HC-Lecture 1 Returns to Education

8/13/2019 HC-Lecture 1 Returns to Education

http://slidepdf.com/reader/full/hc-lecture-1-returns-to-education 1/43

Economics of Human Capital

Lecture 1

HC and the returns to educationIan Walker

Lancaster University Management [email protected]



Overview of lecture

• Explain the theoretical framework for thinkingabout the economics of education.

• Uncover evidence on the “returns to

education”

– Various methods

• Methods

– Revise your understanding of IV, DD, RDD,Matching

– See Angrist and Piscke “Mostly harmlesseconometrics”



Human Capital Theory I

• Theory (Becker (1964)) assumes that individualschoose s to maximise the discounted expectedvalue of their incomes net of the costs ofeducation.

• So, at the optimum s, the PV of the sth

year ofschooling equals the costs of the sth year ofeducation:

where r s is called the internal rate of return.• Optimal investment would imply that one would

invest in the sth year of schooling until if r s=i, the

market rate of interest.

1

1

1 1

T s s s

s st t s

w ww c

r



Human Capital Theory II

• If T is large then the LHS can be

approximated so that

• Then, if c s is sufficiently small,

• Thus one could estimate the returns to s

from seeing how log wages varies with

s.

1

1

s s

s s s

w ww c

r

11log log s s

s s s

s

w wr w w

w



Mincerian Specification

• Mincer (NBER 1974) assumed that r s is aconstant - so , where Y t is potentialearnings and ht is the proportion of period t spent acquiring human capital.

• During full-time education ht =1 so .

• For post-school years, Mincer assumes that ht declines linearly with experience, i.e

• So for x years of post-school work experiencewe get so

• Thus

t t t r Y hY

0

rs

sY Y e

0 0t h h h T t

0exp

x

x s t Y Y r h dt 20

0 0exp2

rs

x

hY Y e r h x x

T

2

0 0log 2 log 1 x xw rs rh x rh T x h X



Important assumptions

• Perfect credit markets – Can be accommodated

– Higher borrowing costs imply lower S*

• S* may be low because low ability• Or because of high r

• Leisure in the utility function

– Lifecycle hours and education jointly determined – Leisure lovers will invest in less S

– Little research on lifecycle framework

• Especially under uncertainty6



Early Empirical Work

• The availability of microdata and ease of estimationresulted in many studies which have simply added anerror term e~N(0, σ 2 ) and estimated the Mincer model byOLS.

• Mincer (1974) used 1960 US Census data and,assuming that x=A-s-6 , found that:

log w I = 6.2 + 0.107s + 0.081 x - 0.0012 x 2

which implies that: r = 0.107, h0 = (0.081/0.107) = 0.76,

and T = (0.107*0.76)/(2*0.0012) = 34 years. • Layard and Psacharopolous (REStuds 79) used the GB

GHS 1972 data and found r =0.097, h0 =0.94 and T =30.

• Thus, these early studies suggested large real returns.See recent papers in Labour Economics 98.



Extensions

• The Mincerian specification has been applied to

cross-section data, not only to estimate r , but

also to address questions such as:

– discrimination by race and by gender, – the effectiveness of training programmes,

– the effects of school quality,

– the return to language skills, and even

– the return to "beauty" (see Hammermesh and Biddle

(JoLE 1998 and AER 1994).



Empirical Problems IFunctional form

• Mincer ’s HCEF can be thought of as an approx

to a more general form:

• In practice researchers have added higherorder terms in S and A to the simple HCEF – Murphy and Welch (JoLE 90) F(.) was a high order

polynomial in A.

– Heckman et al (2001) 50 years of Mincer Equationsshowed AS interactions and S2 important

– In most datasets it would appear that minor

extensions to the simple HCEF captures age/earnings

profiles reasonably well

log ( , )w F S A e



Empirical Problems IIMeasurement of S

• The HCEF assumes linearity in S so that r is aconstant and that S is the relevant measure

• “ Credentials ” matter more than years of

schooling – the “sheepskin” effect – a wage premium for fulfilling

the final year of college, or high school.

• For example CPS post 90 now reports

qualifications rather than years. – Hungerford and Solon (REStats 87) show nonlinearities

– Park (EconLetters 99) estimates an effect of a HSdiploma is 9% and a degree is worth 21% (over and

above the return to the years of education required toacquire the qualification



Empirical Problems IIEndogeneity

• A typical Mincerian specification would be where X includes experience and experiencesquared along with other individual

characteristics. • OLS will be unbiased if the regressor are

exogenous.

• But endogeneity arises whenever

• This might occur for a number of reasons: – Measurement error

– Missing variables

– Ability – Im atience



Ability” bias

• A major pre-occupation has been the

potential for unobservable determinants of

schooling to be correlated with wages.

• That is, suppose:

then OLS on the wage equation would yieldunbiased estimates of r only if cov(ui e)=0.

i i i i

i i i

y X rS e

S Z u



Important issues

• One big issue has been endogeneity of S – coeff on S picks up not just the effect of S on w

• But also the effect of other factors not included that

are correlated with S (like “ability”, A)

– OLS biased upwards

• A smaller issue has been measurement error

– If S contaminated by ME then OLS coeff

“attenuated” (biased towards 0)

• Estimating returns to S (and unobserved

skills) over time has been a very big issue

13



Becker s HC Earnings Function

• Workhorse model of (log) wages• w i = X i β + αSi + ui where X includes a

quadratic in experience (or age)

• But ui = γ Ai + ei and if cov( Ai ,Si ) > 0 – then plim αOLS = α + γ(σAS

2/ σS2) > α if γ>0

• Note that if S = S + v (measurement error)

– then plim αOLS = α.(1 - σ2v / σ2S ) < α if σ2v > 0

• We (think we) have learned quite a lot

about all of this from IV studies

– But probably not the ATE of S on w 14



Minority issues

• A unit of S is the same for everyone – may be quality differences (correlated with S)

• α may also depend on S – Nonlinearity, qualifications, “sheepskin”

• “Separability” assumption – Effect of S on w is independent of age

– α is assumed independent of everything

– but it may depend on other things, αi =α(V i )+v i• Observed and unobserved heterogeneity

• V might include institutions and “grades”

• Some of v may be “luck”, some may be “productivity”

• We know very little about any of this 15





Motivation: understanding why?

• In our simple model – w i = X i β + αSi + ui

– where ui = γ Ai + ei and cov( Ai ,Si )>0

– then plim αOLS = α + γ(σAS2/ σS2)

• Rising var(w ), given S, X , β , and

unobserved A, could be due to:

– α higher returns to education – γ higher returns to unobservable skills

– σ e2 more measurement error in wages

– σ AS greater selectivity in schooling 17



Instrumental variables

Study Sample OLS

%

IV

%

Instruments

Angrist and Krueger

(1991)

US 1970/1980 Census: Men born

1920-29, 1930-39, 1940-49

7.0

(0.000)

10.1

(0.033)

Year * Quarter of Birth;

State * Quarter of Birth

Angrist and Krueger

(1992)

US 1979-85 CPS: Men born 1944-

53 (hence potential Vietnam War

draftees).

5.9

(0.001)

6.6

(0.015)

Draft Lottery Number *

Year of Birth

Card (1995) US NLS: Men aged 14-24 in 1966

sampled as employed in 1976.

7.3

(0.004)

13.2

(0.049)

Nearby college in

county of residence in

1966.

Butcher and Case

(1994)

US PSID 1985: White women

aged 24+

9.1

(0.007)

18.5

(0.113)

Presence of siblings

(sisters)

Uusitalo (1996) Finnish Defence Forces Basic

Ability Test Data matched to

Finnish income tax registers.

8.9

(0.006)

12.9

(0.018)

Parental income and

education, location of

residence.

Meghir and Palme

(1999)

Sweden –

Males 2.8

(0.007)

3.6

(0.021)

Swedish curriculum

reforms.

Duflo (1999) Indonesian – Males 7.7

(.001)

9.1

(0.023)

Indonesian school

reforms – school

building project.

Denny and Harmon

(2000)

ESRI 1987 Data – Males 8.0

(0.006)

13.6

(0.025)

Irish school reforms –

abolition of fees for

secondary schooling.



Instrumental variables

Data OLS IV Instruments

Dearden (1998) UK NCDS: Men 4.8%

(0.004)

5.5%

(0.005)

Family composition, parental

education, social class.

Harmon and

Walker (1995)

UK FES 78-86.

Males 16-64.

6.1%

(0.001)

15.2%

(0.015)

School leaving age changes.

Harmon and

Walker (1999)

UK GHS 92.

Males 16-64.

4.9%

(0.000)

14.0%

(0.005)

School leaving age changes

and educational reforms.

Harmon and

Walker (2000)

UK NCDS: Men 5.0%

(0.005)

9.9%

(0.019)

Measures of peer effects and

education system level

effect.



Alternatives to OLS estimation

• Eliminate“

ability bias”

by controlling for A – But A and S highly correlated

– And our measures of A are often affected by S

• Matching methods assume problem away

– No selection on unobservables• Unbiased estimate of α iff σ AS = 0 is true

• But γ not identified if σ AS = 0 is true

• IV – But IV estimation does not estimate ATE

– IVs may affect people observed from differentyears and cohorts differently• so interpretation of L ATE varies across time

20



Existing literature

• Juhn et al (JPE 1993) - rising var(w ) in US – When var(w ) rose, where, and for who

– Beaudry (JoLE 05), Lemieux (AER 06)

• Cawley et al in Arrow et al (eds) 2000

– A * S * t interaction - hard to identify

• But all US CPS studies problematic

– Because S imputed from data on “some

college”,“college

”, HS graduation

• Induces changes in ME in S

– And changes in w data• Workers have more complex remuneration in more

recent data 21



The twins solution

• Estimate returns to both S and A – over time (and across cohorts)

• Huge panel – identical MZ’s, fraternal DZ’s

– MZ’s may allow us to identify causal effect of S

• Small, but rising fast since early 90’s

– DZ’s then may allow us to infer returns to ability• Large, but falling slowly since early 90’s

• Measurement error problem in S – Important problem for us

– but qualifications are accurately measured

• Address endogenous ΔS with credible (?) IV – Suggests that “ability bias” in MZ diffs is small22



Twins methodology

• Δw i = ΔX i β + α ΔSi + γ Δ Ai + Δei

– where Δ is the within-twin pair difference

• If the twins are MZs, then we eliminate (?)

the unobservables, i.e. Δ Ai = 0 – and usually most ΔX ’s=0

– so regress Δw on ΔS for unbiased estimate of α

• But, within-twin differencing exacerbates MEin S

– ME in ΔSi may be large

• Use IV based on alternative measures of S 23



Existing MZ twins literature

24



Double trouble:Bound & Solon, Neumark (EconEducRev 1999)

• Measurement error in S – S=S*+v where S* is true S

• Differencing S data exaggerates ME bias

– Our S is “normed” from qualifications data

– so ME in ΔS is probably very large

• plim(αWT) = α(1 - r /(1-ρ))

– where r = σ2v/σ2

S , but ρ = cov(S1,S2) ≈ 1

• Need to use IV to deal with ME

– Princeton work uses cross-reported ΔS as IV

– We have lots of x-reports 25



More double trouble: • Why do identical twins differ in S?

• ΔS may not be random

– individual-specific component of A may remain• Need to instrument ΔS for this reason (even if ME=0)

– Education reforms may not work as IVs• Twins have same values of the Z’s?

– Family background probably won’t either• Twins have same

• Bonjour et al (AER 2004)

• But we (think we) do have an IV idea

– and DZ estimate of α provides tighter upper

bound on the true α than OLS does. 26



Bingley and Walker2: Dealing with measurement error

• S comes from admin registers – Low measurement error in qualifications

• So get unattenuated estimates of college premium

– But to get S we need to “norm” the quals data• High var(S) associated with any highest qual

• So we probably have very large ME in S

• Alternative measures of S

– Princeton work uses x-reported S • We have twin’s spouse’s S as well as

conventional x-reports from survey data

28



Bingley and Walker3: Dealing with endogenous ΔS

i

• S dif ferences may not be random – Individual component of A not differenced out

• Need an instrument to purge ΔSi of remaining

A diffs – something that affects twin 1’s S but not twin 2’s

• School size affects if twins can be separated

– Important in DK - teacher gets fixed in grade 1• Twins in 1-class school smaller Δ( ΔS) than in 2+ class

• Expect bigger effect from instruments for DZs

– Since more Δ Ai remains than for MZs

29



Danish data• Merge several administrative

databases via CPR• Use 1970 Census to link

children to mums

– dob identifies multiple births – 1970+ match via birth records

• About 1000 Danish multiplepregnancies each year

– More Danish triplets thanPrinceton has twins• Twins odds about 1 in 80

• Triplet odds about 1 in 800030



Twins sample selection

• Over ½ m twin-year working age obs

– Around 24k pairs over up to 25 years

– Drop the triplets, quads….

• Select MZs, same-sex DZs, age 25-55

• Select if earnings observed (at least twice)

between 1980-2005

• Select working full-time and full-year – to reduce the problem that we have only annual

earnings not hourly wage rate

• 4185 MZ pairs, 6343 DZ pairs31



Variables

• Income data comes from tax returns

– we don’t have good hours of work data

• Schooling data

– Not available for “special” schools

• Few IVF cases yet, and no immigrants• Zygosity questionnaire

– 4 “peas in a pod?” type questions

– 96% match to DNA in small subsample• Christensen et al (Twins Research 2003)

• Christensen et al (BMJ 2006)

– similar test scores at 16 as singletons• Even though they average 900 grams lighter

32





Distribution of ΔS

34

0

10

20

30

40

50

60

0 U to 1 U to 2 U to 3 U to 4 4 or more

%

Men DZ twin pairs

Men MZ twin pairs

Women DZ twin pairs

Women MZ twin pairs

B i lt



Basic resultstwins and singletons compared

• Pool data across waves, adjust std errs• Singleton (we have these too) estimates

– αmS=0.031 (0.0005) αf

S=0.037 (0.0005)

• Treating twins as singletons we get – αm

MZ=0.030 (0.0005) αf MZ=0.037 (0.0006)

– Almost same for DZs

• Twins are just like singletons

• IV (using twin spouse S as IV) – αm

MZ=0.065 (0.0011) αf MZ=0.054 (0.0014)

– Conclusion• Implied very low reliability – 0.5 for m, 0.7 for f35



Basic FE results – twin differences• Expect huge attenuation bias in OLS on twin

differences (ie FE estimation) – MZs αm= 0.005 (0.001) αf = 0.009 (0.001)

– DZs αm= 0.018 (0.001) αf = 0.025 (0.001)

• So FEIV estimates much higher, especiallyfor DZs

– MZs αm= 0.045 (0.010) αf = 0.044 (0.008)

– DZs αm= 0.095 (0.006) αf = 0.054 (0.006)

• Conclusion – Large returns (by DK standards) of 4½ % on

average over 80’s and 90’s36



Returns over time

• Rolling 10 year window over 1980-2002 – MZs yield αt (return to observed skills)

– DZs yield αt + γt (σAS2/σS

2)c

• where γ = return to unobserved skill

• (σAS2/σS

2)c is fixed for all members of cohort c

– So difference between MZ and DZ estimates is

proportional to return to unobserved skills

• We have a long panel

– So its also possible to distinguish cohort effects

37





Extension 2:Endogenous ΔS

• Problem that ΔS might be correlated with Δ A – A is not (entirely) a family effect

– So α biased upwards because of Δ A bias

• Need an IV for ΔS ( even if no ME)?• Usual suspects won’t work

– Need var that affects twin 1’s S but not twin 2’s

– Different classes• We don’t know if twins were separated

– But twins could be separated if 2+ classes

– 46% of schools have single class entry39



Extension 2:Endogenous ΔS

• Twins in 1-class schools have smaller ΔS – MZs Δ1,2+ ΔS = -0.30 male, -0.22 female

– DZs Δ1,2+ ΔS = -0.19 male , -0.14 female

• 1-class twins have same Δw | ΔS as 2-class – Classes affects w only through S

• IV estimation eliminates remaining A bias

• MZs αm = 0.040 (0.009) αf = 0.041 (0.009)• DZs αm = 0.043 (0.015) αf = 0.043 (0.021)

• Conclusion:

– very small Δ A-bias in MZ FE, larger in DZ FE40

E t i 3



Extension 3:Nonlinear effects

• Nonlinear schooling effects – interaction between twin average S and ΔS

– α(S) significantly decreasing in S

– No change in convexity over time• Returns to college vs high school

– No ME in college degree reporting• 1990’s returns to “Bachelor ” about 30%

• 1990’s returns to “Masters” about 15%

– Rising college premium over time• With strong cohort effects

– No rise in returns to unobserved skills41



Extension 4:Self and cross reported S

• Available from the new twins omnibus survey – Match to register data via CPR

• All DK twins included in survey

– Response rate 80%+ of pairs• Little attenuation when using conventional x-

reports as IVs for self-reported S• OLS MZs

αm= 0.038 (0.011)

αf= 0.039 (0.013)

• IV MZs αm = 0.041 (0.017) αf = 0.042 (0.019)

• Other useful information

– Childhood illnesses, birth weight, best friend’s

background and behaviour ...... 42



Conclusion

• There is a lot that we know (or can know)from the data we have – But there is a lot we still don’t know

• Only better data will enable us to know

more – Diminishing returns to econometric ingenuity

have set in

• With much better data there is not much

that cannot be known

43



Next

• Heterogeneity in returns

• Investment in post-schooling skills

• Externalities and peer effects• Intergenerational effects

– See Solon Handbook chapter

44

Documents

HC-Lecture 1 Returns to Education