A New Data Set of Educational Attainment in the World, *

Transcription

1 A New Dt Set of Eductionl Attinment in the World, * Robert J. Brro + Hrvrd University nd Jong-Wh Lee Kore University Revised: November 2011 * We re grteful to UNESCO Institute for Sttistics for providing dt nd UNDP Humn Development Office, Rostislv Kpelyushnikov, Ttjn Skrbecnl for helpfule comments. Ruth Frncisco, Hnol Lee, nd Seulki Shin hve provided vluble reserch ssistnce. Lee thnks the Kore Reserch Foundtion for finncil support. The dt set presented here is vilble online ( + Send correspondence: Robert J. Brro, Deprtment of Economics, Hrvrd University, Cmbridge MA Tel: , Fx: , E-mil: rbrro@hrvrd.edu

2 Abstrct Our pnel dt set on eductionl ttinment hs been updted for 146 countries from 1950 to The dt re disggregted by sex nd by 5-yer ge intervls. We hve improved the ccurcy of estimtion by using informtion from consistent census dt, disggregted by ge group, long with new estimtes of mortlity rtes nd completion rtes by ge nd eduction level. We compre the estimtes with our previous ones (Brro nd Lee, 2001) nd lterntive mesures (Cohen nd Soto, 2007). Our estimtes of eductionl ttinment provide resonble proxy for the stock of humn cpitl for brod group of countries nd should be useful for vriety of empiricl work., Keywords: Eduction, Humn Cpitl JEL No.: I20, J24, O15

3 1. Introduction Mny observers hve emphsized the crucil importnce of humn cpitl, prticulrly s ttined through eduction, to economic progress (Lucs, 1988 nd Mnkiw, Romer nd Weil, 1992). An bundnce of well-educted people goes long with high level of lbor productivity. It lso implies lrger numbers of more skilled workers nd greter bility to bsorb dvnced technology from developed countries. The level nd distribution of eductionl ttinment lso hve impct on socil outcomes, such s child mortlity, fertility, eduction of children, nd income distribution (see for exmple Brro nd Lee, 1994; de Gregorio nd Lee, 2002; Breierov nd Duflo, 2004; Cutler et l., 2006). There hve been number of ttempts to mesure eductionl ttinment cross countries to quntify the reltionship between it nd economic nd socil outcome vribles. Erlier empiricl studies used school enrollment rtios or litercy rtes (Romer, 1990, Brro, 1991, nd Mnkiw, Romer nd Weil, 1992). But lthough widely vilble, these dt do not dequtely mesure the ggregte stock of humn cpitl vilble contemporneously s n input to production. Our erlier studies (1993, 1996, nd 2001) filled this dt gp by constructing mesures of eductionl ttinment for brod group of countries. The figures were constructed t 5-yer intervls from 1960 to The dt showed the distribution of eductionl ttinment of the dult popultion over ge 15 nd over ge 25 by sex t seven levels of schooling. We lso constructed mesures of verge yers of schooling t ll levels primry, secondry, nd tertiry for ech country nd for regions in the world. In this pper, we updte nd expnd the dt set on eductionl ttinment. We extend our previous estimtes from 1950 to 2010, nd provide more, improved dt disggregted by sex nd ge. The dt re broken down into 5-yer ge intervls, nd the coverge hs now expnded to 146 countries by dding 41, including 11 former Soviet republics. The ccurcy of estimtion hs lso improved by incorporting recently vilble census/survey observtions. The new dt set improves on the erlier by using more informtion nd better methodology. 1

4 We construct new estimtes by using informtion from survey/census dt, disggregted by ge group. Previously, we dopted perpetul inventory method, using the census/survey observtions on the eductionl ttinment of the dult popultion group over ge 15 or over ge 25 s benchmrk stocks nd new school entrnts s flows tht dded to the stocks with n pproprite time lg. The flow estimtes were estimted using informtion on schoolenrollment rtios nd popultion structure over time. But this method is subject to bis due to inccurcy in estimted enrollment rtios nd in benchmrk censuses. In the current estimtion, we reduce mesurement error by using observtions in 5-yer ge intervls for the previous or subsequent 5-yer periods. We lso construct new estimtes of () survivl/mortlity rtes by ge nd by eduction; nd (b) completion rtios by eductionl ttinment nd by ge group. These mesures help improve the ccurcy of the bckwrdnd forwrd-estimtion procedure. The dt set improvements ddress most of the concerns rised by critics, including Cohen nd Soto (2006) nd De L Fuente nd Doménech (2006). They noted tht the previous dt set of Brro nd Lee (1993, 2001) shows implusible time-series profiles of eductionl ttinment for some countries. The new procedures hve resolved these problems. In the next section, we summrize the dt nd the methodology for constructing the estimtes of eductionl ttinment nd discuss the modifictions tht hve been mde in the present updte. In section 3, we highlight the min fetures of the new dt set. In section 4, we compre the estimtes with our previous ones (Brro nd Lee, 2001) nd lterntive mesures by Cohen nd Soto (2007). Section 5 presents our conclusions. 2. Dt nd Estimtion Methodology A. The Census dt The benchmrk figures on school ttinment (621 census/survey observtions) re collected from census/survey informtion, s compiled by UNESCO, Eurostt, ntionl sttistic gencies, nd other sources. 1 The census/survey figures report the distribution of eductionl 1 There re dditionl dt vilble from OECD sources for group of OECD countries since We hve decided not to use these dditionl observtions becuse they re not necessrily comptible with the dt from the other sources, in prticulr UNESCO dt for non-oecd countries. As discussed in Brro nd Lee (2001), 2

5 ttinment in the popultion over ge 15 by sex nd by 5-yer ge group, for most cses, in six ctegories: no forml eduction (lu), incomplete primry (lpi), complete primry (lpc), lower secondry (lsi), upper secondry (lsc), nd tertiry (lh). Tble 1 presents the distribution of countries by the number of vilble census/survey observtions since For totl popultion ged 15 nd over, 191 countries hve t lest 1 observtion, nd 112 countries hve 3 or more observtions. Tble 2 shows the distribution of countries by census/survey yer since 1950 (where the underlying figures re pplied to the nerest 5-yer vlue). For totl popultion over ge 15, for exmple, 67 observtions re vilble for 1960, 89 for 1970, 93 for 1980, 84 for 1990, nd 79 for These dt points re used s benchmrk figures on eductionl ttinment. When census provides only numbers for combintion of severl ctegories, such s no forml eduction, incomplete primry, nd complete primry, we use decomposition methods to seprte into ctegories. In mny OECD nd non-oecd countries, vilble census dt do not report dt ccording to these four brod ctegories. 3 Some census dt do not report lu or the proportion of those who hve no forml eduction, nd do report lp, ls, nd lh mong the educted members of the popultion only. To void overestimtion of verge yers of schooling, for census yers with missing lu, we use the illitercy rte, primry enrollment rtio, or lu from other census yers to estimte lu. We then djust lp, ls, nd lh to reflect both the educted nd uneducted members in the totl popultion. In some instnces, dt on lu is not missing but overlpped with other ctegory(ies) or subctegory(ies). Some census dt report the proportion of those who hve reched primry level together with those who hve no forml eduction (lu+lp). A number of countries lso report the combined proportion of those who hve reched secondry schooling or less (lu+lp+ls). Also, some census dt report the combintion of those who hve reched primry or secondry levels (lp+ls). To decompose these overlpping census observtions we most OECD dt come from lbor-force surveys bsed on smples of households or individuls, in contrst to the ntionl censuses in the UNESCO dtbse nd in mny cses, OECD nd UNESCO use different eductionl clssifiction schemes. 2 These census/survey observtions include the countries/territories for which we could not construct the complete estimtes of eductionl ttinment becuse of other missing informtion. Appendix Tble shows the census/survey informtion for the 146 countries for which we hve constructed complete estimtes. 3 Country Notes vilble online t: explin the censuses for which decomposition method ws pplied. 3

6 use enrollment dt. Specificlly, for census yers where lu is combined with other ctegory(ies) or subctegory(ies), we use djusted primry nd/or secondry enrollment rtio by ge group from erlier or lter yers nd the ge distribution profile to decompose the overlpping observtions. 4 B. Estimtion of missing observtions t the four brod levels We clculte from 1950 to 2010 t the five yer intervls the eductionl ttinment of the popultion by 5-yer ge groups. First, we clculte the distribution of eductionl ttinment t four brod ctegories no forml eduction (lu), primry (lp), secondry (ls) nd tertiry eduction (lh). Primry includes both incomplete primry (lpi) nd complete primry (lpc), nd secondry (ls) includes lower secondry (lsi) nd upper secondry (lsc). Tertiry eduction (lh) lso includes both junior-level (lhi) nd higher-level tertiry (lhc). We fill in most of missing observtions by forwrd nd bckwrd extrpoltion of the census/survey observtions on ttinment. The estimtion procedure extrpoltes the census/survey observtions on ttinment by ge group to fill in missing observtions with n pproprite time lg. Let s denote h j, t s the proportion of persons in ge group, for whom j is the highest level of schooling ttined- j=0 for no school, 1 for primry, 2 for secondry, nd 3 for higher t time t. There re 13 5-yer ge groups rnging from =1 (15 19 yers old) to =13 (75 yers nd over). The forwrd extrpoltion method ssumes tht the distribution of eductionl ttinment of ge group t time t is the sme s tht of the ge group tht ws five yers younger t time t-5: h (1) t 1 h where ge group denotes, =3: ge group, =10: ge group. This setting 4 The djusted enrollment rtio is the gross enrollment rtio minus the proportion of repeters. The ge distribution profile is the reltive popultion distribution by ge group within n eductionl ttinment t specific time period. If the gross enrolment rtio is not vilble, the net enrolment rtio is used s proxy for the djusted enrollment rtio. 4

7 pplies to persons who hve completed their schooling by time t-5. As explined below, we djust this formul by considering different mortlity rtes by eduction level for the old popultion ged 65 nd over. For younger groups under ge 25, we dopt different method, considering tht prt of popultion is still in school during the trnsition period from t to t+5. The bckwrd extrpoltion is expressed s: h j h 1, t where ge group denotes, =2: ge group, =9: ge group. (1) Thus, person s eductionl ttinment remins unchnged between ge 25 nd 59. An ssumption here is tht, in the sme 5-yer ge group, the survivl rte is the sme regrdless of person s eductionl ttinment. When we look t informtion from vilble censuses strtified by eductionl ttinment nd popultion structure by ge group in the previous or subsequent 5-yer periods, we find this ssumption holds well for the popultion ged 64 nd under, but not for older ge groups. In typicl country, the mortlity rte is higher for older people who re less-educted. The ssumption of uniform mortlity cn then cuse downwrd bis in the estimtion of the totl eductionl stock. If we consider the differences in survivl rte by eduction levels, the forwrd extrpoltion method is expressed by hj t h 1, (2) where j is the ge-specific survivl rte over the five yers for the popultion in ge group, for whom j is the highest level of schooling. For the popultion ged 60 nd bove ( =11, 12, nd 13), we llow for the different mortlity rtes for the old popultion ged 60 nd bove by eduction levels. By utilizing informtion from vilble censuses by ge group in the previous nd/or next 5- yer periods, we hve estimted the survivl rtes for the old popultion in the ge group, 60 64, 65 69, nd ( =10,11, nd 12) by eduction levels. The estimtion results show tht the more educted people hve lower mortlity rtes. Appendix Notes 1 describes more detils on the estimtion of survivl rtes. 5

8 An importnt issue is how to combine forwrd nd bckwrd-flow estimtes when both re vilble for missing cell. We hve crried out simultion exercise in which we regressed the observed ctul census vlues of the vrious levels of eductionl ttinment on the estimtes generted from forwrd- nd bckwrd-flow estimtes (bsed on both five- or tenyer led nd lgged vlues from ctul censuses). We use the regression results to construct weighted-verge of forwrd nd bckwrd-flow estimtes (see Appendix Notes 1 for more detils on how to combine forwrd-flow nd bckwrd-flow estimtes). Note tht the forwrd nd bckwrd-flow estimtes cnnot be pplicble for the two youngest cohorts between ges 15 nd 24 becuse prt of the popultion is in school during dtes t nd t+5. For these ge groups ( =1: ge group nd =2: 20 24), we construct the estimtes by using the estimtes of the sme ge group in t 5 (or t+5) nd the chnge in (gespecific) enrollment for the corresponding ge groups over time (see Appendix Note 1 for more detils). C. Estimtion of sub-ctegories of eductionl ttinment We hve estimted school ttinment t four brod levels of schooling: no school, some primry, some secondry, nd some higher. We brek down the three levels of schooling into incomplete nd complete eduction by using estimtes of completion rtios. First, we describe our procedure for estimting missing observtions for the subctegories for the primry schooling ctegory. We filled in the missing cells using informtion from the vilble census/survey dt. The completion rte t the primry level is expressed s rtio of people who completed primry schooling but did not enter secondry schooling to people who entered primry school. For the remining missing cells, we filled them in by forwrd nd bckwrd extrpoltion of the census/survey observtions on completion rtios with n pproprite time lg. This procedure pplies to the ge group =3 (25 29) nd bove. 5 If both forwrd nd bckwrd estimtes re vilble, we combine them by using the results of regression of the observed ctul census vlues of the vrious levels of completion rtio on 5 For the countries in which only the completion rtio for totl popultion is vilble, we brek down it into ge groups bsed on the typicl ge profile of completion rtios constructed using the vilble dt of the countries in the sme region. 6

9 the estimtes generted from forwrd- nd bckwrd-flow estimtes (bsed on both 5-yer or ten-yer led nd lgged vlues from ctul censuses). On the other hnd, we ssume tht the completion rtios for ged nd re determined by ge specific profile of completion rtios in ech country (see Appendix Notes 2). We pplied similr methods to estimte missing observtions for the subctegories for secondry nd tertiry schooling. Secondry-school enrollees ged re treted s incompletely educted t the secondry level, nd higher-school enrollees ged re treted s incompletely educted t the higher level. Appendix Notes 2 explins more detils on how to combine forwrd-flow nd bckwrd-flow estimtes of completion rtios. D. Averge Yers of Schooling The number of yers of schooling for the popultion ged 15 nd bove, s t, is constructed s s t A 1 l t s t (3) g where l : the popultion shre of group g in popultion 15 nd bove nd s t : the number of t yers of schooling of ge group ( =1: ge group, =2: ge group,, =13: 75 nd bove). The number of yers of schooling of ge group in time t is s t j h t Dur t (4) where h j the frction of group hving ttined the eductionl level j = pri, sec, ter, nd Dur indictes the corresponding durtion in yers. The durtion dt is constructed by tking ccount of chnges in the durtion system over time in country. We suppose tht chnges in the durtion of schooling t the primry level pplied to new entrnts in primry school (tht is, ges 5 9) t the time of chnge. We use the sme sources nd methodology to construct pnel dt set on eductionl ttinment of femles by ge group. The dt on the distribution of eductionl ttinment mong the popultion, combined with the informtion for ech country on the durtion of 7

10 school t ech level, generte the number of yers of schooling chieved by the verge person t vrious levels nd t ll levels of schooling combined. 3. The Complete Dt Set on Eductionl Attinment, Tbles 3 nd 4 summrize the progress in eductionl ttinment of the popultion ged 15 yers nd bove by region nd by income clssifiction from 1950 to 2010 for the 146 countries tht hve complete informtion. 6 The tble considers two brod groups 24 dvnced countries nd 122 developing countries. The developing group is further broken down into six regions: Middle Est/North Afric (18 countries), Sub-Shrn Afric (33), Ltin Americ/Cribben (25), Est Asi/Pcific (19), South Asi (7), nd Europe nd Centrl Asi (20). Regionl verges re computed by weighting ech country's observtion by its shre in totl popultion of the region. Some of the importnt developments tht represent the progress of developing countries in chieving higher eductionl ttinment re summrized s: In 2010, the world popultion ged 15 nd bove is estimted to hve n verge of 7.9 yers of schooling, incresing stedily from 3.1 yers in 1950 nd 5.3 yers in The overll popultion over ge 15 in high-income economies is estimted to hve 11.3 yers of schooling, compred to 7.2 yers in developing countries. Both Sub-Shrn Africn nd South Asin countries hve the lowest t 5.3 yers on verge. Since 1950, the verge yers of schooling mong the totl popultion ged 15 yers nd bove in developing countries incresed significntly from 2.0 yers to 7.2 yers. In South Asi nd Middle Est/North Afric regions, verge yers of schooling hve more thn 6 The dditionl countries/territories tht hve complete estimtes in the new dt set include Albni, Belize, Burundi, Brunei Drusslm, Cmbodi, Congo, Cote d Ivoire, Egypt, Gmbi, Gbon, Lo People's Democrtic Republic, Luxembourg, Liby, Morocco, Mco Specil Administrtive Region, Mldives, Mlt, Muritni, Mongoli, Nmibi, People's Republic of Chin, Qtr, Reunion, Rwnd, Sudi Arbi, Tong, United Arb Emirtes, Viet Nm, Yemen. The dt set include Croti, Czech Republic, Serbi, Slovki, nd Sloveni s independent countries, replcing the former Yugoslvi nd Czechoslovki. The former USSR is replced by the Russin Republic, Armeni, Azerbijn, Estoni, Kzkhstn, Kyrgyzstn, Ltvi, Lithuni, Republic of Moldov, Tjikistn, nd Ukrine. 8

11 doubled since the 1980s. In South Asi, for instnce, verge yers of schooling mong the totl popultion ged 15 nd over rose from 2.4 yers in 1980 to 5.3 yers in While higher secondry nd tertiry completion nd enrollment rtios ccount for most of the improvements in yers of schooling in dvnced countries, most of the improvements in developing countries re ccounted for by higher primry nd secondry completion nd enrollment rtios (see Figure 1). Averge yers of eduction mong the popultion ged yers in developing countries rose from 3.1 yers in 1950 to 6.83 yers in 1990 nd to more thn 8.90 yers in recent yers (see Figure 1b). The improvements in completion nd enrollment rtios t ll levels mong the younger cohorts in every genertion continully contribute to rising verge yers of schooling s they mture over time. The biggest improvement in verge yers of schooling mong the younger cohorts ws recorded between 1970 nd 1990 in dvnced countries. Figure 2 shows tht developing countries hve successfully reduced illitercy rtes, especilly mong the younger cohorts. Specificlly, the proportion of the uneducted in the totl popultion over ge 15 in developing countries hs declined significntly over the pst six decdes since 1950, from 61.1% in 1950 to 17.4% in Among yer olds, this proportion hs declined from 45.2% in 1950 to 5.9% in Tble 4 summrizes the eductionl ttinment mong mles nd femles by region since It shows tht significnt progress hs been mde by developing countries in terms of reducing gender inequlity in eduction mong the overll popultion over ge 15. The rtio of femle to mle verge yers of schooling incresed from round 62.5% in 1950 to 81.2% in 1990 nd 85.9% by Despite these mjor developments, mny chllenges in mking eduction more inclusive remin. Notwithstnding significnt improvements, the current level nd distribution of eductionl ttinment in developing countries is comprble only to tht of dvnced countries in the lte 1960s (see Figure 1). 9

12 The gp between developing nd dvnced countries in verge yers of schooling mong the overll popultion over ge 15 remins high (4.1 yers in 2010) s it hs nrrowed by only less thn 1 yer in the pst 40 yers. One fctor tht contributed to the slow reduction in this gp is the continued increse in the proportion of the popultion in dvnced countries reching higher levels of eduction. Also, the nrrowing of the gp in verge yers of schooling mong younger cohorts between developing nd developed countries is less thn enough to compenste for the huge gp mong the older cohorts (see Figure 1b). For exmple, while the gp between the verge yers of schooling mong yer olds in developing economies nd dvnced countries hs nrrowed since 1970 by round 1.44 yers in 2010 (3.73 yers in 1970 to 2.29 yers in 2010), this gp hs even widened by round 1.25 yer (from 4.49 yers in 1970 to 5.76 yers) mong those ged 65 yers nd bove (see Figure 1). The chllenge of mking eduction more gender inclusive lso remins in mny developing regions, such s South Asi, Middle Est, nd sub-shrn Afric. The rtio of yers of schooling mong femles to mles remins below 70% in South Asi. The prospects of nrrowing the eductionl ttinment gp between developing nd developed countries gretly rely on the cpbility of developing countries to (1) significntly increse enrollment rtios mong new entrnts (below 15 yers old); nd (2) ctch up with the high rte of survivl from primry to secondry level nd from secondry to tertiry level (15 24 yers old) in developing countries. 4. Comprison with Alterntive Estimtes This section compres our estimtes of eductionl ttinment with other estimtes. First, we wnt to check our new estimtes with our previous estimtes in Brro nd Lee (2001). Tble 5 shows the mens nd stndrd devition of levels nd 10-yer differences of the overlpping observtions between the new Brro-Lee dt set nd Brro nd Lee (2001) estimtes over The two estimtes re highly correlted in both levels nd 10-yer differences, with correltion coefficients over

13 Figure 3 shows tht, on verge, the new Brro-Lee estimtes for verge yers of schooling for dvnced countries re higher thn the previous Brro-Lee estimtes. For developing countries, estimtes of verge yers of schooling until 1990 re slightly lower thn the previous estimtes. Figure 3 lso shows tht the new estimtes disply smoother incresing trend in verge yers of schooling, both for developing nd dvnced countries, thn the previous estimtes. Country level estimtes re lso much smoother over time. Figure 4 compres the new Brro- Lee estimtes with Brro-Lee (2001) estimtes for selected countries. The new estimtes provide smother time profiles of eductionl ttinment in Norwy, the United Sttes, Peru, nd Venezuel. We lso compre the new estimtes with the estimtes by Cohen nd Soto (2007). Cohen- Soto constructed dt set for verge yers of schooling for 95 countries t 10-yer intervls for They dopt dt nd methodology similr to ours. They use forwrd-flow nd bckwrd-flow methods to fill-in missing observtions by extrpolting the census/survey observtions on eductionl ttinment by 5-yer ge group. But there re lso significnt differences. First, Cohen nd Soto use OECD sources for OECD countries nd UNESCO sources for non-oecd countries. 7 As discussed in Brro nd Lee (2001), there exist significnt differences between the OECD dt nd UNESCO censuses. Most OECD dt come from lbor-force surveys bsed on smples of households or individuls, in contrst to the ntionl censuses in the UNESCO dtbse. There re lso significnt differences in the clssifiction of eduction systems between the OECD nd the UNESCO sources. As result, Cohen nd Soto s procedure tends to over-estimte eductionl ttinment for OECD countries (see Figure 5). Second, relying on only OECD sources, which re vilble since the 1990s, underutilizes vilble informtion. For exmple, Cohen nd Soto s estimtion for the United Sttes relies on only two OECD surveys in 1991 nd The dt re then used to estimte missing observtions in the erlier yers by the bckwrd-flow method, wheres for the ge groups for which the bckwrd estimtes re not pplicble, the estimtes re constructed minly by 7 For only few OECD countries including Finlnd, Portugl nd Turkey, Cohen nd Soto combine both OECD nd UNESCO sources. 11

14 lgged enrollment rtes. In contrst, our estimtion for the United Sttes relies on seven UNESCO censuses nd one ntionl census from 1950 to 2005, so tht the census informtion on eductionl ttinment by ge group is used to fill in missing observtions by both forwrd-flow nd bckwrd-flow estimtes. Third, for non-oecd countries, we use substntilly more UNESCO censuses thn Cohen nd Soto. Cohen nd Soto's estimtion uses only 70 UNESCO censuses for 75 developing countries in their smple, compred to 407 for 122 developing countries in our smple. In fct, Cohen-Soto s estimtes for 27 countries (including most sub-shrn Africn countries) rely entirely on enrollment dt. We believe our estimtes bsed on more censuses must contribute to more ccurte estimtion of missing observtions by forwrd-flow nd bckwrd-flow method by ge-group. Finlly, Cohen-Soto do not consider the difference in mortlity rtes by eductionl levels nor the chnge in durtions over time. Tble 5 shows mens nd stndrd devitions of verge schooling yers in levels nd 10- yer differences for the smple of the overlpping observtions between the new Brro-Lee dt set nd Cohen-Soto (2007). The new Brro-Lee estimtes for verge yers of schooling in 1960 re, on verge, lower thn those in Cohen nd Soto (2007). However, the new Brro-Lee estimtes for 2010 re higher on verge. It lso shows tht the new Brro-Lee dt set displys less dispersion thn Cohen-Soto (2007). Lower dispersion is observed cross estimtes for developing countries nd dvnced countries cross time, except for dvnced countries in Figure 5 show tht the estimtes for dvnced countries in the new Brro-Lee dt set re on verge lower thn in Cohen-Soto (2007) for the overll period, Tble 5 shows tht estimte for dvnced countries re less correlted thn those for developing countries. For developing countries, the new Brro-Lee estimtes re on verge very close to Cohen- Soto (2007) estimtes in erlier yers but higher for We estimte relibility rtios for the new Brro-Lee estimtes vis-à-vis Cohen-Soto (2007) in levels nd first 10-yer differences. As used by Krueger nd Lindhl (2001) in checking qulity of schooling dt, the relibility rtio guges the frction of the vribility of 12

15 (unobserved) true vrible in the totl vribility of the vrible mesured with error. Suppose S 1 nd S 2 represent two observed noisy mesures of the (unobserved) true vrible S. Tht is, S 1 = S + e 1 nd S 2 = S + e 2, where e 1 nd e 1 re the mesurement error of S 1 nd S 2. If e 1 nd e 2 re uncorrelted, the relibility rtio of S 1 is defined s R 1 = cov(s 1, S 2 ) /vr(s 1 ) nd hs probbility limit equl to vr(s)/vr(s 1 ). Similrly, the relibility rtio of S 2, R 2 = cov(s 1, S 2 ) /vr(s 2 ) hs probbility limit equl to vr(s)/vr(s 2 ). Cohen-Soto (2007) showed tht their estimtes perform better s compred with Brro nd Lee (2001). It turns out, however, the relibility rtio for the new Brro-Lee estimtes is greter thn tht of Cohen Soto (2007), both in levels nd 10-yer differences in yers of schooling for persons 15 yers nd older. Specificlly, while the new Brro-Lee dt set hs relibility rtios of 1.00 for both levels nd differences, the relibility rtios of Cohen-Soto (2007) re 0.89 for levels nd 0.87 for differences. This mens tht greter proportion of the vribility in observed levels nd chnges in the new Brro-Lee dt set represents true levels nd chnges thn in the Cohen-Soto (2007) dt set. In other words, the new Brro-Lee dt set conveys more signl thn the Cohen-Soto (2007) dt, both in levels nd chnges. 8 Our estimtes of eductionl ttinment provide resonble proxy for the stock of schooling cpitl for brod group of countries. However, the school ttinment does not tke ccount of the skills nd experience gined fter forml eduction. The mesure does not directly mesure the skills obtined t schools nd, specificlly, does not tke ccount for differences in the qulity of schooling cross countries. Figure 6 compres our concept of eductionl ttinment with Hnushek nd Woessmnn s (2009) mesure of humn cpitl qulity, which ws constructed by stndrdizing nd combining vilble interntionl mth nd science test results, covering for 50 countries. 9 Eductionl ttinment nd humn cpitl qulity mesures re highly correlted but humn cpitl qulity is quite diverse for countries with similr levels of eductionl ttinment. 5. Concluding Remrks 8 We hve lso computed relibility rtios of De L Fuente nd Domenech (2006) for the smple of OECD countries. The relibility rtios of the estimtes by De L Fuente nd Domenech re similr to those of our current dt set. The results cn be obtined from the uthors upon request. 9 See Hnushek nd Woessmnn (2009) for more detils bout their methodology for estimting humn cpitl qulity. 13

16 Our new dt set on eductionl ttinment pplies to 146 countries t five-yer intervls from 1950 to The estimtes re disggregted by sex nd by 5-yer ge intervls. These estimtes improve on our previous, widely used dt set by utilizing more informtion nd better estimtion methodology. This improved dt set on eductionl ttinment should be helpful for vriety of empiricl work. 10 Our estimtes of eductionl ttinment provide resonble proxy for the stock of humn cpitl for brod group of countries. The dt set hs been useful for studying the linkges cross countries between eduction nd importnt economic nd socil vribles, such s economic growth, export competitiveness, fertility, income inequlity, democrcy, institutions, nd politicl freedom. We expect tht this new dt set will help to improve the relibility of these types of nlyses. 10 Our erlier estimtes of eductionl ttinment hve been used in mny studies. Up to July 2011, our ppers on eductionl ttinment dt published in 1993, 1996, nd 2001 hve been cited in journls over 790 times, ccording to the Socil Science Cittions Index. The totl number of cittions by ll journl rticles, books, nd working ppers mounts to over 5,900, ccording to Google Scholr. 14

17 References Brro, R.J Economic Growth in Cross Section of Countries, The Qurterly Journl of Economics, 106(2): Brro, R.J. nd J.W. Lee Interntionl Comprisons of Eductionl Attinment, Journl of Monetry Economics, 32, Brro, R.J. nd J.W. Lee Interntionl Mesures of Schooling Yers nd Schooling Qulity, Americn Economic Review, 86, Brro, R. nd J.W. Lee. 1994, Sources of Economic Growth, Crnegie Conference Series on Public Policy, 40: 1. Brro, R. nd J.W. Lee Interntionl Dt on Eductionl Attinment: Updtes nd Implictions, Oxford Economic Ppers 53(3). Breierov, L. nd E. Duflo The Impct of Eduction on Fertility nd Child Mortlity: Do Fthers Relly Mtter Less thn Mothers? NBER Working Pper No Cohen, D. nd M. Soto Growth nd Humn Cpitl: Good Dt, Good Results, Journl of Economic Growth, 12: Cutler, D., A. Deton, A. Llers-Muney The Determinnts of Mortlity, The Journl of Economic Perspectives, 20(3): De Gregorio J. nd J.W. Lee Eduction nd Income Inequlity: New Evidence from cross-country dt, Review of Income nd Welth, 48(3): De L Fuente, A. nd R. Doménech Humn Cpitl in Growth Regressions: How Much Difference Does Dt Qulity Mke?, Journl of the Europen Economic Assocition, 4(1): Hnushek E.A. nd L. Woessmnn Do Better Schools Led to More Growth? Cognitive Skills, Economic Outcomes, nd Custion, NBER Working Pper No Krueger, A.B. nd M. Lindhl Eduction for Growth: Why nd For Whom?, Journl of Economic Literture, 39 (December): Lucs R.E "On the Mechnics of Economic Development," Journl of Monetry Economics, July, Mnkiw, G., D. Romer, nd D. Weil "A Contribution to the Empirics of Economic Growth," Qurterly Journl of Economics, 107. Romer, Pul "Endogenous Technologicl Chnge," Journl of Politicl Economy, October, S71-S102. UNESCO. vrious yers. Sttisticl Yerbook. Pris. 15

18 Tble 1. Brekdown of Number of Countries by Number of Census-Survey Observtions Number of Number of countries observtions All Advnced Developing ( ) MF F MF F MF F Totl Note: The dt refer to census-survey observtions for eductionl ttinment for the totl (MF) nd femle (F) popultions in ech ge ctegory. Tble 2. Brekdown of Number of Countries by Number of Census-survey Yer Census-survey yer (to the nerest 5-yer vlue) Number of countries All Advnced Developing MF F MF F MF F Totl Note: The dt refer to census-survey observtions for eductionl ttinment for the totl (MF) nd femle (F) popultions in ech ge ctegory. 16

19 Tble 3. by Region Trends of Eductionl Attinment of the Totl Popultion Aged 15 nd Over Region Popultion Highest level ttined Averge (no. of Aged 15 No Primry Secondry Tertiry yers of countries) nd over Schooling Totl Completed Totl Completed Totl Completed schooling nd Yer (Million) (% of popultion ged 15 nd over World (146) Advnced (24) Developing (122) By Region Middle Est nd North Afric (18) Sub-Shrn Afric (33) Ltin Americ nd the Crriben (25)

20 Region Popultion Highest level ttined Averge (no. of Aged 15 No Primry Secondry Tertiry yers of countries) nd over Schooling Totl Completed Totl Completed Totl Completed schooling nd Yer (Million) (% of popultion ged 15 nd over Est Asi nd the Pcific (19) South Asi (7) Europe nd Centrl Asi (20)