The Social Value of Education

Robert Topel

University of Chicago

Economists (and others) have generally had little success in estimating the social effects of different investments, and, unfortunately, education is no exception.

Becker, Human Capital (1975)

Social vs. Private Returns

• The private, monetary return to education is one of the most widely studied empirical magnitudes in economics– Consensus: returns are substantial– Appx. 8-15% per year of schooling– 4 years of college raises earnings by about

65%, or a return of over 13%/year

• Why is public funding virtually universal?

Externalities

• When education of one individual confers external benefits (costs) on others, there is a positive economic case for encouraging (discouraging) education

• Private return to schooling may understate the full social benefit of education

A Taxonomy

• Private = Social– Education benefits only the individual– No compelling case for public participation

• Private < Social– Individual’s education benefits others– Public expenditure can enhance efficiency

• Private > Social– Education merely redistributes from poor to

rich

Elements of Private Returns

• Increased individual market productivity• Improved non-market productivity

– Home productivity– Consumption decisions– Production of children’s human capital

• Improved health & longevity• Education as consumption

– Enables consumption of HK goods (ideas)– Matching & assortive mating

Elements of Social ReturnsPrivate < Social

• Social network externalities in production– Education raises the level of economic activity by

more than its private return

• Education & economic growth– The level of education raises economic growth

because educated people produce ideas

• External benefits through social programs– Health– Other income transfers– Equity as a public good

Private < Social(Cont)

• Crime

• Network externalities in consumption

• Voting

• Other “2nd best” considerations– Distorted incentives to invest– Progressive taxes– Artificial compression of skill differentials

Elements of Social ReturnsPrivate > Social

• “Signaling” value of education– Education as a screening device– Private value as a signal, even if no impact on

productivity– No social gain

Measuring Private Returns: A Primer

• To calibrate social returns, we need a benchmark estimate of the size of private returns

• Micro-data on wages, schooling, experience

• Assume:– only cost is foregone earnings– % increase constant over lifetime

• Rate of return is % increase in earnings

Measuring Private Returns (cont)

• lnWi = Xiβ + Siρ + εi

– Si is years of schooling for person i

– ρ is private monetary rate of return

• Versions estimated world-wide– Returns 5-15%– Comparable to returns on other risky assets– Sources of bias empirically unimportant

Difference in Log Average Wages: College and High School Graduates, 1963-2000

Log-difference in mean wages, (college+)-(high school grads)

wagera

t

wageyear1963 1970 1980 1990 2000

.2

.3

.4

.5

.6

Changes in the Price of Skill

4 y

ea

r C

olle

ge

Pre

miu

m

Figure 2. College & Graduate Wage Premiums 1967-1997YEAR

Gra

du

ate

Pre

miu

m

70 75 80 85 90 95

1.40

1.50

1.60

1.70

1.80

1.90

1.55

1.65

1.75

1.85

1.95

2.05

2.15

Rising Returns: Implications for Social Policy

• Rising returns => increased scarcity of skills• Social policies that combat inequality may

exacerbate the problem– Artificial compression of wage distribution– Tax policies– Income redistribution

• Paradox: Public expenditure as “2nd Best” solution to encourage investment– Sweden– Australia

Sweden: Reduced Returns & Reduced Investment

Response of InvestmentF

ract

ion

with

So

me

Co

lleg

e

Fraction of 21-25 Year-olds with Some College 1963-1997YEAR

65 70 75 80 85 90 95

0.25

0.30

0.35

0.40

0.45

0.50

Educational Externalities

• Private returns as a benchmark– E.g. if private (Mincerian) return to a year of

schooling is 10%, does the social return exceed 10%?

• What are the sources of social returns?

• How could we measure them?

• Focus here: productivity and income

Sources of Externalities

• Higher level of productivity– E.g. Lucas (1988)—productive ideas from

social interactions– Productivity of cities– Growth of education leads to growth in output– Growth effect exceeds private return

• Higher growth of productivity– Education as producer of ideas– Level of education leads to growth of output

Growth Accounting and Social Returns

• Output per worker in country j

• With CRS

ln ln lnjt j jt jty h A

ln Pjt jt jt jth X S u

ln Ejt jt jtA S a

Schooling and Growth

• Tractable model of schooling and growth

• is the social return to schooling: private plus external benefits

• Is the impact of schooling on national output larger than it’s impact on individual?

P E

ln ( )P Ejt j jt jt jt jty X S u a

Table 1

The Effects of Education on Labor Productivity

Fixed Country Effects, 1960-1990 (N=719)

(1) (2) (3) (4)

Avg. Years of Schooling

0.23 (22.67)

0.10 (6.21)

Avg. Years of Primary Schooling

0.20 (10.28)

0.06 (2.05)

Avg. Years of Secondary Schooling

0.28 (7.62)

0.14 (5.76)

Country Effects Yes Yes Yes Yes

Year Effects No No Yes Yes

R2 .46 .46 .58 .59

Table 2 The Effects of Education on Productivity and Growth First-Difference Estimator at Various Growth Intervals (dependent variable: jty )

5-year growth (N=608)

10-year growth (N=290)

15-year growth (N=186)

20-year growth (N=101)

5-year growth, fixed effects (N=604)

10-year growth, fixed effects (N=290)

Education:

jtX 0.115 (5.07)

0.115 (5.07)

0.155 (5.23)

0.246 (5.73)

0.022 (1.32)

0.086 (2.85)

Years of schooling: jtX

0.003 (4.85)

0.003 (4.85)

0.003 (4.59)

0.004 (5.93)

0.004 (1.29)

0.009 (2.49)

Ln output/worker: ln jty

-0.004 (1.56)

-0.004 (1.56)

-0.005 (1.77)

-0.009 (2.26)

-0.043 (6.02)

-0.047 (6.03)

lnjt jtX y -0.060 (2.70)

-0.060 (2.70)

-0.041 (1.30)

-0.025 (0.57)

-0.020 (1.25)

-0.049 (2.00)

2R .332 .332 .391 .399 .287 .493 Notes: t-statistics in parentheses. Based on Summers-Heston Mark 5.6 and Barro-Lee (1993) data. All models include year effects. Effects of jtX are evaluated at the mean

level of ln jty .

Alternative Approach: States and Cities

• Does greater average education in an area raise individual earnings, after controlling for individual education?

• Is ? If yes, then taken as evidence of external benefits from education

• Estimates are all over the map

P E

i i i l iw X B S S

0E

Study Data Geogr.

UnitInstrument βE

Rauch (1993)

Census 1980

SMSA OLS 2.8-5.1%

Acemoglu and Angrist (2000)

Census 1950-1990

State Compulsory Schooling Laws, Quarter of Birth

0.4%

Moretti (various)

NLSY 1979, Census 1980-1990

SMSA Age Structure, Land Grant College, Plant opening

20-25%*

Education and Growth of States

• Relative growth of U.S. states—pattern of convergence

• Two issues– Has growth in education contributed to

economic growth of states? (Yes)– Has growth of education produced “spillovers”

that raised total productivity by more than the private returns to schooling? (Maybe)

910

1112

13(m

ean)

me

aned

uc

5.2

5.4

5.6

5.8

66.

2(m

ean)

logw

kwag

e

1940 1960 1980 2000year...

(mean) logwkwage (mean) meaneduc

Evoluation of mean log earnings and mean education

AL

AZ

AR

CA

COCT

DE

DC

FL

GA

ID

ILIN

IAKS

KY

LA

ME

MD

MA

MI

MN

MS

MO

MT

NE

NV

NH

NJNM

NY

NC

ND

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VT

VA

WAWV

WI

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.21

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Gro

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19

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-20

00

4.6 4.8 5 5.2 5.4 5.61940 Log Weekly Wage

Log Weekly Wages, 1940-2000Figure 1-a: Level and Growth of Wages

IV: (1950-2000, using 1940 values)

-0.62(0.08)

AL

AZ

AR

CA

CO

CT

DE

DC

FL

GA

ID

IL

IN

IAKS

KY

LA

ME

MD

MA

MIMN

MS

MO

MT

NE

NV

NH

NJNM

NY

NC

ND

OH

OKOR

PA

RI

SC

SD

TN

TX

UT

VT

VA

WA

WV

WI

WY

34

56

Gro

wth

19

40

-20

00

7 8 9 101940 Average Schooling

Average Years, 1940-2000Figure 1-b: Level and Growth of Schooling

IV:(1950-2000, using 1940 values)

-0.83(0.05)

.2.4

.6.8

(sd)

mea

nedu

c

.1.1

5.2

.25

(sd)

logw

kwag

e

1940 1960 1980 2000year...

(sd) logwkwage (sd) meaneduc

Standard Deviation of log(earnings) and Education

AL

AZ

AR

CA

COCT

DE

DC

FL

GA

ID

ILIN

IAKS

KY

LA

ME

MD

MA

MI

MN

MS

MO

MT

NE

NV

NH

NJNM

NY

NC

ND

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VT

VA

WAWV

WI

WY

.6.8

11

.21

.4L

og

Wa

ge

Gro

wth

3 4 5 6Schooling Growth

Log Weekly Wages and Average Yearsof Schooling, 1940-2000Figure 1-c: Growth in Wages and Schooling

OLS: 0.22(0.03)

AL

AZ

AR

CA

CO

CTDE

DC

FL

GA

ID

ILIN

IA

KS

KYLA

ME

MDMA

MI

MN

MS

MO

MT

NE

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NH

NJ

NMNY

NC

ND

OH

OK

OR PA

RI

SC

SD

TNTX

UT

VT

VA

WA

WV

WI

WY

-.2

-.1

0.1

.2.3

Gro

wth

19

40

-20

00

-.4 -.2 0 .21940 Level

Estimated State Specific Productvity, 1940-2000Figure 2-a: Level and Growth of TFP

Interpretation of the Evidence

• Data suggest that education “drives” growth, and that social return substantially exceeds the private return

• Yet growth in education may be correlated with other, unmeasured, factors that contribute to productivity– Unobserved talent– Changes in demand for skills– Quality of education

Deeper Look at the Data

• Isolate Total Factor Productivity as local effect on wages

• Control for environmental factors affecting “skills” of workers using state of birth– Controls for differences in skills or quality by

birth state and cohort

2-Stage Analysis

First Stage:

(X= Education and Experience Indicators)

Second Stage:

it it t lt bc itw X T u

0 *

'

( 1)

Elt lt

lt lt lt

T E D

a v h

AL

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AR

CA

COCT

DEDC

FLGA

ID

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INIA

KS

KY

LA

ME

MD

MA

MI MN

MS

MOMT

NE

NV

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NJ

NM

NY

NC

ND

OH

OK

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RI

SC

SD

TN

TX

UT

VTVA

WA

WV

WI

WY

-.1

-.0

50

.05

.1S

kill

3 4 5 6Schooling Growth

Growth in Estimated Skills and Mean Years of Schooling, 1940-2000Figure 2-c: Growth in Skills and Schooling

AL

AZ

AR

CA

CO

CT DE

DC

FL

GA

ID

IL IN

IA

KS

KYLA

ME

MDMA

MI

MN

MS

MO

MT

NE

NV

NH

NJ

NMNY

NC

ND

OH

OK

OR PA

RI

SC

SD

TNTX

UT

VT

VA

WA

WV

WI

WY

-.2

-.1

0.1

.2.3

TF

P G

row

th 1

94

0-2

00

0

-.1 -.05 0 .05 .1Skill Growth 1940-2000

Growth in Estimated Skills and State Specific Productivity, 1940-2000Figure 2-d: Growth in Skills and Local TFP

Education and Productivity Growth: U.S. States 1940-2000

10 yr growth 20 yr growth 30 yr growth 60 yr growth

.046(.017)

.026(.018)

.068(.019)

.040(.021)

.067(.017)

.036(.020)

.081(.021)

.023(.024)

1.23(0.44)

1.08(0.40)

1.01(0.34)

1.35(0.38)

R2 .894 .897 .952 .954 .978 .980 .248 .415

0E

lt t lt lt ltT B Educ e

Educ

l

Includes Year FE. No overlapping periods.Figures

Social Returns to Schooling: Where Do We Stand

• Evidence for “excess” social returns is, at best, mixed– Impact of education on TFP is greatly reduced

when growth of other skills is accounted for

• But evidence does indicate that social returns in economic growth are at least as large as private ones– Important contributor to convergence in

incomes and welfare

Other Issues

• Local investments in higher education

• Empirical evidence on the signaling hypothesis