Economics of Human Capital

Lecture 4: Education Production

Ian Walker Lancaster University Management School

Ian.walker@lancaster.ac.uk

This lecture• So far

– Investment in eduction HC

• What else matters for individual HC?– Parental inputs to child HC– Schools

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Intergenerational transmission• Becker’s Woytinsky lecture book 1967

– Becker / Tomes – JPE 1976, JoLE 1986

• Parents (1) altruistic towards child (2)– Max log C1 + β log C2

• Perfect credit market– So invest in child education up to the point where

education returns = 1+r

• But– Contractual issue - incomplete market because of

lack of credible committment– Imperfect credit market 3

“Mobility”• Intergenerational mobility

– concerned with the relationship between the socio-economic status of parents and the socio-economic outcomes of their children as adults.

• Measured in a variety of ways– Income/earnings

– social class / status

– education. 4

Income mobility• Measures of intergenerational earnings and

income mobility– estimation of child (permanent) income against

parental (permanent) income– Log Yc = α + β log Yp + ……..

• Typically child observed when young and parent observed when old

• So include child and parental ages to control for different points in the lifecycle when income measured

• β is the IGE

• 1-β is integenerational mobility 5

ME in income

• Income in one (or several) year is a noisy measure of permanent income– Solon 1992 shows the bias is large

• Controlling for age of p and c may help– But evidence suggests not much

• Better (longer) data helps a lot

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Evidence• Many studies regress child income when adult

against parental income– Or child education, or health or …..

• Positive coefficient– Children’s income (or education ….) may be a consumption

good for the parents– Or credit constraints

• Some studies include parental education– Parental income coeff reduces

• But parental income may affect quality of education rather than quantity

• Parental income measurement error– Attenuates coeff 7

Evidence• Child income when adult often not observed

• So common (as in Becker/Tomes) to run– Schooling = controls + α · log parental income

• This captures a school quality effect– α ≈ 0.3– Small effect: if your twice as rich as me then your

kids will be 10% (α2) richer than mine– But ME might bias α towards 0– Children usually observed at early age in

lifecycle compared to parents– And its probably not linear

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Parents• Long history of research on intergenerational

mobility in social science– Earnings elasticity of father and son’s earnings:

• 0.40 - 0.50 in US (Solon, 1999), 0.60 in UK (Dearden et al 1997)

– Elasticity of educational mobility:• 0.25 to 0.40 in UK (Dearden et al.,1997)

• Mechanism?– Is it causal?– Is it parental education or income or both that

matters?

• UK policy context– Raising min SLA to 18, abolish child poverty

Wider context• Private returns to education widely studied

– High returns suggest possible underinvestment– So encouraging more human capital formation

might be welfare improving

• Growing literature on social returns:– Health and education

• Deaton and Paxson (1999), Lleras-Muney (2002).• Currie and Moretti (2002) – Mother’s education and

child birth weight in developing world (and US).

• Children’s human capital– An externality of sorts

• Survey of correlation studies by Haveman and Wolfe (JEL 1995) suggests strong associations

Intergenerational Transfer: Nurture, Nature, or what?

• Better educated are better at parenting– Higher home productivity as well as in the paid

marketplace

• Better educated make better investments– Including investing in the human capital of their

children

• Better educated are better peers– Cultural transmission

• Better educated have better genes– Unobserved characteristics of the parents may

be genetically transmitted to the children.

Literature ReviewChildren of identical twins• Eliminates (half of) the nature effects?

– As genetically alike as siblings – but cousins – so (slightly) different nurture

• Behrman and Rosenzweig (AER 2002, 2005) and Antonovics and Golberger (AER 2005)– Differences between the children of US MZ twins

• Small effect of father’s education, no effect of mother’s

– But terrible data– Bingley et al (2009): Parental Schooling and Child

Development: Learning from Twins Parents. SFI WP– Much better data

• Conventional effects of DZ mother’s education

• no effect of MZ mothers

Literature ReviewAdoptees• Eliminates the nurture effect?

– But selective adoption? Differential treatment?

• Mostly small samples– Sacerdote (2002), Dearden et al (1997)

• Small effect of adoptive father’s educ on adopted sons• About the same as on natural sons

• Two bigger datasets control for selection– Sacerdote (2007)

• Korean adoptees randomly assigned to US parents• Some impact of adopted mother’s education

– But very small when father’s education included

– Bjorklund et al (QJE 2006)• Swedish data registers

– Use pre-adoption info to control for selection– Finds post-adoption mother’s education matters (a little)

Literature Review Instrumental Variables

• Identifies causal (nurture) effect?– Most studies focus on RoSLA as an IV– Only one study estimates effects on completed schooling

• Children and parents matched from registers

• Black, Devereux and Salvanes (AER, 2005) – Cross sectional variation in SLA in Norway

• Uses completed schooling

– OLS supports evidence of impact, IV does not • but (weak) evidence of mother/son influences• Effect of 0.12 years for low education sample

Literature Review Instrumental Variables

• Early outcomes– Children and parents in same household

• Oreopoulos, Page and Stevens, (JoLE 2006) – Cross sectional variation in Min SLA in USA:

• Outcome is grade repetition:– OLS and IV

• Significant effects for sum of parent’s educations– Insignificant when entered separately

• Other studies– Grade repetition in HE

• Carneiro et al (2007)• Maurin and McNally (2008)

– Suggestive of an effect that parental HE has an effect– But weak IVs

Holmlund, et al, JEL 2011• One large Swedish dataset• Three identification strategies

– Twins, Adoptees and IV (RoSLA)• Twins

– zygosity of twins unknown• Identifies bounds• Small effects of mum’s educ (0-0.06), larger for dad’s (0.1-0.12)

• Adoptees– Some evidence of non-random assignment

• Large effects of mum’s education (0.11), none for dad’s

• IV– RoSLA coincided with other reforms

• And its a local effect• 0.06 years effect of mum’s education, none of dad’s

• Shea (2000): union status as IV – big effects of income on child’s subsequent wages (for

low educated fathers)• Carneiro/Heckman (2002): Credit constraints

– long term factors (parental education) matter for college attendance

• not current parental income

• Jenkins and Schluter (2002): school type– Correlation

• later income matters more than early income – but small effect compared to parental education

• Dearden et al (2002) : EMA– Matched group evidence

• Payment increases participation by about 6%

Does money matter?

What else matters?• Intergenerational correlation studies

– show that education and income matters (to some degree) for children’s living standards

• But what else matters (as well)?• Poor environment

– neighbourhood, housing, teen mum, marriage, schools, peers......

• Adds almost nothing to explanatory power

• Poor parental involvement– Low propensity to plan ahead, high time preference

• Adds about 1/3rd to the explanatory power

School resources• More resources generate better outcomes

– More money, equipment, teachers …….

• But quasi-experimental evidence is mixed– Money

• Some US evidence on redistributions of resources towards needier schools (eg Guryan 2000)

• But some show no effect. Dutch supplement to high immigrant schools (Oosterbeek et al, 2007).

– Equipment• Mostly sceptical evidence on IT and software

– Teachers (class size)• Some large and some small effects• But almost no work on what really matters

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Background to class size• Test score outcomes dominate literature

– Short trem outcome

• Historical OLS/x-tab focus– but CS likely endogenous

• Experiments– Effective randomisation?

• RD / IV “Maimonides’ rule” or demographics– Usually the rule is “fuzzy” so use IV not RD– Uses variation at one grade only– Uses school average CS– Window size – precision vs bias trade off 20

CS variation | C (D ± ε) samplesMaimonides’ (Angrist/Lavy) method

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CS

D

Cohort size

D 2D

3D

ε

D/2

Cohort variation | classes samplesIV (Hoxby) method

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CS

D

Cohort size

C=1 C=2 C=3 C=4

Seminal studies of the causal effect• STAR data - Krueger (QJE 99)

– large significant and lasting (???) effects of lower CS • K, K+1, K+2, K+3 (0.20σ, 0.28σ, 0.22σ, 0.19σ)

– No effects of classroom assistant - sorry

• Maimonides’ rule - Angrist and Lavy (QJE 1999) – Finds similarly large effects of CS cuts in

• K+4, K+5 (0.17σ, 0.26σ)

• Cohort size - Hoxby (QJE 2000)– Connecticut local cohort size variation as IV– Discontinuity from mandated CS caps

• FE - Rivkin et al (Econometrica 2005)– Texan administrative database 23

Recent studies• Browning and Heinesen, "Class size, teacher hours

and educational attainment", Scan JE (2008)• Leuven, Oosterbeek, and Rønning, “Quasi-

experimental Estimates of the Effect of Class Size on Achievement in Norway”, Scan JE (2008).

• Fredriksson, Öckert, and Oosterbeek, “The long-term effects of class size”, QJE (2012)

• Chetty, Friedman, Hilger, Saez, Whitmore Schanzenbach and Yagan “How does your kindergarten classroom affect your earnings?”, QJE 2012

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Issues• Focus has been on education outcomes

– not long term economic effects

• Little work on long term effects of CS– Frederiksson / Chetty QJE papers

• Structural modellers (Keane etc) object to exclusion of other inputs into educational production– Inputs probably negatively correlated with CS– Parents (and maybe teachers) compensate for

CS• Appropriate some of the benefits of small CS 25

Bingley and Walker IZA WP• Reconcile existing estimates• Estimate direct causal effect of CS on

earnings– we can now do this (SSIV)

• We estimate the direct effect of CS on education quantity (ie on S)– permanent effect of CS

• Supplement with MZ twin-based causal estimates of the effect of S on earnings

• Address parental substitution - a bit26

Contrast with previous studies• Previous work mostly estimates CS effect

on (early) test scores– then supplement this with (indirect) correlations

between early test scores and later ones– and corrs between later ones and earnings– Krueger/Whitmore find (weak) corr of early

score with sitting college entrance test (blacks)

• But there is little evidence that there is a long term causal effect of test scores.

• Not much effect of CS on wage rates– Chetty et al: no sig effect (but tries hard)– Frederiksson et al: sig effect only for rich kids27

Our methodRD/IV plus SD• CS driven by rule and by cohort size

– Additional teacher for every (about) 25th child

• Sibling differencing– Differences out family fixed effects– But sibs do not have same ability

• Combine RD/IV with SD– Sibs face different cohort sizes

• Identifying assumption– Parents assumed not to change schools

according to closeness to D28

Danish data• Income data comes from tax returns• Education data from institutions• But we have few observations where we can

observe CS and test scores– Scores at 16 only available from 2001

• We have even fewer observations of people with CS, test scores and incomes in work– Only very young workers

• So we cannot (quite yet) observe effects of CS on incomes directly

• And, as usual, SD increases CS ME– IV actual CS using rule driven CS

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“Child - centric” database• Merged administrative registers

– Enrolled in 8th grade 1981-1990– Left education pre 2000 – same Mum, Dad, school, neighbourhood– 2+ school age children (up to 9 years apart)

• 300k between-sibling differences • about 1000 schools (grade 1-9)

– Includes a neighbourhood peer, and school peer– Geographical information

• Estimate effects of CS on S– Danish Maimonides’ rule is 27

• But effectively 25 30

Distribution of school size

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Summary statistics

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Class size Diff from mean

Frequency % mean std.dev. mean std.dev.

# Siblings

2 251050 83.9 20.17 2.49 1.167 0.937

3 43578 14.6 20.14 2.53 1.383 1.085

4 4136 1.4 19.98 2.56 1.492 1.154

5 435 0.15 19.89 2.62 1.526 1.212

6 84 0.03 18.88 2.94 1.515 1.054

Female 147839 20.16 2.49 1.201 0.963

Male 151444 20.16 2.50 1.206 0.971

Subsequent children 158097

20.09 2.53 1.215 0.976

First child 141186 20.24 2.46 1.191 0.958

Headline estimatesDependent variable is S (years of schooling)

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Family Averages Sibling differences

Log Class size 0.6958 0.0489

0.5082 0.0539

-0.0454 0.0292

-0.0808 0.0314

Male - -0.0337

0.0149 - -0.1946

0.0066

First child - 1.9115

0.945 - 0.3319

0.0099

Age 1 August - -0.1437

0.0020 - -0.0518

0.0010

Intercept 5.0631 0.1466

28.3563 0.3815

7.2629 0.0876

15.9141 0.2099

R-squared 0.0014 0.0541 0.6612 0.6661

# observations 299283 299283 299283 299283

# families 141186 141186 141186 141186

Headline estimates (of 5% ΔCS)RD (vary ε) vs IV (vary window centre)

IV 12 15 18 21 24 RD

CS -0.081 -0.089 -0.112 -0.133 -0.179 -0.223

se 0.031 0.027 0.022 0.016 0.014 0.011

R2 0.67 0.68 0.70 0.72 0.74 0.75

RD ±1 ±2 ±3 ±4 ±5 ±6

CS -0.272 -0.241 -0.236 -0.230 -0.227 -0.223

se 0.091 0.055 0.022 0.017 0.013 0.011

R2 0.51 0.60 0.69 0.71 0.74 0.75

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Why do parents like lower CS?• Parents love their children

– They like it when their kids get more resources– So switch own resources to sib who gets the

bigger CS

• If parents compensated completely for bigger CS we would observe no CS effect on child outcomes

• CS neg corr with maternal work hours – So parents also appropriate part of the benefit of

lower CS

• Parents of bigger / more closely spaced sibships may find it harder to compensate?– Domestic time is limited 35

Sibship size and spacing

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What is -0.25 an estimate of?• Probably upper bound on the average effect

– 0.25 of (σS = 2.5) ≈ 0.6 σS

• Effect of change in (log) 8th grade only– But we can do every grade

• For the first 4 grades the effects are larger

– And we know x-year corr in CS

• Simulating moving from 27 rule to 25 rule– reduce CS by about 1 in all years (about 5%)

• Raises S by about ¼ year• But adds approx 10% to payroll for 8.25 yrs• NPV about 200k Dkkr pc 37

BJW vs Krueger CBA• Krueger = causal effect * correlation * correlation

• Finds Benefits ≈ Double the costs

• BJW has a causal effect estimate of CS on S– But needs an estimate of causal effect of S on income

• Twins– Estimate the effect of difference in S on the difference

in their incomes– 1 year ΔS → 8% Δ Income

• Then – ΔIncome/ΔCS = ΔS/ΔCS x ΔIncome/ΔS = ¼ x 0.08

• PV of 2% of 400k dkr pa at δ=5% ≈ 150k dkr– Benefits ≈ ¾ costs

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Conclusions• 600k sibs => CS has small effects on S

– 5% smaller classes → ¼ year more S• Precise and persistent effect

• 30k twins over 25 years used to estimate causal effect of S– returns to education 8% and precise

• Unit change in CS → 2% rise in lifetime incomes– but DK teachers are expensive

• So CBA → low payoff to ΔCS on average• But large payoff if CS reduction could be

targeted on low income households …39

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Next• Crime

• Becker, Levitt, and other research – on crime and punishment etc.– gun control– Abortion– Drug use– etc

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