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Labor Economic Lecture 10: Human Capital III

Daeho Kim

The Ohio State University Spring 2017

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 1 / 1

Human Capital

I. Theory of human capital as an investment

II. Is education a good private investment?

A. Basic facts for U.S.

B. Empirical Estimate of Returns to Education

C. Heterogeneous Benefits and Costs of Education

III. Is education a good social investment?

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 2 / 1

Homogeneous Treatment Effect (Returns to Educ.) ≡ θ

Yi = α + θ ·Ti + Ui (1)

Omitted Variable Bias: Cov(Ti,Ui ) 6= 0

Conventional wisdom: OLS biased up due to positive ability bias

Angrist and Krueger (1991) use instruments (quarter-of-birth) to reduce ability bias

Ashenfelter and Krueger (1994) use twin differences to reduce ability bias, and use cross-reports as IV to reduce measurement error bias

Findings: IV estimates are greater (often 30% or more) than OLS estimates: θ̂IV > θ̂twin > θ̂ols ≈ 8 10%

Why? Heterogeneous benefits/costs of educ.? (Heterogeneous T.E.?)

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 3 / 1

Heterogeneous Treatment Effect (Returns to Educ.) ≡ θi

Yi = α + θi ·Ti + Ui (2)

θi varies over i (allows for the return to educ. to vary across people)

Can we identify the Average Treatment Effect: E [θi ] = θ

Example: Returns to college for individual i = θi

f (θi ) population density function

c = constant marginal cost of going to college

If θi ≥ c, go to college (Ti = 1) If θi < c, don’t go to college (Ti = 0)

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 4 / 1

ECON 5850: Labor Economics Lecture 10: Human Capital III

[ ]iE θθ =  Average Treatment Effect (ATE) [ ]1|1 == ii TE θθ  Average Treatment Effect on the treated (ATT) [ ]0|0 == ii TE θθ  Average Treatment Effect for untreated (ATU)

c = Marginal Treatment Effect (MTE) – i.e., effect on the marginal person Implication: people with higher benefit of education get more schooling Selectivity Bias  Cov(Ti, θi) > 0 Ti = 1{ θi > c} − Pure “Roy” model: all variations in choice due to heterogeneous benefit (θi) − We CANNOT identify the Treatment Effect of going to college without strong

assumptions − Can’t find even two people with different educ. levels but otherwise identical Ti = 1{θi > ci} − Generalized Roy model: some variations in choice due to heterogeneous cost

(ci) − If costs are uncorrelated with θi (and other unobservables), one can identify

treatment effect (returns to college) using costs ci as instrumental variable − Can find people with the same benefits but with different levels of education

θ = E [θi ]: Average Treatment Effect (ATE)

θ1 = E [θi|Ti = 1]: Average Treatment Effect on the treated (ATT)

θ0 = E [θi|Ti = 0]: Average Treatment Effect for untreated (ATU)

c = Marginal Treatment Effect (MTE) i.e., effect on the marginal person

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 5 / 1

Heterogeneous Treatment Effect (Returns to Educ.) ≡ θi

Implication: people with higher benefit of education get more educ. Cov(θi,Ti ) 6= 0 ⇒ Selectivity Bias

Ti = 1{θi > c}: Pure “Roy” model All variations in choice due to heterogeneous benefit (θi )

CANNOT identify the T.E. of going to college w/o strong assumptions

Can’t find even two people with different educ. but otherwise identical

Ti = 1{θi > ci}: Generalized Roy model

some variations in choice due to heterogeneous cost (ci )

If costs are uncorrelated with θi (and other unobservables), one can identify treatment effect using ci as instrumental variable

Can find people with different levels of education but same benefits

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 6 / 1

Heterogeneous Effect of Education

Yi = α + bi ·Si + Ui (3)

Yi : log of earnings Si : years of education schooling bi : return to education for person i

Cov(Si,Ui ) 6= 0 ⇒ omitted variables bias

Cov(Si,bi ) 6= 0 ⇒ selectivity bias

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 7 / 1

C. Heterogeneous Benefits and Costs of Education (simple graphical analysis)

What causes variation in educational attainment in the population?

– Ability (ai ), Marginal benefits (bi ), Marginal costs (ci )

Earnings production function: gi (Si ; ai,bi )

– Higher ai ⇒ higher Yi at each level of Si (higher y-intercept at Si = 0) – Higher bi ⇒ steeper relation between Yi and Si – bi falls as Si increases ⇒ concave production function: gi (Si ; ai,bi )

Cost function ≈ “indifference” curves: hi (Si ; ci ) – Prefer higher Yi and less Si (education is costly and painful)

– Higher ci ⇒ steeper relation between ci and Si – ci rises as Si increases ⇒ convex cost function: hi (Si ; ci )

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 8 / 1

C. Heterogeneous Benefits and Costs of Education (simple graphical analysis)

ECON 5850: Labor Economics Lecture 10: Human Capital III

Case 1: No heterogeneity in a, b, and c across people − Prediction: everyone gets same level of education − Rejected by data

Schooling S*

g(S; a,b) = production function

h(S; c) = cost/indifference curve

Case 2: Only a varies across people − ak > aj (type-k has higher ability) − Prediction: everyone still gets same level of education since M.B.’s and M.C.’s

are same at optimal choices – i.e., tangent point between production function and cost/indifference curves

Schooling Sj*=Sk*

gk(S; ak,b)

gj(S; aj,b)

h(S; c)

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 9 / 1

C. Heterogeneous Benefits and Costs of Education (simple graphical analysis)

Example: two types of people in population

type-j: (aj,bj,cj )

type-k: (ak,bk,ck )

What kinds of MB’s and MC’s can explain the empirical findings?

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 10 / 1

Case I: No heterogeneity in a, b, and c across people

Prediction: everyone gets same level of education Rejected by data

ECON 5850: Labor Economics Lecture 10: Human Capital III

Case 1: No heterogeneity in a, b, and c across people − Prediction: everyone gets same level of education − Rejected by data

Schooling S*

g(S; a,b) = production function

h(S; c) = cost/indifference curve

Case 2: Only a varies across people − ak > aj (type-k has higher ability) − Prediction: everyone still gets same level of education since M.B.’s and M.C.’s

are same at optimal choices – i.e., tangent point between production function and cost/indifference curves

Schooling Sj*=Sk*

gk(S; ak,b)

gj(S; aj,b)

h(S; c)

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 11 / 1

Case II: Only a varies across people

aj < ak (type-k has higher ability) Prediction: Prediction: everyone still gets same level of education Rejected by data

ECON 5850: Labor Economics Lecture 10: Human Capital III

Case 1: No heterogeneity in a, b, and c across people − Prediction: everyone gets same level of education − Rejected by data

Schooling S*

g(S; a,b) = production function

h(S; c) = cost/indifference curve

Case 2: Only a varies across people − ak > aj (type-k has higher ability) − Prediction: everyone still gets same level of education since M.B.’s and M.C.’s

are same at optimal choices – i.e., tangent point between production function and cost/indifference curves

Schooling Sj*=Sk*

gk(S; ak,b)

gj(S; aj,b)

h(S; c)

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 12 / 1

Case III: Only a and b vary across people

ak > aj and bk > bj (type-k has higher ability and higher MB) Prediction: type-k gets more education than type-j OLS estimate greatly overstates true return to educ. for both types

ECON 5850: Labor Economics Lecture 10: Human Capital III

Case 3: Only a and b vary across people − ak > aj and bk > bj (type-k has higher ability and higher M.B.) − Prediction: type-k gets more education than type-j − OLS estimate greatly overstates true return to education for both types

Schooling Sj*

gj(S; aj,bj)

gk(S; ak,bk)

Slope = b̂ ols

Sk*

True bk ≈ b̂ IV

True bj ≈ b̂ IV

h(S; c)

Case 4: Only c varies across people − ck < cj (type-j has higher M.C.’s and/or distaste for education) − Prediction: type-k gets more education than type-j − OLS estimate close to average effect of education (Average Treatment Effect) –

still understates (overstates) true return to education for type-j (type-k)

Schooling Sj*

aj = ak

Slope = b̂ ols

Sk*

g(S; a,b)

True bj = similar to b̂ IV = True bk

hk(S; ck)

hj(S; cj)

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 13 / 1

Case IV: Only c varies across people

ck < cj (type-j has higher MC and/or distastes for education) Prediction: type-k gets more education than type-j OLS understates true return to educ. for type-j, overstates for type-k, Can explain empirical findings

ECON 5850: Labor Economics Lecture 10: Human Capital III

Schooling Sj*

gj(S; aj,bj)

gk(S; ak,bk)

Slope = b̂ ols

Sk*

True bk ≈ b̂ IV

True bj ≈ b̂ IV

h(S; c)

still understates (overstates) true return to education for type-j (type-k)

Schooling Sj*

aj = ak

Slope = b̂ ols

Sk*

g(S; a,b)

True bj = similar to b̂ IV = True bk

hk(S; ck)

hj(S; cj)

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 14 / 1

Case V: a, b, and c vary across people

ak > aj , bk > bj , ck < cj (k has higher ability& MB, but lower MC) Prediction: type-k gets more education than type-j If c varies enough, then bIV > bols for those with higher c (type-j) Can explain empirical findings

ECON 5850: Labor Economics Lecture 10: Human Capital III

Case 5: a, b, and c vary across people − ak > aj, bk > bj, and ck < cj (type-k has higher ability and M.B., but lower M.C.) − If c varies much more than b, then olsIV bb ˆˆ > when instrument affects education

of those who face higher c (type-j)

Schooling Sj*

ak Slope = b̂ ols

Sk*

Slope = b̂ IV

hk(S; ck)

hj(S; cj)

gk(S; ak,bk)

gj(S; aj,bj)

− Can explain empirical findings − May imply that financial constraints (i.e., imperfect lending markets or

imperfect information) matter in United States − Government may be “under” investing in education − Likely to be even more important in developing countries

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 15 / 1

Case V: a, b, and c vary across people

ECON 5850: Labor Economics Lecture 10: Human Capital III

of those who face higher c (type-j)

Schooling Sj*

ak Slope = b̂ ols

Sk*

Slope = b̂ IV

hk(S; ck)

hj(S; cj)

gk(S; ak,bk)

gj(S; aj,bj)

− Can explain empirical findings − May imply that financial constraints (i.e., imperfect lending markets or

imperfect information) matter in United States − Government may be “under” investing in education − Likely to be even more important in developing countries

May imply that financial constraints matter in United States (i.e., imperfect lending markets or imperfect information)

Likely to be even more important in developing countries

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 16 / 1

III. Is Education a Good Social Investment?

Human capital theory ⇒ education increases productivity of workers ⇒ high estimate of return to education ⇒ good social investment

Signaling theory ⇒ education is just a (costly) signal of one’s ability (imperfect information on worker’s ability) ⇒ bad social investment; does not enhance productivity (just a label)

Signaling? unlikely in studies we have covered

– Compulsory law (quarter-of-birth) study: unclear how staying in school until age 16 is signal of ability

– Twins study: ability held constant and education differences are small

Signaling could be important for GED, MBA (credentials)

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 17 / 1

III. Is Education a Good Social Investment?

School Quality?

– Several studies find association between school inputs (class size, teacher quality) and wages later

– Consistent with inputs having productive effect (quality of primary and secondary schools unobserved to employer – could not be signaling)

– Could partially explain heterogeneity in estimated returns to education – i.e., people attending higher quality schools may have higher returns to education

– Evidence that racial convergence in school quality in segregated South between 1920 and 1940 led to convergence in racial earnings gap in 1960s

Labor Economics (ECON 5850) Lecture 10: Human Capital III Spring 2017 18 / 1