Schooling, Labor-Force Quality, and the Growth of Nations

By ERIC A. HANUSHEK A

Direct measures of labor-force quality fromtest scores are strongly related to growth.consistent with a causal link: direct spenperformance differences; the estimated gquality hold when East Asian countries aquality differences of immigrants are di

unho40

labor-force quality significantly improves ourability to explain growth rates.

huan

ing activities as proxies for relevant humancapital. The most frequently employed measure

-r-ee.,er

i-.-fe

StaResNobenByKleverUnUnJinTwo issues arise in considering the effect ofman capital on economic growth: how shouldy relationship be specified and how should

is either the primary- or secondary-school enrollment rate, used, for instance, in Rome(1990b), Robert J. Barro (1991), and N. Gregory Mankiw et al. (1992) and highlighted in thinfluential sensitivity studies of Ross Levinand David Renelt (1992) and Levine and Sara JZervos (1993). These schooling flow variableshowever, will not accurately represent either threlevant stock of human capital of the laboforce or even changes in the stock during perods of educational and demographic transitionTo deal with these problems, Barro and JongWha Lee (1993) pioneered the development obetter schooling stock variables through the us

* Hanushek: Hoover Institution, Stanford University,nford, CA 94305, and National Bureau of Economicearch; Kimko: Institute for Defense Analyses, 1801

rth Beauregard Street, Alexandria, VA 22311. We haveefited from comments and discussion with Mark Bils,

ron Brown, Stanley Engerman, Douglas Hodgson, Peternow, Paul Romer, Sergio Rebelo, Michael Wolkoff, twoy helpful referees, and participants in seminars at Bostoniversity, Columbia University, the Rand Corporation, theiversity of Oregon, and the University of Rochester.-Yeong Kim provided excellent research assistance.

1184immigrants are educated in their own coestimates of micro productivity effects,magnitude of the growth effects. (JEL O

Recent theoretical analyses of internationaldifferences in growth rates have focused atten-tion on the role of human capital. Most cross-country empirical studies of long-run economicgrowth now include some proxy for humancapital, and these are invariably significant.Data limitations have, however, forced severecompromises. Paralleling analyses of wage de-termination, empirical implementation virtuallyalways employs some readily available measureof the quantity of formal schooling to reflecthuman capital, but this appears inadequate. Theanalysis of international differences in growthrates here suggests that math and science skill isa primary component of human capital relevantfor the labor force. Such cognitive skill of apopulation is not well proxied by measures ofschool quantities or measures of resources de-voted to schools. Accounting for differences inND DENNIS D. KIMKO*

international mathematics and scienceIndirect specification tests are generallyding on schools is unrelated to studentrowth effects of improved labor-forcere excluded; and, finally, home-countryrectly related to U.S. earnings if thetry but not in the United States. The lastwever, introduce uncertainty about the, I20, J24)

human capital be measured? The focus of thispaper is the second issue. This paper does notconsider alternative formulations of the under-lying growth relations but instead is a directapplication of models of endogenous growthdeveloped theoretically by a variety of people(e.g., Richard R. Nelson and Edmund Phelps,1966; Paul Romer, 1990a; Sergio Rebelo,1991). In the simplest formulation, growth ratesare affected by ideas and invention, which inturn are related to the stock of human capitaleither through research and development(R&D) activities or through adoption behavior.These formulations indicate not only why thelevel of output is higher when a country hasmore human capital but also why the growthrate is higher.

Previous investigations of growth have con-centrated on various measures of formal school-

of individual country survey and census data. A school quantity tends to lose significance. The

1185VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHchallenging problem made clear by this alterna-tive, however, comes from the lack of adjust-ment for schooling quality. Few people, forexample, would believe that a year of secondaryschooling in the United States was equivalent toa year at the same grade level in Egypt. Indeed,Barro (1991) explored the inclusion of differ-ences in real school resources as a crude mea-sure of quality differences across countries inhis growth regressions. While he found that thestudent-teacher ratio in primary schools in 1960had a negative relationship to economic growth,the student-teacher ratio in secondary schoolswas statistically insignificant with a positivesigngiving little faith that these adequatelycaptured any quality differences in schools.

There is also a conceptual issue with manyhuman-capital formulations of growth models,since continued growth arising from humancapital frequently requires continued growth inhuman capital. Yet, for simple investmentreasons one does not expect that years ofschooling will expand in an unbounded manner.When phrased in terms of cognitive skills andhuman-capital quality, however, continualquality growth is more natural, and the under-lying growth models are much more readilyinterpreted.

This paper addresses the measurement prob-lem of labor-force quality directly. Rather thanconcentrating on conventional measures ofschooling inputs, we construct new measuresof quality based on student cognitive perfor-mance on various international tests of aca-demic achievement in mathematics and science.Labor-force quality differences measured in thisway prove to have extremely strong effects ongrowth rates.

Direct observations of cognitive skills areavailable for 39 countries which participated ininternational assessments of student achieve-ment at least once, although only 31 countriesalso have the measurement of economic perfor-mance that is needed for subsequent growthestimation. These quality measures can be ex-tended to other countries by imputing missingvalues from international test score regressions.In both the subset with direct testing and in theaugmented data set, the same qualitative con-clusion about growth holds: Labor-force qualityis significant with the correct sign even whenquality measures are also quite robust in theLevine and Renelt (1992) sense of being imper-vious to the precise empirical specification.Moreover, these quality measures are particu-larly important for explaining which countriesare at the top and at the bottom of the distribu-tion of economic growth rates.

Investigations of the empirics of growth suchas this are necessarily subject to a variety ofimportant questions and qualifications related tothe stylized characterizations of different econ-omies and to ambiguity about the underlyingcausal structure. While instrumental variablesstrategies for dealing with the causality issuesare impractical, we pursue three different strat-egies that overall suggest we have identifiedimportant elements of the causal structure ofgrowth. First, if stronger growth leads nations toincrease investment in schools, growth couldcause increased achievement. But direct estima-tion of international production functions doesnot support this as an avenue of effect. Second,if some unmeasured characteristics of countriesaffect both the performance of schools and theperformance of other sectors in the economy,the observed relationship could be spurious.But, estimation of U.S. earnings models forimmigrants that relate to country of schoolingand our cognitive estimates of labor-force qual-ity indicate that our measures of quality aredirectly related to labor-force skills and produc-tivity of individuals. Third, the tests could justbe pinpointing the high growth of East Asiancountries that also score highly on internationaltests. The growth results here, however, hold forsamples of countries which exclude varioussubsets of East Asian countries, although withsomewhat lesser force.

The one caution of the tests involves themagnitude of estimated quality impacts ongrowth. The micro productivity estimates forimmigrants, which have more modest earningsimpacts of quality differences than found in thegrowth equations, suggest uncertainty about thepotential magnitude of causal growth effects.Depending on how the level effects of produc-tivity differences are translated into growth ef-fects, the quality impacts could be noticeablysmaller than those estimated in the growth equa-tionsraising the possibility of other omittedfactors. Nonetheless, even with uncertainty

about magnitudes, we conclude that labor-forcequality is directly related to productivity andgrowth.

I. The Measurement of Labor-Force Quality

Qualitative descriptions of human capital,when considered, generally come from one oftwo sources: measures of schooling inputs (suchas expenditure or teacher salaries) or directmeasures of cognitive skills of individuals.1Employing direct cognitive skill measures hasthe significant advantage of permitting qualitydifferences to arise from factors outside of for-mal schools, while employing measures ofschool inputs has potential advantages if impor-tant aspects of the relevant human capital areonly partially measured by cognitive tests.

statistical techniques and procedures developed inthe United States for the National Assessment ofEducational Progress (NAEP), the main nationaltesting instrument in the United States since 1969.While the IAEP is geared to the U.S. curriculum,the IEA has an international focus not associatedwith the curriculum in any particular country.

The concentration on mathematics and sci-ence corresponds to the theoretical emphasis onthe importance of research and developmentactivities as the source of growth (e.g., Romer,1990a). Able students with a good understand-

1186 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000While we consider both alternatives, the heartof this analysis is the development and use of aconsistent set of cognitive test measures ofquality.

The comparison of cognitive achievementacross countries capitalizes on six voluntary inter-national tests of student achievement in mathe-matics and science that were conducted over thepast three decades.2 Four were administered bythe International Association for the Evaluation ofEducational Achievement (IEA) and two by In-ternational Assessment of Educational Progress(IAEP).3 The IEA, since its establishment in 1959,has a long and unique role in developing compar-ative education research for almost all aspects ofprimary and secondary education. On the otherhand, the IAEP, starting in 1988, builds on the

1 As an alternative, Dale W. Jorgenson and Barbara M.Fraumeni (1992) calculate the human-capital stock fromanalysis of lifetime earnings (by education, age, and sexcategories) and, going even further, adjust for the value ofnonmarket activities.

2 The Third International Mathematics and ScienceStudy (TIMSS) was conducted in 1995 but is not used in thedirect quality measurement. Its results are related to ourlabor-force quality measures below (U.S. Department ofEducation, 1996a, b).

3 Details of participating countries, test administration,and sample sizes can be found in Hanushek and Kim (1995).Lee and Barro (1997) expand international quality measuresby including reading and literacy scores along with morerecent TIMSS data. We do not include reading and literacybecause of concerns about valid testing across languagesand doubts about putting these scores into a common one-dimensional scale with science and mathematics tests.ing of mathematics and science form a pool offuture engineers and scientists. At least for theUnited States, John Bishop (1992) provides sep-arate confirmation of the importance of mathe-matics in determining individual productivityand income. Additionally, while some test in-formation exists for other subjects, it cannot becompared readily with the mathematics and sci-ence scores and therefore is not used here.4

To develop a single measure of labor-forcequality, we combine all of the information oninternational mathematics and science testsavailable for each country through 1991. Thetesting does not directly measure skills of thestock of workers (who received their schoolingat varying times), although the mixture of thedifferent tests employed here does approximatethe relevant time range. While data are hard tocome by, the usual presumption is that qualityof schooling systems evolves slowly over time,in part related to the stationarity of the teachingtechnology and to the slow turnover of teachersand other personnel.5 The approach of combin-ing scores in order to estimate the aggregateskills of the labor force does, nonetheless, pre-clude any consideration of how estimated qual-ity and growth evolve over any subperiods.

Two approaches were taken to combiningthe separate tests available for each country.

4 Reading literacy assessments, for example, are avail-able for 30 countries in 1991 (U.S. Department of Educa-tion, 1994).

5 The test performance in Figure 1 provides some evi-dence about the stability of scores. The United States andUnited Kingdom participate in all six testing programs.Throughout the period, the United Kingdom consistentlyperforms a little better than the United States. Further, witha few exceptions, countries that outperform either theUnited States or United Kingdom on one test also tend to doso when they participate in other tests and vice versa.

Twenty-six performance seriesreflecting dif-ferent age, subtest scores, and yearsare avail-able (for varying subsets of countries), andthese series have different mean percent correct.The first summary method uses a multiplicativetransformation to convert each performance se-ries to a mean of 50. This transformation relieson a strong assumption that the intertemporalmean in world science and mathematics perfor-mance is constant and that the countries takingthe tests are a random draw from the worlddistribution. The second method incorporatesthe additional information that is provided by

The overall NAEP scores for U.S. students

1187VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHthe time series information from the NationalAssessment of Educational Progress (NAEP).At varying times from 1969 to the present, U.S.students aged 9, 13, and 17 have taken NAEPtests in both mathematics and science. Thesetests, constructed on a consistent basis to pro-vide comparisons over time, provide an abso-lute benchmark of performance to which theU.S. scores on international tests can be keyed.Thus, the mean for each international test seriesis allowed to drift in accordance to U.S. NAEPscore drift and the mean U.S. performance oneach international comparison.6 The con-structed measures of schooling quality for eachcountry are the weighted average over all avail-able transformed test scores where weights arethe (normalized) inverse of the country-specificstandard error (s).

Figure 1 gives a graphical depiction of theavailable test information over time. In this,scores for each age-group and subtest are com-bined into a country score on each of the sixunderlying assessments (with the world meanfor each assessment set to 50). The qualitymeasures subsequently used for each countrycombine these scores across years to obtain asingle measure.

6 Since the United States participated in all of the inter-national comparison studies, the performance of U.S. stu-dents participating international tests can be transformed tomimic the performance of U.S. students in NAEP in theclosest time and age-group; see U.S. Department of Educa-tion (1994). Scores of all other countries are adjusted pro-portionately on the basis of matched U.S. score adjustments.The first IEA mathematics test in 1963 and 1964 does nothave an NAEP comparison, because it pre-dated the NAEP.While we experimented with discarding these scores in thecalculation of labor-force quality, subsequent empirical re-sults were unaffected.fell during the 1970s and rose in the 1980s,just the pattern that is seen in Figure 1 for U.S.performance on the separate international tests.Thus, our two alternative measures are highlycorrelated (r 5 0.92). Table 1 shows summarystatistics for the two constructed quality mea-sures for the 31 countries that also have com-plete economic data for the subsequent growthanalysis. The first series, QL1, is based on worldaverage scores of 50 for all six tests; the second,QL2, is benchmarked to the U.S. performanceon the NAEP.

II. Quality Effects on Growth

The underlying formulation guiding this em-pirical work follows from endogenous growthmodels where a countrys growth rate is directlyrelated to the stock of human capital. A varietyof underlying formulations point to this empir-ical specification. In Romer (1990a), humancapital influences the supply of ideas and newtechnologies. In the AK models of Rebelo(1991), growth is directly related to the aggre-gate capital stock that includes human capitalwith the key element being the lack of dimin-ishing returns to human capital. Such modelsalso have earlier antecedents in the models oftechnology adoption of Nelson and Phelps(1966) and Finis Welch (1970), where a coun-trys stock of human capital influences the rateat which it puts in place new technologies andthus its growth rate. While having different pol-icy implications, each can motivate the basicformulation employed here.

The endogenous growth formulation is, ofcourse, not the only model of growth differ-ences, and considerable controversy existsabout the best formulation. (For a discussion ofalternative formulations, see Barro and XavierSala-i-Martin, 1995.) Part of the debate is the-oretically based, largely related to the long-runproperties of the alternative models. Part is em-pirically based. The fundamental issue for em-pirical specifications is whether stocks ofhuman capital or changes in the human-capitalstock should enter into the determination ofgrowth rates. If education is viewed as a directinput into production, then growth rates wouldbe related to growth in the different inputs, andchanges in the human-capital stock would be

1188 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000FIGURE 1. SCORES ON INTERNATIONAL MATH AND SCIENCE TESTS BY YEAR

tM

ipggliPtsesse

dt

TABLE 1SUMMARY STATISTICS FOR CONSTRUCTED LABOR-FORCERES (

S

1189VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHQUALITY MEASU

Qualityhe relevant explanatory factor in growth (e.g.,ankiw et al., 1992). Various aspects of these

nternational growth accounting framework in order to com-are the factorowth versiorowth modeevels (simplnteracted wihelps growt

hat there isimple inputndogenous gchooling attatronger suppvolving ado

8 The inteifferent poino look at ch

measure Median Mean de

QL1 48.76 46.61QL2 54.52 51.28

Notes: See Hanushek and Kim (1995) for a detailthe construction of labor-force quality measures.underlying tests equal to 50. QL2 adjusts all scmance modified for the national time patternEducational Progress. While 39 countries partrestricted to countries that also have the econoanalysis.tandardviation Minimum Maximum

10.86 20.79 60.6513.48 18.26 72.13

ed discussion of the included tests along withQL1 sets the world mean on each of the sixo31 COUNTRIES)consistent with past estimation. Initial incomeotions of

rates.9

actical be-labor forceserved testate futureecause thehrough the

point outlity of the

res based on the U.S. international perfor-of scores on the National Assessment ofnegatively affects growth, supporting nconditional convergence in growth

r accumulation view with various endogenousns. Their empirical application of endogenousls involves adding Barro and Lee schoolinge endogenous growth) and schooling levelsth the countries productivity gap (Nelson andh). They argue from their empirical analysisweak support for viewing human capital as ainto an aggregate production function. Simplerowth models, defined in terms of just level ofined, also receive limited support, but there isort for a Nelson and Phelps version with

ption of best technologies.rnational math and science tests are given atts in time, suggesting that it could be possibleanges in quality over the 30-year period con-

sidered here. This approach is, however, imprcause the emphasis here is on the quality of theand not the quality of students. A change in obperformance of current students might indicgrowth effects but not contemporaneous effects, bachievement change would not have propagated tlabor force.

9 William Easterly and Sergio Rebelo (1993)that using World Bank data reduces the possibialternative models have been tested, but theresults, which depend on specific formulationsand implications, have not been conclusive.7Much of the past discussion has focused on thespecification and interpretation of quantity mea-sures of human capital (cf., Mark Bils and PeterJ. Klenow, 2000). A central argument here isthat the existing testing is likely to be mislead-ing if quality concerns such as those raised inthis paper are key to growth differences.

The emphasis in this paper is the comparisonof alternative empirical versions of endogenousgrowth models with special attention to how theexplanation of cross-country growth is affectedby inclusion of quality measures. This analysiscannot provide tests of alternative growth for-mulations, because just cross-sectional varia-tions in labor-force quality are observed.8

7 For example, Jess Benhabib and Mark M. Spiegel(1994) develop alternative estimation approaches within anTable 2 reports the results of our baselinecross-country regressions that describe growthin average real per capita GDP between 1960and 1990 (Robert Summers and Alan Heston,1991). This begins with a small set of determi-nants of growth rates and investigates themagnitude and stability of the influence oflabor-force quality. Subsequent estimation con-siders expansion to a broader set of countriesand, in the tradition of Levine and Renelt(1992), the potential confounding effects ofother frequently assessed factors.

The simplest models for the sample of 31countries with complete data relate growth toinitial income (Y60) and the Barro-Lee measureof school quantity (S) [column (1)]; an alterna-tive baseline employs these plus the annualgrowth rate in population times 100 (GPOP)[column (4)]. (Variable definitions and sourcesof data are found in Appendix A.) These base-line estimates give rather common results andexplain between 3341 percent of the variationin economic performance for the restricted setof countries considered. The basic results are

icipated in one or more test, these data aremic data required for the subsequent growth

TABLE 2BASELINE ESTIMATES OF 19601990 CROSS-COUNTRY GROWTH MODELS WITH LABOR-FORCE QUALITYate in real per capita GDP (3100) [31 countries])

26)36) (0.146) (0.195) (0.119) (0.139)

20.713 20.038 20.250

4

1190 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000Quantity of schooling (S) 0.548 0.10(0.209) (0.12

Annual population growth(GPOP)

Labor-force quality (QL1) 0.13(Dependent variable: Average annual growth r

(1) (2)Initial per capita income (Y60)

[$1,000]20.609 20.47(0.186) (0.091.4 percentage points per year (e.g., 0.134 z10.86 5 1.46). In contrast, a one-standard-

(0.023)Labor-force quality (QL2)

)

se(3) (4) (5) (6)20.460 20.745 20.481 20.517

(0.103) (0.181) (0.093) (0.112)0.100 0.519 0.106 0.116a concern, since higher income may lead a

deviation increase in the quantity of schooling isassociated with only a quarter-percentage-pointincrease in growth (0.10 z 2.63 5 0.26). (Notethat the school quantity effect falls dramaticallywith inclusion of direct performance mea-sures.)10 The magnitude of the estimated quality

country to reduce its birthrate.The basic model concentrates just on additive

effects of school quantity and quality, but theireffects may be complementary. Some experi-mentation with a linear interaction term pro-duced implausible results for the sampleextremes for both quantity of schooling andmeasured quality. The substitution of logarith-mic models on the other hand yielded virtuallyidentical qualitative results as the basic additivenegative coefficient on initial income arising from potential

measurement error in initial income. Nevertheless, forconsistency with other studies, we rely on Summers andHeston (1991) data for initial income and growth rate cal-culation.

10 This fall in returns to quantity with inclusion of qual-ity is much larger than those typically found in microestimates of wage determination models and those reportedbelow. Bils and Klenow (2000) point out that the simpleestimates of the effects of quantity of schooling are unbe-

lievably large, a situation they attribute to reverse causality.The significantly smaller estimates here when quality ef-fects are considered make the quantity effects more plausi-ble, although, as we discuss below, there is uncertaintyabout the best way to compare micro productivity estimateswith the macro growth equations.Quantity of schooling (S) has a strong, positiveimpact on growth.

The corresponding estimates with the addi-tion of our alternative measures of labor-forcequality, found in the remaining columns, indi-cate a very strong relationship between qualityand per capita growth rates. In the simplestform, adding either quality measure (QL1 orQL2) boosts the adjusted R2 to about 0.7, asubstantial increase from the simpler models.An increase of one standard deviation of labor-force quality, either measured by QL1 or QL2,enhances the real per capita growth rate by over

Constant 2.265 21.900(0.863) (1.004

R2 0.33 0.73

Note: Huber-White estimated standard errors are in parentheeffect is huge, given that the unconditional stan-dard deviation of growth rates for these coun-tries is 1.75 percent. (We return to issues of themagnitude of effects below.)

Replication of the basic models with the ad-dition of population growth [columns (4)(6)]leaves the magnitude and significance of thequality of schooling little changed. The esti-mates of the impact of population growth on therate of economic growth, while always nega-tive, are quite sensitive to specification and arenot significantly different from zero when qual-ity is considered. Also, as with other influencesthat have been estimated in the past, causality is

(0.224) (0.215) (0.211)0.133

(0.024)0.104 0.098

(0.015) (0.015)20.989 4.092 21.756 20.151

(0.910) (0.974) (1.346) (1.142)

0.68 0.41 0.73 0.69

s below coefficients.

models without interactions. Given the paucity gregate resources for schools and characteristicspopulations across countries (Z). As long as nand y are uncorrelated, estimation of equation(3) provides consistent estimates of the produc-tion parameters. The estimation follows themicro level studies of school performance (Ha-nushek, 1979, 1986). While past estimation ofsuch models, both in the United States and indeveloping countries, has failed to find a con-sistent relationship between school resourcesand student performance (Hanushek, 1995,1996), these results do not necessarily carryover to international comparisons. Within-country variations of resources are dwarfed bybetween-country variation, implying that, evenif small marginal differences in resources havelittle effect, the large order-of-magnitude differ-ences found across countries could have impor-tant outcome effects.

We assume that the international level of

1191VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHof data, it remains impossible to investigatesatisfactorily alternative functional forms.

The basic results provide strong support forthe importance of labor-force quality differenceas measured by cognitive achievement in math-ematics and science. They also comprise thebaseline for subsequent analyses both of theavenue of effects and of the generalizability toother countries.

III. Causality, Part A: The Determinantsof Schooling Quality

Growth provides increased resources to a na-tion, and a portion of these resources may beploughed back into human-capital investments,thus suggesting that the relationships previouslyestimated could overstate the causal impact ofhigher labor-force quality. Consider the follow-ing such description:

(1) gi 5 Xib 1 gQLi 1 i(2) Ri 5 Wid 1 hgi 1 n i(3) QLi 5 Zia 1 pRi 1 y i .

Growth ( gi) of nation i is determined by labor-force quality (QL) plus a vector of other factors(X) [equation (1)], while growth also contrib-utes along with other factors W to determiningthe amount of resources devoted to schools andhuman-capital production (Ri) [equation (2)].This formulation highlights the fact that gov-ernments cannot directly affect outcomes butinstead must pursue various indirect policiesthat depend on the organization of schools andthe underlying production function. If, however,resources in combination with other inputs (Z)determine labor-force quality [equation (3)],simple estimation of equation (1) will not pro-vide estimates of the causal effect of quality ongrowth (g). Instead the estimation will also re-flect the impact of growth on quality, embodiedin the structural parameters h and p.

It is infeasible to estimate the complete sys-tem of equations with available data. Instead,the approach here is direct estimation of equa-tion (3), the human-capital production functionthat relates measured labor-force quality to ag-average ability of students does not vary acrosscountries (or at least is exogenous to the otherdeterminants considered here), leading us toconcentrate on standard, readily available re-source measures and aggregate population char-acteristics.11 For the previous growth models,we were interested in measuring the quality ofthe entire labor force, leading to aggregation ofdifferent test scores into a single measure foreach country. Here, however, our interest is theunderlying production relationships, and we canexploit the disaggregated test data to explore

11 The sources of variables, as explained in Appendix A,are mainly from Marlaine E. Lockheed and Adrian Ver-spoor (1991) and Barro and Lees (1993) data set. Forcharacteristics of education system, we consider: pupil/teacher ratio in primary schools (PT-pri) and in secondaryschools (PT-sec), pupils/school ratios, teaching materialsand teacher salary in primary schools, repeaters in primaryschools, percentage of primary-school cohort reaching thelast grade, public recurrent expenditure in primary schoolrelative to GNP, ratio of recurring nominal governmentexpenditure on education to nominal GDP (RECUR), cur-rent expenditure per pupil (PPE), and ratio of total nominalgovernment expenditure on education to nominal GDP (EX-PEND). The school spending variables are converted intospending per pupil by using purchasing-power parity esti-mates from Summers and Heston (1991) along with relevantschool-enrollment data. For socioeconomic variables, weconsider: general education level (schooling quantityS),per capita income at 1960 (Y60) and average income, anddemographic variables (fertility rate, growth rate of popu-lation (GPOP), infant mortality rate, life expectancy atbirth).

TABLE 3PRODUCTION OF MATHEMATICS AND SCIENCE ACHIEVEMENT: COUNTRY- AND COHORT-SPECIFIC SCORES(Dependent variable: Normalized

(1) (2)IEA math1

)

)

)40.80

(5.17) (4.94) (6.55)

1192 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000how school and family resources relate to theperformance of specific cohorts. To estimate theschool production relationships, we considernormalized individual country test scores on thesix separate tests (i.e., the individual countrydata points plotted in Figure 1) and relate themto the relevant cohort-specific family character-istics and school resources (see Appendix B).This approach provides up to 70-country-test-cohort observations with necessary school inputdata, while ensuring that the inputs are exoge-nous to the achievement outcomes.12

Table 3 displays several variants of the pro-duction models. The overall story is that varia-tions in school resources do not have strongeffects on test performance. The estimated ef-

fects of various measures of resources are eitherstatistically insignificant or, more frequently,statistically significant but with an unexpectedsign. This finding holds regardless of the spe-cific measure of school resourceswhetherpupil-teacher ratios, recurrent expenditure perstudent, total expenditure per student, or a va-riety of other measures. The education of par-ents, proxied by the quantity of schooling of theadult population, tends to be positive and sig-nificant at conventional levels. Also, countrieswith higher population growth rates tend tohave lower achievement, consistent with stan-dard arguments about the trade-off betweenquantity and quality of children and the impactof larger family sizes (Gary S. Becker and H.Gregg Lewis, 1973; Robert J. Willis, 1973;Hanushek, 1992). Alternative models (notshown) included region-of-the-world dummyvariables, but these did not change any of the

12 A total of 87 country-test observations are available,but limits on school input data reduce the usable sample.

Number of countries 69 67 70 69 67 70R2 (adjusted) 0.25 0.19 0.25 0.22 0.26 0.25Notes: The sample consists of one observation per country for each of the six test years that each country participated in theinternational testing. Scores are normalized to 50 in each test year. Huber-White estimated standard errors are in parenthesesbelow coefficients.IEA science1

IEA math2

IEA science2

IAEP math and science

Adult schooling (St 2 1) 2.04 1.62(0.82) (0.76

Pupil-teacher ratio in primaryschools (PT-prit 2 1)

Current public expenditureper student (PPEt 2 1)

20.69(0.19)

Total expenditure oneducation/GDP(EXPENDt 2 1)

2165.90(90.66

Annual population growth(GPOPt 2 1)

24.65 24.60(1.68) (1.36

Constant 46.46 52.27test performance in test year t)

(3) (4) (5) (6)44.09 50.15 40.78(5.16) (5.61) (7.03)46.44 54.30 41.98(5.87) (5.48) (7.01)48.49 55.49 41.30(6.04) (5.65) (7.11)45.94 51.66 37.97(6.35) (6.16) (7.62)47.14 52.45 38.24(5.47) (4.91) (6.57)

1.54 2.70 1.75 1.59(0.64) (0.70) (0.73) (0.64)0.066 0.09

(0.16) (0.15)20.766

(0.21)2189.78

(88.69)

22.64 24.86 24.98 22.81(1.96) (1.94) (1.42) (1.91)

estimated school resource effects. Most signif- (4) gi 5 Xib 1 gZia

1 @gy i 1 i 1 gZi ~a 2 a!#

for the remaining n2 2 n1 countries, where thebracketed term indicates the composite errorterm in equation (4).

When and y are uncorrelated for the coun-tries with complete data, estimation of this sys-tem will, under quite general conditions, yieldconsistent estimates of g.13 Clearly, however,the full error term in (4) will have a largervariance than that in (1), so correction forheteroskedasticity is important both to obtainefficient parameter estimates and to obtain con-sistent estimates of the standard errors. If the

1193VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHicantly, the perverse effects of pupil-teacher ra-tios are not a simple artifact of the large classsizes found in many East Asian countries.

Finally, the structure of the testing itselfmight influence the pattern of observed perfor-mance. Variations in school attendance couldlead to variations in scores due to pure selectioneffects, because countries with lower schoolcompletion rates might typically test a moreselective portion of the total age cohort. Themodels in Table 3 were reestimated adding thesecondary-school enrollment rate for the five-year period covering the specific testing pro-gram (not shown). The secondary-schoolenrollment rate was uniformly positive and sta-tistically insignificant (the opposite of whatmight be expected from important selection ef-fects), while the pattern of the school resourceeffects was unaffected.

A significant concern with previous analysesof cross-country growth relationships has beenthe likelihood of simultaneityfast-growingcountries are likely to invest in more schooling,more plant and equipment, and the like. Theeffect of growth on human-capital development,as opposed to the reverse, has specifically beenemphasized, for example, by Jacob Mincer(1996) and Bils and Klenow (2000). The lack ofsystematic income and expenditure effects onlabor-force quality strengthens the causal inter-pretation of labor-force quality in our growthmodels, because p 5 0 eliminates the feedbackloop in equations (1)(3).

IV. An Expanded Sample of Countries

To explore growth differences among coun-tries further, we significantly expand the groupof countries analyzed by projecting labor-forcequality based on observed characteristics. Theestimation strategy concentrates on equations(1) and (3) above. We observe g, X, QL, and Zfor a set of n1 countries, while we just observeg, X, and Z for another set to countries n1 11, ... , n2. We begin by obtaining consistentestimates of a, the effect of country factors onmeasured quality, from estimation of (3) for thefirst set of n1 observations with complete data.We then use this estimate (a) to estimate jointlyequation (1) for the first n1 countries andonly source of heteroskedasticity arises fromestimation of QL for the expanded set of coun-tries in equation (3), a simple two-stage estima-tor that employed different variance estimatesfor the first n1 observations and for the nextn1 1 1, ... , n2 observations would be appro-priate. Because other sources of heteroskedas-ticity are likely, however, we employ moregeneral robust estimation techniques.14

To project labor-force quality in equation (3),we return to the simple cross-sectional sampleof aggregate country values for labor-forcequality, QL1 and QL2, and relate them to aver-age population and schooling characteristics forthe entire 19601990 period. Our primary pur-pose is developing projection equations, and weemploy expanded models that go beyond theprevious production function estimates.

As shown in Table 4, three basic factors are

13 The prior production function estimates plus the fur-ther analysis of U.S. earnings of immigrants (in the text)provide some evidence about the appropriateness of the errorassumption. With a consistent estimate of a, the last term inequation (4) vanishes in the limit, yielding consistent esti-mates of b and g. Based on the prior estimation, we ignorepossible feedback in equation (2) and pRi in equation (3).

14 Subsequent empirical analysis indicates that this sim-ple weighting and the use of Huber-White corrected stan-dard errors yield very similar results (Halbert White, 1980).Note that this estimation problem is not the same as astandard generated regressor case, given the partial observ-ability of QL. Ignoring observed values of QL would effec-tively increase the error variance in (1) and thus reduce theefficiency of the estimator. This approach is also not thesame as errors-in-variables, because it rests on the consis-tency of the underlying estimator in equations (3) and (4).

TABLE 4PREDICTION MODELS FOR LABOR-FORCE QUALITY

Dependent variable 5

(1) (2)Primary-school enrollment

rate (ENROLL-pri)81.50 85.78

(16.54) (23.32)Quantity of schooling (S) 0.714 0.038

(0.53) (0.65)Pupil-teacher ratio in

primary schools (PT-pri)

0.142(0.06)

Number of countries 31 30 30 31 30 302

1194 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000generally important in determining variations inlabor-force quality. Primary-school enrollmentrates strongly influence performance, probablythrough indicating the overall importance thateach country puts on education. Higher popula-tion growth rates are associated with lowerlabor-force quality. Finally, distinct regionaldifferences influence performance with Asiancountries doing best (given the other character-istics).15 The average quantity of schooling isgenerally positively related to performance, al-though it is typically insignificant at conven-tional levels. School resources again are not

strongly related to quality. The incorrect posi-tive sign for pupil-teacher ratio appears whetheror not there is a dummy variable for the Asianregion, a region with traditionally high pupil-teacher ratios and high student performance.The expenditure measures, while positive, arestatistically insignificant.

We utilize the estimates in the second andfifth columns to construct an expanded set oflabor-force quality measures, QL1* and QL2*,which combine observed quality with predictedquality for all countries without observed testdata but with data on the right-hand-sidemeasures. A significant concern, however, isthat relatively few developing countries everparticipated in the testing, implying limitedobservations at the low-achieving end of thedistribution. Because of the thinness of obser-vations at the lower end (see Figure 1), our maingrowth estimates eliminate all countries withpredicted achievement below 20, the lowerbound on actual observations. The subsequent

15 The limited number of countries makes the regionaldifferences suspect. While there are six Asian countries,there are only two African (Mozambique and Swaziland)and one Latin American (Brazil) country. This implies thatthe estimates for Latin American countries are calculatedrelative to the Brazilian mean instead of the world mean.Similarly, African countries are calculated relative to themean for Mozambique and Swaziland.

R 0.73 0.72 0.71 0.68 0.66 0.65

Note: Huber-White estimated standard errors are in parentheses below coefficients.Recurring expenditure oneducation/GDP(RECUR)

Total expenditure oneducation/GDP(EXPEND)

121.07(109.9)

Annual population growth(GPOP)

23.11 23.08(1.76) (1.98)

Asian (51) 5.123 7.52(3.56) (2.76)

Latin American (51) 24.004 23.87(2.31) (2.93)

African (51) 3.170 2.94(2.38) (2.32)

Constant 235.59 237.19(17.20) (22.41)QL1 Dependent variable 5 QL2(3) (4) (5) (6)

86.23 62.36 73.28 75.32(24.81) (24.44) (29.54) (31.30)

0.320 1.651 0.97 1.181(0.64) (0.77) (1.18) (1.14)

20.043(0.13)

55.49 133.23(119.3) (176.1)

170.37(169.1)

22.80 24.105 24.17 23.85(2.06) (2.36) (2.65) (2.62)6.33 12.25 13.77 12.76

(3.07) (6.54) (4.76) (5.02)24.31 21.24 0.203 0.432

(3.39) (3.689) (4.07) (4.53)3.30 11.97 8.71 9.16

(2.68) (5.73) (3.44) (3.72)236.19 213.10 228.40 229.27(24.55) (25.76) (27.65) (30.17)

TABLE 519601990 CROSS-COUNTRY GROWTH MODELS WITH LABOR-FORCE QUALITY FOR AUGMENTED QUALITY SAMPLE[Dependent variable: Average annual growth rate in real per capita GDP (3100)]

1195VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHtwo measures of labor-force quality, which havea simple correlation of 0.95 in the augmented

(1) (2) (3) (4) (5) (6)Initial per capita income (Y60)

[$1,000]20.382 20.390 20.453 20.370 20.384 20.442

(0.081) (0.079) (0.078) (0.084) (0.082) (0.081)Quantity of schooling (S) 0.127 0.117

(0.089) (0.093)Annual population growth

(GPOP)20.097(0.212)

Labor-force quality (QL1*) 0.108 0.104(0.021) (0.023)

Labor-force quality (QL2*)

Assessment available (TEST)

)

ses0.112 0.120 0.103 0.112(0.093) (0.096) (0.100) (0.104)

20.161(0.209)0.76 and 0.78. Importantly, there is no signifi-cant difference in these relationship for the eight

0.076(0.027)

0.094 0.090 0.072country sample.As an independent check on the projections,

the estimates of labor-force quality can be re-lated to the eighth-grade country scores from1995 on the Third International Math and Sci-ence Study testing, or TIMSS (U.S. Departmentof Education, 1996a, b). The correlation of thecombined TIMSS score with QL1* and QL2* is0.67 and 0.66, respectively.17 If South Africa,

newly tested, as opposed to the 24 previouslytested, countries in the TIMSS sample.18 Thehigh correlations also reinforce the previouslyassumed relative stability of schooling systems.

The growth estimates in Table 5, which rep-licate the basic models in Table 2, are veryconsistent with the baseline estimates. Consid-ering QL1*, the first column indicates signifi-cant conditional convergence with higher initialincome translating into lower growth rates.While quantity of schooling is positive, it isstatistically insignificant, and its estimated16 The cutoff, which lies more than two and one-half

standard deviations below the country means, eliminatesnine countries which meet overall data availability criteria.The sampling criterion has slightly different sample impli-cations for the two separate quality measures with 77 com-mon observations. To test the sensitivity of the results totruncation, reestimation of the growth models using allcountries with predicted values of QL1* and QL2* greaterthan zero yielded estimates that are highly statistically sig-nificant but slightly lower in magnitudes from those esti-mated on the more restricted samples.

17 It was possible to construct eighth-grade scores for 32countries that enter into our analysis, including eight coun-

tries not previously directly observed (U.S. Department ofEducation, 1996a, b). The relationship of TIMSS scores andgrowth is explored in Paul T. Decker and Larry M. Radbill(1999).

18 If QL1* and QL2* are regressed on the TIMSS aggre-gate scores, a dummy variable for direct observations ofprior tests or allowance for a different slope on the TIMSSvariable if labor-force quality was observed yields insignif-icant differences.growth estimation, however, is not very sensi-tive to this sampling criteria.16 Also, there ulti-mately proves to be little difference between the

Observed labor-force quality(TEST QL1*)

Observed labor-force quality(TEST QL2*)

Constant 21.606 21.184(0.749) (1.241

Number of countries 78 78R2 0.41 0.42

Note: Huber-White estimated standard errors are in parenthewhich is a full standard deviation below thescore of the next lowest of the 32 matchedcountries, is excluded, the correlations rise to

(0.016) (0.016) (0.021)21.392 20.628(1.455) (1.436)0.054

(0.032)0.034

(0.028)20.475 21.483 20.869 20.657

(1.069) (0.584) (0.984) (0.798)

78 80 80 800.49 0.41 0.41 0.48

below coefficients.

effect on growth is close to what was ob-served previously in Table 2. Most important,labor-force qualitymeasured by QL1*isstatistically significant and very similar inmagnitude to the estimates for the restricted setof countries in the baseline. A one-standard-deviation change in quality translates into aslightly greater than one-percentage-point dif-ference in annual real growth rates. The effectof quality improvements also appears muchmore important than increases in quantity: aone-standard-deviation change in school quan-tity translates into 0.32 percentage points in aver-age growth (and even this might be overstated by

political assassinations or of revolutions andcoups into our models, they are uniformly in-significant, and they do not lessen the impor-tance of variations in labor-force quality.21Importantly, discussions below about the esti-mated magnitude of quality effects raise thepossibility that quality partially proxies forsome set of omitted variables. This sensitivity

1196 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000the arguments of Bils and Klenow, 2000).The remainder of the table demonstrates sta-

bility of the estimated effects of quality. Incolumn (2), the addition of population growthrates has no impact on the estimated qualityeffect. Column (3) provides information on theprojection of labor-force quality in growth byseparating countries with direct observationsfrom those with projections. The point estimateson marginal test score effects (TEST z QL1*)indicate somewhat stronger test influences incountries where there are direct observations,although the coefficient is not significant at the5-percent level.19 As found before, the resultsfrom the alternative quality measure (QL2*) arevirtually the same.

Following Levine and Renelt (1992), a vari-ety of other common measures of economieswere added (not shown), but the importance ofquality differences remains both in terms ofconsistent strength and statistical significance.20Barro (1991) and others have emphasized avariety of political factors which might influ-ence growth. When we introduce measures of

19 The F-test on the addition of both the intercept andslope dummies does reject the hypothesis that both param-eters are jointly zero (F[2, 72] 5 5.59), but slope equalityseems most important.

20 The additional factors included: the ratio of real gov-ernment consumption expenditure net of spending on de-fense and education to real GDP (GCN), the ratio of privateinvestment to GDP (PRIINV), and ratio of total trade toGDP (TRD). While school quantity (S) was insignificant,the consistent result was that labor-force quality remainedstatistically significant, although at times slightly smaller inmagnitude than in Table 5. Alternative functional forms,including log specifications and interactions between qual-ity and the other variables, likewise did not change theoverall results.analysis, however, rules out many commonlyhypothesized candidates.

The estimates using this augmented sampleconfirm the appropriateness of projection to theexpanded set of countries. This expanded sampleprovides increased precision in testing further hy-potheses. It also points to the broader generaliza-tions across world economies that are possible.

V. Causality, Part BThe Quality-Productivity Relationship22

Confusion about causality can also arise from asimple omitted variable problem. To the extentthat other aspects of a country influence bothscores and the success of the economy, the mea-sures of labor-force quality may simply be proxy-ing for the true influences. For example, if growthwere related to more open labor markets, nationswith more open labor markets may also havebetter allocations of workers to teaching and thusbetter student performance. Or, investment inhealth of individuals may lead both to higherproductivity and growth and to better school per-formance. These and other examples could pro-duce the kind of quality-growth relationshipsestimated here, even when cognitive skills ofworkers per se are not driving growth. For exam-ple, consider a situation where a common factor,u, affects both growth of the economy and effi-ciency of the schools, but where measured quality,QL, does not enter into growth:

(5) gi 5 f~u i , Xib! 1 i(6) QLi 5 g~u i , Zia! 1 y i .

21 We average assassinations per million population andnumber of revolutions and coups per year across the ob-served periods. While such measures would impreciselyshow the impact of political upheaval on short-run growth,they should still capture any overall effects.

22 We thank a prior referee for suggesting this analysis.

This is a simplified structural form of thekind of omitted variables problem that has beenhypothesized to enter in one form or another intoestimation and interpretation of many previousgrowth models.23 Without measures of u, it isextraordinarily difficult to deal with such situa-tions, because it generally requires finding instru-mental variables which are correlated with truestudent and worker quality but which are uncor-

on years of school, potential experience (age-

1197VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHrelated with growth.In our analysis, we employ a different strat-

egy. We concentrate on immigrants working inthe United States and relate variations in theirearnings to our measures of labor-force quality.If our measure of labor-force quality does notindicate differences in productivity but ismerely a proxy for other differences in eachcountrys economy, we should see no relation-ship with immigrant earnings differences withinthe U.S. economy. Moreover, by distinguishingwhere each immigrants education was re-ceivedin the home country, in the UnitedStates, or in a combination of the twoit ispossible to relate the quality measures moreclosely to schools than to other characteristicsof the immigrants, be it cultural, family behav-ior, or whatever.

We constructed a sample of all foreign-bornmale workers, aged 2560, with at least $1,000in earnings in 1989 from the 1990 Census ofPopulation 5-percent public use micro data files(PUMS). The PUMS data set provides informa-tion about 1989 labor earnings, schooling at-tained, age, country of origin, and age of entryinto the United States. Two overlapping sam-ples were constructed: (1) those who were bornin a country for which direct quality measureswere available [37 countries]; and (2) those inthe augmented sample that adds countries forwhich quality measures are estimated [87 coun-tries].24 The OLS estimated earnings equationsbegin with the standard Mincer form (Mincer,1974) where log of annual earnings is regressed

23 The same set of problems arise without u entering bothstructural equations if u is correlated with the error in one ofthe equations and enters directly into the other.

24 Countries are included if there are at least 50 immi-grants in the United States meeting the work and earningsrestrictions. Note that a larger set of countries are used inboth samples here, because information on the own-countrygrowth and schooling levels is not required.schooling-6) and its square and then add ourmeasure of labor-force quality (QL2*) based oncountry of origin.

The simple Mincer models in Table 6 formale immigrants (the first column for each ofthe two samples) provide rather standard re-sults: earnings gradients of 9 10 percent peryear of schooling and declining returns toexperience over a career. The interesting por-tion is the estimated effects of quality. In thesample with observed tests, one point of testscore approximately translates into an aver-age of 0.19-percent higher individual earn-ings. The following three columns thendisaggregate the sample by where the immi-grant obtained schooling (based on age ofentry into the United States). Those entirelyeducated in the home country average 0.21-percent higher earnings for each point of testscore, while those educated partially or totallyin the United States show a statistically insig-nificant relationship between home-countrylabor-force quality (QL2*) and individualearnings. With the augmented sample ofcountries on the right-hand side of the table,the pattern of results is the same, and esti-mated quality effects on individual earningsare even stronger.

If the growth effects of labor-force qualitypreviously estimated just reflected some omit-ted factor related to the home country and theefficiency of its markets, we would not expectto see productivity effects for immigrants inthe U.S. economy. Further, if the growth ef-fects simply reflected cultural or family fac-tors and not school achievement and skilleffects, we would expect the influence onproductivity in the U.S. economy to hold re-gardless of where the schooling took place.We interpret the results in Table 6 as provid-ing consistent evidence that our measures oflabor-force quality are related to individualproductivity and signal a causal influence inthe growth relationship.

Nevertheless, while the qualitative evidencesupports a causal relationship between country-specific quality differences and individual produc-tivity, the question remains whether the magnitudeof the estimated effects is sufficient to explain thestrong relationship with growth rates. The priorinvestigation of possible simultaneous provision

quality-growth effects. The individual earnings es- however, provide much larger estimates of

TABLE 6EFFECTS OF SCHOOL QUALITY ON U.S. EARNINGS OF IMMIGRANTS, 1989a

Only immigrants from countries with observed quality measures(n 5 37)

Immigrants from countries with observed or predicted qualitymeasures (n 5 87)

Schooling location

All

Schooling location

United States United Statesly Home only

United Statesand home

United Statesonly

320567080100

00019727

128

en

1198 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000timation, which provides direct evidence about themagnitudes of productivity differences associatedwith varying school-induced skills, holds the pos-sibility that something can be said about the mag-nitude of the growth effects.

Unfortunately, there is no simple way totranslate the individual productivity effects,which relate to levels of income, into aggregategrowth effects. Much depends upon the partic-ular model of growth that is selected. For ex-ample, one approach would be to modelachievement effects as affecting the aggregatesteady-state level of output for an economy withgrowth coming through conditional conver-gence based on initial income levels.25 In this,the relative magnitude of the quality coefficient

quality effects than found in the earnings esti-mation for immigrants, suggesting that morethan just direct productivity effects are enteringinto the growth relationship.

An alternative view from an endogenousgrowth model perspective would relategrowth rates to stocks of human capitalhere, either in terms of quantity or qualityof human capital. In this, strong externalitiesor endogenous growth in terms of the aggre-gate stock of labor-force quality might beable to explain the apparent disparity notedin terms of individual productivity andgrowth effects of quality differences.26 Twothings are important in assessing this. Be-

25 This approach is an extension of Barro and Sala-i-Martin (1995). We thank a referee for suggesting this wayof estimating the growth effects of quality differences.

26 As noted previously, the form could be from, forexample, quality influencing the rate of technologicalchange (Romer, 1990a) or an expanding steady-state levelthrough closing gaps in innovation (Nelson and Phelps,1966) or a variant of an AK model (Rebelo, 1991).of school resources with growth concluded thatthis path for growth effects was inconsistent withthe data. But, this and the further investigation ofvariations related to East Asian countries (see thenext section) are qualitative conclusions and saynothing about the estimated magnitude of

All Home only and home on

Years ofschool

0.089 0.090 0.080 0.103 0.1(0.002) (0.002) (0.002) (0.004) (0.0

Potentialexperience

0.061 0.061 0.069 0.089 0.0(0.002) (0.002) (0.003) (0.004) (0.0

Potentialexperiencesquared

20.0009 20.0009 20.0010 20.0016 20.0(0.0000) (0.0000) (0.0001) (0.0001) (0.0

QL2* 0.0019 0.0021 20.00018 0.0(0.0004) (0.0005) (0.0006) (0.0

Constant 8.154 8.046 7.977 7.881 7.5(0.035) (0.041) (0.056) (0.078) (0.1

Observations 20,644 20,644 12,955 4,956 3,4R2 0.15 0.15 0.13 0.22 0.1

a Mincer earnings models are estimated with the dependimmigrants with 1989 labor-market earnings who were born iare observed or, in the right panel, estimated.and the coefficient on initial income provide anestimate of the impact of quality on steady-statelevels of incomea parameter that would becomparable to the Mincer earnings parameter ifgrowth comes directly from varying levels ofhuman-capital inputs. The growth estimates,

0.103 0.099 0.089 0.117 0.130) (0.001) (0.001) (0.001) (0.003) (0.004)

0.058 0.058 0.067 0.085 0.066) (0.002) (0.002) (0.002) (0.003) (0.006)1 20.0008 20.0008 20.0009 20.0015 20.00112) (0.0000) (0.0000) (0.0000) (0.0001) (0.0002)

04 0.0060 0.0064 20.0025 0.00186) (0.0003) (0.0004) (0.0006) (0.0011)

7.883 7.678 7.589 7.498 7.542) (0.022) (0.024) (0.031) (0.054) (0.093)

3,9840 3,9840 2,6643 8,639 4,5580.23 0.23 0.23 0.26 0.19

nt variable being log of labor earnings. Samples includea country for which measures of labor-force quality (QL2*)

cause the quality coefficient is so large in the is currently uncertainty about how much of the

causal structure rule out many of the most plau-sible factors. Thus, we conclude that the evi-

1199VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHgrowth equations, both absolutely and rela-tive to school quantity, the emphasis must beon the strength of externalities to quality thatdiffer from those for quantity.27 Second, themagnitudes of quality effects in an endoge-nous growth case still appear implausiblylarge. The quality estimates in the baselineand in the augmented growth models suggestthat one standard deviation in test perfor-mance translates into more than 1-percenthigher annual growth in GDP per capita. But,by the estimates of Klenow and AndresRodrguez-Clare (1997 p. 94), the averagegrowth across a broad set of countries that isattributable to technological change is slightlyover 1 percent per yearroughly the same as onestandard deviation of test performance. Thus, theestimated quality effect in growth, even if comingfrom its aggregate influence on technologicalchange, appears too large.

While other models allowing a crosswalk be-

tween quality effects on the level of earningsand on the rate of aggregate growth might rec-oncile the magnitudes,28 we conclude that thereestimated growth effects comes from directcausal influences of measured labor-force qual-ity. A portion could come from omitted vari-ables that are strongly correlated with measuredquality. The exact nature of these omitted vari-ables is unclear, however, because the sensitiv-ity analyses and other considerations of the27 Considerable discussion has surrounded the magni-tude of the effect of school quantity (cf., Bils and Klenow,2000), so the relatively larger quality effects obtained herelead to similar questions, although the underlying structureis less clear.

28 For example, this difference in estimated productivityeffects between micro and macro estimates may reflect anerrors-in-variables problem related to the measurement ofthe quantity of schooling (see Alan B. Krueger and MikaelLindahl, 1999). Their analysis, however, concentrates moreon the estimated effect of changes in human capital,whereas the averages employed here should lessen anyerrors-in-variables problems. Another possibility to recon-cile the magnitude of the micro and macro estimates is thatthe productivity effects in the Mincer equation are poorlyestimated. The Mincer estimation attributes overall countryaverage quality to individuals, instead of including the ap-propriate individual measure. Moreover, the estimates aresensitive to sample. The quality estimates in Table 6 arethree times as large in the augmented sample as in thesmaller sample of test-taking nations. Nonetheless, whileother labor-market factors influence immigrants earningspicture and have some effect on the precise magnitude ofthe estimates, investigation of a variety of more complicatedearnings specifications confirms the overall pattern,strength, and significance of the country-specific labor-forcequality measures in the individual Mincer models for theUnited States. Hanushek and Jin-Yeong Kim (1999) inves-tigate a variety of specifications of the individual earningsmodels, including ones with measures of immigrants lan-dence here suggests that the quality measures doindicate productivity differences. It also con-firms the role of schooling differences acrosscountries, as opposed to cultural, racial, or pa-rental factors, in affecting these quality differ-ences. But, because the micro effects wouldappear to translate directly into smaller growthinfluences, questions about the complete causalstructure remain.

VI. Causality, Part CSensitivityto East Asian Countries

The well-known growth experience of EastAsian countries over our sample period raisesconcern that these results have been dominatedby countries in that region. As seen in Figure 1,East Asian countries tend to score highly on theinternational tests, so it is possible that the testscores might be merely identifying these countrieseven when labor-force quality is not causally re-lated to growth. This can be thought of as a specialcase of the omitted variables discussion of theprevious section.

Table 7 provides evidence about the impact ofthese countries on the estimates of growth rela-tionships. This table compares results for the en-tire sample with results that come from excludingdifferent subsets of East Asian countries. Threesubsets of East Asian countries are explored: FourTigers (Hong Kong, Korea, Singapore, and Tai-wan); High Performing (Four Tigers plus Japan);and Newly Industrialized (High Performing plus

guage ability, race, part-time work status, and selectivity ofimmigration. These alternative specifications affect themagnitude of coefficient estimates but not the overallstrength and significance. Moreover, this latter perspectivewould not change the magnitude of the quality coefficient inthe growth equation, which, independent of the issues aboutcompatibility of the micro and macro estimates, raises con-cerns.

ing rises some when East Asian countries are VII. The Importance of Quality Measurement

TABLE 7THE IMPORTANCE OF EAST ASIAN COUNTRIES

Countries with observed quality me

Fullsample

ExcludingFour

Tigersa

ExcludingHigh

Performingb

E

Ind

2

2

ses.n piwaxa

1200 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000excluded from the larger sample and shows noconsistent change when the sample is restrictedjust to countries with observed test scoresbut itis never statistically significant.

For the sample with observed tests, the effectof labor-force quality drops in magnitude byone-quarter to one-third, depending on the pre-cise sample, and the R2 drops noticeably whenany of the East Asian countries are deleted.These results are consistent with quality ofhuman capital contributing to the growth ofEast Asian economies. Nonetheless, labor-forcequality maintains a strong and significant effecton estimated growth in all subsets of countries.In the augmented samples, similar results hold.

Table 8 provides direct comparisons of esti-mated models with quality measures versus noquality measures or schooling input measures.Without quality measures [columns (13)],school quantity is consistently significant. Fur-ther, from column (2), primary-school pupil-teacher ratio is significant at the 10-percentlevel, but the magnitude is small. Cutting aver-age pupil-teacher ratios in half (to 18 from itscurrent world mean of 36), an extraordinarilyexpensive policy, would increase growth ratesby 0.7 percent per year. At the secondary level,pupil-teacher ratios have a perverse but statisti-cally insignificant effect. Considering total ex-penditure per pupil provides little additionalinformation about growth.

Direct measures of labor-force quality, how-ever, have a very different impact [columns (4)and (5)]. The proportion of variance explained

29 These subsets follow those of the World Bank (1993).High Performing would include China, but China is notincluded in the estimation because of missing data on initialincome for the basic growth models.Indonesia, Malaysia, and Thailand).29 These mod-els are estimated both for samples involving onlydirectly observed test information and for the aug-mented samples (i.e., including countries with pre-dicted tests). In all cases, negative effects of initialincome level are significant, demonstrating condi-tional convergence, although these effects arestronger when the East Asian countries are in-cluded. The estimated effect of quantity of school-

Initial per capita income(Y60)

20.472 20.357 20.328(0.090) (0.092) (0.104)

Quantity of schooling (S) 0.103 0.117 0.106(0.118) (0.116) (0.118)

Labor-force quality (QL1*) 0.134 0.101 0.095(0.020) (0.022) (0.024)

Constant 21.901 21.111 20.929(0.936) (0.934) (1.010)

Number of countries 31 27 26R2 (adjusted) 0.70 0.49 0.39

Note: Huber-White estimated standard errors are in parenthea Four Tigers: Hong Kong, Korea, Singapore, and Taiwanb High Performing: Hong Kong, Korea, Singapore, Taiwac Newly Industrialized: Hong Kong, Korea, Singapore, Ta

and Malaysia did not participate in any of the international eIn short, the importance of labor-force qualityis not merely an artifact of the data driven byEast Asian countries but holds in areas acrossthe world. Outside of East Asia, a one-standard-deviation change in labor-force quality is stillassociated with a 0.71.0-percentage pointhigher growth rate (depending upon the specificsample employed in the estimation).

asures Countries with observed or predicted quality measures

xcludingNewly

ustrializedcFull

sample

ExcludingFour

Tigersa

ExcludingHigh

Performingb

ExcludingNewly

Industrializedc

0.270 20.382 20.308 20.291 20.256(0.086) (0.078) (0.081) (0.084) (0.086)0.085 0.127 0.148 0.140 0.143

(0.113) (0.086) (0.087) (0.089) (0.091)0.091 0.108 0.079 0.075 0.069

(0.023) (0.020) (0.020) (0.020) (0.020)0.966 21.606 20.848 20.709 20.648

(0.986) (0.730) (0.719) (0.739) (0.755)

25 78 74 73 700.40 0.39 0.26 0.22 0.21

below coefficients.

lus Japan.n, Japan plus Indonesia, Malaysia, and Thailand. (Indonesiaminations).

The final two columns of Table 8 incorporatecompared with the other models from Table8. Moreover, the quality measures are especially

TABLE 8COMPARISON OF ALTERNATIVE MEASURES OF SCHOOL QUALITY AND GROWTH

Baseline(1)

School inp(2)

Initial per capita income(Y60) [$1,000]

20.407 20.455 2(0.139) (0.114)

Quantity of schooling (S) 0.529 0.481(0.122) (0.124)

Pupil-teacher ratio in primaryschools (PT-pri)

20.040(0.024)

(1

se

1201VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHboth direct quality measures (QL) and the inputmeasures of the second and third columns.None of the inputs has a significant influence ongrowth after conditioning on either of the labor-force quality measures. These final specifica-tions simply reinforce the higher informationalcontent of the test measures as opposed to theschool inputs.

The importance of adequate measures ofquality becomes clear in Table 9, whichprovides comparisons of the root mean-squarederror (RMSE) in explaining growth rates across

powerful in explaining anomalies in growthrates. The final three columns in Table 8 dividethe countries into slow growers (average annualgrowth less than 1 percent), fast growers (aver-age annual growth greater than 3.5 percent), andthe remainder. The reduction in root mean-squared error comes at the extremes of thegrowth distribution, and especially from betterexplaining rapid growth. The RMSE for fastgrowers falls from about 2.2 percent to 1.7percent when QL1* is used to explain growthdifferences. While the improvement at the bot-tom of the distribution is less in absolute terms,it is still noticeable at about 0.2 percent. Theresults for QL2* are similar.

The previous analyses have concentrated onvariations in growth rates that can be explainedby initial conditions and by quantity and qualityof human capital. At the same time, these highlysimplified models leave out a wide range ofcharacteristics of country economies. Thedistribution of observed growth rates reflects

30 There is an artificially high correlation of the quantityand quality of schooling (r 5 0.71 with QL1*) that comesfrom the projection equation for predicting QL in countriesthat lack direct test information. The separate influences ofquantity and quality, however, are identified by the coun-tries with test observations, and the reduction in estimatedeffect of school quantity seen here simply mirrors thatpreviously seen in the base case for just countries withdirect observations (Table 2).doubles, reaching almost 40 percent. Moreover,quality measures replace quantity in demon-strating the importance of human capital fornational growth.30

Pupil-teacher ratio insecondary schools (PT-sec)

0.027(0.042)

Total expenditure oneducation/GDP (EXPEND)

Labor-force quality (QL1*)

Labor-force quality (QL2*)

Constant 0.933 2.140(0.238) (2.060)

Number of countries 100 96R2 0.23 0.26

Note: Huber-White estimated standard errors are in parenthea consistent set of countries. The root mean-squared error in models with quality falls by 0.2percentage points (in annual growth) when

uts Quality measuresCombined input and

quality(3) (4) (5) (6) (7)

0.408 20.382 20.370 20.393 20.368(0.137) (0.081) (0.084) (0.095) (0.095)0.486 0.127 0.120 0.070 0.065

(0.133) (0.089) (0.096) (0.104) (0.117)0.001(0.026)

0.006(0.024)

20.038(0.044)

20.038(0.045)

14.424.73)

7.388(16.060)

3.968(15.100)

0.108(0.021)

0.112(0.020)

0.094(0.016)

0.100(0.015)

0.558 21.606 21.483 21.113 21.042(0.418) (0.749) (0.584) (1.091) (0.992)

96 78 80 76 780.22 0.41 0.41 0.42 0.42

s below coefficients.

unconditional growth. The countries in italicsare the 13 with a percentile ranking in condi-

open and competitive markets in the UnitedStates.

TABLE 9ROOT MEAN-SQUARED ERROR FOR ALTERNATIVE GROWTH MODELS

1202 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000tional growth that is 20 points or more lower inthe distribution than that in terms of uncondi-tional growth. For example, Egypt, with an av-erage growth rate of 2.9 percent, moves fromthe twenty-seventh-ranked country in uncondi-tional growth to the third-ranked country ingrowth after conditioning on its human-capitalstock. At the same time, Japan, with an averagegrowth rate of 5.3 percent, falls from seventh inunconditional rankings to twenty-fourth afterits favorable growth conditions are taken intoaccount.

The distribution of growth rates after elimi-nating the influence of the measured initial in-

It is interesting to put this in the frameworkof the often-noted growth performance of EastAsia (see World Bank, 1993). After taking intoaccount measures of labor-force quality, Singa-pore, Hong Kong, Korea, Thailand, and Taiwanare still identified as unusually fast growers. Inother words, the East Asian miracle includes asignificant component that is over and above anyemphasis and performance in the development ofhuman capital. At the same time, the Japanesegrowth pattern looks much less unusual. Thus,without minimizing the importance of human cap-ital for development, it is important to note that asignificant component of growth falls elsewhere.the combination of growth conditions andunmeasured factors, and, by the analysis inTable 9, it is clear that the importance of mea-sured and unmeasured factors differs acrosscountries. By taking out the measured effects,we can identify which countries are growingsurprisingly fast or surprisingly slow given hu-man-capital stocks. Figure 2 displays the per-centile distributions of countries in terms ofaverage annual growth rates over the period19601990. Figure 3 displays the distributionafter conditioning on initial income and quan-tity and quality of human capital; i.e., it displayscountries that do significantly better or worsethan would be expected. The countries in bold-face are the 13 with a percentile ranking inconditional growth that is 20 points or morehigher in the distribution than that in terms of

Model (from Table 8)All

countries

A. QL1* quality measureBaseline: C, Y60, S 1.50Input: C, Y60, S, PT-pri, PT-sec 1.50Input: C, Y60, S, EXPEND 1.50Quality: C, Y60, S, QL1* 1.28

Number of countries 76B. QL2* quality measure

Baseline: C, Y60, S 1.52Input: C, Y60, S, PT-pri, PT-sec 1.52Input: C, Y60, S, EXPEND 1.52Quality: C, Y60, S, QL2* 1.31

Number of countries 78come and human capital provides someguidance in looking to identify a richer set offactors that affect growth. For example, theperformance of the United States, identified ashaving significantly faster growth than expectedgiven its human-capital characteristics (movingfrom below the median almost to the top 10percent of the distribution), may partially reflectadditional imperfections in the human-capitalmeasure. None of this analysis incorporatesinformation about higher education, whereU.S. schools are arguably the worlds best.Moreover, in versions of endogenous growthmodels which emphasize ideas and inventions(e.g., Romer, 1990a), higher educations in-put into the production of scientists andengineers would be especially important. Al-ternatively, it may simply reflect the more

Average growth-rate category

,1 percent 13.5 percent .3.5 percent

2.16 0.87 2.162.16 0.87 2.172.14 0.86 2.181.95 0.79 1.7113 47 16

2.08 0.89 2.212.07 0.89 2.222.07 0.88 2.231.90 0.87 1.6715 47 16

AG

1203VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHVIII. Conclusions

Throughout consideration of varying na-tional growth rates, one of the most robustand readily accepted conclusions involves thecentrality of a nations human capital. Thisconclusion has, nonetheless, come from mod-els with very different specifications of hu-man capital. Virtually all have ignored qualityissues, implicitly assuming that any variationsin quality of human capital are small relativeto the importance and variation in pure quan-tity of human capital.

The analysis here explicitly considers the

quality of the labor force as measured bycomparative tests of mathematics and scien-tific skills. A single conclusion emerges fromthe various analytical specifications: Labor-force quality has a consistent, stable, andstrong relationship with economic growth. Aseries of indirect investigations of the under-lying specification are qualitatively consistentwith a causal interpretation. The growth rela-tionship does not appear to be the result ofgrowth causing higher quality through invest-ing resources in schools. Nor does it appear tobe driven by high test performance simplybeing correlated with East Asian countries

FIGURE 3. DISTRIBUTION OF COUNTRIES BY CONDITIONAL GROWTH RATES OF REAL GDP/CAPITA ALLOWING FOR INITIALINCOME AND QUANTITY AND QUALITY OF HUMAN CAPITAL

Notes: Bold (Kenya, Trinidad & Tobago, Honduras, Algeria, Togo, Bolivia, El Salvador, United States, Brazil, India, Iran,Mexico, and Egypt) indicates the country is 20 percentage points or more higher in the conditional distribution than in theunconditional distribution. ITALICS (Mauritius, Yugoslavia, Fiji, Belgium, Barbados, Israel, Congo, Netherlands, Germany,Panama, Japan, Lesotho, and Greece) indicates the country is 20 percentage points or more lower in the conditionaldistribution than in the unconditional distribution.FIGURE 2. DISTRIBUTION OF COUNTRIES BY AVER E ANNUAL GROWTH RATES OF REAL GDP/CAPITA

that, for other reasons, also achieve high impact on growth. At the same time, the simple

1204 THE AMERICAN ECONOMIC REVIEW DECEMBER 2000growth. Finally, by looking at how our qualitymeasures relate to immigrants earnings in theUnited States, we find clear evidence thatinternational test performance relates to produc-tivity differences. Moreover, these productivitydifferences appear related to schooling differ-ences and not cultural factors, family supportand attitudes, and the like. This direct linkage toproductivity suggests a causal impact in inter-national economic performance.

Nonetheless, the estimated impact of qual-ity on growth, indicating that one standarddeviation in mathematics and science skillstranslates into more than one percentagepoint in average annual real growth, alsolooks implausibly large. There is no simpleand agreed upon way to translate the microproductivity differences from individualearnings into effects for economic growth,making it difficult to be precise. If, forexample, quality enters through raising thesteady-state level of income and growth re-flects a process of conditional convergence,the growth equation results are much largerthan the corresponding results for individualearnings. An alternative, which is moreconsistent with the underlying assumed en-dogenous growth approach of this paper,would highlight the role of externalitiesfrom higher levels of human capital. Thegrowth model results, however, imply thatthe externalities must be significantly strongerfor quality than for quantity. The estimatedgrowth effect of one standard deviation ofquality is larger than would be obtainedfrom over nine years in average schooling.Moreover, in absolute terms, this effect isroughly equal to estimates of average ratesof technological progress over this period.These arguments suggest the possibility ofomitted variables in the growth equations, butwe have little indication of what these mightbe. A number of plausible factors have beenruled out by the specification analyses and bythe consideration of alternative models ofcausal effects.

We conclude that labor-force quality differ-ences are important for growth; that these qual-ity differences are related to schooling (but notnecessarily the resources devoted by a countryto schooling); and that quality has a causalestimates of cross-country growth relationshipsappear to overstate the causal impact of quality.The precise cause or magnitude of this over-statement is unclear.

There is also a distinct policy dilemma, be-cause standard school resource policies do notrelate to the variations in quality that have beenidentified. We believe that further investigationof the underlying factors guiding quality differ-ences is important.

APPENDIX A: LIST OF VARIABLES AND SOURCES

Sources of Data

(BL): Barro and Lee (1993 [with 1994 dataupdate])

(ER): Easterly and Rebelo (1993)(KL): King and Levine (1993)(SH): Summers and Heston (1991)(UNESCO): UNESCO Statistical Yearbook

(various years)

Variables in Analysis

Asia, Latin America, and Africa: regional dum-mies for Asian, Latin American, and Sub-Saharan African countries(BL: ASIAE, LAAM, and SAFRICA).

GCN: ratio of real government consumptionexpenditure net of spending on defense andon education to real GDP(ER: HSGVXDXE).

ENROLL-pri: average of total gross enrollmentrate for primary education (BL: Pxx).

EXPEND: average ratio of nominal governmentexpenditure on education to nominal GDP(BL: GEETOT).

GPOP: average of population growth rate (BL:GPOP).

GR: annual average growth rate of per capitareal GDP for the period of 19601990. Ifdata are not available for both end points,subperiods are used for which data are avail-able. Real GDP per capita is SH: RGDPCHin 1985 international prices.

PPE: per pupil current public expenditurecalculated as GDP*(POP)*(Current expend/GDP)/(Primary 1 Secondary students)

[$100] (SH: GDP; UNESCO: current expen-diture, number of primary and secondary stu-dents).

PRIINV: average ratio of private investmentrelative to GDP (BL: INVWB-INVPUB).

PT-pri: average pupil/teacher ratio in primaryschools (BL: TEAPRI).

PT-sec: average pupil/teacher ratio in primaryschools (BL: TEASEC).

QL1, QL2: measures of schooling quality con-structed as described in text; see below.

achievement with predicted values for non-participants; see text and below.

RECUR: ratio of recurring nominal governmentexpenditure on education to nominal GDP(BL: GEEREC).

S: arithmetic average years of schooling for1960, 1965, 1970, 1975, 1980, and 1985 (BL:HUMAN).

TEST: dummy for participants in internationalcomparison studies of student achievement;see text.

The production function estimates (see Table 3) employ a sample combining different testyears in which the dependent variable is the average normalized score for each country and test.Table B1 below describes the dating of exogenous variables for the production function models,based on the specific test year for the performance measure.

19641966 19661973 19801982 19831986 IAEP 1988 IAEP 1991

St 2 1 1960 19601965 19651975 19701980 19751985 19751985EXPENDt 2 1 19601964 19601969 19651974 19701979 19751984 19751984

1205VOL. 90 NO. 5 HANUSHEK AND KIMKO: LABOR-FORCE QUALITY AND GROWTHPT-prit 2 1 19501960 19551965 1960PPEt 2 1 1960 19601965 1965GPOPt 2 1 19601964 19601969 19651970 19651975 19701980 197019801975 19701980 19751985 197519851974 19701979 19751984 19751984TABLE B1DATING OF EXOGENOUS VARIABLES FOR THE PRODUCTION MODELS

IEA mathIEA

science IEA mathIEA

scienceQL1*, QL2*: quality measures expanded tononparticipants and participants in interna-tional comparison studies for student

TRD: ratio of total trade to GDP (KL).Y60: initial income, 1960 [$1,000] (SH: RGD-

PCH).

APPENDIX B: DATA FOR PRODUCTIONFUNCTION ESTIMATES

APPENDIX C: LABOR-FORCE QUALITY DATA

32 CZECHOSLOVAKIA 0

TABLE C1CONTINUED

1206 THE AMERICAN ECONOMIC REVIEW DECEMBER 200033 DENMARK 0 53.48 61.7634 DJIBOUTI 035 DOMINICA 036 DOMINICAN REPUBLIC 0 37.41 39.3437 ECUADOR 0 35.78 38.9938 EGYPT 0 26.01 26.4339 EL SALVADOR 0 21.81 26.2140 ETHIOPIA 041 FIJI 0 50.02 58.1042 FINLAND 1 48.76 59.5543 FRANCE 1 54.15 56.00The following data (Table C1) are generatedfrom the methods described in the text. TEST 5 1if performance is observed, at which time QL1*and QL2* are the observed test data. If TEST 5 0,QL1* and QL2* are projected scores. If blank, thedata necessary for projecting scores or for estimat-ing growth models were missing or the projectedscores were less than 20 (see text).

TABLE C1LABOR-FORCE QUALITY DATA

COUNTRY TEST QL1* QL2*1 ALGERIA 0 28.28 28.062 ANGOLA 03 ARGENTINA 0 42.99 48.504 AUSTRALIA 1 48.13 59.045 AUSTRIA 0 53.20 56.616 BAHAMAS 07 BAHRAIN 0 26.03 23.198 BANGLADESH 09 BARBADOS 0 50.41 59.80

10 BELGIUM 1 53.25 57.0811 BELIZE 012 BENIN 013 BHUTAN 014 BOLIVIA 0 22.10 27.4715 BOTSWANA 0 25.05 31.7116 BRAZIL 1 33.91 36.6017 BULGARIA 018 BURKINA FASO 019 BURUNDI 020 CAMEROON 0 39.00 42.3621 CANADA 1 47.57 54.5822 CAPE VERDE ISLAND 023 CENTRAL AFRICA,

REPUBLIC OF0 24.77

24 CHAD 025 CHILE 1 26.30 24.7426 CHINA 1 59.28 64.4227 COLOMBIA 0 34.78 37.8728 COMOROS 029 CONGO 0 46.04 50.9030 COSTA RICA 0 42.15 46.1531 CYPRUS 0 42.24 46.24COUNTRY TEST QL1* QL2*44 GABON 045 GAMBIA 046 GERMANY, WEST 1 59.03 48.6847 GHANA 0 25.5848 GREECE 0 49.11 50.8849 GRENADA 050 GUATEMALA 051 GUINEA-BISS 052 GUINEA 053 GUYANA 0 45.71 51.4954 HAITI 055 HONDURAS 0 26.43 28.5956 HONG KONG 1 56.93 71.8557 HUNGARY 1 53.85 61.2358 ICELAND 0 48.13 51.2059 INDIA 1 21.63 20.8060 INDONESIA 0 37.98 42.9961 IRAN 1 20.79 18.2662 IRAQ 0 29.34 27.5063 IRELAND 1 47.59 50.2064 ISRAEL 1 51.29 54.4665 ITALY 1 44.59 49.4166 IVORY COAST 067 JAMAICA 0 44.19 48.6268 JAPAN 1 60.65 65.5069 JORDAN 1 39.38 42.2870 KENYA 0 24.43 29.7371 KOREA, REPUBLIC OF 1 56.21 58.5572 KUWAIT 0 28.36 22.5073 LAOS 074 LESOTHO 0 46.14 51.9575 LIBERIA 076 LUXEMBOURG 1 39.45 44.4977 MADAGASCAR 078 MALAWI 079 MALAYSIA 0 47.89 54.2980 MALI 081 MALTA 0 53.16 57.1482 MAURITANIA 083 MAURITIUS 0 49.53 54.9584 MEXICO 0 35.06 37.2485 MONGOLIA 086 MOROCCO 087 MOZAMBIQUE 1 24.26 27.9488 MYANMAR 089 NAMIBIA 090 NEPAL 091 NETHERLANDS 1 56.84 54.5292 NEW ZEALAND 1 52.44 67.0693 NICARAGUA 0 24.19 27.3094 NIGERIA 1 34.15 38.9095 NIGER 096 NORWAY 1 49.60 64.5697 OMAN 098 PAKISTAN 099 PANAMA 0 42.02 46.78

100 PAPUA NEW GUINEA 0 22.58101 PARAGUAY 0 37.99 39.96102 PERU 0 37.83 41.18

109 ROMANIA 0

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Barro, Robert J. Economic Growth in a CrossSection of Countries. Quarterly Journal ofEconomics, May 1991, 106(2), pp. 40743.

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110 RWANDA 0111 SAUDI ARABIA 0112 SENEGAL 0113 SEYCHELLES 0114 SIERRA LEONE 0115 SINGAPORE 1 56.51 72.13116 SOLOMON ISLANDS 0117 SOMALIA 0118 SOUTH AFRICA 0 45.25 51.30119 SPAIN 1 49.40 51.92120 SRI LANKA 0 41.54 42.57121 ST. LUCIA 0122 ST. VINCENT 0123 SUDAN 0124 SURINAME 0125 SWAZILAND 1 35.46 40.26126 SWEDEN 1 47.41 57.43127 SWITZERLAND 1 57.17 61.37128 SYRIA 0 31.66 30.23129 TAIWAN 1 56.28 56.31130 TANZANIA 0131 THAILAND 1 39.83 46.26132 TOGO 0 28.08 32.69133 TONGA 0134 TRINIDAD AND TOBAGO 0 40.57 46.43135 TUNISIA 0 41.79 40.50136 TURKEY 0 41.52 39.72137 UGANDA 0138 URUGUAY 0 46.33 52.27139 UNITED ARAB EMIRATES 0140 UNITED KINGDOM 1 53.98 62.52141 UNITED STATES 1 43.43 46.77142 UNION OF SOVIET

SOCIALIST REPUBLICS1 53.89 54.65

143 VAUATU 0144 VENEZ