Does Schooling Cause Growth? - Pete Kleno · Does Schooling Cause Growth? By MARK BILS AND PETER J. KLENOW* A number of economists ﬁnd that growth and schooling are highly correlated

Does Schooling Cause Growth?

By MARK BILS AND PETER J. KLENOW*

A number of economists find that growth and schooling are highly correlated acrosscountries. A model is examined in which the ability to build on the human capitalof one’s elders plays an important role in linking growth to schooling. The modelis calibrated to quantify the strength of the effect of schooling on growth by usingevidence from the labor literature on Mincerian returns to education. The upshot isthat the impact of schooling on growth explains less than one-third of the empiricalcross-country relationship. The ability of reverse causality to explain this empiricalrelationship is also investigated.(JEL I2, J24, O4)

Robert J. Barro (1991), Jess Benhabib andMark M. Spiegel (1994), Barro and XavierSala-i-Martin (1995), Sala-i-Martin (1997), andmany others find schooling to be positively cor-related with the growth rate of per capita GDPacross countries. For example, we show belowthat greater schooling enrollment in 1960 con-sistent with one more year of attainment isassociated with 0.30-percent faster annualgrowth over 1960–1990. This result is consis-tent with models, such as that of Barro et al.(1995), in which transitional differences inhuman-capital growth rates explain temporarydifferences in country growth rates.

We examine a model with finite-lived indi-viduals in which human capital can grow withrising schooling attainment and thereby contrib-ute to a country’s growth rate. Each generationlearns from previous generations; the ability tobuild on the human capital of one’s elders playsan important role in the growth generated byrising time spent in school. We also incorporateinto the model a positive externality from thelevel of human capital onto the level of tech-nology in use.

We calibrate the model to quantify thestrength of the effect of schooling on growth.To do so, we introduce a measure of the impact

of schooling on human capital based on exploit-ing Mincerian returns to education and experi-ence (Jacob Mincer, 1974) commonly estimatedin the labor literature.1 Our calibration requiresthat the impact of schooling on human capitalbe consistent with the average return to school-ing observed in estimates of the Mincer equa-tion conducted on micro data across 56 separatecountries. We also require that the human-capital returns to schooling exhibit diminishingreturns consistent with the observed higher re-turns to schooling in countries with low levelsof education. We further discipline the calibra-tion by requiring that average human-capitalgrowth not be so high that technological regressmust have occurred on average in the worldover 1960–1990. Our principal finding is thatthe impact of schooling on growth probablyexplains less than one-third of the empiricalcross-country relationship, and likely much lessthan one-third. This conclusion is robust to al-lowing a positive external benefit from humancapital to technology.

If high rates of schooling are not generatinghigher growth, what accounts for the verystrong relationship between schooling enroll-ments and subsequent income growth? One el-ement is that countries with high enrollment

* Bils: Department of Economics, Harkness Hall, Uni-versity of Rochester, Rochester, NY 14627; Klenow: Re-search Department, Federal Reserve Bank of Minneapolis,90 Hennepin Avenue, Minneapolis, MN 55480. We aregrateful to Yongsung Chang and three referees, particularlythe final referee, for useful comments. Saasha Celestial-Oneprovided excellent research assistance.

1 Our approach is very related to the work of Anne O.Krueger (1968), Dale W. Jorgenson (1995), and AlwynYoung (1995), each of whom measures growth in workerquality in a particular country based on the relative wagesand changing employment shares of differing schooling-and age-groups. Our approach is more parametric, but canalso be applied to many more countries.

1160

rates in 1960 exhibit faster rates of growth inlabor supply per capita from 1960 to 1990. Thisexplains perhaps 30 percent of the projection ofgrowth on schooling. A second possibility isthat the strong empirical relation betweenschooling and growth reflects policies and otherfactors omitted from the analysis that are asso-ciated both with high levels of schooling andrapid growth in total factor productivity (TFP)from 1960 to 1990. For example, better enforce-ment of property rights or greater opennessmight induce both faster TFP growth and higherschool enrollments. Finally, the relationshipcould reflect reverse causality, that is, schoolingcould be responding to the anticipated rate ofgrowth for income.

To explore the potential for expected growth toinfluence schooling, we extend the model to in-corporate a schooling decision. Our model buildson work by Gary S. Becker (1964), Mincer(1974), and Sherwin Rosen (1976). A primaryresult is that anticipated growth reduces the effec-tive discount rate, increasing the demand forschooling. Schooling involves sacrificing currentearnings for a higher profile of future earnings.Economic growth, even of the skill-neutral vari-ety, increases the wage gains from schooling.2

Thus an alternative explanation for the Barro et al.findings is that growth drives schooling, ratherthan schooling driving growth. We calibrate themodel to quantify the potential importance of thechannel from growth to schooling, again disci-plined by estimates of empirical Mincer equations.Our calibration suggests that expected growthcould have a large impact on desired schooling.

We conclude that the empirical relationshipdocumented by Barro and others does not pri-marily reflect the impact of schooling ongrowth. We suggest that it may partly reflect theimpact of growth on schooling. Alternatively,an important part of the relation betweenschooling and growth may be omitted factorsthat are related both to schooling rates in 1960and to growth rates for the period 1960 to 1990.

The rest of the paper proceeds as follows. InSection I we lay out the model. In Section II we

document that a higher level of schooling en-rollment is associated with faster subsequentgrowth in GDP per capita (also GDP perworker, and GDP per worker net of physicalcapital accumulation). In Section III we cali-brate the model and explore whether the chan-nel from schooling to human-capital growth iscapable of generating the empirical coefficientfound in Section II. In Section IV we add thechannel from schooling to the level of technol-ogy, to see whether the effect of schooling onhuman capital and technology combined canmimic the empirical relationship. In Section Vwe investigate whether the reverse channel fromexpected growth to schooling can do the same.In Section VI we conclude.

I. A Model of Schooling and Growth withFinite-Lived Individuals

A. The Channel from Schooling to Growth

We start with production technologies sincemuch of our estimation and calibration is basedsolely on them, with no assumptions neededabout preferences or capital markets. Consideran economy with the production technology

(1) Y~t! 5 K~t!a@A~t!H~t!#1 2 a

whereY is the flow of output,K is the stock ofphysical capital,A is a technology index, andHis the stock of human capital. The aggregatestock of human capital is the sum of the human-capital stocks of working cohorts in the econ-omy. For exposition, suppose for the momentthat all cohorts go to school from age 0 to ages(so thats is years of schooling attained) andwork from ages to ageT. Then we have

(2) H~t! 5 Es

T

h~a,t!L~a,t! da

whereL(a,t) is the number of workers in cohorta at time t and h(a,t) is their level of humancapital. Note the efficiency units assumptionthat different levels of human capital are per-fectly substitutable. We generalize (2) to thecase wheres andT differ across cohorts.

2 Andrew D. Foster and Mark R. Rosenzweig (1996) findevidence for a channel from growth to schooling that involvesskill-bias of the technical change. They document that Indianprovinces benefiting from the Green Revolution in the 1970’ssaw increases in returns to, and enrollment in, schooling.

1161VOL. 90 NO. 5 BILS AND KLENOW: DOES SCHOOLING CAUSE GROWTH?

We posit that individual human-capitalstocks follow

(3) h~a,t! 5 h~a 1 n,t!fef~s! 1 g~a 2 s! @a . s.

The parameterf $ 0 captures the influence ofteacher human capital, with the cohortn yearsolder being the teachers. Whenf . 0 the qual-ity of schooling is increasing in the humancapital of teachers.3 The exponential portion of(3) incorporates the worker’s years of schooling(s) and experience (a 2 s), with f9(s) . 0 andg9(a 2 s) . 0 being the percentage gains inhuman capital from each year. Note that the“teachers” that influenceh are at schoolandonthe job. In the special case off 5 1, h growsfrom cohort to cohort even if years of schoolingattained are constant, a` la Robert E. Lucas, Jr.(1988) and Sergio Rebelo (1991). Iff , 1, thengrowth in h from cohort to cohort requires ris-ing s and/orT.

When f 5 0, f(s) 5 us, andg(a 2 s) 5g1(a 2 s) 1 g2(a 2 s)2, equation (3) reducesto the common Mincer (1974) specification.This specification implies that the log of theindividual’s wage is linearly related to that in-dividual’s years of schooling, years of experi-ence, and years of experience squared. Wechoose this exponential form precisely so thatwe can draw on the large volume of microevidence onu, g1, andg2 to quantify the impactof schooling on human capital and growth. Thisapproach differs from that of N. GregoryMankiw et al. (1992), who assume a human-capital production technology identical to thatof other goods (consumption and physical cap-ital). Although (3) is a departure from the priorliterature, we view it as an improvement be-cause it ensures that our estimates of humancapital are consistent with the private returns toschooling and experience seen in micro data.4

In addition to the direct effect of human cap-

ital on output in (1), human capital may affectoutput by affectingA, the level of technology.Richard R. Nelson and Edmund S. Phelps(1966), Theodore W. Schultz (1975), Benhabiband Spiegel (1994), and many others proposethat human capital speeds the adoption of tech-nology. For instance, the growth rate of tech-nology for countryi may follow

~4!9 gAi~t! 5 2h ln

Ai ~t!

A# ~t!

1 b ln hi ~t! 1 j i ~t!

whereA# is the exogenously growing “world tech-nology frontier” andhi(t) 5 Hi(t)/Li(t) is the av-erage level of human capital in countryi.5 Whenh . 0, the closer the country’s technology to thefrontier the slower the country’s growth rate.When b . 0, the higher the country’s humancapital the faster the country’s growth rate. Asstated, one motivation forb . 0 is that humancapital may speed technologyadoption.But an-other motivation is that human capital may benecessary for technologyuse.That is, in (4)9 hu-man capital can be indexing the fraction of frontiertechnology which the country can use.6 Evidencethat human capital plays a role in adoption in-cludes Finis Welch (1970), Ann Bartel and FrankLichtenberg (1987), and Foster and Rosenzweig(1996). Empirical studies finding that human cap-ital is complementary to technology use are plen-tiful, recent examples being Mark Doms et al.(1997), David H. Autor et al. (1998), and EliBerman et al. (1998).

If one integrates (4)9 over time one finds thatthe level of technology in a country should be apositive function of its current and past human-capital stocks. Below we report that there isample evidence that the level of technology [Aconstructed from equation (1)] and the level ofhuman capital [constructed using equation (3)]are positively correlated across countries. Con-ditional on current human capital, however, wedo not find a positive correlation between cur-rentA and past human capital. In terms of (4)9,

3 We ignore nonlabor inputs because evidence suggeststhat teacher and student time constitute about 90 percent ofall costs (see John W. Kendrick [1976] and U.S. Departmentof Education [1996]).

4 Recent papers that have followed our approach includeCharles I. Jones (1998), Boyan Jovanovic and Raphael Rob(1998), Jonathan Temple (1998), Daron Acemoglu and Fab-rizio Zilibotti (1999), and Robert E. Hall and Jones (1999).

5 Li(t) is the sum ofLi(a, t) across cohorts.6 William Easterly et al. (1994), Jones (1998), and Fran-

cisco Caselli (1999) adopt this “use” formulation.

1162 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000

this could mean thath is very high so thattransition dynamics are rapid and economies areclose to their steady-state paths. This wouldsuggest a simple use formulation, with a higherlevel of human capital allowing a higher level oftechnology use:

(4) ln Ai ~t! 5 b ln hi ~t! 1 ln A# ~t! 1 j i~t!.

f

(5) gAi~t! 5 bghi

~t! 1 gA# ~t! 1 « i ~t!.

Equation (5) says that growth in human capitalcontributes to growth indirectly (through growthin A), not just directly [throughH in equation (1)].Note that, because we measureh to be consistentwith Mincerian private-return estimates in (3), thisindirect effect of human capital on technologyrepresents an externality not captured by the indi-vidual worker. Externalities might arise becauseof learning from others who have adopted or be-cause introduction of technology is based on theamount of human capital in the country as a whole(e.g., when there is a fixed cost component totransferring technology).

In Section III we estimate the effect ofschooling on growth using equations (1)through (5), eschewing (4)9 in favor of (4) be-cause the latter fits the data better. In conductingthis growth accounting we can take schoolingdecisions as given (i.e., as data). To quantifypossible reverse causality, however, we mustmodel schooling decisions. For this purpose, wenext specify market structure and preferences.

B. The Channel from Growth to Schooling

We consider a competitive open economyfacing a constant world real interest rater .7

With the price of output in the world normalizedto one each period, firm first order conditionsfrom (1) are

(6) aY~t!/K~t! 5 r 1 d

and

(7) ~1 2 a!Y~t!/H~t! 5 w~t!

where d is the depreciation rate of physicalcapital andw is the wage rateper unit of humancapital. Combining (1), (6), and (7), one caneasily show that

(8) w~t!}A~t!

which means the wage per unit of human capitalgrows at the rategA.

In this economy each individual is finite-lived and chooses a consumption profile andyears of schooling to maximize

(9) E0

T

e2rtc~t!1 2 1/s

1 2 1/sdt 1 E

0

s

e2rtz dt.

Herec is consumption andz is flow utility fromgoing to school. Schultz (1963) and others ar-gue that attending class is less onerous thanworking, especially in developing countries.This benefit of going to school will create anincome effect on the demand for schooling.8

The individual’s budget constraint is

(10)

Es

T

e2rtw~t!h~t! dt $ E0

T

e2rtc~t! dt

1 E0

s

e2rtmw~t!h~t! dt

7 The commonr assumption means that, in our model,the private rate of return to schooling will be equalizedacross countries. This is in contrast to the model of Barro etal. (1995), in which low schooling countries have highreturns to human capital but cannot borrow to financehuman-capital accumulation.

8 We model a utility flow from going to school forconcreteness, but there are other motivations for an incomeeffect: higher education may improve one’s ability to enjoyconsumption throughout life (Schultz, 1963); higher incomemay relax borrowing constraints; and tuition may not risefully with a country’s income (say because goods are usedin education production).


wherem . 0 is the ratio of school tuition to theopportunity cost of student time.9 Individualsgo to school until ages and work from agesthrough ageT.

From (3), (9), and (10), the first-order condi-tion for an individual’s schooling choice is

(11) ~1 1 m!w~s!h~s! 5 zc~s!1/s

1 Es

T

e2r ~t 2 s!@f9~s! 2 g9~t 2 s!#w~t!h~t! dt

which equates the sum of tuition and the oppor-tunity cost of student time for the last year spentin school (the left-hand side) to the sum of theutility flow from attending plus the presentvalue of future earnings gains (the right-handside). The gap between human capital gainedfrom education and that gained from experience[ f9(s)2g9(t2s)] enters because staying inschool means forgoing experience.

The privately optimal quantity of schooling isgenerally not an explicit function of the model’sparameters. To illustrate concepts, however,consider a special case in which it is:f(s) 5 us,g(a 2 s) 5 g(a 2 s), andz 5 0. (Later, whenwe calibrate the model, we considerz . 0 andg and f functions with realistic curvature insanda 2 s.) Usingh(t) 5 h(s)eg(t 2 s) @t . s,w(t) 5 w(s)egA(t 2 s) from (8), and first-ordercondition (11), the privately optimal quantity ofschooling is

(12) s 5 T

2 F 1

r 2 gA 2 gG3 ln F u 2 g

u 2 g 2 m~r 2 gA 2 g!G .

Equation (12) illustrates the channel by whichhigher expected growth inA can induce moreschooling. The interest rater and the growthrate gA enter the schooling decision through

their difference (r 2 gA), so comparative stat-ics of the schooling decision with respect togAmirror those for r , with the opposite sign.Higher growth acts just like a lower marketinterest rate: by placing more weight on futurehuman capital, it induces more schooling. Thebenefit of having human capital is proportionalto the level ofA while working. The cost ofinvesting in human capital is proportional to thelevel of A while in school. Thus higherA in thefuture relative to today, which is to say highergrowth in A, raises the private return to invest-ing in schooling.

Other noteworthy implications of the modelare as follows. A permanently higherlevel oftechnologyA (equivalently, wage per unit ofhuman capital) does not affect the optimalamount of schooling because it affects the mar-ginal cost and benefit of schooling in the sameproportion. Similarly, neither teacher humancapital nor its contribution to learning (f) affectthe schooling decision. These results onA andteacher human capital hinge onz 5 0 (no utilitybenefit to attending class). Regardless of thelevel ofz, a higher life expectancy (T) results inmore schooling, since it affords a longer work-ing period over which to reap the wage benefitsof schooling. Likewise, a higher tuition ratio (m)lowers schooling.

II. The Cross-Country Pattern of Schoolingand Growth

Barro (1991) finds that 1960 primary- andsecondary-schoolenrollment ratesare posi-tively correlated with 1960–1985 growth in realper capita GDP. Column (1) of our Table 1 re-produces this finding using updated RobertSummers and Alan Heston (1991) Penn WorldTables Mark 5.6 data and Barro and Jong-WhaLee (1993) enrollment rates.10 Our measure ofschooling equals six times a country’s primary-school enrollment rate plus six times its

9 We make tuition costs increasing in the opportunitycost of student time because, in the data, tuition rises withthe level of education (see U.S. Department of Education,1996).

10 Our specification differs from Barro’s (1991) in thatwe enter a single schooling variable (rather than primary,secondary, and tertiary schooling separately) and omit ini-tial income as well as other control variables (such as thenumber of coups). If we condition on the natural log of 1960per capita GDP, the coefficient on schooling is 0.598 per-cent (with a standard error of 0.094 percent) and the coef-ficient on initial income is21.215 percent (standard error0.291 percent).


secondary-school enrollment rate plus fivetimes its higher-education enrollment rate. Thiscorresponds to the steady-state average years ofschooling that these enrollment rates imply,with the durations of primary, secondary, andhigher education based on World Bank (1991 p.285) conventions. The estimated coefficient onschooling in column (1) implies that an increasein enrollment rates tantamount to one more yearof attainment is associated with 0.30-percentper year faster growth over 1960–1990 (with astandard error of 0.05 percent).11

Our focus is on whether high enrollments in1960 are associated with rapid subsequentgrowth because high enrollments generate rapidgrowth in human capital or productivity. There-fore, we proceed to net off the contribution ofgrowth in labor supply and physical capital percapita to arrive at a measure of the combinedgrowth in h and A for each country. We firstdeduct the contribution of growth in labor sup-ply by examining growth in income per workerrather than per capita. (Measures of GDP perworker are also taken from the Penn WorldTables.) The result, shown in column (2) ofTable 1, is that an increase in enrollments suf-ficient to produce one more year of schooling is

associated with 0.21-percent faster growth peryear for 1960–1990 (with a standard error of0.05 percent). Thus nearly 30 percent of theprojection of growth in per capita income on1960 schooling, reported in column (1), reflectsfaster growth in labor supply per capita in coun-tries with higher 1960 schooling.

Now, using (1) we can isolate the combinedgrowth in h andA for each country as

gh 1 gA 51

1 2 a~gy 2 agk!

where h is human capital per person,A is aproductivity index,y is GDP per worker, andkis physical capital per worker. We estimatekusing investment rates from the Penn WorldTables and the 1960 capital stocks estimated byKlenow and Andre´s Rodrı´guez-Clare (1997).12

We set physical capital’s share (a) to one-third.The result of regressinggh 1 gA on schoolingin 1960 for the 85 countries with available dataappears in the third column of Table 1. Anadditional year of schooling enrollment in 1960is associated with an increase ingh 1 gA peryear for 1960 to 1990 of 0.23 percent (with astandard error of 0.05 percent). In Section III we

11 Related, Eric A. Hansuhek and Dennis D. Kimko(2000) examine the relationship between thequality ofschooling (measured by standardized math and science testscores) and subsequent economic growth. They find a sig-nificant relationship, even controlling for the quantity ofschooling.

12 Klenow and Rodrı´guez set a country’s 1960K/Y 5I /Y/( g 1 d 1 n), with the investment rateI /Y, the growthrate ofY/L( g), and the population growth rate (n) equal tothe country’s averages over 1960–1970, and withd 5 0.07.

TABLE 1—GROWTH REGRESSED ONRATES AND YEARS OF SCHOOLING

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

Dependent variable GDP per capita GDP per worker Ah† Ah

Schooling 1960 0.300 percent 0.213 percent 0.229 percent 0.476 percent(Enrollment rates) (0.050) (0.050) (0.049) (0.117)

Average years ofschooling, 1960

20.223 percent(0.118)

R# 2 0.23 0.13 0.15 0.22Number of

countries 93 93 85 81

Notes:The dependent variable is the average annual growth rate from 1960 to 1990 of thevariable listed. White-corrected standard errors are in parentheses.Sources:The data is from Summers-Heston (Penn World Tables, Mark 5.6, 1991) and fromBarro and Lee (1996).

† A is a productivity index.h is human capital per person.


break this impact into itsgh andgA componentsfor various specifications of the accumulationtechnology for human capital.

Barro and Sala-i-Martin (1995) employ dataon years of schoolingattainmentin a country’sworking-age population to test the hypothesisthat schooling promotes growth. Column (4) ofTable 1 relates average annual growth from1960 to 1990 to Barro and Lee’s measure of1960 schooling attainment, again with an up-dated data set (Barro and Lee, 1996), as well asto enrollment (years of schooling based on 1960enrollment rates). Growth remains highlycorrelated with enrollment rates. Conditional on1960 enrollment rates, past enrollments (ascaptured by attainment) have no positive rela-tion to growth; in fact, attainment enters with amarginally statistically significant negativeimpact. We view this as suggestive that anycausal impact of 1960 schooling on growthfrom 1960 to 1990 is more likely to reflecttransitional growth in human capital or tech-nology over the period, as opposed to asteady-state influence on growth (as, for in-stance, in AK models). If schooling createssustained growth, then the schooling attain-ment in a country, reflecting past enrollmentrates, should positively, rather than nega-tively, influence growth.

To repeat, an extra year of schooling en-rollments in 1960 is associated with 0.23-percent faster annual 1960 –1990 growth inhuman capital and technology combined. Weproceed as follows to deduce how much ofthis impact reflects a causal effect fromschooling to growth. In the next section wecalculate to what degree countries with higherenrollments in 1960 exhibit faster subsequentgrowth in human capital. In Section IV weallow human capital to add to growth bothdirectly and indirectly by spurring more ad-vanced technology. In Section V we examinethe ability of the reverse channel from ex-pected growth to schooling to explain thestrong correlation between 1960 enrollmentsand growth over 1960 to 1990.

III. Estimating the Impact of Schooling onGrowth in Human Capital

In this section we quantify the growth inhuman capital from 1960 to 1990 for a cross

section of countries. We consider various spec-ifications of the production of human capitaldesigned to be consistent with Mincer (1974)wage equations that have been estimated formany countries. We also allow schooling in-vestments in one generation to improve thequality of education for subsequent generations.We then ask to what extent the faster growth inincome for countries with high schooling en-rollments in 1960 can be attributed to fastergrowth in human capital from 1960 to 1990.

A. Calibrating the Production Function forHuman Capital

Based on equation (3) andg(a 2 s 2 6) 5g1(a 2 s 2 6) 1 g2(a 2 s 2 6)2—aquadratic term in experience, as is standard inthe empirical literature on wages—a worker ofagea will possess a natural log of human capitalgiven by

(13) ln@h~a!# 5 f ln@h~a 1 n!#

1 f~s! 1 g1~a 2 s 2 6!

1 g2~a 2 s 2 6!2.

A time subscript is implicit here. For as manycountries as possible, we construct human-capital stocks for individuals of each age be-tween 20 and 59, using (13) and incorporatingschooling, experience, and teacher human cap-ital specific to each age. We can then calculateaverage human-capital stocks for each countryin 1960 and 1990 by weighting each age’shuman-capital stock by the proportion of thatage-group in the total population of the countryin that year (using population data from UnitedNations, 1994).

To make (13) operational requires data onschooling attainment going back as many yearsas possible. This is of particular importance iffis positive, making the current generation’s hu-man capital depend on past generations’ school-ing. United Nations Education, Scientific, andCultural Organization (UNESCO) (1977, 1983)report country census data on schooling attain-ment of age-groups 20 to 54 or older in years asfar back as 1946 and as recently as 1977. Weexploit this data to construct a time series for


schooling attainment of 20-year-olds for closeto 40 years before the earliest survey.13 Thisconstruction is described in much greater detailin Appendix A. For the countries with the rel-evant data, we estimate the persistence of at-tainment from 1955–1985 and 1925–1955,respectively. Based on this, for a panel of 85countries we “fill in” estimates of the attainmentof 20-year-olds for the years going back beforeattainment data is available in each country. Wealso report results for a 55-country sample forwhich attainment data reach back at least to1935.

Constructing individual human capitals in(13) also requires parameter values for the re-turns to experience,g1 andg2, a parameterizedfunctional form for the impact of schooling,f(s), a value for the parameterf that governsthe intertemporal transmission of human capi-tal, and (whenf . 0) a value for the agedifference between teachers and students,n.

We base the returns to experience and school-ing on estimates of the sources of wage differ-ences (Mincer equations) that have beenexamined with micro data for a large number ofcountries. The canonical Mincer regression es-timates the “returns” to experience and educa-tion using a cross section of individuals (i ’s)

(14) ln~wi ! 5 l0 1 l1si

1 l2~age2 si 2 6!

1 l3~age2 si 2 6!2 1 « i

wherew is the wage,s is years of schooling,(age 2 s 2 6) is experience, and« reflectsmeasurement error, ability, and compensatingdifferentials. In terms of (13), this specificationsetsf 5 0 and makes the impact of schoolinglinear ins. We obtained estimates of (14) for 52countries, largely from the work of GeorgePsacharopoulos (1994).14 In Appendix B we list

the 52 countries and their estimated returns toschooling and experience. Underlying these es-timates are about 5,200 persons per country,with a median sample size of 2,469. We con-centrate on estimates for males since the degreeto which “potential experience” (age2 s 2 6)deviates from actual experience may differ sub-stantially across countries for women.

Our parameter choices forg1 and g2 reflectthe average estimates forl2 andl3 across these52 countries. These average estimates are0.0512 and20.00071, respectively.

For f(s) we posit

(15) f~s! 5u

1 2 cs1 2 c.

We entertainc . 0 because diminishing Mince-rian returns to schooling appear to exist whenwe compare micro-Mincer estimates acrosscountries.

To estimatec in (15), we exploit the fact thatestimated Mincerian returns to education,l1 in(14), equal f9(s) 5 u/sc. Psacharopoulos(1994) reports estimates of Mincerian returns toschooling, together with mean years of school-ing in the sample, for 56 countries.15 We regresscountry Mincerian returnestimateson countryschooling levels for Psacharopoulos’ 56-coun-try sample:

ln~l1! 5 ln~u! 2 c ln~s!

1 @ln~l1! 2 ln~l1!#.

We find c 5 0.58 with a standard error of 0.15.Thatc . 0 means countries with higher school-ing levels display lower Mincerian returns toeducation. For example, as years of enrollmentin 1960 go from 2 to 6 to 10 (e.g., as in fromthe Central African Republic to Fiji to Iceland),the implied Mincerian return on schoolingfalls from 21.6 percent to 11.4 percent to 8.5

13 For countries with nontrivial higher education, a num-ber of 20-year-olds may have not completed their formalschooling. In these cases we base the attainment of 20-year-olds in yeart on the reported attainment of 25-year-olds inyear t 1 5.

14 Psacharopoulos, sometimes with co-authors, con-ducted studies for 23 of our 52 countries. Through refer-ences in Psacharopoulos (1994) we obtained estimates for

another 20 countries. We found independent estimates fornine more countries.

15 We use his sample, as opposed to our 52-countrysample, because this exercise does not require that returns toexperience also be reported, but does require the averageyears of attainment in each sample.


percent.16 These sharply diminishing returnsdepart from the custom in the labor literature ofpositing no diminishing returns.17 For this rea-son we consider two lower values of the curva-ture parameterc, or three in all: 0.58 (our pointestimate), 0.28 (our point estimate minus twostandard errors), and 0 (no diminishing returns).But we note that the case of no diminishingreturns is nearly four standard errors below ourestimate ofc.

For each value ofc we set the value ofu sothat the mean ofu/sc equals the mean Mince-rian return across Psacharopoulos’ 56 countries,which is 0.099. Whenc 5 0.58, u 5 0.32achieves this objective; whenc 5 0.28, u 50.18 does so; whenc 5 0 the required value ofu is, of course, 0.099. These estimated Mince-rian returns to education may overstateu. First,estimates of (14) based on cross sections ofindividuals are biased upward if high-abilityindividuals (those with high«) obtain moreeducation. Second, Mincer’s specification im-poses a constant return to education. For curva-ture parameterc . 0, the return to schooling isconvex to the origin; so by Jensen’s inequalitylinear estimates overstateu. Overstating uwould mean overstating the causal impact ofenrollment in 1960 ongh and growth in output.

We consider a range of values forf, theelasticity of human capital with respect toteacher human capital. The standard Mincerspecification setsf 5 0. Note that values forfmuch above zero greatly increase the total “re-turn” to schooling. For instance, along a steady-state growth path, the return on schooling is

magnified to the extent of1

1 2 f; so forf 5 1⁄2

the Mincerian return to schooling is doubled.We pick an upper value for the range off asfollows. For each value ofc, we pick a value forf sufficiently large that all growth inAh from1960 to 1990, on average for our sample ofcountries, can be attributed to growth in humancapital. We view this as an upper bound on theplausible range forf. Any higher value forfwould imply that 1960–1990 growth in outputper worker, which for our sample of countriesaveraged nearly 1.1 percent per year net of theimpact of growth in physical capital, was asso-ciated with a 30-year period of technologicalregress.

For f . 0 it is necessary to calibraten, theage gap between students and teachers. We setn 5 25. This is slightly less than the averageage gap we calculate between student andworker for countries in the Summers-Hestondata.18

B. Results

For each specification of the human-capitalproduction function (values ofc and f) weregress the calculated annual growth rate inhfor 1960 to 1990, which we denote asgh, onyears of schooling enrollment in 1960 for 85countries with available data. Results appear inTable 2. Recall from Table 1 that one more yearof schooling enrollment in 1960 is associatedwith 0.23-percent faster growth per year inAhfrom 1960 to 1990. (For comparison purposes,the bottom of Table 2 shows that the corre-sponding coefficient for this sample of 85 coun-tries is similar at 0.24 percent.)

We begin in the first panel of Table 2 with thecase of curvature parameterc 5 0.58. Row 1shows that, withf 5 0 so that onlyownschool-ing and experience feeds into human capital, thecoefficient on schooling is actually negative,equaling20.100 percent with a standard errorof 0.015 percent. Hence one cannot argue that1960 enrollment is highly correlated with sub-sequent GDP growth through growth in the

16 Noting that India and China exhibit modest Mincerianreturns despite low schooling attainment (see our AppendixB), we were concerned that this result might be driven byhigh Mincerian returns in small, low schooling-attainmentcountries such as Honduras. When we excluded the 12countries with populations below 5 million, however, weobtained a similar coefficient of20.53 (standard error0.16).

17 When estimated on micro data within countries, thetypical finding is linear returns to education, orc 5 0. SeeDavid Card (1994). As Card argues, ability bias may drivethese estimates toward linearity. The cross-country esti-mates are arguably less subject to ability bias and morelikely to reflect differences in education subsidies and lifeexpectancy.

18 In 1960 the average life expectancy across our sampleof countries was 60.5. If all but six years are spent in schoolor at work, the average age gap between student and workerwill be (60.5 2 6)/2 5 27.25 years. We obtained lifeexpectancy for a person who has successfully reached ageone from Barro and Lee (1993).


quantity of school attainment and experience.(Limiting the analysis to a sample of 55 coun-tries for which we can construct enrollmentrates back at least to 1935 yields an even morenegative impact ongh of 20.137 percent with astandard error of 0.020 percent.)

It may appear surprising that countries withhigher enrollment rates do not display fasterhuman-capital growth from 1960 to 1990. It isimportant to recognize, however, that one moreyear of schooling enrollments in a country in1960 is associated with a very modest increasein schooling attainment in the working popula-tion between 1960 and 1990 of only 0.042 ad-ditional years. This reflects the high persistenceof cross-country differences in enrollment rates.(See Appendix A.) Because countries with highenrollment rates in 1960 also had relatively highenrollments pre-1960, these countries arelargely just maintaining their relatively highattainments. Also, forc 5 0.58 there are con-siderably diminishing returns to schooling.

Consider two countries, each of which hashigher enrollments in 1960 than in past years.Both countries will exhibit growth in humancapital. But the country expanding on a rela-tively low level of enrollments will displaysomewhat faster growth in human capital. Wesee shortly that forc 5 0, higher enrollmentrates in 1960 are associated with highergh,though the magnitude is small.

The rightmost column of Table 2 reports that,for this specification, the average growth rate inhuman capital for the 85 countries for 1960 to1990 equals 1.39 percent. By comparison, theaverage rate of growth forAh equals 1.60 per-cent. Thus the specification in column 1,c 50.58, f 5 0, implies that over 85 percent ofgrowth in Ah can be attributed to growth inhuman capital. More generally, we find for allspecifications considered that growth in humancapital is primarily responsible for averagegrowth in Ah for 1960 to 1990.

Row 2 reports results forf 5 0.19. Forc 5

TABLE 2—GROWTH IN HUMAN CAPITAL REGRESSED ONSCHOOLING

Schooling 1960(Enrollment rates) R# 2 Meangh

f 5 0 20.100 percent 0.35 1.39 percent(0.015)

c 5 0.58f 5 0.19 20.091 0.29 1.60

(0.015)

f 5 0 20.007 20.01 1.11(0.011)

c 5 0.28 f 5 1⁄3 0.029 0.06 1.43(0.012)

f 5 0.46 0.054 0.19 1.60(0.012)

f 5 0 0.048 0.23 0.94(0.009)

c 5 0 f 5 1⁄3 0.087 0.50 1.18(0.009)

f 5 0.67 0.171 0.80 1.60(0.009)

Notes:The dependent variable is the average annual growth rate of human capital from 1960to 1990. 12 c andf are the respective exponents on years of schooling and teacher humancapital in the human-capital production function. The number of countries in the sampleequals 85. For these 85 countries, the regression for growth in human capital plus technology[Table 1, col. (2)] is:gh 1 gA 5 0.238 S60, R# 2 5 0.18.

(0.054)


0.58 this value is the upper bound on the plau-sible range forf. That is, higher values forfwould imply that technology regressed on av-erage for the 85 countries from 1960 to 1990.Even for this higher value off the schoolingcoefficient remains negative at20.091 percent,and statistically significant. (The coefficient isyet more negative, equaling20.131 percentwith standard error 0.021 percent, if we confinethe regression to those 55 countries for whichwe have attainment data back to 1935 or ear-lier.) Hence, even incorporating estimates ofrising school quality reflecting rising humancapital of teachers, the correlation of 1960 en-rollment with subsequent growth in human cap-ital accounts for none of the dramaticassociation of 1960 schooling with faster in-come growth from 1960 to 1990.

As discussed above, this benchmark case withc 5 0.58 features steeply diminishing Mincerianreturns to schooling. Results forc 5 0.28 arepresented in the second panel of Table 2. Whenf 5 0, so that human capital of elders does notdirectly augment human capital of the young, wefind no impact of 1960 enrollment rates on humancapital growth,gh, from 1960 to 1990. (The coef-ficient equals20.007 percent with standard error0.011 percent.) The next row presents results rais-ing f to 1⁄3. For f 5 1⁄3 there is now a positiveeffect of 1960 schooling ongh, equaling 0.029percent (standard error 0.012 percent). Neverthe-less, this effect remains only one-eighth the size ofthe projection ofgh 1 gA on 1960 schoolingenrollments. By construction, this implies that allbut one-eighth of this projection reflects fastergrowth inA in countries with high schooling ratesin 1960. Forc 5 0.28, as opposed to 0.58, a largervalue forf can be considered without driving theaverage value ofgh above the average value ofgh 1 gA. For the upper value off 5 0.46 theimpact of 1960 schooling ongh equals 0.054 per-cent (standard error 0.012 percent). This still rep-resents less than one-fourth of the projection ofgh 1 gA on schooling, with more than three-fourths attributable to faster growth in technology.Note, however, that this arguably exaggerates thevalue off, the impact of elders’ human capital,and the importance of growth in human capital asit leaves no role for advances in technology inaverage growth from 1960 to 1990.

Finally, results for no curvature (c 5 0) aregiven in the bottom panel of Table 2. The caseof f 5 0 corresponds to a standard Mincer

specification. The projection ofgh on the 1960years of schooling enrollment generates a coef-ficient of 0.048 percent (with standard error of0.009 percent). This is one-fifth of the sizeneeded to explain the projection ofgh 1 gA on1960 enrollments, implying that 80 percent ofthe explanation for faster growth can be attrib-uted to faster growth in technology. Forf 5 1⁄3the estimated impact of schooling ongh equals0.087 percent (standard error 0.009 percent),implying that country differences ingh contrib-ute over one-third of the differences ingh 1 gAassociated with schooling in 1960. Forc 5 0 itis possible to takef up to as high as 0.67without driving the average value forgh abovethe average value forgh 1 gA. For this upper-most value off 5 0.67, the estimated impact ofschooling ongh is substantial, equaling 0.171percent (standard error 0.009 percent). This, bycontrast to the other specifications, implies thattwo-thirds of the country differences ingh 1 gAassociated with schooling in 1960 can be attrib-uted to thegh component.

We conclude that pure growth in human capitalaccounts for a minority of the observed relationbetween schooling and income growth, mostprobably less than one-third. The exception is ifthere are no diminishing returns to the investmentin schooling and we take the power on the previ-ous generation’s human capital, parameterf, toequal our imposed upper bound. Then we canaccount for a majority of the schooling-growthrelation with human-capital growth. But note thatthis specification is extreme in a couple of re-spects. The lack of diminishing returns to school-ing is strongly contradicted by the cross-countryevidence on schooling returns in Psacharopoulos(1994). In fact, a value forc of 0 is nearly fourstandard errors below our point estimate ofc.Secondly, the very high value forf of 0.67 im-plies thataveragegrowth in human capital for the85 countries accounts for all ofaveragegrowth inAh of 1.6 percent per year, allowing no role forimprovements in technology from 1960 to 1990.19

19 One might also object to the very high value forf of0.67 on the grounds that it requires an implausibly strongimpact of parent and teacher human capital on the outcomesof students. For instance, researchers such as Hanushek(1986) and James J. Heckman et al. (1996) have difficultycorrelating schooling outcomes with teacher inputs. Suchevidence, however, may not capture all channels by whicha person can be affected by the human capital of their elders.


To illustrate this point, suppose we only requirethat c be within three standard deviation of itsestimate, so thatc 5 0.13, and that technologicalgrowth, on average, be strictly positive but verysmall, so that it contributes only one-tenth (0.2percent per year) of the observed average growthin income per worker for these 85 countries.These conditions are sufficient to restrict the in-tergenerational parameterf to equal 0.34. Fur-thermore, these restrictions imply that oneadditional year of schooling enrollment in 1960 isassociated with 0.065 percent fastergh for 1960 to1990 (with standard error 0.011 percent). Thisexplains only 30 percent of the magnitude of theprojection ofgh 1 gA on 1960 enrollments re-ported in Table 1.20

IV. Estimating the Impact of Schooling onGrowth in Technology

Higher school enrollment in 1960 may beassociated with faster growth inA becausegrowth in human capital facilitates adoption oftechnology. [See the discussion and referencessurrounding equations (4)9, (4), and (5) in themodel section above.] If workers need morehuman capital to use more advanced technol-ogy, then growth in human capital can bringimprovements in technology. Our human-capital stocks should reflect the private wagegain to the adopting worker. But if there areexternal effects to that adoption, it will show upas higherA where human capital is higher.

Suppose that, based on equation (4) above,we regress the log level ofA in 1990 on the log

level of human capital,h, in 1990 for our sam-ple of 85 countries.21 We measure human cap-ital based on the parameter valuesc 5 0.28 andf 5 1⁄3. This is intermediate to the cases exam-ined in Section III. This exercise yields an es-timated elasticity ofA with respect toh of 0.77(standard error 0.13).22 If one interprets this asan unbiased estimate ofb in equation (4), thenthis is consistent with an external benefit three-quarters as large as the private benefit to humancapital. Of course,A may be high in countrieswith high human capital because they are bothcaused by, say, government policies favoringinvestments of all types. If so, then the ordinaryleast-squares (OLS) estimate of the external ef-fect is biased upward.23

Consider the very high (OLS) estimated elas-ticity of A with respect toh of 0.77. It is importantto recognize that this elasticity implies that thecombined direct and indirect (throughA) impactsof growth in human capital on income growthwould be extremely large for the 1960 to 1990period. As reported in Table 2, forc 5 0.28 andf 5 1⁄3, the averagegh for 1960–1990 for the 85countries equals 1.43 percent per year. The elas-ticity of 0.77 implies a combined impact ofgrowth inh on gh 1 gA of 2.53 percent per year.But the total growth ingh 1 gA on average acrossthe 85 countries equals only 1.60 percent per year.This discrepancy would require that technology,holding human capital constant, must have re-gressed at 0.93 percent per year. We view this asimplausible.

20 From Table 2, we see that for countries with high 1960schooling to exhibit much highergh requires an importantrole for risingquality of schooling, reflecting rising humancapital of teachers and a value forf considerably above 0.In an earlier version of this paper (Bils and Klenow, 1998),we show that growth in the quality of schooling can implyrelatively higher wages for younger cohorts, biasing theestimated Mincerian return on experience below its truereturn. This downward bias should be most pronounced forcountries with the most rapid growth in their quality ofschooling. If cross-country differences in growth partlyreflect differences in the rate of growth of the quality ofschooling, then we should observe flatter age-earnings pro-files in countries which have displayed more rapid growth.We test this prediction by relating differences in the esti-mated return to experience for 52 countries to differences intheir growth rates of per capita income. We find no evidencethat faster growth affects the wages of the young relative tothose of the old.

21 Heckman and Klenow (1997) follow a similar strategyin order to gauge the potential for externalities from humancapital.

22 When we added lags of the human-capital stocks tothis regression, none entered positively and significantly. Interms of our model section, the data favor specification (4)over (4)9. For this reason we maintain the interpretation thata higher level of human capital raises the level of technol-ogy rather than its transitional growth rate.

23 The natural attack on this simultaneity problem is toinstrument for country differences in human capital withvariables that influence human capital but are otherwiseexogenous to a country’s level of technology. In practice itis very difficult to find cross-country variables that are bothrelevant predictors of schooling and arguably valid instru-ments. In an earlier draft (Bils and Klenow, 1998) weattempted to instrument for a country’s human capital usinglife expectancy in the country or, alternatively, a set ofvariables depicting climate in the country. We found a veryhigh elasticity ofA with respect to instrumented countrydifferences inh. We presented considerable evidence, how-ever, that our instruments were not valid.


We explore this connection further in Table3. Here we vary the impact of human capital ontechnology while at the same time imposingthat technology, holdingh constant, did notregress on average for our 85 countries.24 Foreach elasticity ofA with respect toh, this re-quires putting an upper bound on the parameterf such that the combined direct and indirectimpact of growth in human capital ongh 1 gAdoes not explain more than 100 percent of itsaverage value across countries for 1960–1990of 1.60 percent. We then ask how much of thefaster growth observed ingh 1 gA in countrieswith high 1960 schooling can possibly be attrib-uted to the direct plus indirect (technology)effects of faster growth in human capital inthose countries.

Table 3 again considers values for the curva-ture parameterc equal to 0.58, 0.28, and 0,starting in the top panel withc 5 0.58. For

comparison, the first row presents the case ofhhaving no impact onA. This duplicates resultsfrom Table 2. The upper bound onf, for c 50.58, is 0.19. Note that for this benchmark case,countries with relatively high 1960 schoolinghaveslowergrowth in human capital, with thecoefficient equaling20.091 percent. The sec-ond row assumes a positive elasticityb of Awith respect toh equal to 0.15. This value forbis the largest we can entertain, while at the sametime keeping the parameterf that links humancapital across generations nonnegative andkeepingaverageresidual technological growthnonnegative for the 85 countries. For this caseas well, countries with higher 1960 schoolingexhibit slower growth in human capital, thecoefficient equaling20.100 percent. Thus mag-nifying increases in human capital to capture aninfluence on technology (last column of Table3) only makes this negative impact larger inmagnitude.

The middle panel of Table 3 treats the case ofc 5 0.28. The first row repeats the case fromTable 2 ofb 5 0, with f set at the upper boundof 0.46. The impact of 1960 schooling ongh

24 Our approach is similar to an exercise of Becker’s(1964 Ch. 6), who estimates the “room” for human-capitalexternalities in the level of residual TFP growth.

TABLE 3—GROWTH IN HUMAN CAPITAL, WITH INDUCED GROWTH IN TECHNOLOGY, REGRESSED ONSCHOOLING

(1) (2) (3)

Critical value forf Impact of 1960schooling ongh

Combined impact ongh 1 gA

b 5 0 0.19 20.091 percent 20.091 percent(0.015) (0.015)

c 5 0.58b 5 0.15 0 20.100 20.115

(0.015) (0.017)

b 5 0 0.46 0.054 0.054(0.012) (0.012)

c 5 0.28 b 5 1⁄3 0.11 0.002 0.003(0.012) (0.015)

b 5 0.42 0 20.007 20.010(0.011) (0.016)

b 5 0 0.67 0.171 0.171(0.009) (0.009)

c 5 0 b 5 1⁄3 0.35 0.090 0.120(0.009) (0.013)

b 5 0.71 0 0.048 0.082(0.009) (0.015)

Note: b 5 elasticity of A (technology) with respect toh (human capital);f 5 the exponent on teacher human capital inhuman-capital production; 12 c 5 the exponent on years of schooling in human-capital production.


equals 0.054 percent, less than one-fourth of theextent thatgh 1 gA projects on 1960 schooling.The next row assumes thatA exhibits an elas-ticity b of 1⁄3 with respect toh, so increases inh raise the level of technology. Note, however,that it is now necessary to reducef from 0.46down to 0.11 in order that growth in humancapital not explain more than 100 percent ofaveragegh 1 gA. This reduces the impact of1960 schooling ongh from 0.054 percent all theway down to 0.002 percent. Even allowing forthe indirect impact ofgh on gA, the total impactof schooling ongh 1 gA is now only 0.003percent, and is not statistically different thanzero. Thus allowing for a positive impact ofhuman capital on technology, because it neces-sitates lowering the upper bound forf, theimpact of elders’ human capital, actually re-duces the potential ability of schooling differ-ences to explain differences ingh 1 gA. Thethird row of the middle panel considers thelargest elasticity ofA with respect toh that ispossible without driving the parameterf nega-tive. This reinforces the message from the sec-ond row. Taking the elasticity to 0.42, anddriving f down to 0, makes the measured im-pact of 1960 schooling ongh slightly negative.Therefore, even thoughgh indirectly raisesgAby 0.42 percent, the combined effect of school-ing on gh 1 gA is less than obtained for largervalues off with less of the indirect channelthrough technology use.

The final panel of Table 3 repeats the exercisefor c 5 0 (no curvature). Comparing rows 1 and2, if we allowgA to increase by1⁄3 percent for eachpercentage-point increase ingh, then it becomesnecessary to reduce the upper bound onf from0.67 to 0.35. This reduces the impact of 1960schooling ongh by almost one-half (from 0.171percent to 0.090 percent). It more than offsets theindirect channel ofgh ongA, reducing schooling’sability to explain country differences ingh 1 gAfrom 0.171 percent to 0.120 percent. Raising theelasticity ofA with respect toh to 0.71, the highestvalue possible without loweringf below 0, againcuts the impact of schooling ongh by almost onehalf to 0.048 percent, resulting in a still lowercombined impact of schooling ongh 1 gA of0.082 percent.

In sum, allowing for a channel from humancapital to technology does not alter our conclu-sion from Section III: differences in growth

rates of human capital explain a relatively smallfraction of the cross-country relationship be-tween schooling and subsequent growth.

A. Levels Accounting

Our focus is on interpreting the strong corre-lation observed between 1960–1990 growthrates and 1960 levels of schooling. Klenow andRodrıguez-Clare (1997) and Hall and Jones(1999) also employ our approach of using theMincerian return on schooling to measure hu-man capital across countries, but focus primar-ily on the relative contributions of human andphysical capital versus TFP in cross-countrydifferences in income levels. These papers ex-amine special cases of our human-capital tech-nology: linearity in the Mincer specification(c 5 0) in Klenow-Rodrı´guez, no intergenera-tional link in human capital (f 5 0) in Hall-Jones, and no externality from human capital totechnology (b 5 0) in either. Both papers at-tribute greater importance to differences in TFPacross countries than to differences in humancapital.

We can examine the robustness of theKlenow-Rodrı´guez/Hall-Jones levels account-ing exercise by varying the curvature parameterc and allowing for large external effects ofschooling either through “teaching” (f . 0) ortechnology (b . 0). As in our calculations fromTables 2 and 3, we restrict the size of theseexternal effects only by the requirement that theimplied impact from growth in human andphysical capital does not explain more than 100percent of the average growth in income perworker for 1960 to 1990 for our sample of 85countries. That is, that there is no technologicalregress on average for these countries.

The results for various parameter values ap-pear in Table 4. They can be summarized asfollows. Regardless of how we specify the pro-duction of human capital, we find that differ-ences in physical capital contribute 46 percentof the differences in per capita income. Moreexactly, conditional on income per worker in1990 being 1 percent higher than the meanacross countries, one should expect1⁄3 ln(K/L)to be 0.46 of 1 percent above the mean acrosscountries. The remaining contribution of 54 per-cent is similarly attributed to the term2⁄3ln( Ah). How this 54 percent is attributed to


human capital (h) and TFP (A) is not overlysensitive to the choice of the curvature param-eterc. In particular, for the case of no externaleffects (f andb both zero), the contribution ofA is about 2.5 times that forh, regardless of thevalue ofc.

Not surprisingly, raising the value off, theimpact of elders’ human capital, increases therelative contribution ofh. For c 5 0.58, thehighestf can be is only 0.19. For this case, thecontribution of TFP remains 75 percent largerthan that from human capital. For lower valuesof c, f can be higher without average growth inhuman capital exceeding average growth inAh.For c 5 0.28, the maximal value forf of 0.46implies that differences in human capital arecomparable in importance to differences inTFP. Forc 5 0, it is conceivable to raisef to0.67, at which point the differences in humancapital contribute nearly 50 percent more thandifferences in TFP.

Similar to the growth exercises in Table 3, al-lowing for externalities from human capital totechnology does not expand the importance ofhuman capital, once we scale back the impactf

of elders’ human capital to avoid implying tech-nological regress.

As with our discussion of Table 2, we wouldargue that plausible parameter values wouldallow for some diminishing returns to schoolingand at least very modest technology gains. Sup-pose we again only require thatc be withinthreestandard deviation of its estimate, soc 50.13, and that technological growth contributesat least one-tenth (0.2 percent per year) of theobserved average growth in income per workerfor these 85 countries. These conditions, whichrestrict f to 0.34, imply a contribution fromhuman capital of 21.6 percent (standard error of1.3 percent) and from TFP of 32.1 percent (stan-dard error of 2.1 percent). So differences in TFPare about 50 percent more important than dif-ferences in human capital.

V. Estimating the Impact of Expected Growthon Schooling

As we stressed in Section I, our model containsa channel by which higher expected growth inAcan induce more schooling. We now calibrate the

TABLE 4—CONTRIBUTIONS OF HUMAN CAPITAL AND TFP TO 1990 INCOME PERWORKER

Fractional contribution to income per worker from†

(1) (2)

2⁄3(1 1 b)ln(h) 2⁄3[ln(A) 2 bln(h)]

b 5 0, f 5 0 0.169 (0.009) 0.368 (0.019)c 5 0.58 b 5 0, f 5 0.19 0.220 (0.012) 0.318 (0.021)

b 5 0.15,f 5 0 0.195 (0.011) 0.342 (0.020)

b 5 0, f 5 0 0.154 (0.008) 0.383 (0.018)b 5 0, f 5 0.46 0.276 (0.016) 0.262 (0.024)

c 5 0.28 b 5 1⁄3, f 5 0.11 0.232 (0.013) 0.305 (0.021)b 5 0.42,f 5 0 0.219 (0.012) 0.318 (0.021)

b 5 0, f 5 0.67 0.142 (0.008) 0.395 (0.018)b 5 0, f 5 0.67 0.314 (0.020) 0.223 (0.027)

c 5 0 b 5 1⁄3, f 5 0.35 0.274 (0.016) 0.263 (0.024)b 5 0.71,f 5 0 0.243 (0.013) 0.294 (0.022)

Notes:b 5 elasticity ofA (technology) with respect toh (human capital);f 5 the exponenton teacher human capital in human-capital production; 12 c 5 the exponent on years ofschooling in human-capital production.

† The contribution of factorX to income per worker, ln(Y/L), is defined as cov(ln(Y/L),X)/var(ln(Y/L)), equaling the coefficient from regressing ln(Y/L) on X. Given that the threefactors,1⁄3ln(K/L), 2⁄3(1 1 b)ln(h), and2⁄3[ln( A) 2 bln(h)] sum to ln(Y/L), the contribu-tions of the three factors must sum to one. The contribution from physical capital,1⁄3 ln(K/L),is estimated at 0.463 with standard error 0.014 across all these specifications for theproduction and impact of human capital.


model to determine whether this channel is up tothe quantitative task of matching the coefficientfrom the regression of 1960–1990 annual growthin Ahon 1960 enrollment [0.23 percent in column(3) of Table 1].

With diminishing Mincerian returns to bothschooling (c . 0) and experience (g2 , 0) andwith country-specific expected growth inA,first-order condition (11) from the model saysthat the privately optimal level of schooling incountry j solves

(16) 11 m 5 z~annuityj!

1 Esj

T

e~gAj 1 g1 1 g2 ~a 2 sj ! 2 r !~a 2 sj !

3 @usj2c 2 g1 2 2g2~a 2 sj !# da.

Here the “annuity” is the annuity value ofhigher expected growth, that is, how much ex-pected future growth boosts today’s consump-tion relative to today’s earnings.25 Higherexpected growth induces more schooling bylowering the effective discount rate and, whenz. 0, by raising wealth.

Using (16) we construct predicted schoolinglevels (sj’s) for 93 countries. We then regressactual 1960–1990gAj on these predicted school-ing levels. We allow the actual 1960 countryschooling levels to deviate from the schoolingpredicted by (16) according to a country-specificerror termvj. This error term reflects measure-ment error and omitted factors such as country-specific education subsidies. Suppose that thev’sare orthogonal to 1960–1990gA’s so that pre-dicted schooling from (16) and growth covaryonlybecause of the impact of expected growth onschooling. Then adding thev’s would raise the

variance of schooling (to its observed variance)without affecting the covariance between school-ing and growth, thereby reducing the coefficientobtained by projecting growth on constructedschooling. This is appropriate, however, as it isnot meaningful to judge the ability of the reversechannel to generate the observed correlation be-tween schooling and growth if predicted schoolingis much less variable than observed schoolinglevels.26

To obtainsj ’s and implement this procedurewe need measures of expected growth,E( gAj),for each country. We consider three possibili-ties: that countryj anticipated1⁄4, 1⁄3, or 1⁄2 of itsex post1960–1990gAj relative to the worldaverage. That is, we setE( gAj) 5 1⁄4gAj 13⁄4gAavg etc. For example, if Hong Kong aver-aged 6-percent growth compared to 2-percentgrowth for the world as a whole over 1960–1990, we consider expected growth in HongKong in 1960 to be 3 percent, 3.33 percent, or 4percent. This would imply that the variance ofexpected growth is1⁄16, 1⁄9, or 1⁄4 of the varianceof realized growth. This seems reasonable inlight of theR2’s reported in Table 1, for exam-ple, 0.24 for the regression ofAh growth oninitial schooling enrollment alone.

The last step to obtainsj ’s is to set parametervalues. The parameterc governs the degree ofdiminishing Mincerian returns to schooling. Aswe described in Section IV, our point estimateis 0.58. In addition toc 5 0.58 we considerc5 0.28, two standard deviations below our pointestimate. We found that the model implies ex-treme sensitivity of schooling decisions tochanges in parameter values whenc 5 0. Forexample, schooling rises fully one year for eachone-year increase in life expectancy.27 Relatedto this, if we proceed and setc 5 0 in (16) wefind that, despite the model’s omission of fac-tors such as country-specific education subsi-dies, predicted schooling levels vary more than

25 Specifically, from (11) z multiplies c(s)1/s/(w(s)h(s)). We sets 5 1 because the empirical literatureprovides little guidance on whether it is above or below one.We assume that persistent level differences in per capitaincome have proportional effects on consumption and earn-ings, leavingc(s)/(w(s)h(s)) unaffected. Differences inexpected growth, in contrast, should raisec(s) relative tow(s)h(s) by the annuity value of that growth, i.e., by thefactor 1 1 r ¥ ((1 1 gA)t 2 1)/(1 1 r )t. We sum over30 years (growth from 1960–1990), andr is set to matchmean predicted and actual schooling levels in 1960.

26 Because it is orthogonal togAj , we need not observev j. We can instead regressgAj onsj from (16) (which omitsv j) and then scale the coefficient down by the variance ofsj

relative to the variance of actual 1960 schooling. This isequivalent to including an orthogonalv j.

27 In an earlier version of this paper (Bils and Klenow,1998) we estimated using cross-country data that schoolingrises by only about1⁄8 to 1⁄4 of a year for each one-yearincrease in life expectancy.


actual schooling levels. Thus we report resultsonly for c 5 0.58 andc 5 0.28, for which thevariances of predicted schooling fall well shortof the variance of actual schooling in 1960.

We useu 5 0.323 whenc 5 0.58 andu 50.176 whenc 5 0.28. These values ensure thatthe average Mincerian return implied forPsacharopoulos’ 56-country sample matchesthe actual average of 9.9 percent. We setg1 50.0512 andg2 5 20.00071, the average Mince-rian coefficients on experience and experience-squared across the 52-country sample for whichwe have such estimates. We setm 5 0.5 so thattuition costs are one-half as large as the oppor-tunity cost of student time. We base this onKendrick’s (1976) evidence that instructioncosts and the opportunity cost of student timeare roughly equal in the United States, and theidea that students pay one-half of instructioncosts. We set life expectancyT equal to its 1960average over our 93-country sample of 54.5.(We subtract six years from the literal 60.5average so that, as in the model, schooling be-gins at age 0.)

We set the wealth effect parameterz based onRobert Haveman and Barbara Wolfe’s (1995)survey of micro estimates of the effect of familyincome on schooling attainment. They report arange of elasticities of log years of attainmentwith respect to log family income of 0.02 to0.20. We setz so that the elasticity in the model(evaluated at the 6.2 years implied by mean1960 schooling enrollment) is at the upper endof this range, or 0.20. We do this because, as weshall see, the wealth effect turns out to be tooweak to generate much of the estimated coeffi-cient of growth on schooling.

Finally, depending on the case (the value forcurvaturec, the share of growth expected, andwealth effect excluded or included), we set thereal interest rater to as low as 0.093 or as highas 0.105 to ensure that average predicted 1960schooling enrollment matches the actual aver-age of 6.2 for the 93 countries.

Using these parameter values we can calcu-late the responses of optimal schooling in (16)to changes in expected growth, life expectancy,and the Mincerian return on schooling. Startingat 6.2 years of schooling, a 1-percent higherexpected growth rate induces 1.4 more years ofschooling whenc 5 0.58 and 2.5 more yearswhenc 5 0.28. One more year of life expectancy

induces 0.03 and 0.04 more years of schooling,respectively, under the two values ofc. And a1-percent-point higher Mincerian return to school-ing engenders 1.1 and 1.9 more years in the twocases. Are these responses reasonable? A fewstudies, Robert J. Willis and Rosen (1979), Rich-ard Freeman (1986), and David Meltzer (1995),have estimated the response of schooling to itsMincerian rate of return. They obtain estimates inthe 0.3 to 0.7 range, compared to our calibratedmodel values of 1 to 2. Thus, even with substantialcurvature, our model implies large schooling re-sponses compared to the limited estimates in theliterature.

The top panel of Table 5 reports coefficientsfrom regressing 1960–1990 growth rates ofA onpredicted schooling levels from (16) for the caseof curvaturec 5 0.58. (All entries in Table 5 arecoefficients scaled down to incorporate thev errorterms.) In the first row, with no wealth effect (z 50), the coefficients are 0.10 percent, 0.14 percent,and 0.20 percent. The coefficients are increasingin the fraction of subsequent growth which isanticipated. The more that growth is foreseen, thebigger its effect on schooling and the larger therole of reverse causality. Excluding thev’s, thevariance ratios (variances of predicted schoolingrelative to that of actual schooling) rise from 3percent to 12 percent across the three columns.The second row in Table 5 repeats the exerciseexcept with a wealth effect (z . 0). With thisadditional effect of expected growth on schooling,the coefficients are higher but very modestly so(less than 0.02 percent higher). All of the coeffi-cients in the top panel of Table 5 fall short of theempirical coefficient of 0.23 percent, but theysuggest that more than one-third of the empiricalrelationship could reflect reverse causality.

The bottom panel of Table 5 reports coeffi-cients for the case ofc 5 0.28. Since diminish-ing Mincerian returns to schooling mitigate theimpact of expected growth on schooling, lessdiminishing returns (a smallerc) means a largerreverse channel. With no wealth effect, the co-efficients are 0.21 percent, 0.28 percent, and0.41 percent (with variance ratios of 13 percent,23 percent, and 52 percent when thev’s areomitted). Again, even a large wealth effectmakes a minor contribution, boosting the coef-ficients less than 0.02 percent.

Table 5 shows that, for plausible parametervalues, the reverse causality channel is strong


enough to generate the empirical coefficient of0.23 percent in the absence of any effect ofschooling on the growth rate. The qualifier onthese Table 5 results is that they reflect a de-mand for schooling that is considerably moreresponsive to schooling’s Mincerian return thanimplied by several micro studies.

VI. Conclusion

Barro (1991) and others find a strong positivecorrelation between initial schooling enrollmentand the subsequent growth rate of per capitaGDP across countries. Using evidence from thelabor literature and historical attainment datafrom UNESCO (1977, 1983), we calibrate amodel to determine how much of this relation-ship reflects causality running from schooling togrowth. We find that the channel from school-ing to growth is too weak to plausibly explain

more than one-third of the observed relationbetween schooling and growth. This remainstrue even when we take into consideration theeffect of schooling on technology adoption.Thus our primary conclusion is that the bulk ofthe empirical relationship documented by Barroand others should not be interpreted as reflect-ing the impact of schooling on growth.

We also calibrate a model channel from ex-pected growth to schooling. We find that thischannel is capable of generating much of theempirical coefficient (even assuming most ofrealized growth is unexpected). Another impor-tant consideration, however, is that part of therelation between schooling and growth may re-flect omitted factors that are related both toschooling rates in 1960 and to growth rates forthe period 1960 to 1990. Identifying the natureand importance of any such factors is a subjectfor further study.

TABLE 5—CALIBRATED REVERSE CAUSALITY CHANNEL

(1) (2) (3)Expected growth

51⁄4 gAj 13⁄4 gAavg

Expected growth51⁄3 gAj 1

2⁄3 gAavg

Expected growth51⁄2 gAj 1

1⁄2 gAavg

No wealth effect(z 5 0)

0.101 percent 0.135 percent 0.201 percent

c 5 0.58With a wealth effect

(z . 0)0.119 0.151 0.214

No wealth effect(z 5 0)

0.208 0.276 0.406

c 5 0.28With a wealth effect

(z . 0)0.227 0.293 0.420

Notes:Dependent variable: Average annual 1960–1990 growth rate ofA.Right-hand-side variables: 1960 schooling predicted by the model. Schoolings predicted by the model solves 11 m

5 z~annuity! 1 *sT e~ gA 1 g1 1 g2 ~a 2 s!2r !~a 2 s!@us2c 2 g1 2 2g2~a 2 s!# da.

1 2 c 5 the exponent on years of schooling in human-capital production.Other parameter values:u 5 0.323 or 0.176, depending onc (so that Mincerian return averages 9.9 percent average across

56 countries).g1 5 0.0512,g2 5 20.00071 (average coefficients in Mincerian returns to experience across 52 countries).m 5 0.5 (student-paid instruction costs relative to the opportunity cost of student time).r 5 0.093 to0.105 (ensures predicted 1960 schooling matches the actual average of 6.2 for 93 countries).T 5 54.5 (average life expectancy 60.5 from Barro and Lee [1993] minus the six years before school).z 5 (value which generates an income elasticity of schooling of 0.20 as in Haveman and Wolfe, 1995).gAavg 5 0.01515 the average growth rate across the 93 countries from 1960–1990.Coefficients are scaled by the variance of predicted schooling relative to the variance of 1960 schooling.


APPENDIX A: CONSTRUCTION OFHUMAN-CAPITAL STOCKS FOR1960AND 1990

We construct estimates of the growth in human-capital stocks from 1960 to 1990 by country asfollows. We first construct an estimate of human capital for workers at each age from 20 to 59 forboth 1960 and 1990. We then weight these age-specific human capitals into aggregates for 20- to59-year-olds using data on population weights by age from the United Nations (1994).

As discussed in Section III, our measure of human capital for an individual of agea at time t isbased on the Mincerian model of human-capital accumulation, generalized for an impact fromhuman capital of the previous generation:

ln@h~a, t!# 5 f ln@h~a, t 2 25!# 1us1 2 c

1 2 c1 g1@a 2 s~a, t! 2 6# 1 g2@a 2 s~a, t! 2 6#2.

This formulation assumes that the relevant cohort for an individual’s human capital is 25 yearsolder (approximately the difference in the average age of workers and teachers across countries).We setc 5 0.58. As described in the text, this reflects the lower return to schooling in countrieswith more years of schooling that Psacharopoulos (1994) finds, and we estimate, in his56-country sample of estimates of the Mincer equation. We also present results for two smallervalues forc: c 5 0.28, which represents our point estimate forc minus two standard errors ofthe estimate, andc 5 0. We then setu to match the average return to schooling of 9.9 percentacross the 56 countries. We choose the parametersg1 and g2 to yield the average experience-earnings profiles observed for a 52-country sample for which we have profile slope estimates(Appendix B). This requires respective values forg1 andg2 of 0.0512 and20.00071. (Forf .0 the parameterg1 must be revised upwards modestly to maintain the steepness of experience-earnings profiles in the presence of rising school quality.)

Given these parameter choices, the only remaining input in the calculation is educationalattainment. Because an individual’s human capital is a function of the human capital in past cohorts(the teachers) whenf . 0, it is important that we obtain information on schooling going back as faras possible. We construct country-specific time series for schooling attainment for 20-year-olds forthe years 1970 to 1990 from data on primary, secondary, and higher enrollment rates in theBarro-Lee (1993) data. For prior to 1970 we construct a series for educational attainment based oncountry censuses of schooling attainment by age cohort conducted in various years between 1946and 1977. These surveys are compiled by the United Nations and reported in the two UNESCOpublications (1977, 1983),Statistics of Educational Attainment and Illiteracy 1945–1974andStatistics of Educational Attainment and Illiteracy 1970–1980.For 32 countries we use two or moresurveys taken in that country in differing years.

The surveys provide the fraction of population of each age bracket achieving each of sixpossible levels of attainment: no schooling, some primary, completed primary, some secondary,completed secondary, and some post secondary. We assign respectively the values 0, 3, 6, 9, 12,and 14.5 years of schooling to these qualitative categories, in accord with World Bank (1991)estimates of the duration of these levels of education. The definition of age cohorts differssomewhat across surveys. The most common classification is according to the age-groups15–19, 20 –24, 25–34, 35– 44, 45–54, 55– 64, and 651. We do not use age categories below age20 or above age 65. (For countries with nontrivial higher education, a number of 20-year-oldsmay have not completed their formal schooling. In these cases we measure the attainment of20-year-olds in yeart by the attainment of 25-year-olds in yeart 1 5.) We then project backin time to construct a history of attainments of 20-year-olds that generates the age distributionsof schooling we observe at the dates of the census surveys. To take a concrete example, a 1951survey for Columbia shows 2.00 years of schooling for persons aged 55 to 64. The midpoint ofthis bracket is age 59.5. A person aged 59.5 in 1951 was age 20 in midyear 1910. Therefore we


set attainment of a 20-year-old in mid-1910 equal to 2.00 years. Similarly, the attainment of 2.40years for 45- to 54-year-olds in 1951 yields attainment of 2.40 years for a 20-year-old inmid-1920, and so forth.

Many cells are missing in the UNESCO data. For instance for the 1952 Chilean survey we knowhow many persons received primary schooling only, and we do not know what fraction of theseliterally completed the schooling. By contrast, for the 1970 Chilean survey we do know. If twoconsecutive cells are missing in a survey, such as not knowing how many persons had some orcompleted secondary schooling, we do not use the survey. If only one cell is missing we attempt tointerpolate based on later or previous survey information for that country. For instance, for Chile wecan interpolate the fraction of 25–34-year-olds in 1952 who had completed primary schooling basedon the fraction of 45–54-year-olds in 1970 who had completed. When this is not possible, weinterpolate based on observed ratios in countries with similar schooling distributions using predictedvalues based on regressions.

Between the Barro-Lee enrollment rates and the UNESCO censuses we are able to constructattainment of 20-year-olds for as many as 12 different dates ranging from 1990 back to as early as1906. More exactly, we were able to construct attainment back to 1935 or before for 55 countries,to 1925 or before for 32 countries, and to 1915 or before for 21 countries. For each country weinterpolated attainment for the years between our data points.

It remains necessary to project attainment back before our available data. Forf . 0 we need toproject attainment back arbitrarily far, though iff is much less than one the weights on theseprevious attainments will decline rapidly. We use three separate equations for backcasting: One for1955 and after, one for 1925 to 1955, and a third for prior to 1925. For 1955 and after we backcastusing the equation ln[s(20, t)] 5 1.0216 ln[s(20, t 1 1)] 2 0.0706.This equation is consistentwith the results of regressing attainment of 20-year-olds in 1955 on attainment of 20-year-olds in1985 for the countries where both series are available. Similarly, for 1925 to 1955 we use an equationln[s(20, t)] 5 1.0047 ln[s(20, t 1 1)] 2 0.0226,which is based on regressing 1925 attainmenton 1955 attainment. The coefficient in this latter equation is not significantly different from one.Based on that, prior to 1925 we simply assume that attainment decreases by 1.77 percent per year.This is the average rate of increase for the years 1925 to 1955.

The outcome is that we are able to construct human-capital stocks for 1960 and 1990 for 85 of the93 countries used in the basic growth regression in column (1) of Table 1. For 55 of these countriesthese stocks reflect information on enrollments going back at least as far as 1940.


APPENDIX BTABLE B1—52-COUNTRY SAMPLE OF MINCER REGRESSIONCOEFFICIENTS

Country Experience Experience2 Schooling YearNumber of

observations Reference

Argentina 0.052 20.00070 0.107 1989 2965 PAustralia 0.064 20.00090 0.064 1982 8227 PAustria 0.039 20.00067 0.039 1987 229 PBolivia 0.046 20.00060 0.073 1989 3823 PBotswana 0.070 20.00087 0.126 1979 492 PBrazil 0.073 20.00100 0.154 1989 69773 PBritain 0.091 20.00150 0.097 1972 6873 PCanada 0.025 20.00046 0.042 1981 4642 PChile 0.048 20.00050 0.121 1989 26823 PChina 0.019 20.00000 0.045 1985 145 PColombia 0.059 20.00060 0.145 1989 16272 PCosta Rica 0.042 20.00050 0.105 1989 6400 PCote d’Ivoire 0.053 20.00008 0.207 1985 1600 PCyprus 0.092 20.00140 0.098 1984 3178 PDenmark 0.033 20.00057 0.047 1990 5289 R&SDominican Republic 0.055 20.00080 0.078 1989 436 PEcuador 0.054 20.00080 0.098 1987 5604 PEl Salvador 0.041 20.00050 0.096 1990 4094 PGreece 0.039 20.00088 0.027 1985 124 PGuatemala 0.044 20.00060 0.142 1989 8476 PHonduras 0.058 20.00070 0.172 1989 6575 PHungary 0.034 20.00059 0.039 1987 775 PIndia 0.041 20.00050 0.062 1981 507 PIndonesia 0.094 20.00100 0.170 1981 1564 PIreland 0.061 20.00100 0.079 1987 531 C&RIsrael 0.029 20.00046 0.057 1979 1132 PItaly 0.010 20.00027 0.028 1987 197 PJamaica 0.083 20.00110 0.280 1989 1172 PKenya 0.044 20.00200 0.085 1980 1600 A&SSouth Korea 0.082 20.00140 0.106 1986 4800 PMalaysia 0.013 20.00004 0.094 1979 605 PMexico 0.084 20.00100 0.141 1984 3425 PMorocco 0.068 20.00070 0.095 1970 2422 PNetherlands 0.035 20.00049 0.066 1983 1888 PNicaragua 0.050 20.00080 0.097 1978 962 PPakistan 0.106 20.00060 0.097 1979 1568 PPanama 0.066 20.00080 0.126 1989 5436 PParaguay 0.058 20.00090 0.103 1989 1084 PPeru 0.053 20.00070 0.085 1990 1625 PPhilippines 0.023 20.00060 0.119 1988 4283 PPoland 0.021 20.00036 0.024 1986 5040 PPortugal 0.025 20.00040 0.094 1985 21823 PSingapore 0.062 20.00100 0.113 1974 1247 PSpain 0.049 20.00060 0.130 1990 635 AR&SSweden 0.049 20.00000 0.026 1981 2996 ASwitzerland 0.056 20.00069 0.072 1987 304 PTanzania 0.041 20.00100 0.067 1980 1522 A&SThailand 0.071 20.00088 0.091 1971 3151 CUruguay 0.051 20.00070 0.090 1989 6567 PUnited States 0.032 20.00048 0.093 1989 8118 K&PVenezuela 0.031 20.00030 0.084 1989 1340 PWest Germany 0.045 20.00077 0.077 1988 2496 K&P

Sources:A 5 Mahmood Arai (1994)A&S 5 Jane Armitage and Richard Sabot (1987)AR&S 5 Alfonso Alba-Ramirez and Maria Jesus San Segundo (1995)C 5 Carmel U. Chiswick (1977)C&R 5 Tim Callan and Barry Reilly (1993)K&P 5 Alan B. Krueger and Jo¨rn-Steffen Pischke (1992)P 5 Psacharopoulos (1994)R&S 5 Michael Rosholm and Nina Smith (1996).


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Does Schooling Cause Growth? - Pete Kleno · Does Schooling Cause Growth? By MARK BILS AND PETER J. KLENOW* A number of economists ﬁnd that growth and schooling are highly correlated