A New Test of Borrowing Constraints forEducation

Meta Brown John Karl Scholz Ananth Seshadri

University of Wisconsin - Madison

April 2009

My Plan

After a brief introduction, I will present a model that, wehope, makes clear our strategy for identifying borrowingconstraints.

I’ll discuss our central empirical results using data from theHealth and Retirement Study (HRS).

I hope to have time to discuss a substantial number ofextensions and looks at robustness.

MotivationPrior evidence for constraints

Educational borrowing constraints may impede efficienthuman capital investment (Becker 1964).

Empirical evidence consistent with borrowing constraintsinclude

Manski and Wise (1983), Kane (1994), Hauser (1993):Parental income positively associated with schooling.Card (1995): Proximity to college matters.Card (1998): OLS estimates of return to schooling below IV.

More recent work challenges this view

Cameron & Heckman (1998, 2001); Carneiro & Heckman(2002); Heckman & Lochner (2000); Keane & Wolpin (2001);and Cameron & Taber (2004)

All studies interpret data through the lens of a unitary model -single decision maker.

Our Alternative ApproachChildren and parents may not always agree

If parents and children behave as a single actor, it is notsurprising that borrowing constraints are unimportant.Parents with college-age children typically have extensiveaccess to credit.

In contrast, college-age children are likely to be constrainedsince they generally cannot borrow against future humancapital. A more relevant question is, do parents choose torelieve the constraint?

HRS parents report that 33% of their children who went tocollege did so without their financial backing.

25 percent (16 percent) of children whose parents had$200,000 to $400,000 (over $400,000) of net worth in 2000received no parental financial support for college.

Our Alternative ApproachPolicy Context

U.S. financial aid policy (like the prior academic literature onborrowing constraints for education) assumes that parents who areable to pay for college are willing to pay for college:

Students’ access to federal loans and grants is contingent onparents’ income and assets.

But parents are under no legal obligation to make their”Expected Family Contributions” (EFCs).

The standard for students to be independent is strict: Namely,the child needs to be an orphan, veteran, parent, 24 or older,a grad student, or married.

Do borrowing constraints affect the educational attainment ofstudents whose parents do not meet their EFCs?

Anecdotal EvidenceFrom the Becker-Posner blog

“Currently if you are under 25 and not in graduate school you areconsidered dependent on your parents’ income and have to includetheir income on your FAFSA which will count against you whenfiguring your expected family contribution. For those of us who didnot receive any financial support from parents other than cosigningloans this is a real kick in the ass. Not only is my family lowermiddle-class and unable to contribute to my education, but thegovernment will tell me that they expected them to contribute andwill punish me by lowering my available loans total.”

Posted by Diana on January 11, 2005 at 11:10am in response to”Government’s Role in Student Loans-BECKER”

Our Alternative ApproachA simple analytic model points to a new way to examine this issue

We model interactions between parents and children as adynamic non-cooperative game, following the intuition ofBruce and Waldman (1991).

Parents care about their own consumption and their children.Children, however, care only about their own consumption(”one-sided” altruistic preferences).

Questions the model addresses:

Do children’s borrowing constraints ever lead to inefficientequilibrium investments?If so, for which combinations of the primitives (parentalresources, degree of altruism, and the shape of the humancapital production function)?In what circumstances, if any, will financial aid affectequilibrium human capital investment?

ModelObjectives, constraints and timing

Preferences

Uk(ck1 , ck

2 ) = u(ck1 ) + βu(ck

2 )

Up({

c it

}i=p,k; t=1,2

)= u(cp

1 ) + βu(cp2 ) + αUk(ck

1 , ck2 )

Physical capital: ai invested in 1 returns Rai in 2 for i = p, k

Human capital: ep & ek returns h(ep + ek + τ) to the child in pd 2

Choices, constraints & timing:

In 1 Parent moves, choosing cp1 + g1 + ep + ap ≤ xp; g1, e

p ≥ 0.

Child chooses ck1 + ek + ak ≤ g1; ak , ek ≥ 0.

In 2 Parent chooses cp2 + g2 ≤ Rap;

Child consumes ck2 = Rak + h(e) + g2.

Period 2There is a discontinuity in optimal second period transfers

Parent maxg2≥0

{u(Rap − g2) + αu(Rak + h(e) + g2)

}

g2(RaP ,Rak +h(e)) =

g2 s.t. u′(Rap − g2) = αu′(Rak + h(e) + g2)

where u′(Rap) < αu′(Rak + h(e))0 otherwise

(1)

Second period transfers are compensatory, since they decrease withthe child’s income and assets.

Period 1Children may overconsume and credit constraints for college may arise rationally

Child’s Euler equation

u′(ck1) = β max

{R, h′(e)

} (1+

∂g2

∂(Rak + h(e))

)u′(ck

2) (2)

We show ek= ak= 0. There are two cases to consider. Wheng2> 0

u′(cp1) = αu′(ck

1); u′(cp1) = βRu′(cp

2); (3)

h′(e) = R; u′(cp2) = αu′(ck

2)

If g2 ≥ 0 binds, however

u′(cp1) = αu′(ck

1); u′(cp1) = βRu′(cp

2); u′(ck1) = βh′(e)u′(ck

2 );

h′(e) > R; u′(cp2) > αu′(ck

2 )

Description of equilibriumTwo regions based on whether second period transfers are made

Partition the xp × α× h space into 2 regions

Region 1

→ xp and/or α large and/or h′(·) to R quickly

→ g2 > 0, h′(e) = R

→ Strategic concerns; efficient HC investment

Region 2

→ xp and/or α small and/or h′(·) to R slowly

→ g2 = 0, h′(e) > R

→ No strategic concerns; but underinvestment in HC

When does financial aid matter?Our central Proposition

Proposition 2: In any equilibrium in which g2 > 0, ∂(ep+ek )∂τ = −1.

Financial aid does not influence totaleducational attainment.

In any equilibrium in which g2 ≥ 0 binds,∂(ep+ek )

∂τ > −1. Financial aid increases totaleducational attainment.

Empirical strategyOur model calls for data on parent-child pairs, g2, and financial aid

The model implies the response of educational attainment tofinancial aid should differ for g2 > 0 and g2 = 0 families.

No data set we know contains full financial aid information,realized educational attainment, and post-schooling transfers.

However, we can go to the HRS for educational attainmentand post-schooling transfers, if we can find an informativefinancial aid proxy.

A consistent feature of U.S. federal aid formulas generatessubstantial aid variation with family structure:

EFC(I,A) calculated at the parent level

At the student level, Aid = COA -EFC(I,A)

NTherefore a student’s federal aid can vary substantially withthe number of siblings he or she has in college.We use birth spacing as a proxy for financial aid.

Is Birth Spacing a Reasonable Proxy for Financial Aid?Evidence from the NLSY-97 suggests it is

ParameterIndependent variable (Std error)Sibling-years of overlap in first term of college 358.44**

(179.52)Parent's 1997 income, 1000s -23.84***

(6.38)Parent's 1997 income squared, 10000s 7.14***

(2.33)Parent's 1997 net worth, 1000s -2.19**

(0.98)Parent's 1997 net worth squared, 10000s 0.06*

(0.03)AFQT percentile -28.97*

(16.69)AFQT percentile squared 0.63***

(0.15)Constant 3,152.17***

(463.69)Observations 2608R-squared 0.06* significant at 10%; ** significant at 5%; *** significant at 1%

Appendix Table 2: OLS Estimates of Financial Aid, NLSY-97

The Data Used to Examine Our Central PropositionThe Health and Retirement Study

U.S. national panel study initiated in 1992.

Cohorts: HRS (born between 1931-1941); in 1998 additionalcohorts were added, including the AHEAD (born before 1923);CODA (1923-1930); and War babies (1942-1947).

For much of the analysis we start with 13,091 families in the1998 HRS. We restrict the sample by requiring:

Those with complete information on the child’s DOB,education, gender, gift information, and relationship to theHRS respondent.Children who are 24 or older in 2000 with at least one siblingThe main sample is reduced to 9,471 families with 34,593children.The module sample (see next slide) goes from 427 families to334, with 1,262 children.

HRS Measures of Post-College TransfersThe HRS poses two specific, gift questions that are useful to this study

We rely on transfers reported by parents over the period 1998-2004in response to the Waves 4, 5, 6 & 7 questions:

”Including help with education but not shared housing or sharedfood (or any deed to a house), in the last 2 years did [theRespondent or Spouse] give financial help totaling $500 or more toany of their children or grandchildren?”

An even more ideal question was asked of a smaller group ofrespondents in the 1994 Wave 2 Transfers Module:

“Other than contributions toward education expenses, have youever given substantial gifts to your grown children?”

Central Empirical Model

Many observable and unobservable factors influence schoolingdifferences between two arbitrarily chosen individuals, includingparental attitudes and investments in their children, and heritablecomponents of aptitude.

We account for time invariant family-specific factors by estimatingthe following model.

eis = ωi + Xis β + γois + ε is ,

wherei = 1, ...,N familiessi = 1, ...,Si children of family ieis education of child s of family iωi family i fixed effectXis exogenous characteristics of child s of family iois years of overlap in college ages of child s with family i sibs

Central ResultsBirth spacing affects schooling, but only for the no-gift samples

Table 2: Family Fixed Effect Estimates of Years of Schooling, HRS, Gift v. No Gift

Gifts No Gifts Gifts No GiftsParameter Parameter Parameter Parameter

Independent variable (Std error) (Std error) (Std error) (Std error)Child gender, male=1 -0.242*** -0.086 -0.249 -0.314**

(0.087) (0.088) (0.195) (0.134)

Child age -0.014 -0.048*** -0.008 -0.051***(0.013) (0.012) (0.029) (0.018)

Oldest child indicator 0.147 0.296** 0.079 0.290(0.117) (0.121) (0.258) (0.186)

Youngest child indicator 0.119 -0.089 0.187 -0.056(0.124) (0.126) (0.265) (0.194)

Sibling-years of overlap 0.034 0.105*** -0.050 0.094**in college ages (0.031) (0.030) (0.064) (0.046)

Number of Children 16,892 17,701 467 795Number of Families 4890 4581 125 209R-squared 0.5934 0.6521 0.5713 0.5941Adjusted R-squared 0.4276 0.5304 0.4073 0.4454

* indicates significance at the 10 percent, ** at the 5 percent, and *** at the 1 percent level.

1998-2004 Gifts to Children Transfer Module Gifts to Children

The Results and Next Steps

A student with a sibling 5 years (or more) younger or older,will get roughly one semester less schooling than an otherwiseidentical twin.

Themes and variation

Overlap won’t matter for low-income families (who get fullfinancial aid) or high income families. Use net worth terciles todistinguish groups.Make use of historical changes in financial aid.The margin should be college: it is.Identification in the fixed effects models come from familieswith three or more children. This, in a sense, throws away alot of information. Are results robust to random effects?Split the sample by altruism.

Sensitivity AnalysesThe effects hold in the middle net worth tercile of the no-gift sample

Table 3: Family Fixed Effect Estimates of Years of Schooling, HRS

1998-2004 Gifts to ChildrenGifts No Gifts Gifts No Gifts

Parameter Parameter Parameter ParameterIndependent variable (Std error) (Std error) (Std error) (Std error)Child gender, male=1 -0.241** -0.088 -0.341 -0.379*

(0.0878) (0.089) (0.0204) (0.153)Child age 0.014 -0.048** -0.014 -0.067**

(0.013) (0.012) (0.029) (0.023)Oldest child indicator 0.145 0.297* 0.094 0.331

(0.117) (0.121) (0.273) (0.216)Youngest child indicator 0.119 -0.089 0.547 -0.274

(0.125) (0.127) (0.286) (0.224)Sibling-years of overlap 0.020 0.070 0.048 0.071in college ages*Tercile 1 (0.045) (0.046) (0.103) (0.063)

Sibling-years of overlap 0.048 0.189** 0.060 0.197*in college ages*Tercile 2 (0.051) (0.047) (0.083) (0.082)

Sibling-years of overlap 0.040 0.046 -0.044 -0.047in college ages*Tercile 3 (0.055) (0.054) (0.128) (0.114)

Number of Children 16,824 17,609 364 582Number of Families 4869 4557 92 150R-squared 0.59 0.65 0.59 0.57Adjusted R-squared 0.43 0.53 0.44 0.41* significant at 5%; ** significant at 1%

Transfer Module Gifts to Children

Sensitivity AnalysesFinancial aid got much more generous in 1978 - results are larger then

Table 4: Family Fixed Effect Estimates of Years of Schooling, HRS, Around Reform

College Entry1998-2004 Gifts to Children Gifts No Gifts Gifts No Gifts

Parameter Parameter Parameter ParameterIndependent variable (Std Error) (Std Error) (Std Error) (Std Error)Child gender, male=1 -0.0707 -0.146 -0.443** -0.0104

(0.113) (0.121) (0.142) (0.157)Child age 0.00553 -0.0610** -0.00152 -0.0211

(0.0191) (0.0182) (0.0296) (0.0327)Oldest child indicator 0.128 0.338* 0.204 0.229

(0.145) (0.159) (0.201) (0.242)Youngest child indicator 0.0184 -0.164 0.258 0.0487

(0.172) (0.187) (0.196) (0.215)Sibling-years of overlap -0.231** 0.239** 0.111 -0.0145in college ages*Tercile 1 (0.0688) (0.0684) (0.0656) (0.0829)

Sibling-years of overlap 0.0710 0.143* 0.0403 0.284**in college ages*Tercile 2 (0.0716) (0.0670) (0.0828) (0.0874)

Sibling-years of overlap -0.0296 0.0692 0.114 0.0533in college ages*Tercile 3 (0.0745) (0.0758) (0.0929) (0.0974)

Number of Children 8180 11,036 8712 6636Number of Families 3133 3579 3416 2623R-squared 0.7339 0.6559 0.6248 0.7327Adjusted R-squared 0.5682 0.4903 0.3821 0.5572* significant at 5%; ** significant at 1%

Post-reformPre-reform

Sensitivity AnalysesResults are robust using cross-sectional variation: the RE estimates

Table 5: Family Random Effect Estimates of Years of Schooling, HRS1998-2004 Gifts to Children: Gifts No gifts

Independent variable Parameter (SE)Sibling-years of overlap 0.03 0.07** in college ages (0.03) (0.03)Number of children 0.01 -0.26**

(0.12) (0.11)Number of children squared -0.01 0.01

(0.01) (0.01)Child gender, male=1 -0.25*** -0.13

(0.08) (0.08)Child age 0.02*** -0.01

(0.01) (0.01)Oldest child indicator 0.12 0.12

(0.10) (0.11)Youngest child indicator 0.13 0.06

(0.11) (0.12)Parent's 2000 income in 100,000s 0.04 0.59

(0.15) (0.42)Income squared in billions -0.00 -0.02

(0.00) (0.01)Parent's 2000 net worth in millions 0.37*** 0.39

(0.13) (0.26)Net worth squared in 100 billions -2.24** -0.98

(0.92) (0.76)Black 0.44** 0.63***

(0.20) (0.23)Hispanic 0.33 -0.94***

(0.30) (0.27)Parent's education less than HS -0.75*** -0.75***

(0.18) (0.20)Parent some college 0.70*** 0.91***

(0.17) (0.25)Parent college graduate 1.27*** 0.98**

(0.22) (0.39)Parent post graduate education 1.72*** 1.79***

(0.23) (0.44)Mean family effect 13.02*** 14.74***

(0.43) (0.50)Total number of children 16565 17327Number of families 4820 4488* indicates significance at the 10 percent, ** at the 5 percent, and *** at the 1 percent level.

Parameter (SE)

Sensitivity AnalysesAltruism: financial aid matters less for more altruistic families

Table 6: Family Fixed Effect Estimates of Years of Schooling, HRS 2000 Economic Altruism Module

Altruism ModuleParameter

Independent variable (Std error)Child gender, male=1 -0.0877

(0.203)Child age -0.0464

(0.0313)Oldest child indicator 0.581*

(0.276)Youngest child indicator 0.134

(0.286)Sibling-years of overlap 0.0982in college ages*Give 3/4 (0.0894)

Sibling-years of overlap 0.644**in college ages*Give 1/2 (0.109)

Sibling-years of overlap 0.398*in college ages*Never give (0.157)

Number of Children 3292Number of Families 914R-squared 0.3035Adjusted R-squared 0.0332* significant at 5%; ** significant at 1%

Conclusions

We develop a theory of human capital investment thatrecognizes the distinct roles of parents and children.

The model reveals an identifiable category of students who arelikely to be meaningfully borrowing constrained.

Estimates using HRS and NLSY97 data are consistent with theexistence of such constraints.

Hence, we think the literature suggesting there are noimportant financial barriers to college is mistaken.

Aid policy is incomplete to the extent that it leaves children ofnoncontributors under-funded.

Policy prescriptions based on these results are unclear:Though increasing financial aid is would move the HC ofnoncontributors’ children toward the efficient level, manychildren of contributors would receive inframarginal subsidies.