Human capital and productivity

Human capi al and p oduc i i y Angel de la Fuen e* Ins i u o de Análisis Económico (CSIC) Janua y 2011 Abs ac This pape su eys he empi ical li e a u e on human capi al and p oduc i i y and summa izes he esul s o my own wo k on he subjec . On balance, he a ailable e idence sugges s ha in es men in educa ion has a posi i e, signi ican and sizable e ec on p oduc i i y g ow h. Acco ding o my es ima es, mo eo e , he social e u ns o in es men in human capi al a e highe han hose on physical capi al in mos EU coun ies and in many egions o Spain. Keywo ds: human capi al, p oduc i i y, g ow h, measu emen e o JEL Classi ica ion: O40, I20, O30, C19 _____________________ * This pape has been p epa ed o a special issue o No dic Economic Policy Re iew on p oduc i i y and compe i i eness. I d aws hea ily on join wo k wi h R. Doménech and o he coa ho s ha has been pa ially inanced by he Eu opean Commission, he OECD, he esea ch depa men o BBVA and he Spanish Minis y o Science and Inno a ion ( h ough g an no. ECO2008-04837/ECON and i s p edecesso s). 1 1. In oduc ion One o he mos dis inc i e ea u es o he "new" heo ies o economic g ow h has been he b oadening o he ele an concep o capi al. While adi ional neoclassical models ocused almos exclusi ely on he accumula ion o physical capi al (equipmen and s uc u es), mo e ecen con ibu ions ha e a ibu ed inc easing impo ance o he accumula ion o human capi al and p oduc i e knowledge and o he in e ac ion be ween hese wo ac o s. The empi ical e idence, howe e , has no always been consis en wi h he new heo e ical models. In he case o human capi al, in pa icula , a numbe o s udies ha e p oduced discou aging esul s. Educa ional a iables a e o en no signi ican o e en en e wi h he "w ong" sign in g ow h eg essions, pa icula ly when hese a e es ima ed using di e enced speci ica ions o panel echniques. The accumula ion o nega i e esul s in he li e a u e du ing he second hal o he nine ies gene a ed a g owing skep icism abou he ole o schooling in he g ow h p ocess and e en led some au ho s (see in pa icula P i che , 2001) o se iously conside he easons why educa ional in es men may ail o con ibu e o p oduc i i y g ow h. Many esea che s in he a ea, howe e , held on o mo e op imis ic iews. They (we) a gue ha he nega i e esul s ound in ce ain s udies can be explained by echnical p oblems ha ha e a lo o do wi h he di icul y o measu ing human capi al co ec ly. This a icle p o ides a quick e iew o se e al s ands o a li e a u e ha p o ides e idence in suppo o his hypo hesis and a mo e de ailed summa y o my own wo k on he subjec . The pape is o ganized as ollows. Sec ion 2 ske ches he heo e ical amewo k ha has guided mos s udies o he con ibu ion o educa ion o economic g ow h, e iews he main empi ical speci ica ions used in he li e a u e and b ie ly discusses some o i s key esul s. Sec ion 3 highligh s some o he sho comings o he c oss-coun y schooling da a se s mos commonly used in he ea ly empi ical li e a u e, discusses hei implica ions o a emp s o es ima e he con ibu ion o educa ion o p oduc i i y g ow h and in oduces a con enien indica o o da a quali y ha can be used o quan i y he in o ma ion con en o al e na i e schooling se ies and o es ima e he size o he bias caused by measu emen e o . Sec ion 4 summa izes he main indings o a se ies o pape s I ha e w i en mos ly in collabo a ion wi h Ra ael Doménech. In hem, we cons uc new a ainmen se ies o 21 OECD coun ies and o he egions o Spain, de elop measu es o he in o ma ion con en o hese and o he schooling se ies and es ima e a a ie y o g ow h speci ica ions o bo h samples. Using hese esul s we ha e also cons uc ed a se o me a- es ima es o he coe icien o human capi al in an agg ega e Cobb-Douglas p oduc ion unc ion ha co ec o he downwa d bias gene a ed by measu emen e o . Wi h his co ec ion, we ind ha he con ibu ion o in es men in human capi al o p oduc i i y g ow h is posi i e, qui e sizable and implies a he espec able social e u ns ha , o mos e i o ies in ou wo samples, compa e qui e a o ably wi h hose on physical capi al. 2 2. Human capi al and economic g ow h: an o e iew o he li e a u e Theo e ical models o human capi al and g ow h a e buil a ound he hypo hesis ha he knowledge and skills embodied in humans di ec ly aise p oduc i i y and inc ease an economy's abili y o de elop and o adop new echnologies. In o de o explo e i s implica ions and open he way o i s empi ical es ing, his basic hypo hesis is gene ally o malized in one o wo (no mu ually exclusi e) ways. The simples one in ol es in oducing he s ock o human capi al (which will be deno ed by H h oughou his pape ) as an addi ional inpu in an o he wise s anda d agg ega e p oduc ion unc ion linking na ional o egional ou pu o he s ocks o p oduc i e inpu s (gene ally employmen and physical capi al) and o an index o echnical e iciency o o al ac o p oduc i i y (TFP). The second possibili y is o include H in he model as a de e minan o he a e o echnological p og ess ( ha is, he a e o g ow h o TFP). This in ol es speci ying a echnical p og ess unc ion ha may include as addi ional a gumen s some indica o o in es men in R&D and a measu e o he “ echnological gap”, ha is, o he dis ance be ween each coun y’s p oduc i e echnology and he bes p ac ice on ie . In wha ollows, I will e e o he i s o hese links be ween human capi al and p oduc i i y as le el e ec s (because he s ock o human capi al has a di ec impac on he le el o ou pu ) and o he second one as a e e ec s (because H a ec s he g ow h a e o ou pu h ough TFP). Box 1 de elops a simple model o g ow h wi h human capi al ha o malizes he p eceding discussion and inco po a es bo h e ec s. Box 1: A desc ip i e model o human capi al and g ow h ____________________________________________________________ This box de elops a simple model o g ow h and human capi al ha has wo componen s: an agg ega e p oduc ion unc ion and a echnical p og ess unc ion. The p oduc ion unc ion will be assumed o be o he Cobb-Douglas ype: (B.1) Yi = Ai Ki α kHi α hLi α l whe e Yi deno es he agg ega e ou pu o coun y i a ime , Li is he le el o employmen , Ki he s ock o physical capi al, Hi he a e age s ock o human capi al pe wo ke , gene ally measu ed by school a ainmen , and Ai an index o echnical e iciency o o al ac o p oduc i i y (TFP) which summa izes he cu en s a e o he echnology and, possibly, omi ed ac o s such as geog aphical loca ion, clima e, ins i u ions and endowmen s o na u al esou ces. The coe icien s α i (wi h i = k, h, l) measu e he elas ici y o ou pu wi h espec o he s ocks o he di e en ac o s. An inc ease o 1% in he s ock o human capi al pe wo ke , o ins ance, would inc ease ou pu by α h%, holding cons an he s ocks o he o he ac o s and he le el o echnical e iciency. Unde he s anda d assump ion ha (B.1) displays cons an e u ns o scale in physical capi al and labo while holding a e age a ainmen cons an , (i.e. ha α k + α l = 1), we can de ine a pe capi a p oduc ion unc ion ha will ela e a e age labo p oduc i i y o a e age schooling and o he s ock o capi al pe wo ke . Le ing Q = Y/L deno e ou pu pe wo ke and Z = K/L he s ock o capi al pe wo ke and di iding bo h sides o (B.1) by o al employmen , L, we ha e: (B.2) Q = AZ α kH α h ____________________________________________________________ 3 Box 1 -- con inued ____________________________________________________________ The echnical p og ess unc ion desc ibes he de e minan s o he g ow h a e o o al ac o p oduc i i y. I will assume ha coun y i's TFP le el can be w i en in he o m: (B.3)Ai = B Xi whe e B deno es he wo ld " echnological on ie " (i.e. he maximum a ainable le el o e iciency in p oduc ion gi en he cu en s a e o scien i ic and echnological knowledge) and Xi = Ai /B is (an in e se indica o o ) he " echnological gap" be ween coun y i and he wo ld on ie . I will be assumed ha B g ows a a cons an and exogenous a e, g, and ha he g ow h a e o Xi is gi en by (B.4) Δ xi = γ io - λ xi + γ Hi whe e xi is he log o Xi and γ io a coun y ixed e ec ha helps con ol o omi ed a iables such as R&D in es men . No ice ha his speci ica ion inco po a es a echnological di usion o ca ch-up e ec . I λ > 0, coun ies ha a e close o he echnological on ie will expe ience lowe a es o TFP g ow h. As a esul , ela i e TFP le els will end o s abilize o e ime and hei s eady-s a e alues will be pa ly de e mined by he le el o schooling. ____________________________________________________________ Some ecen heo e ical models sugges ha he accumula ion o human capi al may gi e ise o impo an ex e nali ies ha would jus i y co ec i e public in e en ions. The p oblem a ises because some o he bene i s o a mo e educa ed labo o ce will ypically "leak ou " and gene a e ou pu gains ha canno be app op ia ed in he o m o highe ea nings by hose who unde ake he ele an in es men , he eby d i ing a wedge be ween he p i a e and social e u ns o educa ion. Lucas (1988), o example, sugges s ha he a e age s ock o human capi al a he economy-wide le el inc eases p oduc i i y a he i m le el holding he i m's own s ock o human capi al cons an . I is also commonly assumed ha he a e e ec s o human capi al on echnical p og ess include a la ge ex e nali y componen because i is di icul o app op ia e p i a ely he ull economic alue o new ideas. Aza iadis and D azen (1990), and implici ly Lucas (1988) as well, s ess ha younge coho s a e likely o bene i om he knowledge and skills accumula ed by hei elde s, hus gene a ing po en ially impo an in e gene a ional ex e nali ies ha ope a e bo h a home and in school. The li e a u e also sugges s ha human capi al can gene a e mo e di use "ci ic" ex e nali ies, as an inc ease in he educa ional le el o he popula ion may help educe c ime a es o con ibu e o he de elopmen o mo e e ec i e ins i u ions. F om heo y o da a: al e na i e app oaches o empi ical analysis Empi ical s udies o he e ec s o human capi al on p oduc i i y (o mo e b oadly, o he de e minan s o economic g ow h) ha e ollowed one o wo al e na i e app oaches. The i s one in ol es he speci ica ion and es ima ion o an ad-hoc equa ion ela ing g ow h in o al o pe capi a ou pu o a se o a iables ha a e hough o be ele an on he basis o in o mal heo e ical conside a ions. The second app oach is based on he es ima ion o a s uc u al ela ion be ween he le el o ou pu o i s g ow h a e and he ele an explana o y a iables 4 ha is de i ed om an explici heo e ical model buil a ound an agg ega e p oduc ion unc ion and, possibly, a echnical p og ess unc ion o he ype desc ibed in Box 1. This basic amewo k o he "s uc u al" analysis o he de e minan s o g ow h can gi e ise o a la ge numbe o empi ical speci ica ions. Some o he mos common examples a e discussed in Box 2. The p oduc ion unc ion can be es ima ed di ec ly wi h he ele an a iables exp essed Box 2: Some common empi ical speci ica ions ____________________________________________________________________________________ Fo es ima ion pu poses i is gene ally con enien o wo k wi h he p oduc ion unc ion w i en in loga i hms o in g ow h a es. Using lowe case le e s o deno e loga i hms, and he combina ion o lowe case le e s and he symbol " Δ " o deno e g ow h a es, he p oduc ion unc ion gi en by equa ion (B.1) in Box 1 yields he ollowing wo speci ica ions: (B.5) yi = ai + α kki + α hhi + α lli + ε i (B.6) Δ yi = Δ ai + α k Δ ki + α h Δ hi + α l Δ li + Δε i whe e ε i and Δε i a e s ochas ic dis u bances. One di icul y ha a ises a his poin is ha bo h o hese equa ions con ain e ms ha a e no di ec ly obse able (in pa icula he le el o TFP, ai , o i s g ow h a e, Δ ai ). To p oceed wi h he es ima ion, i is necessa y o make u he assump ions abou he beha io o hese e ms. Di e en assump ions will gene a e di e en econome ic speci ica ions. The simples possibili y is o assume ha he a e o echnical p og ess is cons an o e ime and ac oss coun ies, i.e. ha Δ ai = g o all i and . In his case, g can be es ima ed as he eg ession cons an in equa ion (B.6) and ai is eplaced in equa ion (B.5) by aio + g , whe e aio and g gi e ise o coun y-speci ic cons an s and a common end espec i ely. An al e na i e and mo e sophis ica ed app oach is o speci y Δ ai in equa ion (B.6) as a unc ion o o he a iables. One possible speci ica ion is he one gi en by he echnical p og ess unc ion desc ibed by equa ions (B.3) and (B.4) in Box 1. When da a on ac o s ocks o hei g ow h a es a e no a ailable (o a e no conside ed eliable), a gene alized Solow model can be used o app oxima e hese a iables in e ms o obse ed in es men a es. In such a model, long- e m equilib ium alues o ac o a ios a e simple unc ions o in es men a es, and he beha io o hese a ios away om such an equilib ium can be app oxima ed as a unc ion o in es men a es and ini ial income pe wo ke . I we a e willing o assume ha mos coun ies a e easonably close o hei long- un equilib ia, equa ion (B.5) can be eplaced by an equa ion ela ing ou pu pe wo ke o in es men a es in physical and human capi al. O he wise, he ele an equa ion will in ol e he g ow h a e o ou pu and i will include ini ial ou pu pe wo ke as an addi ional eg esso in o de o pick up ansi ional dynamics along he adjus men o he long- un equilib ium. Two a he s anda d speci ica ions o he esul ing s eady s a e and con e gence equa ions (which do no allow o a e e ec s) would be (B.7) qi = aio + g + α k 1- α k- α h ln ski δ +g+ni + α h 1- α k- α h ln shi δ +g+ni and (B.8) Δ qi = g + β (aio + g ) + β ⎝ ⎜ ⎛⎠ ⎟ ⎞ α k 1- α k- α h ln ski δ +g+ni + α h 1- α k- α h ln shi δ +g+ni - β qi whe e q is he log o ou pu pe wo ke , sk and sh s and o in es men in physical and human capi al measu ed as a ac ion o GDP, n o he a e o g ow h o employmen o he labo o ce and δ o he a e o dep ecia ion (which is assumed o be he same o bo h ypes o capi al). The pa ame e β measu es he speed o con e gence owa ds he long- un equilib ium o s eady s a e and can be shown o be a unc ion o he deg ee o e u ns o scale in bo h ypes o capi al conside ed join ly and o he leng h o he pe iod o e which we a e aking obse a ions. ____________________________________________________________________________________ 5 in le els o in g ow h a es when eliable da a a e a ailable o he s ocks o all he ele an p oduc ion inpu s. Al e na i ely, i s pa ame e s can be eco e ed om o he speci ica ions (con e gence and s eady s a e equa ions) ha a e designed o es ima ion when only da a on in es men lows ( a he han ac o s ocks) a e a ailable. These speci ica ions can be de i ed om a p oduc ion unc ion by eplacing ac o s ocks o hei g ow h a es by con enien app oxima ions in e ms o in es men a es using he p ocedu e de eloped by Mankiw, Rome and Weil (1992) wi hin he amewo k o a gene alized Solow model wi h se e al ypes o capi al. Empi ical e idence: a bi d’s eye iew A la ge numbe o empi ical s udies ha e analyzed he ela ionship be ween human capi al and economic g ow h using he di e en speci ica ions I ha e ou lined abo e.1 Ea ly a emp s in his di ec ion, by and la ge, p oduced posi i e esul s ha ended o con i m economis s’ adi ionally op imis ic iews ega ding he mac oeconomic payo o in es men in educa ion. Landau (1983), Baumol e al (1989), Ba o (1991) and Mankiw, Rome and Weil (1992), among many o he s, ind ha a a ie y o educa ional indica o s ha e he expec ed posi i e e ec on ou pu g ow h. Du ing he second hal o he nine ies, howe e , a new ound o empi ical pape s p oduced a he disappoin ing esul s on he e ec s o schooling on agg ega e p oduc i i y. Unlike mos p e ious s udies, mos o hese pape s used pooled quinquennial da a and elied on ei he panel echniques o he use o di e enced speci ica ions o con ol o unobse ed coun y he e ogenei y. In his se ing, educa ional a iables a e o en ound o be insigni ican o e en en e wi h he "w ong" sign in g ow h eg essions. (See o ins ance Benhabib and Spiegel (1994), Islam (1995), Caselli, Esqui el and Le o (1996) and P i che (2001)). While some esea che s ha e been willing o ake such coun e in ui i e esul s a ace alue, many o he s ha e been a he skep ical (see o ins ance Ba o (1997)). These au ho s ha e ended o a ibu e nega i e esul s on schooling and g ow h o a ious econome ic and speci ica ion p oblems and o poo da a quali y. Measu emen e o , in pa icula , has been widely ecognized o be a po en ially impo an p oblem o wo easons. Fi s , because he se ies o a e age yea s o schooling commonly used in he li e a u e a e likely o con ain a lo o noise and, second, because yea s o schooling can be expec ed o be a e y impe ec measu e o skills in any e en . The i s p oblem, in addi ion, is likely o be pa icula ly impo an in a panel se ing, whe e pa ame e es ima es ely hea ily on he ime-se ies a ia ion o he da a, because measu emen e o a ising om changes in classi ica ion and da a collec ion c i e ia ends o gene a e a lo o spu ious ola ili y in he schooling se ies ha will make i di icul o iden i y i s con ibu ion o p oduc i i y g ow h. Al hough i is oo ea ly o he issue o ha e been conclusi ely se led, my eading o he e idence accumula ed o e he las decade o so is op imis ic. We ha e good easons o belie e 6 ha he nega i e esul s ound in some o he p e ious li e a u e can indeed be la gely a ibu ed o de iciencies in he human capi al da a used in ea lie s udies. Pape s ha make use o imp o ed da a se s on a ainmen o allow o measu emen e o s ongly sugges ha inc eases in a e age schooling do indeed ha e a subs an ial impac on p oduc i i y g ow h. Resul s a e gene ally e en s onge and sha pe when di ec measu es o skill le els a e used o p oxy o human capi al, sugges ing ha imp o emen s in he quali y o schooling can ha e an e en la ge e ec on agg ega e ou pu han inc eases in i s quan i y. The wa e o nega i e esul s on he g ow h e ec s o educa ion ha a i ed in he second hal o he nine ies is clea ly associa ed wi h he in oduc ion o panel da a echniques. While ea ly s udies elied on c oss-sec ion da a (wo king wi h a single obse a ion pe coun y ha desc ibed a e age beha io o e a pe iod o se e al decades), s udies in he second g oup ha e used se e al obse a ions pe coun y, aken o e sho e pe iods, and ha e employed panel echniques o di e enced speci ica ions ha basically elimina e he c oss-sec ion a ia ion in he da a be o e p oceeding o he es ima ion. While heses es ima ion echniques ha e he impo an ad an age ha hey con ol o unobse able di e ences ac oss coun ies, hey also ha e some disad an ages. Pe haps he main one is ha hey a e mo e sensi i e o measu emen e o in he da a as e o s end o be g ea e in he ime-se ies han in he c oss-sec ion dimension because hey end o cancel ou when we wo k wi h a e ages o e long pe iods. This sugges s, as I ha e al eady no ed, ha a possible explana ion o he nega i e esul s ob ained in panel da a s udies has o do wi h he poo quali y o he schooling da a ha ha e been used un il ecen ly in he g ow h li e a u e. As we will see below, mos o he ea lie da abases on in e na ional schooling le els con ain la ge amoun s o noise ha can be aced back o a ious inconsis encies o he p ima y da a used o cons uc hem. The exis ence o his noise induces a downwa d bias in he es ima ion o he coe icien s ha measu e he impac o human capi al ( ha is, a endency o unde es ima e hei alues) because i gene a es spu ious a iabili y in he s ock o human capi al ha is no ma ched by p opo ional changes in he le el o p oduc i i y. A numbe o ecen s udies p o ide e idence ha is consis en wi h his hypo hesis. S a ing wi h K uege and Lindhal (K&L 2001), some au ho s ha e cons uc ed s a is ical indica o s o he in o ma ional con en o di e en a ainmen se ies ( eliabili y a ios) ha can be used o calcula e he likely size o he a enua ion bias and conclude ha he alue o his a io is su icien ly low o explain he lack o signi icance o educa ional indica o s in p e ious s udies. O he au ho s, including Cohen and So o (2007), de la Fuen e and Doménech (D&D, 2001a and b and 2006) and Ba o and Lee (2010), ha e ied o imp o e he signal- o-noise a io in he schooling se ies by exploi ing new sou ces o in o ma ion and in oducing di e en co ec ions. They ind ha he esul s conce ning he impac o educa ion on g ow h imp o e conside ably when hese e ised se ies a e used. I will e u n o hese issues in much g ea e de ail in he ollowing wo sec ions. 1 Fo a mo e de ailed su ey o he ele an li e a u e, see sec ion 3 o he Appendix o de la Fuen e and Ciccone (2003). 7 Ano he in e es ing de elopmen is he use o c oss-coun y da a on di ec measu es o skill which may p o ide be e p oxies o he s ock o human capi al han yea s o schooling. While such da a a e s ill a he sca ce, some ecen pape s sugges ha his is likely o be a e y ui ul line o esea ch. Hanushek and se e al coau ho s2 cons uc indica o s o labo o ce quali y using mean coun y sco es in a numbe o in e na ional s uden achie emen es s in ma hema ics, science and eading, while Coulombe e al (2004) use da a d awn om IALS, an in e na ional s udy on he skill le el o he adul popula ion conduc ed by he OECD and S a is ics Canada. In bo h cases, he esul s o g ow h eg essions poin o e en la ge ou pu e ec s han hose ob ained using e en e ised a ainmen da a. While no en i ely ee o p oblems, hese es ima es do sugges ha he quali y o educa ion is likely o be a leas as impo an as i s quan i y and ha he e u n o imp o emen s in schooling quali y could be ex ao dina ily high, o no only a e hei expec ed bene i s la ge, bu he ele an cos s will gene ally be much lowe han hose o inc easing a ainmen o hey do no in ol e a u he sac i ice o s uden ime and ou pu . 3. C oss-coun y da a on schooling: p oblems and consequences Mos go e nmen s ga he in o ma ion on a numbe o educa ional indica o s h ough popula ion censuses, labo o ce su eys and specialized s udies and su eys. Va ious in e na ional o ganiza ions collec hese da a and compile compa a i e s a is ics ha p o ide easily accessible and (supposedly) homogeneous in o ma ion o a la ge numbe o coun ies. The mos comp ehensi e egula sou ce o in e na ional educa ional s a is ics is UNESCO's S a is ical Yea book. This publica ion p o ides easonably comple e yea ly ime se ies on school en ollmen a es by le el o educa ion o mos coun ies in he wo ld and con ains some da a on he educa ional a ainmen o he adul popula ion, go e nmen expendi u es on educa ion, eache /pupil a ios and o he a iables o in e es .3 The UNESCO en ollmen se ies ha e been used in a la ge numbe o empi ical s udies o he link be ween educa ion and p oduc i i y. In many cases his choice e lec s he easy a ailabili y and b oad co e age o hese da a a he han hei heo e ical sui abili y o he pu pose o he s udy. En ollmen a es can p obably be conside ed an accep able, al hough impe ec , p oxy o he low o educa ional in es men bu hey a e no necessa ily a good indica o o he exis ing s ock o human capi al since a e age educa ional a ainmen (which is o en he mo e in e es ing a iable om a heo e ical poin o iew) esponds o in es men lows only g adually and wi h a e y conside able lag. In an a emp o emedy hese sho comings, a numbe o esea che s ha e cons uc ed da a se s ha a emp o measu e di ec ly he educa ional s ock embodied in he popula ion o labo o ce o la ge samples o coun ies du ing a pe iod o se e al decades. These da a se s ha e gene ally been cons uc ed by combining he a ailable da a on a ainmen le els wi h he 2 See among o he s Hanushek and Kimko (2000) and Hanushek and Wossman (2008 and 2009). 3 O he use ul sou ces include he UN's Demog aphic Yea book, which also epo s educa ional a ainmen le els by age g oup and, in ecen yea s, he OECD's annual epo on educa ion in i s membe coun ies (Educa ion a a Glance), which con ains a g ea deal o in o ma ion abou he inpu s and ou pu s o he educa ional sys em. 8 UNESCO en ollmen igu es o ob ain se ies o a e age yea s o schooling and o he composi ion o he popula ion o labo o ce by educa ional le el. The bes known ea ly a emp s in his line a e he wo k o Ky iacou (1991), he i s e sions o he Ba o and Lee da a se (1993, 1996 and 2000) and he se ies cons uc ed by Wo ld Bank esea che s (Lau, Jamison and Loua (1991), Lau, Bhalla and Loua (1991) and Neh u, Swanson and Dubey (NSD, 1995). In de la Fuen e and Doménech (D&D, 2006) we b ie ly e iew he me hodology used in hese s udies and compa e he di e en da a se s wi h each o he , ocusing in pa icula on he OECD, whe e he quali y o he a ailable in o ma ion should in p inciple be be e han in de eloping coun ies. The analysis o he di e en se ies e eals e y signi ican disc epancies among hem in e ms o he ela i e posi ions o many coun ies and implausible es ima es o ime p o iles o a leas some o hem. Al hough he a ious s udies gene ally coincide when compa isons a e made ac oss b oad egions (e.g. he OECD s. LDCs in a ious geog aphical a eas), he disc epancies a e e y impo an when we ocus on he g oup o indus ialized economies. Ano he cause o conce n is ha exis ing es ima es o en display ex emely la ge changes in a ainmen le els o e pe iods as sho as i e yea s (pa icula ly a he seconda y and e ia y le els). To a la ge ex en , hese p oblems ha e hei o igin in he de iciencies o he unde lying p ima y da a. As Beh aman and Rosenzweig (1994) ha e no ed, he e a e good easons o wo y abou he accu acy and consis ency o UNESCO's da a on bo h a ainmen le els and en ollmen a es. Ou analysis o he di e en schooling da a se s con i ms his diagnos ic and sugges s ha many o he p oblems de ec ed in hese da a can be aced back o sho comings o he p ima y s a is ics, which do no seem o be consis en , ac oss coun ies o o e ime, in hei ea men o oca ional and echnical aining and o he cou ses o s udy, and e lec a imes he numbe o people who ha e s a ed a ce ain le el o educa ion and, a o he s, hose who ha e comple ed i . A enua ion bias and a measu e o da a quali y The poo quali y o c oss-coun y schooling da a is a se ious conce n because i ends o obscu e he ela ionship be ween he a iables o in e es and gene a es a endency o unde es ima e he impac o human capi al on p oduc i i y. To unde s and he o igin o he a enua ion bias caused by measu emen e o , assume ha he le el o p oduc i i y, Q, is a linea unc ion o he s ock o human capi al, H, gi en by (1) Q = bH + u whe e u is a andom dis u bance. Gi en his ela ionship, a ia ions in he s ock o human capi al, H, will induce changes in Q, and he ela i e magni ude o he a ia ions in hese wo a iables will allow us o es ima e he alue o he coe icien b. Now, i H is measu ed wi h e o , ha is, i wha we obse e is no H i sel bu a noisy p oxy o i , say (2) P = H + ε , 15 Figu e 1: Es ima ed α s s. SUR eliabili y a io -0.25 0 0.25 0.5 0.75 1 -0.25 0 0.25 0.5 0.75 1 ca chup e di le els p ed SUR eliabili y a io ca ch-up di e ences ixed e ec s le els ˆ ! s es ima e wi hou measu emen e o In de la Fuen e and Doménech (2002 and 2006) we use a p ocedu e o his ype o ob ain consis en me a-es ima es o α s. Wo king wi h he h ee linea speci ica ions es ima ed abo e ( ha is, wi h all o hem excep o he ca ch-up model) and wi h di e en assump ions abou he na u e o measu emen e o (and in pa icula abou i s co ela ion ac oss da a se s and wi h he emaining explana o y a iables in he model), we ob ain di e en es ima es o α s which a e hen adjus ed o accoun o he possible bias gene a ed by he ac ha we a e wo king wi h he a e age a ainmen o he en i e popula ion a he han ha o employed wo ke s. In his manne , we gene a e a a he b oad ange o possible alues o α s. Unde wha we conside o be he mos plausible assump ions, ou esul s imply alues o α s be ween 0.70 and 0.80. I is wo h no ing ha ou smalles lowe bound o his pa ame e is 0.57. This is almos wice as la ge as Mankiw, Rome and Weil's (1992) es ima e o 1/3, which could p obably ha e been conside ed a consensus alue o his pa ame e in he ea ly 90s and came hen o be seen as oo op imis ic in he ligh o he nega i e esul s in he li e a u e e iewed in an ea lie sec ion. Ou es ima es, by con as , poin o a conside ably highe igu e and sugges ha in es men in human capi al is an impo an g ow h ac o whose e ec s ha e been unde es ima ed in p e ious s udies as a esul o he poo quali y o schooling da a. 16 4.4. Regional esul s o Spain Ou analysis o Spanish egional da a yields quali a i ely simila conclusions ega ding he con ibu ion o schooling o p oduc i i y. In de la Fuen e and Doménech (2008), we es ima e a ca ch-up speci ica ion using biennial da a o he Spanish egions co e ing he pe iod 1965-95. The speci ica ion is iden ical o he one es ima ed abo e o he OECD sample excep in ha physical capi al is now disagg ega ed in o wo componen s, one o which is he s ock o p oduc i e in as uc u es ( anspo and wa e supply ne wo ks and u ban s uc u es). As a p oxy o he s ock o human capi al, we use ou own census-based a ainmen se ies and an al e na i e es ima e o a e age yea s o schooling cons uc ed using Mas e al's (MPUSS, 2002) se ies on he b eakdown o he wo king-age popula ion by a ainmen le el which is, in u n, based on Labo Fo ce Su ey da a. Table 3: G ow h es ima es wi h al e na i e schooling se ies and speci ica ions ______________________________________________ [1] [2] [3] [4] S da a om: MPUSS D&D MPUSS D&D α s -0.013 0.835 -0.013 0.835 (0.11) (2.04) (0.11) (4.13) adj. R2 0.749 0.753 0.757 0.763 egional e ec s all all signi . signi . ______________________________________________ No es: - All equa ions include pe iod dummies. - Whi e's he e oscedas ici y-consis en a ios in pa en heses below each coe icien . - The employmen a io has been d opped om he equa ion due o i s lack o signi icance. The es ima es o he human capi al pa ame e ob ained wi h bo h schooling se ies a e epo ed in Table 3. All equa ions con ain pe iod dummies. Equa ions [1] and [2] con ain a ull se o egional dummies, and equa ions [3] and [4] e ain only hose egional ixed e ec s ha we e signi ican in he i s i e a ion. Inspec ion o he able e eals wo in e es ing esul s ega ding he coe icien o human capi al ( α s). Fi s , his pa ame e goes om being non-signi ican when he MPUSS (2002) da a a e used o ha ing a la ge and signi ican alue wi h ou a ainmen se ies. This esul is consis en wi h ou es ima es o he in o ma ion con en o he wo se ies, as he ele an eliabili y a io is 0.900 o ou da a and only 0.035 o MPUSS's a ainmen se ies when bo h a e measu ed in loga i hmic di e ences. Second, ou es ima e o α s o he Spanish egions (0.835) is highe han hose epo ed abo e o he OECD da a using a simila speci ica ion (0.540 wi h a ull se o coun y dummies and 0.394 when only he signi ican ixed e ec s a e e ained). Again, he explana ion seems o lie a leas pa ly in he in o ma ion con en o he di e en da a se s ( he ele an eliabili y a io o he c oss-coun y a ainmen se ies in D&D (2006) was 0.246). In ac , ou es ima e o α s using Spanish egional da a lies well wi hin he ange o he me a-es ima es ob ained by D&D (2006) o OECD coun ies a e co ec ing o measu emen e o . 17 4.5. Some implica ions The esul s summa ized in he p e ious sec ions ha e some impo an implica ions. I a e age schooling en e s he p oduc ion unc ion wi h a coe icien wi hin he ange o alues we ha e es ima ed, di e ences in school a ainmen a e one o he key sou ces o p oduc i i y di e en ials ac oss bo h he OECD coun ies and he egions o Spain and in es men in educa ion yields a a he subs an ial e u n ha , in mos e i o ies, compa es qui e a o ably wi h ha a ailable om al e na i e in es men oppo uni ies. Figu e 2: Con ibu ion o schooling o ela i e p oduc i i y in 1995 -10% 0% 10% 20% PV Ca Ma Na Ri A Va Cn Cn Ba Mu CL As CM An Ex Ga schooling o he ac o s -20% - Key: An = Andalucia; A = A agón; As = As u ias; Ba = Balea es; Cn = Cana ias; Cn = Can ab ia; CL = Cas illa y León; CM = Cas illa la Mancha; Ca = Ca aluña; Va = Valencia; Ex = Ex emadu a; Ga = Galicia; Ma = Mad id; Mu = Mu cia; Na = Na a a; PV = País Vasco; Ri = Rioja. While I don' ha e he space ha I would need o go in o de ail, I don' wan o close his sec ion wi hou a leas a b ie elabo a ion on hese wo s a emen s. Using he es ima es gi en in Table 3 and he unde lying da a, in D&D (2008) we ha e calcula ed he con ibu ion o schooling o he ela i e p oduc i i y o he Spanish egions, de ined as log eal ou pu pe job measu ed in de ia ions om he (unweigh ed) sample a e age o he same a iable. Figu e 2 shows he decomposi ion o each egion's ela i e p oduc i i y in o a schooling-induced componen and a esidual ha cap u es he join impac o all o he ac o s. Using eg ession weigh s o a e age he di e en egions, we ind ha he sha e o schooling in ela i e p oduc i i y was 40% in 1995 -- ha is, ha o he ypical Spanish egion schooling accoun s o 4/10 o he p oduc i i y gap wi h he sample a e age.11 A simila calcula ion o he OECD sample implies a sha e o schooling in ela i e p oduc i i y o 30%. 11 We de ine he ela i e p oduc i i y o egion i (q eli) as he di e ence be ween he egion’s log ou pu pe employed wo ke and he a e age alue o he same a iable in he sample. The con ibu ion o human capi al o ela i e p oduc i i y (csi) is ob ained mul iplying he coe icien o his ac o , α s , by he ela i e le el o schooling (measu ed in log di e ences wi h he geome ic sample mean). A e cons uc ing hese wo a iables o each egion, we es ima e a eg ession o he o m csi = a ∗ q eli + ei 18 Ou es ima es also imply ha he social e u ns o educa ion a e qui e espec able.12 Combining ou esul s on he p oduc i i y e ec s o human capi al wi h ough es ima es o i s impac on employmen and wi h da a on educa ional expendi u e, we es ima e social a es o e u n anging om 10.1% o 12.6% in Spain and om 8.3% o 11.5% in he EU15.13 In bo h samples, hese e u ns compa e qui e a o ably in mos cases wi h hose a ailable om al e na i e in es men oppo uni ies. This sugges s ha in mos o hese e i o ies a ma ginal ealloca ion o in es men esou ces in a o o educa ion would be socially desi able. 5. Conclusion Academic economis s ha e adi ionally been a he op imis ic abou he con ibu ion o educa ion o economic de elopmen and ha e o en assigned o he accumula ion o human capi al a cen al ole in o mal models, pa icula ly in he ecen li e a u e on endogenous g ow h. The esul s o ea ly empi ical s udies on he de e minan s o economic g ow h ha e been la gely consis en wi h his iew. Du ing he second hal o he nine ies, howe e , a new ound o empi ical pape s p oduced a he disappoin ing esul s on he subjec ha spa ked a li ely con o e sy in he li e a u e be ween "skep ics" and "belie e s" in he salu a y e ec s o schooling on agg ega e p oduc i i y g ow h. This pape con ains a selec i e and a he pa isan e iew o some o he ele an li e a u e. A e se ing he s age, i ocuses on a p oblem ( he poo quali y o c oss coun y schooling da a) ha may help explain he discou aging esul s ound in some in luen ial s udies, on possible ways o o e come i , and on wha happens when his is done. I ha e a gued ha , due o a ious de iciencies o he p ima y da a, he schooling se ies used in he ea ly empi ical li e a u e on g ow h and human capi al con ain a conside able amoun o noise ha gene a es a e y subs an ial downwa d bias in es ima es o he pa ame e ha measu es he con ibu ion o educa ional a ainmen o p oduc i i y. This conclusion is based on he es ima ion o a s a is ical indica o o he in o ma ion con en o he schooling se ies mos commonly used in he li e a u e. I is also ein o ced by he inding o a clea endency o human capi al coe icien s o ise and become mo e p ecise as he in o ma ion con en o he schooling da a inc eases. When his ela ionship is ex apola ed o cons uc es ima es o he alue o he schooling coe icien ha would be ob ained in he absence o measu emen e o , he exe cise sugges s ha he ue alue o he elas ici y o ou pu wi h espec o he s ock o human capi al is almos ce ainly no lowe han 0.60 -- ha is, a ound wice as high as he mos op imis ic es ima e o e e ence in he ea lie li e a u e on g ow h and human capi al. whe e ei is a andom dis u bance. The coe icien ob ained in his manne , a ≅ csi/q eli , measu es he ac ion o he obse ed p oduc i i y di e en ial ha can be a ibu ed o human capi al in he sample as a whole. 12 The social a e o e u n o schooling is de ined as he discoun a e ha equa es he p esen alue o he inc eases in ou pu induced by a ma ginal inc ease in a e age a ainmen o he p esen alue o he explici and oppo uni y cos s o schooling. 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