1 AN ECONOMISTS' VIEW OF SCHOOLING SYSTEMS 1 Lous Lévy-Garboua TEAM, CNRS and Unversty of Pars I- Panthéon-Sorbonne Nathale Damoselet Mnstère de l Educaton and Unversty of Pars V-René Descartes Gérard Lassblle, Insttut de Recherche sur l Econome de l Educaton (IREDU), CNRS, Djon (France) Luca Navarro-Gomez Unversty of Malaga, Span Summary Ths paper presents a smple theory of schoolng systems based on the assumpton that schoolng systems produce two knds of human captal: a general ablty-enhancng knowledge referred to as "educaton", and many types of skll-specfc knowledge referred to as vocatonal "tranng". The theory predcts that the dfferentaton of supply of tranng leads to the expanson of general educaton as well as tranng. If skll-specfc talents can be detected later than the general ablty, early sortng of pupls by ablty wll not be effcent. The dualty and effcency of school producton s llustrated by a sample of 16 schoolng systems of ndustralsed countres. Keywords: schoolng systems, educaton and tranng, dfferentaton, sortng, effcency.
2 1. Introducton 2 The am of the present paper s to provde a smple theory and descrpton of schoolng systems from an economc perspectve. The theory dstngushes between educaton and tranng, whch may be combned n varous proportons by schoolng systems for the producton of dfferentated sklls. The descrpton s based on a core-sample of sxteen ndustralsed countres whch was determned by the avalablty of comparable data from varous sources and the answers gven by educaton experts to a questonnare talored to our needs 1. The sxteen countres formng our sample are Austra, Canada, France, Germany, Greece, Hungary, Italy, Japan, Netherlands, Norway, Portugal, the Russan Federaton, Span, Sweden, UK, USA. The consderable dfferentaton typcally observed n schoolng systems s nconsstent wth the assumpton of homogeneous human captal made n much of economc lterature. Thus secton 2 presents a smple economc theory of schoolng systems relaxng ths assumpton and makng an mportant dstncton between the provson of general educaton and vocatonal tranng. In secton 3, we show a varety of ndexes of average educaton, skll (human captal at market value), and types of dfferentaton and screenng for our man sample of sxteen countres. Then secton 4 relates productve effcency at country level wth the dfferentaton of schoolng systems. Our man conclusons are summarsed n secton A smple theory of schoolng systems A schoolng system s the nsttuton whch allocates socal knowledge prmarly to young ndvduals. Drawng on Becker s (1964) semnal dstncton between general and specfc human captal, we may say that schoolng provdes both general knowledge and occupatonspecfc knowledge. General knowledge can be used n all frms and all occupatons, whle occupaton-specfc knowledge can be used n all frms but only n specfc occupatons (note that frm-specfc knowledge cannot be provded by the schoolng system). We focus our
3 3 attenton here on the dual provson of general and occupaton-specfc,.e. vocatonal, knowledge by schoolng systems above the common-core syllabus. The standard assumpton of homogeneous human captal and capactes tends to understate the extent of optmal dfferentaton of schoolng systems 2. Under ths standard assumpton, a dfferentated schoolng system would be descrbed as a common-core syllabus followed by a varety of vocatonal currcula of optonal length. But ths s not a good descrpton of what schoolng systems actually offer. What s beng observed s that students may decde to receve further general educaton before they engage n vocatonal tranng. Further educaton s seen as a general but optonal prerequste for enhancng the acquston of sklls by vocatonal tranng. 2.1 The basc model It wll be assumed that the schoolng system provdes, above the common-core educaton, both further general educaton E and a varety of skll-specfc tranng T, = (1,..., s) at unt prce. Each pupl combnes school nputs wth hs own capactes to embody one of the s dfferentated sklls S. We wrte the skll s ndvdual producton functon as β S ( E, T ) = t A( E) T, (1) where t (>0) s a gven -specfc capacty, called talent, A (E) desgnates the ndvdual s general ablty, and 0 < β < 1. The crucal assumpton we make s that the general ablty s not entrely gven by brth and cultural transmsson, but also captures the learnng skll acqured through educaton wth S ( E) 0, and S (0) 1. ' 0 0 = A ( E ) S 0( E ) (2) The general learnng skll unformly rases the margnal productvty of tranng n the acquston of all non-learnng sklls. It s assumed to be a non-decreasng concave functon of the amount of further educaton, for nstance
4 α S 0 ( E) = 1+ ae, (3) 4 wth a > 0, 0 α < 1. The parameter a descrbes the student s cogntve ablty by the end of the common-core educaton. We shall further assume that there are a small number of paths leadng to the producton of any skll due to large set-up costs n the producton of educaton. For nstance, E mght only take two values, 0 or 1, f students are gven a choce among pure tranng and one perod of general educaton followed by tranng. We do not make the same assumpton for tranng because tranng s partly suppled by frms as a jont product of ther actvty. Thus, the amount of tranng s chosen optmally by each ndvdual. Fnally, we assume decreasng margnal returns on both educaton and tranng, and the Inada condton ' ( E,0) = +. The ratonal behavour of a student s descrbed by the choce of skll type and school nputs E and T whch maxmse the net returns from hs general educaton and vocatonal tranng on the dscrete set of educatonal optons E = ( 0,1,..., n) S max, E, T p S ( E, T ) E T (4) subject to (1), (2), (3), and non-negatvty constrants on the amount of tranng T 0. The Inada condton ensures that some tranng wll always be provded T > 0. It should be noted that the -specfc talent t and the prce of skll (.e. specfc human captal), p, cannot be ndependently dentfed 3. Henceforth, n the followng paragraphs, we drop the latter varable and adopt a nomnal defnton of specfc talents (.e. p t ). Thus a 1% ncrease of the rate of return to skll results n an equal rse of -specfc talent for all students, and a 1% ncrease n the borrowng rate of a student, reflectng the latter s dmnshng opportuntes, entals a 1% declne of all hs nomnal talents. Although the present analyss emphasses varatons of specfc talents among students, we should not forget that varatons of the rates of return on
5 5 sklls and of the average borrowng rate may also have large aggregate effects on the outputs of schoolng systems n a cross-country comparson. The conclusons that would be drawn from the model by omttng prce effects would only hold for countres of smlar ncome level per capta nsofar that the dstrbuton of opportuntes may then be assumed to vary lttle between these countres. For space lmtatons, all proofs are omtted here but can be found n our workng paper (Lévy-Garboua et al 2002). The soluton of program (4) has ntutve appeal. Students ratonal behavour may be descrbed as f they frst chose the specfc occupaton for whch they have more (nomnal) talent. Then, they choose the optmal mx of educaton and tranng condtonal on ths choce of occupaton. The man proposton follows: PROPOSITION 1 If cogntve abltes and skll-specfc talents dffer among students but are perfectly known both by themselves and by schools, t s not optmal to sort students nto the more general and the vocatonal path on the bass of ther cogntve ablty alone. The optmal sortng rule s descrbed by the followng condton, whch combnes nformaton on cogntve ablty and skll-specfc talents: β β 1 β β 1 1 β β t. ( 1+ a) 1 β 1 > 1 Moreover, students who prefer the educaton-cum-tranng path always engage n longer specfc tranng and, a fortor, n longer studes than those engaged n pure tranng. The latter predcton s n lne wth countless observatons of complementarty between educaton and tranng. Besdes, snce the more talent a student has for a skll, the more he wll be nclned to opt for educaton (proposton1), ths has an mportant corollary: COROLLARY The dfferentaton of vocatonal studes ncreases the demand for general educaton (and longer studes), for gven dstrbutons of cogntve abltes and skll-specfc talents.
6 6 We beleve that ths corollary provdes a strong and, to some extent, new ratonale for the vocatonalsaton and lengthenng of studes, as well as the massfcaton of further general educaton that took place n ndustralsed countres. 2.2 Screenng In actual practce, schools and unverstes screen students who are not perfectly aware of ther cogntve ablty and skll-specfc talents. Because the general ablty apples to a great many tasks, t wll often be detected early n the course of common-core (.e. prmary and lower secondary) educaton. On the other hand, the assessment of an ndvdual s return-maxmsng skll-specfc talent must often awat the later dfferentaton of currcula snce each talent can only be detected on a sngle set of tasks. The present dscusson s summarsed by the followng assumpton: ASSUMPTION Students return-maxmsng skll-specfc talents cannot be detected as early as ther cogntve ablty. The presence of a lag between the tmes when general ablty and talents can be detected precsely generates a trade-off between the frst-best choces of educaton and skll. PROPOSITION 2 As far as educaton s concerned, early screenng by general ablty s optmal as soon as ths can be detected. However, such early screenng s neffcent as far as the producton of sklls s concerned, for whch screenng should occur later on. The postponement of screenng untl the upper secondary level, where talents can be assessed wth some precson, has often been advocated as a means of reducng nequalty.
7 7 However t may also be justfed for effcency reasons f abltes and talents are not strongly correlated. Its adopton by market economes entals a vocatonalsaton of schools at the relatve expense of general educaton. Thus our theory relates the potental declne of educatonal standards to the postponement of dfferentaton by ablty untl occupatonspecfc talents can be assessed. 3. An economc descrpton of schoolng systems In order to show the relevance of our theoretcal dstncton between educaton and tranng for understandng the productve effcency of schoolng systems, we must measure these two outputs of schoolng systems and how the latter dfferentate n matchng heterogeneous capactes and sklls. The approprate ndcators have been derved from avalable statstcs and the answers of selected educaton experts to a questonnare. Twenty-three experts 4 from sxteen OECD countres flled ths questonnare n These sxteen countres form the man sample that wll be used below for statstcal analyss. 3.1 The producton of educaton and sklls Average scores obtaned n standardsed tests are commonly taken to be good ndcators of school performance, assumng that the dstrbuton of abltes between pupls s the same n all countres. However, the theoretcal dscusson of secton 2 makes t clear that they are not concerned wth vocatonal tranng and essentally descrbe the average level of the general ablty produced by general educaton. A better ndcator of market sklls, or total human captal per pupl, should reflect the market value of school outputs. (Insert table 1 about here) Varous measures of the producton and dstrbuton of human captal (educaton-cum-tranng) and ts educaton component appear n table 1 for our sample of sxteen ndustralsed countres. The most comprehensve ndex of total human captal per pupl at 1994 market value 5 (HTOT) s shown n column 1. It was derved from OECD s statstcs (0ECD 1996:tables R11.1, R12.1)
8 8 on the dstrbuton of graduate output between four hghest completed levels of educaton (lower secondary, upper secondary, non-unversty and unversty sector). Each level was mputed a market value ndex through the mean earnngs of employed male graduates of 25 to 64 years of age at ths level relatve to the mean earnngs at upper secondary level (OECD 1996 :table R22.1). A proxy for the same total human captal ndex one generaton back (HTOT0) was obtaned by weghtng the same value ndexes wth the dstrbuton of the populaton 25 to 64 years of age between the four levels of graduaton (OECD :table C1.1). The derved estmate of the rate of human captal growth per pupl n a generaton (.e. IH= (HTOT-HTOT0)/HTOT0) s gven n column 2. Inequalty of the dstrbuton of human captal s summarsed n column 3 by the varance of the 1994 value ndexes between the four levels of graduaton (INEQ). The objectve growth of human captal s paralleled n column 4 wth an subjectve ndcator for the declne of educatonal standards, derved from the nformed opnon of the selected experts. Whle all of the sampled countres have undergone postve, and often substantal, growth n one generaton, educaton experts frequently expressed the opnon that educatonal standards had declned. An nterpretaton of the latter s percepton wll be gven n secton 4. Fnally, ths descrpton of the output of schoolng systems s completed n column 5 by the scores obtaned n standardsed mathematcs and scence tests by pupls at grade seven (SCORE), who are theoretcally thrteen years old. These results were gathered n for a sample of 24 countres by the Internatonal Assocaton for the Evaluaton of Educatonal Achevement n ts thrd nternatonal study on mathematcs and scence. These countres nclude our own sample of 16 countres, wth the excepton of Italy. We consder ths last varable to be a good aggregate ndex of the general ablty produced by educaton. (Insert fgure 1 about here) Clearly, HTOT and SCORE do not descrbe the same schoolng output. The rank correlaton (Spearman s rho) between these two varables s only (n=14) and the assumpton that they are stochastcally ndependent cannot be rejected. By plottng these two varables along two
9 9 axes, Fgure 1 shows that a parabolc relaton would ft the data better than a straght lne 6. Greece, Portugal, and Span, whch are the least developed countres of the sample, rank low along the two dmensons, Japan s clearly the hghest performer n the producton of educaton and Norway has the lead n the producton of sklls. If the three low-performers were left out of the dagram, the slope would even become slghtly negatve. Whereas dfferences n opportuntes generate a postve correlaton of educaton and sklls, a negatve correlaton between educaton and sklls emerges from dstnctve patterns of dfferentaton across countres. 3.2 Dfferentaton and screenng If we use our theoretcal dstncton between one sngle general ablty and many knds of occupaton-specfc talents, we see that the sortng of students, whether t s by ablty or by talent, must produce sharply dfferent socal outcomes. Snce general ablty as opposed to occupaton-specfc talents possessed by an ndvdual determnes the extent of hs market opportuntes, only the dfferentaton by ablty unambguously produces a rankng of students. We may speak of vertcal dfferentaton on one hand and horzontal dfferentaton on the other hand. In our questonnare, the amount of vertcal dfferentaton s attested by the use of three potental means of sortng students by ther general ablty: a standardsed test, grades and the reference of the school. The amount of horzontal dfferentaton can be traced by the use of two common means of assessng occupaton-specfc talents: preferences of the famly or the student, and choce of optonal courses. These fve crtera of dfferentaton were lsted separately by experts for lower secondary and upper secondary levels. Ths nformaton s summarsed below by table 2, whch ndcates the frequency of use of each of these means of dfferentaton n our sample of sxteen countres 7. (Insert table 2 about here) The frst three columns ndcate that the vertcal dfferentaton of students s equally present n the lower and the upper levels of secondary schoolng and the last two ndcate that horzontal dfferentaton prevals at the upper level. Ths shows that educaton takes place at both levels
10 10 and tranng eventually starts at the upper level. Moreover, the fgures demonstrate that sortng by ablty domnates sortng by talent n the lower level, whle the reverse s true n the upper level. Ths s consstent wth our assumpton that the general ablty can be detected rather early but the occupaton-specfc talents can hardly be known before the specfc tranng has taken place. Another proof of the last asserton can be found n the ncreased severty of screenng between the lower and upper levels of secondary educaton. Screenng scores have been derved from our survey among educaton experts by addng up three ndcators of downstreamng, class repeatng and drop-out 8, each measured on an ordnal 0-4 scale 9. The resultng ndex measures the amount of screenng takng place at each level of educaton on a 0-12 scale n a way whch allows comparson between levels. Screenng ncreases from a score of 3.2 n the lower level to 4.7 n the upper level of secondary educaton and ths dfference s sgnfcant at the 1% confdence level (t=2.82, df 28). The addton of frequences of use for all fve means of dfferentaton yelds country scores of total dfferentaton at the two levels of secondary educaton (DIFLOW, DIFUP). Total dfferentaton ncreases wth level wthout excepton. Ths pcture s confrmed by a t-test of dfference between the means of the lower and the upper levels. The mean scores of total dfferentaton are 1.2 for the lower level and 2.2 for the upper level, and they are unequal at the 5% confdence level (t = 2.168, d.f. 30) 10. Ths result s consstent wth the theoretcal predcton that students should be sorted by a combnaton of ablty and talents, whch optmally requres postponement of dfferentaton untl talents can be assessed wth suffcent precson. Fgure 2 plots the total dfferentaton scores at the two levels of secondary educaton. It separates two groups of countres wthout ambguty. Canada, Greece, Italy, Japan, Norway, Portugal and Span have no dfferentaton of any knd at the lower secondary level (DIFLOW=0). These countres have n common that all pupls must follow a common-core syllabus from the tme of entry nto prmary educaton to the end of compulsory educaton (Lassblle, Navarro-Gomez 2000). At the other end of the spectrum, France, Germany, the Netherlands and the USA are
11 11 strongly dfferentated at both levels of secondary educaton. In between, le countres whch may be further classfed n two groups by closer nspecton. Hungary and Sweden offer no knd of horzontal dfferentaton. Austra, Russa and the UK form a resdual group of average dfferentaton, whether we take the dstrbuton of total dfferentaton between levels or between vertcal and horzontal means. (Insert fgure 2 about here) 4. The productve effcency of schoolng systems In ths secton we test two mplcatons of our theory of schoolng systems, namely proposton 2 and the corollary of proposton 1: a) Snce ablty can be detected earler than talents, t s not optmal to make an ntensve use of dfferentaton too early, say at the lower secondary level, for producng sklls. However, t wll be optmal to do so for producng educaton; b) Horzontal dfferentaton enhances the aggregate demand for general educaton and tranng. 4.1 A frst set of results Table 4 presents the results of regressons for the output measures that appeared n table 1. The explaned varables are HTOT (col. 1), SCORE (col. 2), INEQ (col. 3) and DECLINE (cols.4-5). These are all explaned essentally by two supply varables, the amount of dfferentaton at the lower secondary and upper secondary levels (DIFLOW, DIFUP), and by one demand varable, the average level of human captal one generaton back (HTOT0). (Insert table 4 about here) The frst set of mplcatons amounts to the predcton of a negatve effect of DIFLOW on HTOT (actng as a proxy for average sklls) and a postve effect on SCORE (actng as a proxy for average educaton). The second mplcaton s a postve effect of DIFUP (actng as a proxy for horzontal dfferentaton) on HTOT (actng as a proxy for aggregate educaton-cumtranng). Both sets of mplcatons are confrmed n columns 1 and 2 of table 4. The three
12 12 coeffcents descrbng these effects are sgnfcant at the 5% level wth the predcted sgn. The trade-off between educaton and sklls s strkngly llustrated by the offsettng effects of lowerlevel dfferentaton and upper-level dfferentaton on these two outputs. Lower-level dfferentaton s good for the producton of general educaton (SCORE) and bad for the producton of occupaton-specfc sklls (HTOT). Late dfferentaton s good for the producton of sklls. Lookng back at fgure and table 1, Norway turns out to be the best performer because t has managed to suppress school-leavers at lower secondary level and has developed a large vocatonal non-unversty sector. These results are obtaned on a small sample and must be treated wth cauton. However, the qualtatve conclusons were replcated wth smlar but dfferent varables and samples. An nstance of ths s gven by the comparson of column 5 wth column 4. Comparson of columns 4 and 2 shows that the percepton of declnng standards (see, on the same topc, Baudelot and Establet 1989) addresses the relatve declne of educaton n the total output of schoolng systems. Ths nterpretaton s confrmed by the regresson of column 5. STTPRIM desgnates the rato of students to teachng staff n prmary educaton for 1994, as gven by OECD (1996: table P32 (publc and prvate)). Ths s postvely related to early dfferentaton f educaton expendtures are constraned. For a gven budget, larger class sze s the prce for havng more dfferentaton that obvously uses more teachers 11. Therefore, DIFLOW and STTPRIM both capture aspects of early dfferentaton and have a negatve effect (sgnfcant at the 5% level) on DECLINE. Indeed, the selected experts dd not stress the declne of educatonal standards n France, Germany and the Netherlands whch have strongly earlydfferentated schoolng systems on both accounts. The converse s true for Italy. By ntroducng the level of human captal one generaton back n the regressons, the dynamcs of educaton and human captal can be analysed. The coeffcent of ths varable s postve and smaller than one n column 1, but close to one n column 2. These results suggest the convergence of the human captal or skll output of schoolng systems but the lack of convergence of the educaton output. For nstance, table 1 shows that Canada, Germany, the
13 13 Netherlands, Sweden and the USA have been expandng slowly n comparson wth developng countres lke Italy, Portugal, and Span. Fnally, the results of column 4 suggest that the dsperson of human captal wthn countres (INEQ) s not ncreased by early dfferentaton. 4.2 A second set of results Our frst results may be open to crtcsm n that they are based on a small sample of countres and on qualtatve or even subjectve explanatory varables. Fortunately, we were able to replcate, on a larger sample and wth more and well-accepted ndcators, the regresson analyss concernng the scores obtaned n standardsed mathematcs and scence tests (SCORE) by pupls n grade seven and grade eght. Twenty-four countres are ncluded n ths analyss, encompassng the sxteen countres of our man sample. In the twelve "non-dfferentated" systems 12, all the pupls had normally completed the same currculum when they took the tests; whle the pupls n the twelve "dfferentated" systems 13 had been sorted nto several streams after completng the common-core syllabus (see Lassblle and Navarro-Gomez (2000) for a full descrpton of the dfferentaton and other varables). On average, pupls n dfferentated systems perform better than pupls n non-dfferentated systems. For example, at grade seven, pupls n the frst systems acheved a score of 502, whle the second acheved only 477. In order to show the extent to whch the characterstcs of the two systems affect pupls achevement, n Table 5 we regress the mathematcs test scores n grades seven and eght on the followng objectve varables: the rato of the length of common-core syllabus to the length of compulsory educaton (an ndex of non-dfferentaton of systems whch takes value 1 for "nondfferentated" systems and values smaller than one for "dfferentated" systems), the pupl/teacher rato, the nstructonal tme from the frst year of prmary educaton up to the age when pupls took the tests, the percentage of pupls enrolled n the prvate sector, and the degree of decentralsaton of systems, estmated on the bass of the share of central government fundng. The test scores n the seventh and eghth grades are adjusted wthn the framework of a fxed-effect model. To take nto account the correlaton between the results obtaned n each grade, the varance-covarance matrx s corrected for heteroscedastcty by clusterng
14 14 observatons by country (see, for example, Greene 1997). Gven the avalablty of data, the estmaton covers fourteen countres, yeldng twenty-eght observatons. Among these, seven countres have dfferentated and seven have non-dfferentated educaton systems. (Insert table 5 about here) Dfferentated systems obtan better results than non-dfferentated systems, all thngs beng equal. The effect of the structure of the system s far from neglgble, as the tmng of dfferentaton of pupls nto streams explans about 15 percent of the dfference n scores between pupls. Snce the dfferentaton ndex retaned here s manly concerned wth early (vertcal) dfferentaton, ths fndng confrms the results obtaned n table 4 (column 2), namely that early dfferentaton s good for educaton. The generally accepted dea among educators that non-dfferentated systems are the best way to maxmse the producton of educaton s probably wrong. Even the superorty of these systems for reducng socal nequaltes at an early age seemed questonable n table 4. The results n Table 5 also show that the pupl/teacher rato has a negatve mpact on pupls scores after allowng for dfferentaton. Ths result s smlar to those obtaned by other studes (see, for example, Hanushek 1986). The total number of school hours, whch dffers wdely across countres, has no sgnfcant effect on achevement n mathematcs. However, the nstructonal tme n prmary educaton explans the good performance of certan countres better than the nstructonal tme n secondary educaton. These results confrm that margnal returns are decreasng n the acquston of learnng sklls. Furthermore, the regresson results ndcate that countres where prvate educaton s more wdespread perform sgnfcantly better than countres where t s more lmted. Once agan, prvate educaton wdens the choce set of famles and chldren and thus operates lke another knd of dfferentaton by choce (ths pont s developed n Damoselet and Lévy-Garboua 2000, 2001). Fnally, centrally managed educaton systems perform as well as decentralsed ones, after controllng for dfferentaton.
15 5. Concluson 15 Ths paper has made a basc dstncton between general educaton and vocatonal tranng. Educaton contrbutes to the producton of the learnng skll, whch s a general nvestment for producng many other sorts of occupaton-specfc sklls n combnaton wth specfc tranng. The dversty of marketable sklls ntroduces a polcy trade-off for schoolng systems between educaton and non-learnng sklls. If the objectve was to maxmse the net returns to educaton alone, students should be sorted by ther cogntve ablty alone. But f the objectve s to maxmse the net returns to both educaton and many knds of specfc tranng, then students should be gven an opton to receve further general educaton before they engage n vocatonal tranng and be sorted between these alternatve paths accordng to some combnaton of ther cogntve ablty and occupaton-specfc talents. Early dfferentaton s good for educaton but s bad for the producton of sklls. Furthermore, the horzontal dfferentaton of schoolng systems at a later stage nduces a rsng demand for both educaton and tranng. REFERENCES Baudelot, R., and G. Establet (1989), Le nveau monte, Pars: Seul. Becker, G. S. (1964), Human Captal, 1 st edton, New York: Columba Unversty Press for the NBER. Damoselet, N. (1998), Effets des systèmes scolares sur le comportement éducatf ndvduel, L Actualté Economque, (74), Damoselet, N. and L. Lévy-Garboua (2000), L effcacté de la dfférencaton et de la sélecton scolare: une comparason économque des systèmes éducatfs, Econome Publque, (6), Damoselet, N. and L. Lévy-Garboua (2001) Comparason des systèmes éducatfs: une approche économque, n Raymond Boudon, Nathale Bulle, and Mohamed Cherkaou (eds), Ecole et Socété: les paradoxes de la démocrate, Pars: PUF, pp Greene, W. (1997), Econometrc Analyss, 3d edton, London: Prentce-Hall Internatonal, Inc.
16 Hanushek, E.A. (1986), The Economcs of Schoolng: Producton and Effcency n Publc 16 Schools, Journal of Economc Lterature, (24), Internatonal Bureau of Educaton (1997), World Data on Educaton: , Geneva: Internatonal Bureau of Educaton. Lassblle, G. and L. Navarro Gómez (2000), Organzaton and Effcency of Educaton Systems: some emprcal fndngs, Comparatve Educaton, (36), OECD (1996), Educaton at a Glance, Pars: OECD. UNESCO (1996), Statstcal Yearbook, Pars: UNESCO.
17 Table 1 17 Country The producton and dstrbuton of educaton and sklls n 16 schoolng systems Total human captal per pupl at 1994 market value (upper secondary=100) HTOT Rate of growth of human captal n a generaton(%) IH Inequalty INEQ Opnon on the declne of educatonal standards DECLINE Score n math. and sc. test n grade seven SCORE Austra Canada France Germany Greece Hungary n.a Italy Japan n.a Netherlands Norway Portugal Russan Fed n.a Span Sweden UK USA
18 Table 2 18 The frequency of use of varous means of dfferentaton n lower secondary and upper secondary levels level means By standardsed test By grades By reference of the school By preferences of famly or student By optonal courses Lower secondary 1* Upper secondary * The range of varaton of all the ndcators s Table 3 Regresson analyss of schoolng outputs HTOT SCORE INEQ DECLINE DECLINE Constant (2.83)* (6.75)** (2.15) (0.02) (5.59) HTOT (4.72)** (2.11) (1.34) (0.66) - DIFLOW (3.15)* (3.58)** (0.57) (2.14) (2.63) DIFUP (2.95)* (1.98) (1.52) (0.29) - PTRPRIM (2.68) R² Number of observatons Absolute value of t-statstcs n parentheses. * sgnfcant at 5% level; ** sgnfcant at 1% level.
19 Table 4 Adjustment of mathematcs test scores n grades 7 and 8 19 SCORE Constant (9.11)** (14.81)** I (2.66)* (2.17)* PTR (2.05)* (3.08)** INSTIME a n.a. (0.73) INSTIMEP (1.52) INSTIME (0.91) SIZEPRIV (2.06)* (3.68)** DECENTR (0.27) (0.37) Adjusted R² F Number of observatons Note: Fxed-effect model corrected for heteroscedastcty by clusterng observatons by country. Absolute value of t-statstcs n parentheses; * sgnfcant at 5% level; ** sgnfcant at 1% level. a/ INSTIME= nstructonal tme n prmary level (INSTIMEP)+ nstructonal tme n secondary level - up to thrteen or fourteen years of age - (INSTIMES). Sources: Internatonal Bureau of Educaton (1997), OECD (1996) and UNESCO (1996) for nstructonal tme; UNESCO (1996) for the sze of prvate sector; OECD (1996) for the degree of centralsaton.
20 Fgure 1 20 Comparng the performance of schoolng systems along two dmensons: educaton and sklls 571 Japan score Netherla Austra Hungary Canada Germany Sweden Russan USA France UK Norway Span Greece 423 Portugal htot
21 Fgure 2 21 Comparng total dfferentaton of schoolng systems n the lower secondary and upper secondary levels 4 Netherlands 3 France USA Germany DIFLOW 2 Hungary Austra Russan 1 Sweden UK Japan Italy Greece Canada Span Portugal Norway DIFUP
22 Notes 22 1 We are grateful to Wm Groot and Jean-Jacques Paul for helpng us n the preparaton of the questonnare and the selecton of experts. 2 Some amount of dfferentaton s optmal, even f human captal and capactes are assumed homogeneous, when students dffer n capactes (see Damoselet 1998). 3 If human captal yelded a constant rental prce w over an nfnte duraton of lfe and f r was the constant ndvdual s borrowng rate, the prce of skll for an ndvdual of unt -specfc talent would be: p = w r. 4 Snce the lst of topcs reflected the economc ssues rased by schoolng systems, due weght was gven to ther economcs background n the selecton of experts. 5 See Damoselet and Lévy-Garboua (2000, 2001) for a detaled descrpton of ths ndcator. 6 Ths statement s unambguously supported by the data. We regressed SCORE on a quadratc functon of HTOT and found strong non-lnearty. 7 Frequences may vary by steps of 0.5 because, n some countres, two experts responded to the questonnare ndependently and dsagreed n ther answers. 8 Down-streamng means that a student may swtch from a hgher educaton level to a lower educaton level. Class repeatng means that a student wll not be gven access to the next level f he does not meet the academc requrements. Lastly, drop-out descrbes a student leavng an nsttuton of educaton wthout a dploma or certfcate never, 1 - not very often; 2 - sometmes; 3 - frequent; 4 - very frequent. 10 Ths ndex of total dfferentaton gves more weght to ablty than talent snce the questonnare mentons three crtera of vertcal dfferentaton and only two crtera of horzontal dfferentaton. An equal weghtng of the two knds of dfferentaton would stll renforce our concluson. 11 The substtuton between dfferentaton and the reducton of class sze s further attested by the absence of correlaton between the expendture per student and the rato of students to teachng staff at
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