differ-ences in work experience play a role as well.

The difference in children’s annual attainment (ln At ) forthe two types of mothers is large, as can be seen in FigureA2. With high γ5, Type I mothers are better at utilizingresources from welfare programs to nurture their childrenand as a result each year of welfare and work contributemore to the cognitive development.

The fact that we have more Type I mothers is encour-aging. First, since the effects of employment are mostlypositive, policies that are pro-employment will be beneficialto most children’s attainment. On the other hand, policiesthat curb welfare use will not affect children born to Type Imothers ex-post, as their mothers do not use welfare much tobegin with. As for children born to Type II mothers, reducingwelfare use actually is beneficial for at least half of them,given that the marginal effect of welfare use is negativefor children with more than the median level of observedcognitive ability endowment.

Overall, allowing mothers to have varying levels ofwelfare stigma and efficiency utilizing welfare resourcesadds greatly to our model’s ability to capture the effectsof work and welfare on children’s attainment. Having typesalso enhances our understanding of the potential channelswelfare reform initiatives contribute to these effects.

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WELFARE REFORM AND CHILDREN'S EARLY COGNITIVE DEVELOPMENT