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Education, Growth, and Income Inequality
Education, Growth, and Income Inequality
Education, Growth, and Income Inequality
Education, Growth, and Income Inequality
Education, Growth, and Income Inequality
Thijs van Rens2008, Review of Economics and Statistics
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A joint Initiative of Ludwig-Maximilians-Universität and Ifo Institute for Economic Research
Working Papers
EDUCATION, GROWTH AND INCOME
INEQUALITY
Coen Teulings
Thijs van Rens*
CESifo Working Paper No. 653 (4)
January 2002
Category 4: Labour Markets
CESifo
Center for Economic Studies & Ifo Institute for Economic Research
Poschingerstr. 5, 81679 Munich, Germany
Phone: +49 (89) 9224-1410 - Fax: +49 (89) 9224-1409
e-mail: office@CESifo.de
ISSN 1617-9595
¯
An electronic version of the paper may be downloaded
• from the SSRN website: www.SSRN.com
• from the CESifo website: www.CESifo.de
* We would like to thank Mikael Lindahl and Daniele Checchi for sharing their datasets.
We are also grateful to Robert Shimer, Giorgio Primiceri and Alan Krueger for helpful
comments.
CESifo Working Paper No. 653
January 2002
EDUCATION, GROWTH AND INCOME INEQUALITY
Abstract
When types of workers are imperfect substitutes, the Mincerian rate of return
to human capital is negatively related to the supply of human capital. We
work out a simple model for the joint evolution of output and wage dispersion.
We estimate this model using cross-country panel data on GDP and Gini
coefficients. The results are broadly consistent with our hypothesis of
diminishing returns to education. The implied elasticity of substitution fits Katz
and Murphy’s (1992) estimate. A one year increase in the stock of human
capital reduces the rate of return by about 2 per cent. The combination of
imperfect substitution and skill biased technological change closes the gap
between the Mincer equation and GDP growth regressions almost
completely.
JEL Classification: E20, J24, O10, O15.
Coen Teulings
Tinbergen Institute
Erasmus University
Burg. Oudlaan 50
3062 PA Rotterdam
The Netherlands
Teulings@few.eur.nl
Thijs van Rens
Princeton University
Department of Economics
001 Fisher Hall
Princeton NJ 08544-1021
U.S.A.
1
I nt r oduct ion
If workers wit h various levels of educat ion were perfect subst it ut es, relat ive wages would
be independent of t he dist ribut ion of human capit al. However, st udies int o t he subst it ut ability of worker types, for example K at z and Murphy (1992), have shown t hat
t his is not t he case. T hen, a simple economic argument est ablishes t hat t he Mincerian
rat e of ret urn should be negat ively relat ed t o t he average years of educat ion among t he
workforce. Raising t he average years of educat ion in t he economy makes low-skilled
workers more scarce, raising t heir wages, while at t he same t ime increasing t he supply
of highly educat ed workers, t hereby reducing t heir wages. This mechanism reduces t he
ret urn t o human capit al.
T he relat ion between GDP and educat ion at t he aggregat e level is a simple re‡ect ion
of a Mincerian earnings funct ion at t he micro level, when ext ernalit ies of educat ion can
be ignored, as is suggest ed by a number of recent st udies (Heckman and K lenow, 1997;
Acemoglu and Angrist , 1999). T his simple t heory of imperfect subst it ut ion between
workers wit h di¤erent levels of human capit al has joint implicat ions for GDP and income
dispersion. The e¤ect of an increase in t he mean level of educat ion on GDP should
decline wit h t he level of educat ion. Hence, we expect a negat ive second order e¤ect of
increases in t he educat ion level on growt h. Since wages are t he main source of income for
most families, measures of income inequality should be posit ively relat ed t o t he ret urn t o
educat ion. T he average level of educat ion in t he economy a¤ect s t he ret urn t o schooling
negat ively. Hence, it compresses t he wage dist ribut ion. The main idea of t his paper is
t o simult aneously est imat e t he e¤ect of t he average educat ion level on GDP and income
dispersion.
T he applicat ion of t he Mincerian earning funct ion as t he driving force in t he relat ion
between GDP and educat ion put s t his paper in t he ext ensive st ream of research int o t he
cross count ry relat ion between educat ion and growt h. In Barro and Sala-i-Mart in (1999),
a higher educat ion level makes t he labor force more able t o deal wit h t echnological
innovat ions, yielding a relat ion between t he level of human capit al and t he growt h of
out put . Barro and Sala-i-Mart in found indeed t hat t he level of educat ion has a st rong
and signi…cant e¤ect on fut ure GDP growt h, as did Benhabib and Spiegel (1994) in an
earlier st udy. T he e¤ect of t he growt h in educat ion on t he growt h of out put , condit ional
on t he e¤ect of t he level of educat ion, is insigni…cant in t heir regressions. T hese result s
cast doubt on t he relevance of t he Mincer equat ion for t he aggregat e level, increasing
t he popularity of human capit al based endogenous growt h models.
Following K rueger and Lindahl (2000), we argue t hat t hese conclusion are due t o a
2
number of misspeci…cat ions. Measurement error at t enuat es t he coe¢ cient for t he growt h
in educat ion. However, just Krueger and Lindahl’s argument does not …ll t he whole
gap between t he Mincer equat ion and t he GDP growt h regression. T he long run rat e of
ret urn t o educat ion remains above any reasonable est imat e. Gallup, Sachs and Mellinger
(1999) show t hat geography mat t ers for GDP. Proximity t o t he sea for t ransport and
a t emperat e climat e t o avoid t ropical diseases are great advant ages t o a count ry. A
combinat ion of …xed e¤ect s due t o geography, imperfect subst it ut ion between types of
labor, and skill biased t echnological progress brings us much closer t o a full reconcilliat ion
of t he GDP dat a and t he Mincer equat ion. Count ries wit h a favorable geography are
richer and can t herefore invest more in human capit al. Hence, human capit al variables
pick up part of t he favorable …xed geography e¤ect . The init ial advant age in human
capit al increases in t he course of t ime due t o skill biased t echnological progress. T his
gives t he impression t hat educat ion yields a higher growt h of GDP, not a higher level.
Previous st udies on t he relat ion between inequality and growt h have focused on t he
e¤ect of t he one upon t he ot her, some papers arguing t hat growt h reduces inequality
(t he so called K uznet s curve), ot hers highlight ing t he e¤ect of inequality on growt h
(see Bénabou 1996 for a survey). Our approach di¤ers from t his lit erat ure, in t hat
we t ake bot h inequality and growt h as dependent variables, simult aneously det ermined
by t he level of human capit al. If t he average educat ion level has a negat ive e¤ect on
inequality and a posit ive e¤ect on growt h, as implied by our model, t hen t his provides an
explanat ion for t he negat ive correlat ion between inequality and growt h t hat has spurred
t his lit erat ure.
T he t heoret ical framework we apply is derived from an assignment model wit h het erogeneous workers and het erogeneous jobs, see Teulings (2001). Highly educat ed workers have a comparat ive advant age in complex jobs. The ret urn t o educat ion is t herefore
higher in more complex jobs. When t he supply of highly educat ed workers increases,
t here are insu¢ cient complex jobs for t hem. Some high skilled workers have t o do less
complex jobs, where t heir human capit al has a lower ret urn. This yields a negat ive
relat ion between t he aggregat e supply of educat ion and it s Mincerian rat e of ret urn. We
t est t his relat ionship by ent ering a second order t erm in educat ion in a GDP regression.
Furt hermore, educat ion should ent er negat ively in a regression of t he variance of log
wages, since a reduct ion of t he Mincerian rat e of ret urn compresses wage di¤erent ials.
T he simple model we present in t he next sect ion formalizes t hese ideas. We also use our
est imat es t o derive t he compression elasticity: t he percent age decline in t he ret urn t o
human capit al per percent increase in t he value of it s st ock. T his concept relat es our
result s t o K at z and Murphy’s (1992) est imat e of t he elast icity of subst it ut ion between
3
low- and highly skilled workers, providing a check on t he int erpret at ion of our est imat ion
result s.
Our empirical work uses Barro and Lee’s (1999) panel dat a on GDP and educat ion
and Deininger and Squires’ (1996) dat a on Gini coe¢ cient s for 100 count ries over t he
period 1960-1990. Alt hough t he micro labor lit erat ure has shown t hat t he log-linear
Mincerian wage equat ion is st rikingly robust (see Card 1999 for a survey), t he est imat ed
ret urns for di¤erent count ries vary subst ant ially (Psacharopoulos 1994; Bils and K lenow
1998). T his paper exploit s t his variat ion t o est imat e t he degree of subst it ut ability
between worker types. We will also present direct evidence of diminishing ret urns t o
educat ion from a cross sect ion of Mincerian rat es of ret urn est imat ed from micro dat a
for various count ries.
Empirical research in t his area is t roubled by t he issue of causality: does a higher
educat ion level lead t o higher GDP or is it t he ot her way around. T he same problem applies t o t he relat ion between educat ion and income inequality. Indeed, Bils and K lenow
(1998) have argued t hat t he posit ed causat ion from educat ion t o growt h should be reversed. However, t heir argument s apply t o t he endogenous growt h relat ion, and not t o
t he Mincerian relat ion invoked here.1 Our solut ion t o t he endogeneity problem relies on
t he t ime-lags in t he causat ion from GDP t o average level of schooling of t he populat ion.
First , t he polit ical syst em has t o decide on spending of addit ional t ax revenues on educat ion. Then, new t eachers have t o be t rained and schools have t o be built . Only t hen
t he …rst new cohort can undergo t he improved t raining. It will t hen t ake some years or
so before t he …rst cohort of bet t er educat ed st udent s ent er t he labor market . It t akes
several new cohort s of bet t er educat ed workers before t here is a not iceable e¤ect on t he
average level of educat ion of t he workforce. We argue t herefore, t hat it is reasonable t o
assume t hat GDP only a¤ect s educat ion level wit h a lag of at least 10 years. We explore
whet her our result s are driven by a few count ries t hat experience high growt h during
t he sample period (e.g. Asian t igers).
Our empirical result s provide st rong support for a negat ive relat ion between t he
supply of human capit al and it s ret urn. Moreover, t he est imat ion result s are also largely
mut ually consist ent quant it at ively: a one year increase in t he st ock of human capit al
reduces it s ret urn by about 2 percent age point s. T his est imat e is consist ent wit h K at z
and Murphy’s (1992) est imat e of t he elast icity between low and high skilled workers.
We account for skill biased t echnological progress by ent ering cross e¤ect s of t ime
1
Bils and K lenow (1999) argue t hat if endogenous growt h is due t o t he role of educat ion di¤using
t he most recent st at e of t echnology, t hen t he educat ion of new cohort s should be more valuable, leading
t o a negat ive correlat ion between growt h and t he ret urn t o experience.
4
dummies and educat ion. T his relat es our analysis t o O’Neill (1995). He asks t he quest ion
as t o why t he huge invest ment s in human capit al by LDCs have not cont ribut ed t o a
convergence in GDP between LDCs and t he indust rialized world. His explanat ion relies
on skill biased t echnological progress: “ T he recent shift in product ion t echniques t oward
high-skilled labor has result ed in a subst ant ial increase in t he ret urns t o educat ion.
T his t rend, when combined wit h t he large disparit ies t hat st ill exist in educat ion levels
between t he developed and less developed count ries, has led t o an increase in inequality
despit e t he signi…cant reduct ion in t he educat ion gap t hat has occurred over t he last 20
years.” (p.1299). Our result s con…rm his analysis.
T he int eract ion t erms of educat ion and t ime dummies allow inference on t he pace of
skill biased t echnological change. T he GDP and inequality regressions yield quant it at ively similar est imat es, suggest ing skill biased t echnological change t o account for a 3%
t o 4% increase in t he ret urn t o educat ion per decade. This is equivalent t o t he reduct ion
in t he ret urn t hat would be achieved by a 0.8 year increase in t he average level of schooling, about as much as t he act ual increase in t he educat ion level over period covered by
our sample. Finally, our analysis reduces t he di¤erence between t he long and t he short
run rat e of ret urn t o educat ion from a fact or 6, as in K rueger and Lindahl (2000), t o
less t han 2. One can t herefore conclude, wit h some exaggerat ion, t hat T inbergen’s race
(1975) between educat ion and t echnology and Mincer’s earnings funct ion rule t he world.
T he paper is st ruct ured as follows. In sect ion 2, we present a simple Walrasian model
wit h imperfect subst it ut ion between types of labor. Sect ion 3 discusses t he dat a and
present s t he est imat ion result s. Sect ion 4 concludes.
2
2.1
T heor et ical fr am ewor k
A simple gr owt h model wit h em phasis on human capit al
Consider t he long run growt h pat h of an economy wit h physical and human capit al.
All market s are perfect ly compet it ive, so t hat wages equal marginal product ivity. We
specify bot h a simple aggregat e product ion funct ion and a Mincerian earnings funct ion.
First , consider t he Mincerian earnings funct ion. Let wi t be t he log wage of worker i
at t ime t and let si t be t he years of schooling she at t ained; wi t is assumed t o sat isfy t he
Mincerian earnings funct ion:
wi t = ! 0 (St ; t) + ! 1 (St ; t) si t + ¾ui t ´ wt (si t ; ui t )
(1)
where St is t he average educat ion level of t he workforce in t he economy, ui t is a mean
zero unit variance random variable represent ing ot her charact erist ics of workers (like
5
experience and innat e ability) and ¾is it s st andard deviat ion. Bot h t he int ercept ! 0 (¢)
and t he Mincerian rat e of ret urn t o human capit al ! 1 (¢) vary over t ime and wit h t he
average educat ion level of t he workforce. Equat ion (1) is const rained t o be linear in si t ,
implying t hat t he rat e of ret urn t o educat ion at part icular point in t ime t is independent
of t he years of schooling of an individual worker. T his assumpt ion plays an import ant
role in t he subsequent analysis.
Next , consider t he aggregat e product ion funct ion. Let out put per worker be governed
by a const ant ret urns t o scale Cobb Douglas product ion funct ion:
yt
ht
=
´
®ht + (1 ¡ ®) kt
¯ 1St ¡
2
1
2 ¯ 2St
(2)
+ ¯ 3St t + ¯ 4t
where yt is log out put per worker, kt log capit al per worker and ht is log average pro¯
dh t
> 0. The …rst t erm in t he expression for ht
duct ivity. We assume St < ¯ 1 , so t hat dS
t
2
measures t he e¤ect of schooling. T he second t erm measures t he diminishing ret urns t o
educat ion: t he higher t he mean level of educat ion of t he workforce, t he smaller t he ret urn t o addit ional schooling. T he t hird t erm capt ures t he e¤ect of skill biased t echnical
progress, while t he …nal t erm re‡ect s neut ral t echnical progress: ot her t hings equal, t he
ret urn t o educat ion increases over t ime when ¯ 3 > 0.
First , consider t he role of capit al in t his economy. Firms maximize pro…ts per worker,
yielding a …rst order condit ion for t he opt imal capit al st ock:
RK t = (1 ¡ ®) Yt ) kt = yt + ln (1 ¡ ®) ¡ ln r
(3)
where Yt and K t denot e t he exponent ials of t he corresponding lower case variables, and
R is t he rent al rat e of capit al which we assume t o be const ant over t ime. Equat ion (3)
re‡ect s t he st andard result for a Cobb Douglas t echnology t hat t he share of capit al in
out put is equal t o 1 ¡ ®. We assume t hat …rms adjust t heir capit al st ock su¢ cient ly
fast , so t hat we can ignore deviat ions from it s equilibrium value. Then, combining t he
FOC for capit al and t he product ion funct ion:
yt
=
kt
=
1¡ ®
(ln (1 ¡ ®) ¡ ln r )
®
1
¯ 1St ¡ 21 ¯ 2St2 + ¯ 4t + ¯ 3St t + (ln (1 ¡ ®) ¡ ln r )
®
¯ 1St ¡
2
1
2 ¯ 2 St
+ ¯ 4t + ¯ 3St t +
(4)
T he equat ions for log out put and capit al are ident ical, up t o a const ant t erm. Est imat ion
of t he separat e cont ribut ions of human and physical capit al on t he basis of equat ion (2)
is t herefore problemat ic, due t o endogeneity of kt . In t he absence of measurement
6
error in bot h St and kt , equat ion (2) is unident i…ed since ¯ 1St ¡ 12 ¯ 2St2 + ¯ 4t + ¯ 3St t
is collinear wit h kt . In t he presence of measurement error, t he relat ive magnit udes
of t heir coe¢ cient s merely re‡ect s t he precision of t heir measurement . Krueger and
Lindahl (2000) argue t hat capit al dat a are correlat ed t o out put by const ruct ion, since
invest ment dat a …gure in bot h series. Hence, measurement error in bot h series are likely
t o be correlat ed. T his explains why t hey …nd 1 ¡ ® t o be much higher t han one would
expect on t he basis of capit al’s share in out put (about 0.35). We shall t herefore omit
capit al from all our regressions and report est imat ion result s for equat ion (4) only.
Next , consider t he role of types of labor in t his economy. We have a similar condit ion
for labor as for capit al, aggregat ing over all individuals:
Z Z
®Yt =
Wt (s; u) f t (s; u) dsdu
(5)
where f t (s; u) is t he joint cross-sect ional density of s and u, and Wt (s; u) ´ exp (wt (s; u))
is t he wage rat e of an individual wit h s years of schooling and charact erist ics u. Labor
get s a share ® of t ot al out put .
Marginal product ivity t heory implies t hat t he increase in out put from adding one
worker wit h charact erist ics (s; u) t o t he workforce of t his economy raises out put by
Wt (s; u). T his implicat ion ext ends t o t he (marginal) e¤ect of new human capit al: a
marginal increase in t he years of educat ion of worker i will raise out put by:
@Wt (si t ; ui t )
@Yt
=
= Wt (si t ; ui t ) ! 1 (St ; t)
@si t
@si t
(6)
where Yt denot es aggregat e out put , and Wt (si t ; ui t ) is given by t he Mincer equat ion (1).
Equat ion (6) st at es t hat t he increase in out put due t o an increase in t he schooling level
of worker i by an amount h, equals t he gain in out put due t o t he addit ion of a worker
wit h charact erist ics (s + h; u) minus t he loss in out put due t o t he removal of a worker
wit h charact erist ics (s; u).
Consider an increase of t he years of educat ion of all workers by an equal amount
dsi t = ds for all i . By const ruct ion, t he average years of educat ion St changes by t hat
same amount : dSt = ds, t hus shift ing t he marginal dist ribut ion of educat ion t o t he right .
(si t ;u i t )
T hen, each worker’s wageincreases by an amount @W t @
ds = Wt (si t ; ui t ) ! 1 (St ; t) ds.
si t
T he change in t ot al out put is obt ained from t he product ion funct ion (2):
@Yt
ds = (¯ 1 ¡ ¯ 2St + ¯ 3t) ®Yt ds
@St
7
By equat ion (6), t he e¤ect of t his increase in St on aggregat e out put is equal t o t he sum
over all workers of t he increases in individual wages. T hus:
Z Z
@Wt (s; u)
@Yt
=
f t (s; u) dsdu
@St
@s
Z Z
(¯ 1 ¡ ¯ 2St + ¯ 3t) ®Yt = ! 1 (St ; t)
Wt (s; u) f t (s; u) dsdu
=
! 1 (St ; t) ®Yt
where t he t hird equality follows from equat ion (5). T he second line relies on t he linearity
of t he Mincerian earnings funct ion (1) in si t , for ot herwise ! 1 (St ; t) could not be brought
out side t he int egral.
Dividing t hrough by t he labor share, we obt ain an expression for t he ret urn t o
educat ion:
! 1 (St ; t) = ¯ 1 ¡ ¯ 2St + ¯ 3t
(7)
T he increase in log aggregat e out put is equal t o Mincerian rat e of ret urn t o educat ion.
Or, in ot her words, t he privat e ret urn t o educat ion, as measured in a cross sect ion
analysis on individual wages, is equal t o t he social rat e of ret urn, as measured in a t ime
series analysis of log aggregat e out put . T his conclusion does not come as a surprise,
since in t his Walrasian world, t here are no ext ernal e¤ect s of schooling decisions.
T he ret urn t o educat ion ! 1 (¢) det ermines relat ive wages of workers wit h various
levels of educat ion. If ¯ 2 were 0, t hen t he relat ive wages would be independent of
St and workers wit h di¤erent levels of educat ion would be perfect subst it ut es. Wit h
¯ 2 > 0, an increase in t he mean level of educat ion in t he economy reduces t he rat e of
ret urn t o educat ion. Teulings (2001) provides a product ion t echnology t hat yields t his
implicat ion.2
2.2
I nequalit y and t he compr ession elast icit y
An increase in t he level of educat ion reduces t he ret urn on furt her invest ment s in human
capit al by ¯ 2dSt . T his fall in t he ret urn on human capit al compresses wage di¤erent ials. We use t his relat ion t o analyze t he int eract ion between t he evolut ion of out put
and income dispersion D t . For simplicity, capit al income is assumed t o be dist ribut ed
2
Because we do not need an expression for ! 0 (St ; t) for our empirical applicat ion, it is not present ed
here. However, t he declining marginal ret urn t o educat ion implies t hat a below average educat ed worker
gains from an increase in t he mean level of human capit al, whereas an above average worker looses out
(in bot h cases, keeping const ant t he human capit al of t hat worker).
8
proport ional t o labor income, so t hat t he log wage dist ribut ion and t he log income
dist ribut ion di¤er only by t heir …rst moment . We assume t hat si t and ui t are joint ly
normally dist ribut ed, wit h correlat ion ½. Furt hermore, we assume t hat t he variance of
si t is const ant over t ime V (si t ) = V .3 We can t hen derive an expression for t he variance
of log income D t = V (wi t ) from t he Mincer equat ion (1).
Dt
=
! 1 (St ; t) 2 V + 2! 1 (St ; t) V 1=2¾½+ ¾2
=
µ0t ¡ µ1t St + µ2St2
(8)
where
µ0t
=
(¯ 1 + ¯ 3t) 2 V + 2 (¯ 1 + ¯ 3t) V 1=2¾½+ ¾2
µ1t
=
2¯ 2 (¯ 1 + ¯ 3t) V + 2¯ 2V 1=2¾½
µ2 =
¯ 22V
T he variat ion in income due t o t he educat ion component is equal t o t he variance of
years of educat ion, mult iplied by t he ret urn t o educat ion. T he second equality follows
from subst it ut ion of equat ion (7). Equat ion (8) est ablishes cross equat ion rest rict ions
on t he equat ions for out put and income dispersion. When informat ion on ½; ¾and V is
available, t hese rest rict ions can be t est ed. Not ice t hat if ¯ 2 = 0, D t would not depend
on St .
T he coe¢ cient ¯ 2 relat es in a simple way t o earlier empirical …ndings, like K at z
and Murphy’s (1992) est imat e of t he subst it ut ion elast icity between low- and highskilled workers of 1.4. For t his purpose, we de…ne t he compression elasticity ° as t he
percent age reduct ion in t he ret urn t o human capit al per percent increase in t he value
of it s st ock. T his elast icity can be calculat ed from equat ions (1) and (2) as t he relat ive
reduct ion of t he ret urn t o human capit al per year increase in St , divided by t he e¤ect
of t his increase in t he level of schooling on t he log value of t he st ock of human capit al:
° (St ; t) ´ ¡
¡ @! 1 (St ; t) =@St
¯2
@ln ! 1 (St ; t)
=
=
@ln H t
! 1 (St ; t) @ht =@St
(¯ 1 ¡ ¯ 2St + ¯ 3t) 2
(9)
Equat ion (9) implies t hat t he compression elast icity is increasing in St . This implicat ion is imposed by t he quadrat ic speci…cat ion for ht adopt ed in equat ion (2) and
3
T his is a crucial assumpt ion for t he analysis. If V varies over t ime, t he linear form of M incerian
equat ion (1) would collapse, see Teulings (2001) for det ails. A n increase in V raises labor supply in bot h
t ails of t he schooling dist ribut ion. T his reduces relat ive wages in t he t ails. In t he empirical sect ions, we
shall adopt a pragmat ic approach, by including Vt as an addit ive cont rol variable in our regressions.
9
should not be t aken at face value. However, Teulings (2001) shows t hat t he compression elast icity is indeed increasing in t he level of human capit al in t he special case of a
Leont ief product ion t echnology over di¤erent types of labor.4
T he compression elast icity relat es t o t he K at z and Murphy elast icity of subst it ut ion
between high and low-skilled labor ´ low-high by t he following relat ion, see Teulings (2001):
1
° (St ; t) =
(10)
´ low-high D t
Using Kat z and Murphy’s (1992) est imat e of ´ low-high = 1:4 and using a typical value
for wage dispersion in t he Unit ed St at es of D t »
= 0:36, t he compression elast icity is of
t he order of magnit ude of 2 for t he Unit ed St at es. We will use equat ions (9) and (10)
t o compare K at z and Murphy’s est imat e t o our est imat ion result s.
2.3
W hy linear it y of t he M incer equat ion is im por t ant
T he int erpret at ion of t he second order e¤ect of years of educat ion on GDP as being
caused by imperfect subst it ut ability of worker types relies on t he linearity of t he Mincer
equat ion in si t . In t hesubsequent argument , we ignore t echnological progress and assume
ui t and si t t o be uncorrelat ed for convenience. Suppose t hat workers wit h various levels
of schooling are perfect subst it ut es (so ! 0 and ! 1 do not depend on St ), but t hat t he
Mincerian earnings funct ion (1) is concave in t he years of educat ion:
wi t = wt (si t ; ui t ) = !
0
+ ! 1si t ¡
2
1
2 ! 2si t
+ ¾ui t
(11)
T hen, repeat ing t he derivat ion of equat ion (7), we get :
Z Z
@Yt
@Wt (s; u)
=
f t (s; u) dsdu
@St
@s
Z Z
(¯ 1 ¡ ¯ 2St ) ®Yt =
(! 1 ¡ ! 2s) Wt (s; u) f t (s; u) dsdu
In appendix A we show t hat t he int egral has an analyt ic solut ion, and t he above expression can be writ t en as:
¶
µ
!2
!1
¡
St ®Yt
(12)
(¯ 1 ¡ ¯ 2St ) ®Yt =
! 2V + 1 ! 2V + 1
4
In t hat case, t he compression elast icity sat is…es (dropping t he t ime dependence for convenience)
° (S) = ° (0) exp [° (0) !
10
1
(0) S]
Hence, t he model implies:
¯2=
!2
! 2V + 1
T his expression yields an alt ernat ive int erpret at ion for ¯ 2 > 0. Inst ead of imperfect
subst it ut ion between types of labor, t he negat ive second order e¤ect of educat ion on
out put is now int erpret ed as declining marginal ret urns t o human capit al for each individual worker. In t his case t he aggregat e ret urn t o human capit al also declines when
t he human capit al st ock increases since every worker moves along it s schedule of declining marginal ret urns. We can derive an equat ion for income inequality D t for t his
int erpret at ion which is observat ionally equivalent t o equat ion (8). Again, t his yields an
alt ernat ive int erpret at ion of a negat ive e¤ect of St on income inequality. In fact , any
combinat ion of concavity of t he Mincerian earnings funct ion and imperfect ion in t he
subst it ut ability of worker types can explain ¯ 2 > 0. Dat a on out put and t he variance of
log income alone do allow t o disent angle bot h models. However, as observed by Krueger
and Lindahl (2000), t he abundant empirical evidence on t he Mincerian earnings funct ion
does not suggest any syst emat ic non-linearit ies in t he relat ion between log wages and
years of schooling. We shall t herefore int erpret t he second order e¤ect in t he log out put
equat ion as evidence t hat di¤erent types of labor are imperfect subst it ut es.
3
3.1
Em pir ical evidence
D at a sour ces
Our empirical analysis is largely based on dat a from two sources: t he Barro and Lee
(1996, 1993) dat a on educat ional at t ainment and t he Deininger and Squire (1996) dat a
on income inequality. These dat aset s were supplement ed wit h dat a on real GDP per
worker from t he Penn World Table (Summers and Hest on 1991) mark 5.6a.
T he Barro and Lee dat aset cont ains det ailed dat a on educat ional at t ainment for 114
count ries for t he period 1960-1990 in int ervals of 5 years. Barro and Lee report t he
fract ion of t he populat ion t hat at t ained a cert ain educat ion level, as well as t he average
durat ion of t his educat ion level. T hey use t hese dat a t o const ruct t he average educat ion
level of t he populat ion in years. We also calculat e a rough est imat e of t he variance of
t he educat ion dist ribut ion.5
5
Barro and Lee calculat e average years of educat ion from at t ainment dat a (percent age of t he populat ion t hat have at t ained a cert ain level of schooling) combined wit h dat a on t he typical durat ion of
11
Deininger and Squire (1996) use result s from a large number of st udies and assess
t heir comparability. T heir dat aset cont ains Gini coe¢ cient s of t he income dist ribut ion
for 115 count ries from 1947 t o 1996. We use only t he ‘high quality’ dat a for t he period 1960-1990. The ‘high quality’ label is provided by Deininger and Squire on t he
basis of t hree crit eria: dat a are (i ) based on a nat ional household survey, (ii ) which
is represent at ive of t he populat ion, and (iii ) in which all sources of income have been
count ed. T he t ot al number of observat ions in t he high quality sample is 693. T he dat a
cont ain missing values due t o limit at ions t o t he t ime period of dat a availability, and
due t o missing observat ions wit hin t hat t ime period. For virt ually all count ries, dat a
are available only every two or …ve years or at irregular int ervals. We const ruct dat a
for 5 year int ervals from 1960 t o 1995 by linear int er- and ext rapolat ion.6 T his met hod
yields a dat aset cont aining 370 observat ions for 98 count ries. Only for 58 count ries we
have t hree or more observat ions. We calculat ed t he variance of log income from t he
Gini coe¢ cient s, assuming t hat log income is dist ribut ed normally. T he det ails of t his
calculat ion can be found in appendix B.
Table 1 summarizes t he main variables in t he combined dat aset .7
3.2
D ir ect est imat es of diminishing r et ur ns t o educat ion
Before present ing t he est imat ion result s for our main dat aset , we present some est imat es
of t he e¤ect of t he mean years of schooling on t he ret urn t o human capit al as measured
direct ly from individual dat a. In t able 2 we have ranked a large number of count ries
each level of schooling (1996, p.218). We can express t he calculat ion as:
S = f pr i Spr i + f sec (D pr i + Ssec ) + f h i g h (D pr i + D sec + Sh i gh )
where S is average years of schooling in t he t ot al populat ion, f l ev el is t he fract ion of t he populat ion
t hat has at t ained a cert ain educat ion level (no educat ion, primary educat ion, secondary educat ion or
higher educat ion), D l ev el is t he typical durat ion of t he di¤erent educat ion levels, and Sl ev el is t he average
durat ion of a cert ain educat ion level for t hose people t hat have not cont inued t o at t ain a higher educat ion
level. Int uit ively Sl ev el < D l ev el due t o early drop-out .
T he calculat ion of average years of schooling in t his expression is just an expect ed value, which suggest s
t he following proxy for t he variance in educat ion wit hin each count ry (cf. Checchi 1999):
2
2
2
2
V (S) = f pr i Spr
i + f sec (D pr i + Ss ec ) + f h i gh (D pr i + D sec + Sh i gh ) ¡ S
For int erpolat ion we use xbt = n +n p x t ¡ p + n +p p x t + n , where n is t he t ime span t ill t he next observat ions
and p · 2 is t he t ime span since t he previous observat ion. For ext rapolat ion we use t he observat ion t hat
is closest by. T his procedure is e¢ cient if t he Gini follows a random walk, as is almost t rue empirically.
7
T he dat a are available at ht t p:/ / www.princet on.edu/ ~t vanrens/ paper.
6
12
for which such est imat es of t he ret urn t o schooling are available. The dat a are obt ained
from Bils and Klenow (1998) and include est imat es from Psacharopoulos (1994) and
ot her aut hors (sources in t he t able). We have plot t ed t he ret urn t o educat ion against
t he average schooling level in …gure 1, panel A. Apart from Jamaica, t here is a clear
negat ive relat ionship between t he two. T he ret urn t o educat ion is plot t ed against income
inequality in Panel B. T his relat ion document s t hat inequality is indeed st rongly relat ed
t o t he ret urn t o educat ion.
Table 3 present s t he result s for some simple regressions on t hese dat a. Obviously,
t hese est imat es should be int erpret ed wit h some care. The dat a in t able 3 provide
t he best est imat es t hat are available for many count ries, but it is not clear t o which
ext end t hese est imat es are comparable across count ries. In part icular, t he underlying
st udies di¤er in whet her and how t hey account for ability bias and measurement error.
Nevert heless, t he est imat es are informat ive. T hey show t hat t he ret urn t o educat ion is
about 16% for count ries wit h an educat ion level of zero, and decreases by about 0.7%
for every year of educat ion. For t he average educat ion level of 5.3 years in our sample,
t his would correspond t o a ret urn t o schooling of 12%. In t he US, wit h an average
educat ion level of 12 years of schooling in 1990, t he ret urn t o educat ion would be about
7.5%. T his simple cross sect ion analysis provides t herefore …rst evidence of t he negat ive
relat ion between t he ret urn t o educat ion and t he mean years of schooling in t he economy.
T he t ime dummies suggest t hat t here has been skill biased t echnological progress from
1985 t o 1990, raising t he ret urn t o human capit al by 4%. However, t here is lit t le act ion
before 1985. The est imat ion result s even suggest a negat ive skill bias in t hat period,
but t he result s are insigni…cant . Weight ing count ries by log GDP per worker or log
populat ion size does not a¤ect t hese conclusions.
3.3
Est imat ion r esult s for G D P
We apply an error correct ion version of equat ion (4) for out put as a st art ing point for our
empirical analysis. We replace t he t ime t rends in skill biased and neut ral t echnological
progress by dummies t o allow for variat ions in t heir pace. Indexing count ries by j , t he
equat ion we est imat e is:
¢ yj t
=
¡ ±yj t ¡ 1 + ¢ ¯ 0t + ±¯ 0t ¡ 1 + ¯ 1t ¢ Sj t ¡ 12 ¯ 2¢ Sj2t
¡
¢
+ ¢ ¯ 1t + ±¯ 1t¡ 1 Sj t ¡ 1 ¡ 21 ±¯ 2Sj2t ¡ 1 + vj t
=
¡ ±yj t ¡ 1 + ° 0t + ° 1t ¢ Sj t + ° 2¢ Sj2t + ° 3t Sj t ¡ 1 + ° 4Sj2t¡
13
(13)
1
+ vj t
where vt is an error t erm. The short run ret urn t o human capit al is ° 1t + 2° 2Sj t ¡ 1, while
t he long run ret urn is (° 3t + 2° 4Sj t ¡ 1) =±. K rueger and Lindahl (2000) have shown t hat
est imat es of t he ret urn t o human capit al from t his type of model are st rongly a¤ect ed by
at t enuat ion bias because of measurement error when using short t ime int ervals. However, t he longer t he t ime int erval, t he great er t he risk of reverse causality. As argued
in t he int roduct ion, we t ake it t o be unlikely t hat shocks t o GDP have a major impact
on t he mean level educat ion wit hin 10 years. Hence, we apply a 10 year observat ion
int erval. T his implies t hat we have at most 3 observat ions on t he change in educat ion
for each count ry, 1960 t ill 1990.
Est imat ion result s for equat ion (13) are report ed in Table 4. Column (1) replicat es
K rueger and Lindahl (2000, Table 3). The result s di¤er slight ly because we use GDP
per worker rat her t han GDP per capit a. The short run e¤ect of 8% addit ional GDP per
year educat ion is roughly consist ent wit h t he micro lit erat ure on t he Mincerian earnings
funct ion. T he long run e¤ect t akes a long t ime t o mat erialize, as can be seen from
t he low coe¢ cient of t he level of GDP lagged. However, t he long run e¤ect is 6 t imes
larger t han t he short run e¤ect (0.00297/ 0.00616 = 48 log point s increase in GDP per
addit ional year of educat ion), exceeding by far any est imat e of t he Mincerian rat e of
ret urn.
Column (2) of Table 4 adds t he crucial second order e¤ect in educat ion. It s coe¢ cient
has t he expect ed negat ive sign and is signi…cant at t he 5% level. T he second order t erm
is about 1/ 20 of t he …rst order t erm, bot h for t he short and t he long run t erms. T his
rat io of one over 20 will be a recurrent t heme in all our est imat es. This regression implies
a ret urn t o educat ion in t he range of -1.7% t o 10% for an average educat ion level of 12
t o 4 years. When we allow for skill biased t echnological change as in column (3) t he
coe¢ cient ° 1 seems t o increase subst ant ially, but t his is because t he reference cat egory
for t he t ime dummy int eract ions is 1990. Alt hough t he short run cross-e¤ect s of t ime
dummies and educat ion are not very precisely measured, t hey provide some informat ion
regarding t he nat ure of t echnological progress. T heir negat ive sign is evidence of skill
biased t echnological progress: keeping const ant t he average educat ion level, t he ret urn
t o educat ion has gone up over t he period. The pace of skill biased t echnological progress
increased dramat ically during t he eight ies, raising t he ret urn by as much as 6.7%. To
get some idea about t he size of t he impact of skill biased t echnological progress, we can
use t he second order t erm for educat ion t o calculat e t he increase in average years of
0:067
= 4 years. T he e¤ect of skill
educat ion t hat is required t o o¤set t his increase: 2¤0:0085
biased t echnological progress on t he ret urn t o schooling in t he eight ies (one decade) was
about twice as high as t he e¤ect of t he increase in t he average educat ion level over t he
14
whole sample period (t hree decades). T he long run coe¢ cient s yield a similar pict ure.
Not e however t hat t he long run ret urn t o educat ion is st ill 6 t imes higher t han t he short
run ret urn.
We report some speci…cat ion t est s in columns (4) t hrough (6). Column (4) adds
t he variance in t he years of educat ion. This does not a¤ect t he result s. In columns
(5) and (6) observat ions are weight ed by log GDP per worker and log populat ion size
respect ively. Again, t his does not make much di¤erence. T he WLS est imat es show t hat
our result s are not driven by a few very poor or very small count ries, and are consist ent
wit h t est s t hat show t hat t here is no het eroskedast icity in t he residuals.
We also est imat ed t he model wit h random and …xed e¤ect s. T hese regressions
st rongly suggest t he presence of count ry speci…c …xed e¤ect s. T his does not come as a
surprise. Gallup, Sachs and Mellinger (1999) have shown t he import ance of geography
for growt h and GDP. Access t o open sea or navigable rivers is an import ant advant age.
Count ries wit h a t emperat e climat e do much bet t er t han count ries in t he t ropical zone.
T he aut hors present evidence t hat t he e¤ect of climat e is likely t o be due t o t ropical
diseases, in part icular malaria. Where t hese fact ors are largely …xed (t here is some reduct ion in t he number of count ries where malaria is endemic), we should allow for …xed
e¤ect s in our est imat ion.
OLS est imat ion of equat ion (13) is inconsist ent in t he presence of …xed e¤ect s as yt¡ 1
is correlat ed wit h t he …xed e¤ect . Also, OLS in …rst di¤erences would be inconsist ent
because of t he lagged dependent variable. We t herefore use t he met hodology set out in
Blundell and Bond (1998). We respecify equat ion (13) as:
yj t
=
° 0t + (1 ¡ ±) yj t ¡ 1 + ° 1t Sj t ¡ (° 1t ¡ ° 3t ) Sj t ¡
+ ° 2Sj2t
¡ (° 2 ¡
° 4) Sj2t ¡ 1
+ f j + "j t
1
(14)
where we assume:
E [" j t f j ] =
0
E [" j t " j t ¡ s ] =
0 for s 6
= 0
E [" j t Sj t ¡ s ] =
0 for s ¸ 0
T he t hird assumpt ion re‡ect s our ident ifying assumpt ions t hat shocks " j t in log GDP
t ake at least t en years t o have a signi…cant e¤ect on St . T he e¢ cient GMM est imat or
of equat ion (14) uses t he following moment condit ions (Arellano and Bond 1991)
E [¢ " j t yj t ¡ s] =
0 for s ¸ 2
E [¢ " j t Sj t ¡ s] =
0 for s ¸ 1
15
which follow direct ly from our assumpt ions on t he error t erm above. We est imat ed t his
model using t he DPD98 for Gauss package (Arellano and Bond 1998). Table 5 gives t he
est imat ion result s. Column (1) is ident ical t o column (3) in t able 4, but now present ed
in levels as in equat ion (14). Column (2) repeat s column (1) in …rst di¤erences. Bot h
est imat ors are inconsist ent . Column (3) present s t he GMM est imat ion result s using t he
above moment condit ions. The result s are insigni…cant , as was t o be expect ed given t he
small number of observat ions and short t ime dimension of our dat a.
Blundell and Bond (1998) suggest joint ly est imat ing equat ion (14) in …rst di¤erences
and in levels. T his result s in an e¢ ciency gain, part icularly in panels wit h a short t ime
dimension, because t he est imat or uses addit ional moment condit ions. We have t o make
one addit ional assumpt ion:
E [f j ¢ Sj t ] = 0
T hen, two addit ional moment condit ions are available:
E [(f j + " j t ) ¢ yj t ¡ s] =
0 for s ¸ 1
E [(f j + " j t ) ¢ Sj t ¡ s] =
0 for s ¸ 0
Columns (4) and (5) present t he est imat ion result s using all moment condit ions, where
we use a two st ep procedure t o account for t he covariance st ruct ure in t he error t erms
in column (5). We t ake column (5) as t he benchmark for our discussion. T he Sargan
t est -st at ist ic for t he validity of inst rument s is 12.65 wit h 12 degrees of freedom (p-value
is 39.5%), accept ing t he over-ident ifying rest rict ions. T he rat io of t he …rst and second
order t erm of St is st ill about 20, bot h for t he cont emporaneous and t he lagged e¤ect .
However, t he long run e¤ect is now much closer t o t he short run e¤ect t han in Table 4:
0:13
t he short run e¤ect of t he …rst order t erm is 0:46 and t he long run e¤ect 0:46¡
1¡ 0:63 = 0:89,
less t han 2 t imes t he short run ret urn. T his is as close as our analysis will bring us t o t he
Mincerian wage equat ion. Finally, t here is clear evidence of skill biased t echnological
progress, raising t he ret urn t o educat ion by about 4.5% during t he eight ies and about
3.5% during t he ninet ies (keeping const ant t he mean level of educat ion).
T he est imat e for t he diminishing ret urns t o educat ion ¯ 2 = 2° 2 = ¡ 0:048 is about 7
t imes higher t han t he direct est imat e in t able 3. The combinat ion of allowing for …xed
e¤ect s and skill biased t echnological change is crucial for t his result . T here is a clear
int uit ion for t his. Geography gives some nat ions an init ial advant age over ot hers. These
count ries can a¤ord a higher level of invest ment in human capit al, raising t heir level of
St . Hence, St is correlat ed wit h t he …xed e¤ect and is likely t o pick up some of t he e¤ect s
16
of geography in a regression wit hout …xed e¤ect s. Next , count ries wit h a high level of St
see t heir init ial advant age increased by skill biased t echnological progress. When we do
not allow for t his type of t echnological progress by including t ime dummies crossed wit h
St , t his e¤ect shows up as endogenous growt h due t o a high init ial level of educat ion.
A combinat ion of T inbergen’s race between educat ion and t echnology, Mincer’s ret urn
t o human capit al and Gallup, Sachs and Mellinger’s geography gives t herefore a …ne
descript ion of t he evolut ion of GDP between 1960 and 1990.
T he ret urns t o educat ion by decade, evaluat ed at t he average educat ion level across
count ries in our sample are as follows.
Average educat ion level St
Ret urn t o Educat ion
1970
3.83
19.9%
1980
4.56
20.8%
1990
5.32
20.6%
Not ice t hat t he numbers are not st rict ly comparable over t ime because some count ries do
not have dat a on educat ion for t he whole sample period. T he number for 1980 is about
twice t imes Krueger and Lindahl’s est imat e of 8.5%. However, t he ret urn is much lower
in t he OECD count ries. It is even negat ive for t he count ry wit h t he highest educat ion
level, t he Unit ed St at es (St = 12 in 1990).8 A 0.8 year increase in t he mean value of St
during eight ies su¢ ces t o o¤set t he e¤ect of skill biased t echnological progress, which
seems t o be a more realist ic number t han t he 4 years calculat ed on t he basis of t able 3.
T he race between educat ion and t echnology has no clear winner: t he upward e¤ect of
t echnology is o¤set by t he increase in t he average educat ion level across t he world.
From equat ion (9) we can calculat e t he compression elast icity evaluat ed at t he average educat ion level in 1990 using t he est imat es of column (5): ° (5:3; 1990) = 1:14. T his
is lower t han t he value of 2 implied by Kat z and Murphy’s (1992) est imat e of t he elast icity of subst it ut ion between highly and low-skilled workers. However, t heir est imat e
applies t o t he Unit ed St at es. We cannot calculat e t he complexity dispersion paramet er
for t he Unit ed St at es due t o it s est imat ed negat ive rat e of ret urn t o human capit al, but
t heory suggest s t hat t he complexity dispersion paramet er is increasing in St , see t he
discussion in Sect ion 2.2. Hence, our est imat ion result s are reasonably consist ent wit h
K at z and Murphy’s elast icity of subst it ut ion.
As point ed out by Krueger and Lindahl (2000), a short er observat ion period exacerbat es t he consequences of measurement error in ¢ St . In t able 6 we report t he est imat ion
8
One expect s t his result t o be due t o t he rest rict ed funct ional form of t he model, using only a quadrat ic
in educat ion. We t ried including a t hird order t erm, but t he dat a cont ain insu¢ cient variat ion t o allow
reliable est imat ion.
17
result s for K rueger and Lindahl’s speci…cat ion and for our baseline regression (t able 4,
column 3) using 5, 10 and 20 year changes. Reading t he t able horizont ally, we see t hat
¡ ¢
t he coe¢ cient est imat es for ¢ St and ¢ St2 increase as we use longer t ime int ervals.
From column (1) t o column (3) t he number of observat ions drops from 607 t o 292.
Nevert heless t he signi…cance of t he paramet er est imat es increases subst ant ially. The
long run coe¢ cient s do not change much. Moving from a 10 t o a 20 year observat ion
period raises t he coe¢ cient s even furt her, t hough not by far as much as in K rueger and
Lindahl’s speci…cat ion. This result is problemat ic for t he conclusions of K rueger and
Lindahl. Measurement error provides a just i…cat ion for using long t ime int ervals, but
t here is no clear rule as t o how long t he int erval should be. Whereas t he long run ret urn
is 6 t imes higher t han t he short run ret urn when measured by using 10 year int ervals,
one can increase t he est imat e of t he short run ret urn t o almost any level by using longer
and longer t ime di¤erence int ervals. Therefore, t he smaller di¤erence between long and
short run ret urn and t he lower sensit ivity of t he est imat ion result s t o t he di¤erencing
int erval applied, makes one feel more comfort able about t he int erpret at ion of t he result s.
Columns (7) and (8) repeat t he est imat ions for 20 year t ime int erval wit h t he K yriacou
(1991) dat a for educat ion. T he result s are largely similar t o t he Barro and Lee educat ion
dat a.
Table 7 present s a robust ness check. Our result s might be driven by a few count ries
wit h except ionally high growt h rat es and except ionally high invest ment in human capit al, bot h persist ing over t he whole 30 year period covered. T his would open a channel
for reverse causality by t he following st ory: some count ries grow fast over prolonged period, and use t heir addit ional revenues t o invest in educat ion. In t hat case, t he increase
in t he average level of educat ion in t his observat ion period is just a predict or of t he
raise in educat ion during t he previous observat ion period. Hence, we exclude …rst t he
10 highest and lowest observat ions on ¢ yt ; ¢ St ; yt and St in a number of regressions.
Obviously, t his compression of t he variat ion in t he dat a reduces t he signi…cance of t he
coe¢ cient s. However, t he crucial coe¢ cient ° 2 never changes sign and is quit e st able.
3.4
Est imat ion r esult s for inequalit y
As st art ing point , we est imat e an ext ended version of equat ion (8):
D j t = µ0t + µ1t Sj t + µ2Sj2t + µ3Vj t + " j t
(15)
where we added Vj t as a cont rol variable as discussed in sect ion 2.2. Again, we use a
t en year observat ion period. T he dat a on income inequality are less comparable across
18
count ries t han t he dat a on GDP growt h and educat ion level. In part icular, t he Gini
coe¢ cient s in t he Deininger and Squire dat aset are based on di¤erent de…nit ions: some
use income and ot hers expendit ure dat a, some are based on t he household as a reference
unit and ot hers on t he individual, some are based on gross and ot hers on net income. As
suggest ed by Deininger and Squire (1996) we include dummy variables in t he regressions
t o cont rol for changes in t he de…nit ion of t he income variable.
T he OLS est imat ion result s for equat ion (15) are report ed in t able 8. Columns (1)
t o (3) present result s for t he model in levels. Column (1) present s t he full model. The
main variables St and St2 have t he expect ed sign, t hough t he lat t er is not signi…cant .
Not e however, t hat just t he signi…cance of µ1t is su¢ cient evidence for ¯ 2 > 0, since
neit her St nor St2 would have any e¤ect on income dispersion if ¯ 2 = 0. If t he correlat ion
½between ui t and si t were zero, t he model would imply t hat t he …rst and second order
e¤ect s in t his regression di¤er by t he same rat io as t he …rst and second order e¤ect s in
¡ ¯2
µ2
= °° 2 , see equat ion (8). In our est imat es of t he GDP
= 2¯
t he GDP equat ion: µ1t
1t
1t
equat ion we found a rat her robust rat io of one over 20 between t he second and …rst order
e¤ect s. In column (1), t his rat io is much lower. T his would be consist ent wit h a posit ive
correlat ion between years of schooling and ot her worker charact erist ics, ½> 0, but due
t o t he lack of precision in t he measurement of µ2, we cannot draw st rong conclusions.
T his is document ed by t he result s in column (2): dropping t he t ime variat ion in µ1t
raises µ2 by a fact or 2. We t ake column (2) as a benchmark.
Test ing cross equat ion rest rict ions between (8) and (13) requires informat ion on V; ½;
and ¾. An est imat e for V can be found in t able 1: V »
= 12:6. Since we do not have a
reliable est imat e for ½, t he subsequent calculat ions are based on ½= 0.9 The est imat ion
result s in column (5) of t able 5 for 1990 imply:
µ1t
=
µ2 =
2¯ 2 (¯ 1 + ¯ 3t) V = 4° 2° 1t V = 0:57
¯ 22V = 4° 22V = 0:03
T he est imat ed values for µ1t in column (2) of t able 8 are a fact or 7 smaller t han what
one would expect on t he basis of est imat e of t he GDP growt h equat ion. T he est imat e
for µ2 is a fact or 18 t oo small.
9
T his provides a lower bound on t he e¤ect of educat ion on wage dispersion
³
´
µ1t = 2¯ 2 (¯ 1 + ¯ 3 t) V + 2¯ 2 V 1=2 ¾½= 2¯ 2 ¯ 1 + ¯ 3 t + V ¡ 1=2 ¾½ V
A n upper bound can be found by set t ing ½ = 1 and ¾2 equal t o t he t ot al variance of log wages:
1=2
¾ = D t ' 0:75 from t able 1. In t hat case V ¡ 1=2 ¾½= 0:21, about half t he size of ¯ 1 + ¯ 3 t which is
between 0.38 and 0.46, see Table 5. Hence, set t ing ½= 0 will not great ly a¤ect t he conclusions in t he
t ext .
19
T wo remarks are in place here. First , t he est imat es for µ1 and µ2 (in absolut e value)
are posit ively correlat ed: a low est imat e for µ1 generat es a low est imat e for µ2 as well.
Const raining t he rat io between t he …rst and second order e¤ect t o 20, t he est imat e goes
up t o µ1 = ¡ 0:15 (t¡ value: 9:39), reducing t he di¤erence wit h it s expect ed value on t he
basis of t he GDP model t o a fact or 4.
Second, in t he derivat ion of equat ion (8) we assumed t hat capit al income is dist ribut ed proport ionally t o labor income. This assumpt ion is clearly incorrect . Since
capit al income account s for a large share on income inequality and since inequality is
unrelat ed t o t he ret urn t o human capit al, t he empirical e¤ect of St on inequality can be
expect ed t o be smaller t han predict ed by equat ion (8).
T he proxy for t he variance of t he schooling dist ribut ion t hat we include as a cont rol
variable in t he regressions is insigni…cant . T his suggest s t hat t he direct e¤ect of schooling
on t he income dist ribut ion (a more homogeneous human capit al dist ribut ion leads t o
less income dispersion) is less import ant t han t he indirect , general equilibrium e¤ect
(a higher average educat ion level reduces t he ret urn t o human capit al and t herefore
compresses t he income dist ribut ion). However, since we only have a crude proxy for t he
variance of educat ion, we may expect it s coe¢ cient t o be at t enuat ed t owards zero. In
any case it s inclusion does not a¤ect t he ot her coe¢ cient est imat es.
Column (3) ent ers …xed e¤ect s as a robust ness check. T hough t he sign of t he coe¢ cient s remains consist ent wit h t he model, t hey are no longer signi…cant . An alt ernat ive
way t o eliminat e count ry speci…c e¤ect s is by …rst di¤erencing equat ion (15). Est imat ion result s for t his model are present ed in columns (4) t rough (7). Column (4) present s
t he result s when bot h St and St2 are included. Bot h µ1t and µ2 are insigni…cant , but
have t he expect ed sign. Column (5) present s t he most robust t est of t he model: t est ing
¯ 2 > 0 by ent ering only St while allowing for …xed count ry e¤ect s by …rst di¤erencing.
T he coe¢ cient for St is signi…cant .
T he posit ive and signi…cant int ercept document s a rising t rend in income inequality,
keeping educat ion const ant . This t rend can be explained by t he e¤ect of skill biased
t echnological progress. Using t he result s in column (5) we can evaluat e t he size of t his
D t =@St
e¤ect . From equat ion (8) we have @@
D t =@t = ¯ 2=¯ 3 (again set t ing ½= 0). Hence, we can
est imat e ¯ 2=¯ 3 as t he rat io of t he coe¢ cient for ¢ St and t he const ant t erm, yielding
¯ 2=¯ 3 = 5:6. From t he GDP regression in t able 5, column (5) we can ret rieve ¯ 2=¯ 3 as
¡ ¢
2 £ t he coe¢ cient on ¢ St2 divided by est imat e for skill biased t echnological progress,
t hat is, 3.5 % per decade. Hence ¯ 2=¯ 3 = 1:4. Based on t he est imat es for GDP one
would have expect ed a four t imes higher int ercept in t he inequality regression. T his
calculat ion indicat es t hat t here are ot her fact ors compressing inequality, which o¤set
20
t he e¤ect of skill biased t echnological progress.
Columns (6) and (7) present result s when we weigh observat ions by log GDP per
worker and log populat ion size. Like in t he GDP growt h equat ion, t his does not make
a lot of di¤erence. We present a …nal robust ness check in column (8). As point ed out
by At kinson and Brandolini (1999), addit ive dummy variables may be insu¢ cient t o
cont rol for changes in de…nit ions of t he Gini coe¢ cient . We t herefore dummied all 21
observat ions wit h a de…nit ional change separat ely. T his correct ion is clearly asking t oo
much from t he dat a (t he number of observat ions is only 77), and all coe¢ cient est imat es
become insigni…cant , t hough t he coe¢ cient for ¢ St st ill has t he expect ed sign.
3.5
I nequalit y and gr owt h
T he posit ive e¤ect of educat ion on GDP and it s negat ive e¤ect on inequality imply
a negat ive correlat ion between inequality and GDP. We est imat ed t he global average
ret urn t o educat ion at around 21%, and t he e¤ect of educat ion on t he variance of t he log
income dist ribut ion at around -8% (evaluat ed at t he average educat ion level St = 4:56
in 1980). These est imat es imply a correlat ion between GDP and t he variance of log
wages of
Cor r (yj t ; D j t ) =
¡ 0:08 ¢0:21 ¢V (Sj t )
V (yj t ) ¡
1=2
V (D j t ) ¡
1=2
= ¡ 0:42
where we used t he variance of t he average educat ion level across count ries and t ime, and
t he st andard deviat ions of yj t and D j t from t able 1. The observed correlat ion between
yj t and D j t in our sample is ¡ 0:20, and t he correlat ion between ¢ yj t and ¢ D j t is ¡ 0:29.
Most of t he exist ing lit erat ure has focused on t he relat ion between inequality and
GDP growth (see Bénabou 1996 for a survey). However, since GDP growt h is correlat ed
wit h t he level of GDP (correlat ion coe¢ cient 0.24), t he negat ive correlat ion between
¢ yj t and D j t (correlat ion is ¡ 0:13) t hat has spurred t his lit erat ure, may very well be
due t o t he negat ive correlat ion between yj t and D j t caused by educat ion and possible
ot her t hird fact ors. Inst ead, t he lit erat ure has focused on a causal relat ion between
inequality and growt h, an approach t hat has recent ly been quest ioned by Quah (2001).
Quah argues t hat because most of t he variat ion in inequality is across count ries and most
of t he variat ion in growt h is across t ime, it is unlikely t hat inequality has an empirically
relevant e¤ect on growt h. Our result s o¤er support for t his argument . Modelling GDP
and inequality as being joint ly det ermined by educat ion implies an even larger negat ive
correlat ion t han is observed in t he dat a. This approach seems more promising t han
looking for a causal relat ion between inequality and growt h or vice versa.
21
4
Concluding r em ar ks
We have shown t hat t he evolut ion of GDP, t he Gini coe¢ cient and t he rat e of ret urn
t o educat ion can be capt ured by a simple Walrasian model of imperfect subst it ut ion
between workers wit h various levels of educat ion in t he presence of skill-biased t echnological progress. Human capit al ent ers as a fact or of product ion in t his simple const ant
ret urns t o scale Cobb-Douglas economy. We derived easy t o int erpret relat ions between
educat ional at t ainment , GDP and income inequality t hat can be est imat ed from crosscount ry panel dat a.
Our empirical result s provide st rong support for t he negat ive relat ion between t he
supply of human capit al and it s ret urn. The implied ret urn t o schooling in di¤erent
count ries is well in line wit h evidence from micro dat a. Our est imat es provide a simple
explanat ion for t he negat ive correlat ion between inequality and growt h based on t he
comovement of t hese variables wit h t he average educat ion level. Our result s suggest
t hat t his mechanism is quant it at ively more import ant t han a causal relat ionship between
inequality and growt h.
A
N on-linear M incer equat ion
To get expression (12) in t he t ext , we …rst used t he assumpt ion t hat si t and ui t are
uncorrelat ed t o int egrat e out over u
Z Z
(! 1 ¡ ! 2s) Wt (s; u) f t (s; u) dsdu
Z Z
¢
¡
=
(! 1 ¡ ! 2s) exp ! 0 + ! 1s ¡ 21 ! 2s2 + ¾u f t (s) f (u) dsdu
Z
¢
¡
=
(! 1 ¡ ! 2s) exp ! 0 + ! 1s ¡ 21 ! 2s2 + 21 ¾2 f t (s) ds
Second, not ice t hat since f t (s) is t he pdf of a normal (wit h mean St and variance V ),
¢
¡
exp ! 0 + ! 1s ¡ 21 ! 2s2 + 21 ¾2 f t (s) can be rewrit t en as a const ant A ¤t t imes t he pdf of
a normal wit h mean ¹ ¤t and variance V ¤
¢
¡
exp ! 0 + ! 1s ¡ 21 ! 2s2 + 12 ¾2 f t (s)
!
Ã
2
1
(s
¡
S
)
t
2
2
= p
exp ! 0 + ! 1s ¡ 21 ! 2s + 12 ¾ ¡ 12
V
2¼V
!
Ã
A¤
(s ¡ ¹ ¤t) 2
= p t exp 21
V¤
2¼V ¤
22
where
¹ ¤t =
! 1V + St
! 2V + 1
Furt hermore, from equat ion (5) we have
Z Z
Z
¡
®Yt =
Wt (s; u) f t (s; u) dsdu =
exp !
Hence
+ ! 1s ¡
2
1
2 ! 2s
+
1 2
2¾
¢
f t (s) ds = A ¤t
Z Z
(!
B
0
1
¡ ! 2s) Wt (s; u) f t (s; u) dsdu = ! 1®Yt ¡ ! 2¹ ¤t®Yt
G ini coe¢ cient and t he var iance of log incom e
¤
£
Let W 2 W ; W denot e income wit h density f (W ), dist ribut ion funct ion F (W ) and
mean M . F (W ) measures t he share of t he populat ion wit h income lower t han W . Let
Z (W ) denot e t he cumulat ive share of t ot al income earned by people wit h income lower
t han W . By de…nit ion:
1
Z (W ) =
M
ZW
xf (x)dx
(16)
W
T he graph of t he Lorenz curve has F (W ) on t he horizont al and Z (W ) on t he vert ical
axis. The Gini coe¢ cient G 2 [0; 1] is given by twice t he area between t he Lorent z curve
and t he 45-degree line.
Z1
G = 1¡ 2
Z1
Z dF = 2
0
1
M
By change of variables, using dZ =
2
G=
M
F dZ ¡ 1
0
W f (W )dW , t his expression can be writ t en as:
ZW
W f (W ) F (W ) dW ¡ 1
W
23
¡
¢
Assume income t o be log normally dist ribut ed so t hat F (W ) = © w¡¾¹ and M =
1 2
e¹ + 2 ¾ , where w ´ ln W and ¹ and ¾2 are t he mean and variance of w. By change of
variables v = w¡¾¹ ) dW = ¾e¾v+ ¹ dv, t he Gini coe¢ cient can writ t en as:
2
G=
M
Z1
0
¡ w¡ ¹ ¢ µ
¶
w¡ ¹
¾
W
©
dW ¡ 1 = 2e¡
¾W
¾
Á
1 2
¾
2
Z1
e¾v Á(v) © (v) dv ¡ 1
¡ 1
which maps t he Gini coe¢ cient t o t he variance of t he log income dist ribut ion ¾2. Numerically evaluat ing t his expression for di¤erent values of ¾shows t hat t he relat ionship
is virt ually linear in t he relevant range. Variances of log income of 0, 0.1, 0.2, 0.3 and
0.4 correspond t o Gini coe¢ cient s of 52.05, 56.33, 60.39, 64.20 and 67.78 respect ively.
R efer ences
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[2] Arellano, Manuel and St eve Bond (1991). Some Test s of Speci…cat ion for Panel
Dat a: Mont e Carlo Evidence and an Applicat ion t o Employment Equat ions. Review
of Economic Studies, vol.58 no.2, pp. 277-297.
[3] Arellano, Manuel and St ephen Bond (1998). Dynamic Panel Data Estimation Using
DPD98 for Gauss. mimeo, available at : ht t p:/ / www.cem….es/ ~arellano/
[4] At kinson A.B. and A. Brandolini (1999). Promise and Pitfalls in the
Use of
“ Secondary” Data-Sets: I ncome I nequality in OECD Countries.
mimeo, available at : ht t p:/ / www.nu¤.ox.ac.uk/ economics/ people/ at kinson.ht m or:
ht t p:/ / www.bancadit alia.it / pubblicazioni/ t emidi
[5] Barro, Robert J. and Xavier Sala-i-Mart in (1999). Economic Growth. Cambridge
MA: MIT Press (…rst MIT Press edit ion, originally published by McGraw-Hill,
1995).
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(dat aset available at : ht t p:/ / www.worldbank.org/ research/ growt h/ ddbarlee.ht m).
24
[7] Barro, Robert J. and Jong Wha Lee (1996). Int ernat ional Measures of Schooling Years and Schooling Quality. American Economic Review, vol.86 issue 2 Papers and Proceedings May 1996,
pp.218-223
(dat aset
available
at :
ht t p:/ / www.nber.org/ dat a
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ht t p:/ / www.worldbank.org/ research/ growt h/ ddbarle2.ht m).
[8] Bénabou, Roland (1996). Inequality and Growt h. In: NBER Macroeconomics Annual 1996, Ben S. Bernanke and Julio Rot emberg (eds.). Cambridge MA: MIT
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[9] Benhabib, Jess and M. Spiegel (1994). T he Role of Human Capit al in Economic
Development : Evidence from Aggregat e Cross-Count ry Dat a. Journal of Monetary
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[10] Bils, Mark and Pet er J. Klenow (1998) Does Schooling Cause Growt h or t he Ot her
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[12] Card, David (1999). T he Causal E¤ect of Educat ion on Earnings. Chapt er 30 in
t he Handbook of Labor Economics, Volume 3, O. Ashenfelt er and D. Card (eds.).
Amst erdam: Elsevier.
[13] Checchi, Daniele (1999). Does Educational Achievement Help to Explain I ncome I nequality? mimeo, Universit à degli St udi di Milano Bicocca. Available at
ht t p:/ / www.eco-dip.unimi.it / pag_ pers/ checchi/ checchi1.ht m.
[14] Checchi, Daniele (2000). I nequality in I ncomes and Access to Education. A CrossCountry Analysis (1960-1995). mimeo, Universit à degli St udi di Milano Bicocca.
Available at ht t p:/ / www.eco-dip.unimi.it / pag_ pers/ checchi/ checchi1.ht m.
[15] Checchi, Daniele and Luca Flabbi (1999). I ncome and Educational Distribution
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[16] Deininger, K laus and Lyn Squire (1996). A New Dat a Set Measuring Income Inequality. World Bank Economic Review, vol.10 no.3, pp.565-591 (dat aset available
at : ht t p:/ / www.worldbank.org/ research/ growt h/ dddeisqu.ht m).
25
[17] Gallup, J.L., J.D. Sachs and A.D. Mellinger (1999). Geography and economic development . NBER Working Paper No.6849.
[18] Heckman, James J. and Pet er J. K lenow (1997). Human Capital Policy. mimeo,
University of Chicago. Available at : ht t p:/ / www.klenow.com/ .
[19] K at z, Lawrence F. and Kevin M. Murphy (1992). Changes in Relat ive Wages, 19631987: Supply and Demand Fact ors. Quarterly Journal of Economics, vol.107 issue
1, pp.35-78.
[20] K rueger, Alan B. and Mikael Lindahl (2000). Educat ion for Growt h: Why and
For Whom? NBER Working Paper No.7591. Fort hcoming in Journal of Economic
Literature, vol.39 nr.4 (Dec 2001).
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A Cross-Count ry St udy of t he Convergence Hypot hesis. New York University C.V. Starr Center for Applied Economics Working Paper RR 9126
(www.econ.nyu.edu/ working) (dat aset available on request ).
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World Development, vol.22 no.9, pp.1325-1343.
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[25] Summers, Robert and Alan Hest on (1991). T he Penn World Table (Mark 5): An
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Nort h Holland.
26
Table 1. Description of the main variables in the dataset
Variable
yt
Obs
Mean Std.Dev.
1060
8.611
1.037
Min
6.122
∆y t
429
0.021
0.027
-0.066
Dt
370
0.560
0.319
0.100
92
0.000
0.017
-0.052
St
775
4.240
2.848
0.040
∆S t
328
0.066
0.066
-0.225
Vt
662
12.657
5.834
1.043
∆Vt
273
0.249
0.297
-0.888
∆Dt
Max
Description and source
11.172 Log real GDP per worker, 1985 intl. prices, Chain
index (PWT 5.6a).
0.101 10 year changes in real GDP per worker.
(annualized)
1.552 Variance of log income. Calculated from Gini
coefficient income distribution (Deininger and Squire).
0.051 10 year changes in variance of income.
(annualized)
12.000 Average years of education attained by the population
over 25 years of age (Barro and Lee).
0.387 10 year changes in average years of education.
(annualized)
35.823 Variance of the education distribution (rough estimate
constructed on the basis of Barro and Lee data).
1.361 10 year changes in variance of education.
(annualized)
Table 2. Return to education in several countries
PWT 5.0
country
code
123
126
114
118
107
115
50
83
110
89
85
131
121
41
127
68
113
53
117
78
75
21
77
104
66
94
124
29
54
129
97
61
109
72
74
51
92
67
100
98
70
4
62
125
60
56
71
69
86
58
20
59
Average years of schooling
population over 25
year
educ. level
Country
Poland
Sweden
Greece
Italy
Austria
Hungary
Canada
China
Denmark
Israel
India
Australia
Netherlands
Tanzania
Switzerland
Bolivia
Germany West
Dom. Rep.
Ireland
Venezuela
Peru
Kenya
Uruguay
Thailand
USA
Malaysia
Portugal
Morocco
El Salvador
UK
Pakistan
Nicaragua
Cyprus
Ecuador
Paraguay
Costa Rica
Korea
Argentina
Singapore
Philippines
Chile
Botswana
Panama
Spain
Mexico
Guatemala
Colombia
Brazil
Indonesia
Honduras
Cote d'Ivoire
Jamaica
POL
SWE
GRC
ITA
AUT
HUN
CAN
CHN
DNK
ISR
IND
AUS
NLD
TZA
CHE
BOL
DEU
DOM
IRL
VEN
PER
KEN
URY
THA
USA
MYS
PRT
MAR
SLV
GBR
PAK
NIC
CYP
ECU
PRY
CRI
KOR
ARG
SGP
PHL
CHL
BWA
PAN
ESP
MEX
GTM
COL
BRA
IDN
HND
CIV
JAM
85
80
85
85
85
85
80
85
90
80
80
80
85
80
85
90
90
90
85
90
90
80
90
70
90
80
85
70
90
70
80
80
85
85
90
90
85
90
75
90
90
80
90
90
85
90
90
90
80
90
85
90
8.7
9.45
6.89
5.75
7.17
7.93
10.23
4.04
11.21
9.11
2.72
10.02
8.29
.
8.99
4.11
8.83
3.76
7.87
4.89
5.5
2.46
6.69
3.54
12
4.49
3.45
.
3.4
7.66
1.74
2.83
7.56
5.36
4.72
5.4
8.03
7.77
4.38
6.73
6.16
2.29
7.55
6.25
4.34
2.56
4.25
3.56
3.09
3.68
.
4.51
Return to Education
year
ret. to educ
86
81
85
87
87
87
81
85
90
79
81
82
83
80
87
89
88
89
87
89
90
80
89
71
89
79
85
70
90
72
79
78
84
87
89
89
86
89
74
88
89
79
89
90
84
89
89
89
81
89
85
89
.024
.026
.027
.028
.039
.039
.042
.045
.047
.057
.062
.064
.066
.067
.072
.073
.077
.078
.079
.084
.085
.085
.09
.091
.093
.094
.094
.095
.096
.097
.097
.097
.098
.098
.103
.105
.106
.107
.113
.119
.121
.126
.126
.13
.141
.142
.145
.154
.17
.172
.207
.28
Education data from Barro and Lee. Return to education data from Bils and Klenow (1998).
Original sources return to education: Rosholm and Smith 1996 (Denmark), Calan and Reilly 1993 (Ireland),
Armitage and Sabot 1987 (Kenya and Tanzania), Alba-Ramirez and San Segundo 1995 (Spain), Arai 1994
(Sweden), Chiswick 1977 (Thailand), Krueger and Pischke 1992 (USA and Germany) and Psacharopoulos 1994
(all other countries); see Bils and Klenow for full references.
Table 3. Direct estimates of diminishing returns to schooling (OLS estimates)
(1)
OLS
(2)
OLS
excl. Jamaica
(3)
WLS
(GDP/w)
(4)
(5)
(6)
WLS
WLS
WLS
(GDP/w)
(population)
(population)
excl. Jamaica
excl. Jamaica
St
-0.00708
-0.00638
-0.00721
-0.00649
-0.00673
-0.00614
(3.23)
(3.68)
(3.41)
(3.86)
(3.18)
(3.49)
(year=70)
-0.02297
-0.01538
-0.02100
-0.01382
-0.02247
-0.01620
(0.81)
(0.69)
(0.75)
(0.62)
(0.85)
(0.74)
(year=80)
-0.03538
-0.02759
-0.03542
-0.02819
-0.03556
-0.02902
(2.49)
(2.44)
(2.52)
(2.51)
(2.55)
(2.49)
(year=85)
-0.04061
-0.03381
-0.04012
-0.03365
-0.04270
-0.03700
(3.06)
(3.21)
(3.13)
(3.28)
(3.30)
(3.42)
Constant
0.15663
0.14513
0.15725
0.14591
0.15451
0.14490
(10.33)
(11.95)
(10.50)
(12.07)
(10.34)
(11.54)
Observations
49
48
49
48
49
48
R-squared
0.36
0.40
0.37
0.41
0.36
0.39
Absolute value of t statistics in parentheses. Dependent variable is the Return to Education as in table 2. WLS
regressions are weighted by log GDP per worker or log population size. The dummy for 1975, and the dummy for
1985 in column (6), was dropped because there were no observations.
Table 4. GDP growth equation
(1)
OLS
(3)
OLS
(baseline
model)
0.24335
(4)
OLS
with V[educ]
0.24508
0.24717
0.24814
∆S t (year=70)
(3.84)
-0.00848
(2.16)
-0.09705
(3.09)
-0.00881
(1.75)
-0.07495
(3.94)
-0.00840
(2.18)
-0.09901
(3.99)
-0.00898
(2.32)
-0.09956
∆S t (year=80)
(1.87)
-0.06732
(1.34)
-0.07423
(1.95)
-0.07728
(1.89)
-0.06933
(1.35)
(1.42)
-0.00461
(1.60)
(1.39)
0.01231
(5.51)
-0.00058
(3.36)
-0.00386
(3.14)
-0.00339
(3.02)
0.01218
(5.57)
-0.00059
(3.46)
-0.00323
(2.65)
-0.00276
(2.48)
∆S t
∆ (St2)
(2)
OLS
0.08546
0.17025
(4.11)
(3.25)
-0.00780
(2.07)
∆Vt
St-1
St-12
St-1(year=70)
St-1(year=80)
Vt-1
0.00297
(4.31)
0.00857
(4.45)
-0.00045
(2.67)
0.01217
(5.42)
-0.00058
(3.29)
-0.00349
(2.80)
-0.00300
(2.63)
(0.73)
0.00902
(3.21)
-0.00034
(1.60)
-0.00325
(2.39)
-0.00391
(3.14)
0.00037
(1.03)
-0.00723
(2.81)
0.05516
(7.25)
0.04659
(6.12)
0.02040
(1.04)
250
0.38
4.65
0.0321
(5)
WLS
(GDP/w)
(6)
WLS
(population)
-0.00616
-0.00787
-0.00839
-0.00848
-0.00812
(2.99)
(3.74)
(4.04)
(4.07)
(4.08)
(year=70)
0.03449
0.03506
0.05590
0.05769
0.05427
(10.21)
(10.34)
(8.17)
(8.21)
(8.05)
(year=80)
0.02120
0.02179
0.04017
0.04269
0.03832
(6.54)
(6.82)
(5.77)
(5.99)
(5.61)
Constant
0.03816
0.04033
0.02715
0.02735
0.02601
(2.34)
(2.51)
(1.67)
(1.66)
(1.66)
Observations
292
292
292
292
292
R-squared
0.32
0.34
0.37
0.37
0.37
F-statistic1
11.29
9.56
11.08
11.27
11.29
p-value
0.0009
0.0022
0.0010
0.0009
0.0009
Absolute value of t statistics in parentheses.
1
H0: Long-run effect (coefficient St-1 divided by minus coefficient yt-1) equals short-run effect (coefficient
∆S t ). The F-tests reject the null when the p-value is smaller than 0.05.
yt-1
Table 5. GDP growth equation: Dynamic panel data estimates
(1)
OLS in
levels
St
0.24335
0.71161
(4)
BlundellBond,
1-step
0.37104
(5)
BlundellBond,
2-step
0.46365
∆S t 70
(2.48)
-0.00744
(1.31)
-0.06567
(1.03)
-0.06484
(1.07)
0.07700
(4.26)
-0.02025
(4.09)
-0.06592
(6.33)
-0.02420
(5.94)
-0.07970
∆S t
(2)
OLS in
first difs
(incons.)
0.21467
(3)
ArellanoBond
St 70
(3.84)
-0.00848
(2.16)
-0.09705
St 80
(1.87)
-0.06732
∆S t 80
(0.82)
-0.05795
(0.04)
-0.10613
(1.12)
-0.02990
(1.59)
-0.03461
St-1
(1.35)
-0.05954
∆S t −1
(0.95)
-0.00040
(0.10)
-0.31410
(0.48)
-0.05333
(0.66)
-0.12747
∆S t −1 70
(0.01)
0.00002
(0.00)
0.00240
(0.32)
-0.01429
(0.32)
0.31557
(0.70)
0.00225
(0.41)
-0.01259
(2.28)
0.00778
(1.84)
-0.02127
∆S t −1 80
(0.04)
-0.02123
(0.37)
0.31499
(0.29)
-0.00615
(0.77)
-0.01405
(0.26)
0.11605
(1.37)
(0.17)
1.05351
(1.54)
0.36002
(3.92)
-0.26536
(3.03)
184
0.26
0.22577
(0.30)
-0.64783
(1.21)
184
(0.10)
0.71236
(7.62)
-0.20276
(2.87)
-0.59898
(7.50)
2.17565
(3.18)
286
(0.28)
0.62961
(7.53)
-0.20986
(3.57)
-0.61523
(9.50)
2.81648
(4.73)
286
St2
St-1 70
(1.04)
0.00272
(0.64)
-0.02478
St-1 80
(0.48)
-0.06210
St-12
yt-1
(yr=70)
(yr=80)
Const.
(1.15)
0.91608
(44.07)
0.55900
(8.17)
0.40168
(5.77)
0.27154
(1.67)
292
0.95
∆ (St2)
∆ (St-12)
∆yt-1
(yr=80)
Const.
Obs.
Obs.
R-sq
R-sq
Nr of
Nr of
102
102
countries
countries
Absolute value of t statistics in parentheses, based on robust standard errors.
102
Table 6. GDP growth equation: the effect of measurement error
(1)
(2)
5 year changes
∆S t
0.03991
0.06276
(2.74)
∆S t (year=65)
(1.12)
-0.00293
(1.02)
0.09728
∆S t (year=70)
(1.35)
-0.00882
∆S t (year=75)
(0.18)
0.01557
∆S t (year=80)
(0.28)
-0.01051
∆S t (year=85)
(0.22)
0.04885
∆ (St2)
(3)
(4)
10 year changes
(baseline model)
0.08546
0.24335
(4.11)
(3.84)
-0.00848
(2.16)
(5)
(6)
20 year changes
0.15236
0.29273
(3.00)
(2.52)
-0.01655
(1.77)
(7)
(8)
20 year changes,
Kyriacou data
0.13828
0.24317
(4.37)
(2.46)
-0.00989
(1.26)
-0.09705
(1.87)
-0.06732
(1.35)
(0.82)
0.01441
0.00297
0.01217
0.00368
0.01176
0.00526
0.01074
(6.21)
(4.31)
(5.42)
(3.88)
(4.21)
(4.47)
(3.15)
St-12
-0.00064
-0.00058
-0.00062
-0.00042
(3.89)
(3.29)
(2.29)
(1.32)
St-1(year=65)
-0.00526
(3.09)
St-1(year=70)
-0.00510
-0.00349
(3.03)
(2.80)
St-1(year=75)
-0.00447
(2.89)
St-1(year=80)
-0.00534
-0.00300
(3.50)
(2.63)
St-1(year=85)
-0.00263
(1.77)
yt-1
-0.00706 -0.00913 -0.00616 -0.00839 -0.01179 -0.01306 -0.01294 -0.01354
(3.79)
(4.80)
(2.99)
(4.04)
(4.42)
(4.96)
(4.44)
(4.61)
(year=65)
0.03189
0.05489
(7.02)
(6.08)
(year=70)
0.03398
0.05876
0.03449
0.05590
(7.71)
(6.62)
(10.21)
(8.17)
(year=75)
0.02259
0.04379
(5.22)
(4.87)
(year=80)
0.01977
0.04715
0.02120
0.04017
(4.62)
(5.32)
(6.54)
(5.77)
(year=85)
-0.00457
0.00631
(1.08)
(0.66)
Constant
0.04808
0.03376
0.03816
0.02715
0.09750
0.09286
0.09354
0.08605
(3.25)
(2.17)
(2.34)
(1.67)
(4.87)
(4.81)
(4.48)
(4.06)
Observations
607
607
292
292
97
97
79
79
R-squared
0.22
0.26
0.32
0.37
0.22
0.29
0.28
0.31
Absolute value of t statistics in parentheses.
Estimates in columns 1, 3 and 5 correspond to Krueger and Lindahl (2001) table 3. The results differ slightly because
we use GDP per worker rather than GDP per capita as the dependent variable.
St-1
0.00349
(5.48)
Table 7. Subsample robustness of the GDP growth equation
(1)
Without 10
countries with
highest growth
in education
0.23695
(2)
Without 10
countries with
highest growth
in GDP
0.18019
(3)
Without 10
countries with
highest
education level
0.20674
(4)
Without 10
countries with
highest GDP
∆S t (year=70)
(3.34)
-0.01001
(2.44)
-0.07701
(2.86)
-0.00981
(2.47)
-0.00388
∆S t (year=80)
(1.30)
-0.05366
(0.95)
0.00993
(4.28)
-0.00044
(2.50)
-0.00284
(2.27)
-0.00204
(1.78)
-0.00690
(3.11)
0.05228
(7.57)
0.03481
(4.92)
0.02054
(1.21)
269
0.36
∆S t
∆ (St2)
St-1
St-12
St-1(year=70)
St-1(year=80)
yt-1
(year=70)
(year=80)
Constant
Observations
R-squared
Countries
excluded from
the sample
Congo
Egypt
China
Hong Kong
Jordan
Korea
Taiwan
Austria
Cyprus
Romania
(6)
Without 10
countries with
lowest GDP
0.22825
(5)
Without 10
countries with
lowest
education level
0.21525
(2.81)
-0.00391
(0.76)
-0.11270
(3.31)
-0.00653
(1.47)
-0.10193
(3.26)
-0.00574
(1.38)
-0.10266
(3.56)
-0.00696
(1.71)
-0.11475
(0.07)
0.00191
(1.99)
-0.06663
(1.81)
-0.06577
(1.94)
-0.08831
(2.16)
-0.07981
(0.04)
0.00926
(4.11)
-0.00042
(2.47)
-0.00266
(2.17)
-0.00183
(1.62)
-0.00590
(2.75)
0.04693
(6.94)
0.03057
(4.36)
0.01657
(1.01)
268
0.36
(1.20)
0.00900
(2.92)
-0.00037
(1.28)
-0.00161
(0.94)
-0.00163
(1.11)
-0.00766
(3.40)
0.05104
(6.64)
0.03589
(4.65)
0.02804
(1.60)
265
0.38
(1.20)
0.01131
(4.42)
-0.00056
(2.73)
-0.00288
(1.95)
-0.00231
(1.74)
-0.00815
(3.63)
0.05416
(7.36)
0.03822
(5.18)
0.02746
(1.58)
268
0.37
(1.72)
0.01084
(4.16)
-0.00048
(2.46)
-0.00359
(2.61)
-0.00358
(2.84)
-0.00798
(3.80)
0.05703
(7.21)
0.04533
(5.60)
0.02665
(1.55)
272
0.35
(1.56)
0.01118
(4.71)
-0.00048
(2.64)
-0.00364
(2.75)
-0.00353
(2.90)
-0.00874
(3.76)
0.05828
(7.60)
0.04420
(5.67)
0.03153
(1.64)
266
0.37
Botswana
Swaziland
Hong Kong
Japan
Korea
Singapore
Taiwan
Malta
Bulgaria
Romania
Absolute value of t statistics in parentheses.
Canada
USA
Denmark
Finland
Sweden
Australia
New Zealand
Czechoslovakia
East Germany
Soviet Union
Canada
USA
Bahrain
Kuwait
Belgium
France
Germany
Netherlands
Switzerland
Australia
Benin
Centr. Afr. Rep.
Gambia
Mali
Mozambique
Niger
Sierra Leone
Sudan
Afghanistan
Nepal
0.23387
Centr. Afr. Rep.
Lesotho
Malawi
Mali
Niger
Rwanda
Togo
Uganda
Zaire
Myanmar
Table 8. Income inequality
St
St2
St 60
St 70
St 80
Vt
(yr=60)
(yr=70)
(yr=80)
1{inc}
1{hh}
1{gr}
(1)
OLS in
levels
(2)
OLS in
levels
(3)
FE in
levels
-0.07192
-0.08573
-0.05534
(2.47)
0.00085
(0.38)
-0.03155
(0.95)
-0.02715
(1.51)
0.00623
(0.41)
0.00065
(3.05)
0.00170
(0.78)
(1.62)
0.00365
(1.56)
0.00105
-0.00070
(0.20)
0.11027
(0.60)
0.13346
(1.37)
-0.06782
(0.67)
0.09302
(1.70)
-0.04313
(1.20)
0.26680
(6.98)
(0.33)
-0.05257
(0.76)
0.00491
(0.10)
-0.02754
(0.68)
0.09840
(1.81)
-0.03647
(1.03)
0.26782
(7.00)
(0.20)
-0.00012
(0.00)
-0.01062
(0.44)
-0.03376
(1.79)
0.25144
(4.08)
-0.00107
(0.04)
0.00693
(0.13)
(4)
OLS in
first difs
(5)
OLS in
first difs
(6)
WLS
(GDP/w)
(7)
WLS
(popul)
-0.09820
-0.05611
-0.05718
-0.05394
(8)
OLS with
dums for
def. ch.
-0.01934
∆ (St2)
(1.40)
0.00320
(0.66)
(1.96)
(2.01)
(1.94)
(0.77)
∆Vt
0.00094
-0.00176
-0.00169
-0.00269
0.00065
(0.13)
(0.29)
(0.29)
(0.47)
(0.13)
-0.00801
(1.49)
-0.00554
(1.28)
0.04095
(3.89)
-0.00059
(0.11)
-0.00487
(0.42)
-0.00846
(1.59)
-0.00562
(1.30)
0.04155
(3.98)
0.00007
(0.01)
-0.00527
(0.46)
-0.00835
(1.57)
-0.00560
(1.30)
0.04169
(3.89)
-0.00008
(0.01)
-0.00550
(0.48)
-0.00779
(1.53)
-0.00459
(1.11)
0.04030
(3.93)
-0.00065
(0.12)
-0.00458
(0.42)
-0.00474
(1.03)
-0.00351
(0.88)
∆S t
(yr=70)
(yr=80)
∆1{inc}
∆1{hh}
∆1{gr}
dumms
Const.
Obs.
R-sq
Nr of
countries
0.73888
(10.48)
262
0.47
0.76879
(11.35)
262
0.46
0.55529
(5.48)
262
0.21
71
Const.
Obs.
R-sq
Nr of
countries
F-stat1
p-value
yes
0.01011
(2.72)
77
0.29
0.01056
(2.90)
77
0.29
0.01039
(2.90)
77
0.28
0.01008
(2.85)
77
0.27
0.00571
(1.71)
77
0.63
4.34
0.0000
Absolute value of t statistics in parentheses.
1
H0: Dummies for definitional changes jointly insignificant. The F-tests reject the null when the p-value is smaller than 0.05.
Table 9. Subsample robustness of the inequality equation
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Without 10
countries
with highest
growth in
education
Without 10
countries
with highest
growth in
GDP
Without 10
countries
with highest
inequality
growth
Without 10
countries
with highest
education
level
Without 10
countries
with highest
GDP
Without 10
countries
with highest
inequality
Without 10
countries
with lowest
inequality
∆S t
-0.07871
-0.07214
-0.00494
-0.06751
-0.06705
-0.04840
-0.05793
∆Vt
(2.22)
-0.00315
(2.00)
-0.00174
(0.17)
0.00083
(1.89)
-0.00717
(2.03)
-0.00005
(1.71)
-0.00095
(1.82)
-0.00111
(0.45)
-0.00933
(1.63)
-0.00487
(1.02)
0.04134
(3.88)
-0.00038
(0.07)
-0.00527
(0.45)
0.01152
(2.98)
69
0.32
(0.26)
-0.00874
(1.44)
-0.00559
(1.13)
0.04150
(3.79)
-0.00020
(0.03)
-0.00516
(0.43)
0.01121
(2.84)
66
0.31
(0.16)
-0.00724
(1.57)
-0.00423
(1.05)
0.02620
(2.99)
0.01535
(2.88)
-0.00723
(0.77)
0.00252
(0.73)
61
0.39
(0.86)
-0.01193
(1.87)
-0.00892
(1.82)
0.04344
(3.90)
-0.00052
(0.08)
-0.00419
(0.34)
0.01474
(2.98)
64
0.33
(0.01)
-0.00853
(1.33)
-0.00661
(1.36)
0.04132
(3.34)
0.00088
(0.15)
-0.00292
(0.17)
0.01241
(2.81)
64
0.32
(0.16)
-0.00967
(1.84)
-0.00465
(1.09)
0.03678
(3.60)
0.00538
(0.94)
-0.00624
(0.56)
0.00909
(2.55)
73
0.30
(0.16)
-0.00831
(1.36)
-0.00548
(1.16)
0.04167
(3.79)
0.00028
(0.05)
-0.00549
(0.45)
0.01068
(2.61)
70
0.28
(year=70)
(year=80)
∆(def=inc)
∆(def=hh)
∆(def=gr.)
Constant
Obs.
R-squared
Countries
excluded
from the
sample
Congo
Egypt
China
Hong Kong
Jordan
Korea
Taiwan
Austria
Cyprus
Romania
Botswana
Swaziland
Hong Kong
Japan
Korea
Singapore
Taiwan
Malta
Bulgaria
Romania
Guatemala
Brazil
Chile
Venezuela
China
Hong Kong
Thailand
Australia
New Zealand
Soviet Union
Absolute value of t statistics in parentheses.
Canada
USA
Denmark
Finland
Sweden
Australia
New Zealand
Czechoslov.
E. Germany
Soviet Union
Canada
USA
Bahrain
Kuwait
Belgium
France
Germany
Netherlands
Switzerland
Australia
Gabon
Guinea Biss.
Lesotho
Malawi
Sierra Leone
South Africa
Zimbabwe
Guatemala
Honduras
Brazil
Belgium
Hungary
Uk
Bulgaria
Czechoslov.
Romania
Latvia
Slovak Rep.
Slovenia
Ukraine
Figure 1. Return to education, education and inequality
A. Diminishing returns to education
.3
Return to Education
JAM
.2
IDN HND
BRA
COL
MEX
GTM
ESP
CHL PHL
BWA
.1
PAK
SGP
PRY CRI
ECU
NIC SLV
MYS
PRT
THA
KEN
VEN PER
DOM
BOL
IND
PAN
ARG
KOR
CYP
GBR
URY
USA
IRL
NLD
DEU
CHE
ISR
CHN
AUT
GRC
ITA
AUS
DNK
CAN
HUN
SWE
POL
0
0
1
2
3
4
5
6
7
8
Average years of schooling
9
10
11
12
B. Returns to education and inequality
.3
Return to Education
JAM
CIV
.2
HND
IDN
BRA
GTM
COL
MEX
ESP
.1
GBR
PAK
USA
IRL
NLD
PAN
PHL
SGP
KOR
CHL
CRI
MYS
THA
BOL
VEN
DOM
AUS
DNK
CHN
CAN
HUN
ITA
SWE
POL
0
.4
.5
.6
.7
.8
.9
Standard deviation log income
1
1.1
1.2
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RELATED TOPICS
EconomicsEconometricsHigher EducationHuman CapitalEconomic InequalityIncome DistributionApplied EconomicsPanel DataIncome inequalityGrowthInequalityRate of returnTechnological ProgressElasticity of SubstitutionProductivity GrowthWage DifferentialGDP GrowthSkill Biased Technological ChangeEconomics statistics