On the Effects of FDI on Local Human Capital Formation

Transcription

1 On th Effcts of on Local Human Captal Formaton Muhammad Asal Adolfo Crstóbal Campoamor August, 0 ABSTRACT Ths papr lnds both thortcal and conomtrc support to th noton of optmal lvls. It dos so by uncovrng an nvrtd-u-shapd rlatonshp btwn and ducatonal ffort. Th optmalty of a partcular nflow dpnds on th ducatonal ncntvs nducd by on th local, htrognous populaton. Thos ncntvs ar formd n th fac of uncrtanty and asymmtrc nformaton btwn th multnatonal and ts potntal workrs. Our stmats confrm th sgnfcanc of a postv (lnar) and a ngatv (non-lnar) mpact of pr capta on trtary schoolng, both n dvlopd and dvlopng countrs. Kywords: Asymmtrc Informaton; ; Human Captal; Sklls; Tournamnts. JEL Classfcaton: F3, H5, J4. RESUMEN El prsnt papr prsta tanto argumntos tórcos como soport conométrco a la da d un nvl óptmo d. Lo hac dscubrndo una rlacón con forma d U nvrtda ntr y sfurzo ducatvo. La optmaldad d un flujo lmtado d dpnd d la formacón d ncntvos para ducars ntr la poblacón local, qu s a su vz htrogéna n térmnos d dstrza o habldad. Estos ncntvos s forman n prsnca d ncrtdumbr nformacón asmétrca ntr la multnaconal y sus potncals mplados. Nustras stmacons rvlan la xstnca (y sgnfcatvdad) d un mpacto postvo (lnal) y otro ngatvo (no lnal) d la nvrsón xtranjra drcta sobr la scolarzacón trcara, tanto n paíss dsarrollados como n vías d dsarrollo. ISET (Intrnatonal School of Economcs at Tbls Stat Unvrsty). 6 Zandukl Strt, 008 Tbls (Rpublc of Gorga). m.asal@st.g. Unvrsdad Autónoma d Madrd. Dpartamnto d Análss Económco: Toría Hstora Económca. C/ Francsco Tomás y Valnt, Madrd (Span). adolfocrstobal@gmal.com.

2 Kywords: Informacón Asmétrca; ; Captal Humano; Habldad; Comptcón. Clasfcacón JEL: F3, H5, J4.. INTRODUCTION It has bn wdly rportd by th ltratur on multnatonal corporatons (hncforth MNCs) th rol playd by th lattr n th xpanson of formal ducaton n th host countrs. As mphaszd by Blomström and Kokko (00), MNCs provd attractv mploymnt opportunts to hghly sklld graduats n natural scncs, ngnrng and busnss scncs, whch may b an ncntv for gftd studnts to complt trtary tranng 3. Accordng to ths da, n ordr to accss th staff of rputd multnatonals, potntal workrs nd to qualfy as ducatd labor forc. Thrfor, vn whn not all of thm wll ffctvly work for such multnatonals, ths ralty wll nduc on ths workrs an ffort of human-captal formaton wth sgnfcant spllovrs for th rst of thr countrs. In prncpl, t s straghtforward that mor, manng bttr condtons of mployablty at hghr wags, should stmulat human-captal formaton to b slctd by multnatonals. That s, th rlaton btwn nflows and ducatonal nvstmnt s monotoncally ncrasng whn th local populaton s homognous. Howvr, onc w ntroduc som ablty-htrognty among natv workrs, such rlaton bcoms non-monotonc: a vry larg MNC staff mpls a hgh lklhood to b mployd for th hgh-ablty natvs, whch wll tnd to rduc thr ffort thn; and th lowr ffort xrtd by th most capabl wll b accompand (as a racton) by mor laznss by all othrs. Thrfor, undr crtan condtons w suggst that th abov-mntond rlaton btwn pr capta and schoolng n rcpnt countrs shows approxmatly an nvrtd-u shap. 4 Thr s n prncpl no rason why th MNCs wll tnd to maxmz th aggrgat ffcncy unts of th local human captal, bcaus thr ar many othr stratgc prorts for thm. Thrfor, t may b n th ntrst of th local govrnmnt to us som nstrumnts n ordr to ntrnalz th xtrnal ffcts, whch wll spll ovr most 3 Abundant mprcal studs also suggst that multnatonal corporatons tnd to ras th dmand for ducaton n dvlopng countrs, as thr plants ar oftn mor sklld-labor-ntnsv than th rst of th conomy (s, for nstanc, Fnstra and Hanson (997)). 4 Unlk Hoffmann (003), who usd a gnral-qulbrum modl to xplor th mchancs of th complmntarty (and two-way causalty) btwn human-captal accumulaton and, w consdrd a partal-qulbrum framwork.

3 of th productv sctors. Furthrmor, human-captal accumulaton s not th only prorty to b consdrd by th host-country govrnmnt. Productv lnkags wth local sctors, multpl forms of tchnology transfr, or just th valu addd gnratd by may b vn mor sgnfcant (.g. Markusn and Vnabls (999)). Nvrthlss, w trd to mphasz th potntal non-monotoncty of th prvous rlaton, togthr wth som causal xplanatons for such phnomnon, whos rlvanc wll b confrmd n th mprcal sctons of our papr. Indd, our mprcal stmats confrm th sgnfcanc of both a postv, lnar mpact of on trtary schoolng, and of a ngatv mpact of, both n dvlopd and dvlopng countrs. To th bst of our knowldg, ths s th frst papr to ncorporat a non-lnar ffct of n th analyss of human-captal accumulaton. Zhuang (008) usd a dffrnc-n-dffrncs approach n whch th rvrs-causalty problm was addrssd usng dumms of polcy changs as ndpndnt varabls, nstad of masurd n dollars. On th othr hand, Chcch t al. (007) usd xplctly an varabl as a rgrssor, but only capturd ts postv lnar ffct on human-captal formaton. Th rst of th papr s organzd as follows: scton dscrbs an llustratv modl; sctons 3 and 4 prsnt th data and th stmaton procdur; scton 5 contans th rsults and scton 6 an appndx lstng th countrs n our sampl.. AN ILLUSTRATIVE MODEL In our modl thr must b a chanc for all potntal workrs (sklld and unsklld) to b lgbl for a job n MNCs. Othrws th gans would b crcumscrbd to th hghsklld workrs. Thrfor, som nos n th ducatonal and/or th poltcal systm of th host country must play a rol, by prvntng th MNCs from usng a fully-nformd rcrutng polcy. That sam nos s also rsponsbl for som uncrtanty on th part of th applcants, who wll slct thr optmal ducaton ffort as a functon of th probablty to b slctd by th MNCs... Educaton as an nstrumnt to b hrd by multnatonals Our thortcal framwork s a varaton of Lazar and Rosn (98) s modl of tournamnts. In ths partcular sttng thr ar l local workrs comptng for h jobs offrd by th MNCs. Th total sz of th populaton (l) s dvdd nto a proporton ½ of hgh-ablty typs (lt us call thm typ-) and a proporton ½ of low-ablty typs 3

4 (typ-). Th formr typs own θ ffcncy unts of labor (θ>), whras th lattr own just on ffcncy unt. Howvr, th typ of ach ndvdual s not obsrvabl to th mployr. H nds to us a slcton procss n ordr to choos th (prsumably) bst mploys for th MNC, though such slcton dpnds on an mprfct tst. W assum that, n ths modl, mor formal ducaton mprovs th chanc to b slctd by th MNC, that s, t plays th rol of a sgnalng dvc. Howvr, schoolng also hlps th MNC to mprov th qualty of ts pool of mploys, snc th most capabl ndvduals wll b mor ducatd. Gvn that th most capabl workrs ar also mor productv, ths mpls that schoolng wll channl dsproportonally th sklld workrs to th MNC, rasng th aggrgat productvty (and valu addd) of th conomy. From that pont of vw, t can b sad that schoolng also has an aggrgat productvty ffct. Lt th prsonal outcom of any ndvdual n th tst dpnd on hs own tranng ffort ( ) and an lmnt of randomnss (η ), whr th random varabl η follows an unform dstrbuton ovr th ntrval [-a,a], a>0 for all. Mor spcfcally, lt us dnot by g th tst scor of ndvdual and assum that g That randomnss (η ) obscurs th tru typ of th ndvdual to th ys of th mployr, gvn that a good (or a bad) rsult n th tst could b obtand (undr dffrnt crcumstancs) by any of th two typs. W can ntrprt th varanc of η as an nvrs masur of th qualty of th ducatonal systm n th host country. Th magntud of such varanc s masurd by th paramtr a. Dspt th mprfctons n th tst, th multnatonal frm dcds to rcrut th bst h scors, whr h stands for th sz of th local staff n th multnatonal corporaton. That varabl (h) wll also dtrmn th rlatv ncntvs of both typs to gt ducatd and, subsquntly, th x-post qualty of th hrd staff. Th way to b slctd n th tst s batng at last l-h compttors, whr l s th total numbr of canddats nvolvd n th slcton procss. That s, all workrs wll b ntrstd n applyng for a job n th multnatonals, gvn that th MNC offrs a hghr wag than th on avalabl locally (w F - w H =Δw>0, whr F and H stand for forgn and hom, rspctvly). Frst of all, t s ntutv that gvn dntcal prfrncs (n th form of dsutlty) wth rspct to ffort th hgh-ablty typs wll tnd to xhbt a hghr ncntv to 4

5 5 acqur ducaton, snc thy wll njoy from th sam wag gap, but appld to a hghr numbr of ffcncy unts of labor. W wll show ths fact by obtanng th probablty that any workr (of typ ) gts a hghr scor than any othr workr (of typ j;,j Є(,)), as follows: a a d P g g P j a j j j j j 4 4 ) ( () whr w hav consdrd an unform, ndpndnt probablty dstrbuton for th random varabls η and η j, and assumd that a s bg nough to nsur that probablts ar always postv and lowr than on. Lt us dnot by γ th paramtr masurng th ntnsty of th ffort dsutlty by both typs of ndvduals. Now w ar rady to prsnt th maxmzaton problm facd by th workrs of both typs: (4) whr (3),, a p p a a p w p Max Wlfar w p Max Wlfar h l h l W hav dnotd by p th probablty that an agnt shows a hghr scor than anothr on, condtonal on th typ (=,) of th formr. In (3) w ar ncorporatng th fact that, n ordr to b hrd by a multnatonal, any canddat must dfat othr (l-h) potntal workrs. Lt us dnot by z= - th dffrnc btwn th ducaton fforts of both typs, so that p = a z p 4.Thn, by pluggng th quatons n (4) nto th maxmands gvn by (3) and takng th corrspondng frst-ordr condtons, w com up wth th followng racton functons: (5) h l h l a z a w h l a z a w h l If w now subtract both trms n (5), w can charactrz th dstanc btwn th optmal fforts mad by both typs as follows:

6 lh lh w z z z ( l h) (6) 8a 8a 8a Furthrmor, w can clos th systm by mposng a consstncy rqurmnt, whch guarants that th workrs` xpctatons ar ratonal: th ffctv sz of th MNC staff must b qual to th sum of th probablts to b hrd. 5 Such rqurmnt can b xprssd as follows: lh lh l lh lh l z z h p p (7) 8a 8a Thrfor, our whol conomc systm can b charactrzd by th quatons (6) and (7) n th two ndognous varabls h and z. If w xamn carfully both quatons abov, t s straghtforward that both xprssons wll hold f h s clos nough to l (h l-), and f z s clos nough to zro (z 0+). 6 Howvr, w blv that nothng substantal hngs on that proxmty to th cornr solutons, snc w wll b stll abl to plot th shap of th (admttdly small) ndvdual fforts wth rspct to th nflow. Our xrcs wll consst n takng comparatv statcs (on th ffort lvls) wth rspct to th wag gap; obtanng (and plottng) th labor ncom gnratd by 7 that corrsponds to such valus of th gap; and also plottng th rlatonshp btwn and th aggrgat tranng ffort of th local populaton. W consdr two possbl objctv functons (or crtra) to b maxmzd by th govrnmnt n th host country: thr th labor ncom gnratd by, or th aggrgat ducatonal ffort also nducd by. In th lattr cas, snc our proposd objctv wll b promotng up to th pont whr aggrgat ducatonal ffort s maxmzd, w wll drv som conclusons concrnng th avalabl polcy nstrumnts for th govrnmnt. In othr words, th wag gap s xognous for us, whras (undrstood hr as th local labor ncom gnratd by th MNC) and th ffort lvls ar our ndognous varabls... Calbraton and dagrammatc rsults Snc th systm of non-lnar quatons xprssd by (6) and (7) has no analytcal soluton, w nd to solv t numrcally for som plausbl valus of th paramtrs. In partcular, w hav followd Ghosh and Whally (007) s paramtrzaton wth 5 In othr words, condton (7) mans that th MNC can xactly fulfll ts proms to hr th bst h scors. 6 Thos two condtons ar also a guarant that th maxmzaton problms spcfd n (3) ar concav. 7 W assum that th potntal profts gnratd by th MNC wll b rpatratd to th hom country. Thrfor, th host country wll b ntrstd xclusvly n th labor ncom stmmng from. 6

7 z=- Dltaw P-P + rspct to th unts-trm n th dsutlty of ffort functon (γ=). Goldn and Katz (999) suggst an avrag rturn to ach yar of collg n th USA of 0.3, whch amounts to a lowr bound for θ=.5. W wll dscuss latr th mplcatons of changng our paramtr a, whch for th momnt wll tak a valu a=830, whl l=.7. A usful dfnton wll b for us HC lh lh l z z 8 8 a a (8) That s, th varabl HC capturs th aggrgat unts of ffctv labor usd n th MNC. Morovr, w hav normalzd (wthout loss of gnralty) th domstc wag w H to zro. Thrfor, th labor ncom dstrbutd by th MNC among th domstc workrs (that s, th valu addd that rmans n th host country) s HC w (9) Snc w ar ntrstd n th mprcal mplcatons of our numrcal rsults, w hav ncludd n vry horzontal axs of Fgur th varabl, as dfnd n quaton (9). W can clarly obsrv (n th last panl) that and Δw ar postvly corrlatd, whch conforms wll wth Fnstra and Hanson (997) s fndngs wth Mxcan data. Fgur (a=830) 5 x x x

8 .3. Intrprtaton of th fgurs Hghr wag gaps and nflows ar lkly to nduc addtonal tranng on th part of both hgh-ablty and low-ablty workrs. Howvr, th ncntvs ar n prncpl strongr for th most capabl popl, gvn thr xtra unts of ffctv labor, whch translats nto hghr wags pr hour workd. That s th rason why, as starts to rach vry sgnfcant valus, th aggrgat ffctv unts of labor grow substantally and sklld workrs ncras thr tranng ffort at a fastr rat. But that stuaton wll only last up to a crtan pont. Whn both and th wag gap ar qut hgh and MNCs hr a sgnfcant fracton of th populaton, sklld typs wll start to fl that th rlatv gans from addtonal ffort ar lowr than thr dsutlty. Whn thy vntually dcd to rlax, vrybody wll also dcd to do so, as w can obsrv n th panl that shows th aggrgat ffort lvls. Undr such crcumstancs, t maks sns for th govrnmnt n th host country to wondr: Should w rally promot so much, whn that s (locally) rducng th ducatonal achvmnt of our workrs, and th MNCs wll nd up rlasng many unducatd, unsklld mploys for th rst of th conomy? In othr words, n trms of Fgur th govrnmnt may wondr whthr =50 s bttr for th local conomy than =00, although n th lattr cas th wag gap s stll hghr (s th lowr panl on th rght). What could th govrnmnt do to nhanc th xrton of ducatonal ffort, whl allowng for mor? Intrstngly, a good answr would b ncrasng th lvls of corrupton n th admnstraton/ducatonal systm. If w rasd th valu of a from 830 to 835, lowrng thrfor th prcson of th tsts n th host country, thn typ- s would hav to work hardr to dffrntat thmslvs, whch would also push typ- s, as w can obsrv n fgur. Howvr, ths procss could not prsst forvr, snc vntually an xtrmly corruptd systm would compltly abort any ffort by both typs. Fnally, w would obtan agan an optmal lvl of n trms of ducatonal ffort; though such ffort would b hghr ths tm (compar th scond panls on fgurs and ). Fgur (a=835) 8

9 z=- Dltaw P-P + x x x Just to conclud wth th scton, lt us mphasz th followng da: f th sngl prorty of th govrnmnt wr maxmzng a wghtd avrag of th local wlfar lvls n (3), thn thr would b no uppr bound for th local targt. Nvrthlss, f th govrnmnt antcpatd futur layoffs by th multnatonal and apprcatd th adaptablty and rdploymnt capacty of th workrs, probably thy could lmt to nhanc th aggrgat ducatonal ffort. An nstrumnt that sms to rconcl both crtra s a hgh corrupton lvl n th ducatonal sctor, although that s partcularly lkly to b damagng n othr rspcts. 9

10 3. DATA W us data from th World Bank's World Dvlopmnt Indcators. 8 Th data covr 67 countrs, for th yars 000 and 005. Basd on th IMF country classfcaton thr ar 8 dvlopd and 39 dvlopng countrs n th data. Tabl TablMans rports summary statstcs of our man varabls of ntrst, for th yar 005. Tabl : Summary Statstcs 005 All Dvlopd Dvlopng Man Std. Error Man Std. Error Man Std. Error Ltracy rat Schoolng yars Scondary ducaton Trtary ducaton (Bll. USD) pr capta (000' USD) GDP (pr capta) Expndtur on ducaton Pupl-Tachr rato Mortalty rat Land (000 sq. km) Obsrvatons Sourc: Authors' calculaton, WDI data. Th varabls scondary and trtary ducaton rprsnt th gross nrollmnt rato, whch s th rato of total nrollmnt rgardlss of ag to th whol ag group whch offcally corrsponds to th rlvant ducaton lvl. Ths, as wll as th ltracy rat, ar xprssd n prcntag ponts. For xampl, about 90% of th populaton agd 6-8 n dvlopd countrs ar nrolld n som sort of hgh school. s th nt flow of Forgn Drct Invstmnt n bllons of currnt USD. W also dfn -PC whch s (n bllons of USD) dvdd by th populaton (n mllons); thrfor, th pr capta, -PC, s dfnd n thousands of currnt USD. 8 < accssd March/5/0. 0

11 GDP pr capta s also xprssd n currnt USD. It s vdnt from th tabl that GDP pr capta n dvlopd countrs s almost nn-fold that n dvlopng countrs. Mortalty rat s xprssd n prcntag ponts; and t s worth notng that n dvlopng countrs ths s tn tms hghr than n dvlopd countrs. Fnally, Land s th country's total ara xcludng watr bods,.., laks and major rvrs. Ths s xprssd n thousands of squard-km. 4. ESTIMATION On of th man tstabl hypothss suggstd by our thortcal analyss s that th ncras n forgn drct nvstmnt n a country nducs an ncras n th human captal of th country, xmplfd by hghr partcpaton rats n hghr ducaton, but at a dcrasng rat. Evntually, xcdng som (hgh) lvl of, ths wll start nducng a dcln n schoolng attanmnt. To tst ths hypothss w run th followng rgrsson by OLS whr HC X (0) HC, sgnfyng human captal, s thr th nrollmnt rat n trtary ducaton or th nrollmnt rat n scondary school n country. W also consdr th ovrall avrag yars of schoolng as a masur of human captal; ths, howvr, s not th bst masur of human captal bcaus of ts nablty to dstngush btwn prmary or advancd lvls of schoolng. Bsds, w do not hav prvous (for th yar 000) lvls of avrag schoolng, whch dos not facltat a comprhnsv stmaton of th rlatonshp rgardng ths varabl. 9 rprsnts th pr capta n country, n thousands of USD. s th rror trm. Othr control varabls ar ncludd n th vctor X for country. Ths control for macro varabls n th conomy, lk GDP pr capta, whch s probably corrlatd wth ducaton outcoms as w xpct rchr countrs to hav mor rsourcs allocatd to ducaton; also thy control for ducaton nput varabls, lk th log of publc xpndtur on ducaton (pr capta), th pupl-tachr rato, th mortalty rat, and a dummy varabl whch taks on th valu f country s a dvlopd country. 9 Ths smply mans that w wll not b abl to carry out th proxy-varabl stmaton for ths varabl as t wll bcom clar shortly.

12 In th ducaton ltratur, rsarchrs gnrally nclud varabls about ducaton nputs. Two major masurs of ducaton nputs ar th pupl-tachr rato and th publc xpndtur on ducaton. Th pupl-tachr rato s th numbr of pupls nrolld n prmary school dvdd by th numbr of prmary school tachrs. Th publc xpndtur on ducaton s th govrnmnt spndng on ducatonal nsttutons (prvat and publc) and ducatonal actvts (admnstraton, subsds, studnts, tc...). As all ths ar blvd to affct ducaton outcoms n a country, t s ncssary to control for thm n th rgrsson analyss n ordr not to confound thr ffct wth that of th lvls n th country. Mortalty rat s ncludd n th rgrsson bcaus t convys som nformaton about povrty (as mortalty rat s hghr n poorr countrs), but also ths may affct ducatonal chocs: ducatonal attanmnt s an nvstmnt dcson, th rturn of whch dpnds on th lf-span [s Eggr t al. (005), Chcch, D Smon, and Fan (007)]. 4. Endognous Although w blv that changs n th lvls of n som country affct th lvls of ducaton n that country, t s also qually convncng that th currnt lvls of ducaton affct. Forgn compans mght b attractd to nvst n countrs wth hghr potntal, xmplfd by a mor sklld (ducatd) labor forc. Thr also xst thortcal modls that confrm ths ntuton of rvrs causalty btwn and human captal (s Hoffmann 003). Thrfor, s suspctd to b an ndognous varabl n our man quaton of ntrst. To show ths, assum that whr () z s a wht nos (homoskdastc, srally uncorrlatd rror trm) that s ndpndnt of varabls ncludd n th modl, partcularly and. And z stands for possbl varabls that ar omttd from th rgrsson, bcaus thy ar thr not avalabl or unobsrvabl, that mght b corrlatd wth our varabl of ntrst, namly. If that s th cas, thn our OLS stmats of quaton (0) wll b basd and nconsstnt. To addrss ths concrn w us two dffrnt mthods. Frst, to control for z, th unobsrvabl varabls n th rror trm that may b corrlatd wth, w nclud a proxy varabl. Ths varabl, f not xactly z, has to b rlatd to t. W choos th lag of th dpndnt varabl as a proxy varabl n our analyss. For xampl, n th

13 cas of trtary nrollmnt, w nclud n th rgrsson an addtonal varabl whch s trtary nrollmnt n th yar 000, rcallng that our analyss focus on th yar 005. Th ncluson of such a varabl controls for dffrncs btwn th countrs n our cross-sctonal data that could not othrws b capturd by our ncludd varabls. Th sam da appls for th othr masur of human captal, scondary nrollmnt. Th scond approach that w us s th nstrumntal varabls approach (two stag last squars, SLS). Th da s to captur th part of that s orthogonal to z, and masur ts ffct on th human captal masur. To do that, w us th ovrall populaton dnsty, dfnd as th numbr of rsdnts pr on squar klomtr, as an nstrumnt for. In our sampl w fnd that th corrlaton coffcnt btwn pr capta and populaton dnsty s about 0.45, confrmng ts rlvanc hr. On th othr hand, t s not vry lkly that land ara has an ffct on th lvl of ducaton n a country, or an ffct on th ndvdual choc of nvstmnt n ducaton, lndng support to th xcluson rstrcton, whch smply mans that th populaton dnsty s not part of, or s not corrlatd wth, th varabls ncludd n z. Th us of a vald nstrumnt allows us to stmat (th prdctd valu of ) by runnng th followng (frst stag) rgrsson by OLS: whr 0 X Dnsty () Dnsty s th populaton dnsty n country. W thn us th prdctd n th man rgrsson nstad of (th scond stag). On fnal pont worth mphaszng s that w hav n our man rgrsson th varabl also. If s dmd ndognous as dscussd abov, thn t follows that s also ndognous (bng a functon of an ndognous varabl). On wll b tmptd to us nstad of n th scond stag stmaton. Howvr, ths s not corrct, from a mthodologcal vw. 0 Thrfor, to gt an nstrumnt for w us a nonlnar form of th varabls ncludd n th frst stag, and calculat follows: as X 0 Dnsty 3 (3) 0 Actually, ths approach s rfrrd to as th forbddn rgrsson, n th conomtrc ltratur. S Wooldrdg (00) for mor dtals. 3

14 Whr s smply th squar of th prdctd valus n rgrsson (). Th rgrsson n (3) wll gv us th prdctd valu of, namly wll us nstad of n our man rgrsson. 5. RESULTS, whch w W carry out th analyss for thr ndvdual masurs of schoolng: scondary nrollmnt, trtary nrollmnt, and avrag yars of schoolng; thn w dfn a gnral masur of schoolng basd on a wghtd combnaton of scondary and trtary nrollmnt. Tabl shows th man rsults of our analyss for th scondary nrollmnt rato. It shows rsults from th nav OLS stmaton, th proxy-varabl stmaton, and th nstrumntal-varabls stmaton. Th dpndnt varabl n all rgrssons s th scondary nrollmnt rato. Tabl : Th Effct of on Scondary Enrollmnt pr capta OLS Proxy IV ( pr capta) ln GDP pr capta ln Publc Expndtur Pupl-Tachr Rato Mortalty Rat Dvlopd Country Scondary nrollmnt R Obsrvatons NOTE: t-statstcs n parnthss. (*) s sgnfcant at th 0% lvl, (**) at th 5%, and (***) at th %. Dvlopd Country s a dummy varabl that taks on th valu f th country s dvlopd and zro othrws. S txt for dtals. Not that, for symmtry, w us th sam varabls n th frst stag of both and, namly, X, Dnsty, and. 4

15 Th frst column rports th smpl OLS rgrsson of scondary nrollmnt aganst th rlvant varabls. It s vdnt from th tabl that GDP has a postv and sgnfcant ffct on school nrollmnt. As xpctd, th pupl-tachr rato and th mortalty rat hav a ngatv and vry sgnfcant ffct on school nrollmnt. Th sgn of th coffcnt of publc xpndturs on ducaton s countrntutv, nonthlss t s not statstcally dffrnt from zro n ths rgrsson. Th most ntrstng fndng n ths tabl s that has th quadratc ffct on scondary school nrollmnt, confrmng our thortcal modl. A postv and a ngatv, pont to th fact that th schoolng- rlatonshp can b dscrbd by an nvrtd U-shap graph. Th scond column s an OLS rgrsson that uss a laggd dpndnt varabl, namly scondary nrollmnt n 000, as a proxy for th unobsrvabl varabls n th rror trm that affct currnt nrollmnt and mayb rlatd to. Rsults from ths rgrsson ar smlar to ths from th OLS rgrsson, and also confrm th nvrtd U-shap rlatonshp btwn schoolng and. Th last column rports th two-stag-last-squars rgrsson output for scondary nrollmnt. Although th xpctd, postv ffct of GDP and ngatv ffct of mortalty rat and pupl-tachr rato s onc agan confrmd, th coffcnts ar not statstcally sgnfcant anymor (and thr sgns ar countrntutv). Tabl 3 rports th analog rsults for trtary nrollmnt. All stmaton rsults pont to th mportant obsrvaton that an nvrtd-u shap capturs th rlatonshp btwn and trtary nrollmnt. 5

16 Tabl 3: Th Effct of on Trtary Enrollmnt pr capta OLS Proxy IV ( pr capta) ln GDP pr capta ln Publc Expndtur Pupl-Tachr Rato Mortalty Rat Dvlopd Country Trtary nrollmnt R Obsrvatons NOTE: t-statstcs n parnthss. (*) s sgnfcant at th 0% lvl, (**) at th 5%, and (***) at th %. Dvlopd Country s a dummy varabl that taks on th valu f th country s dvlopd and zro othrws. S txt for dtals. Othr varabls, xcludng publc xpndtur on ducaton, also rcv coffcnts wth th rght ntutv sgn, and ar statstcally sgnfcant. Th nstrumntal varabls stmaton rsults (column 3) ar now vry statstcally sgnfcant wth th rght sgns. Tabl 4 rports rsults for th cas of avrag yars of schoolng. As dscussd arlr, ths varabl s mor problmatc masur of human captal, and a sgnfcant rlatonshp s not xpctd n ths cas. 6

17 Tabl 4: Th Effct of on Avrag Yars of Schoolng pr capta OLS.0.33 ( pr capta) ln GDP pr capta.57.8 ln Publc Expndtur.0.5 IV Pupl-Tachr Rato Mortalty Rat Dvlopd Country R Obsrvatons NOTE: t-statstcs n parnthss. (*) s sgnfcant at th 0% lvl, (**) at th 5%, and (***) at th %. Dvlopd Country s a dummy varabl that taks on th valu f th country s dvlopd and zro othrws. S txt for dtals. Both OLS and IV stmats of th ffct of on th avrag yars of schoolng ar not statstcally sgnfcant, although th sgn of th IV stmats s n ln of our prvous rsults. Also, as mntond arlr, snc w do not hav th laggd valu of schoolng (n 000) w could not carry out a proxy varabl stmaton for ths varabl. 5. A Gnral Masur of Schoolng In ths scton w dfn a gnral masur of schoolng, quvalnt n natur to th avrag yars of schoolng usd arlr, but s dffrnt n th sns that t gvs hghr wght to trtary ducaton n ln wth our thortcal prdctons. In partcular, w dfn th gnral schoolng masur GS, as th follows: GS % Scondary % Trtary 3.3 Ths masur translats hgh-school nto yars of schoolng, and trtary ducaton nto 5.39 yars of schoolng. Th da hr s to captur th ncrasd gan n 7

18 productvty assocatd wth hghr ducaton. W thn us ths masur of schoolng to stmat th ffct of usng smlar functonal forms as wr usd n prvous sctons. Man rsults ar summarzd n Tabl 5. Tabl 5: Th Effct of on Schoolng, a Gnral Masur of Schoolng pr capta OLS Proxy IV ( pr capta).5.7 ln GDP pr capta ln Publc Expndtur Pupl-Tachr Rato Mortalty Rat Dvlopd Country SCL R Obsrvatons NOTE: t-statstcs n parnthss. (*) s sgnfcant at th 0% lvl, (**) at th 5%, and (***) at th %. Dvlopd Country s a dummy varabl that taks on th valu f th country s dvlopd and zro othrws. Th dpndnt varabl s GS a gnral masur of schoolng basd on a lnar combnaton of trtary and scondary ducaton. S txt for dtals..65 Th tabl rvals sgnfcant and consstnt stmats of th -schoolng rlatonshps. Th postv coffcnt of and th ngatv coffcnt of squard, vald and sgnfcant undr all thr stmaton mthods, confrm th nvrtd- U shap of th ducaton- found so far. A rlatonshp of ths shap allows us to calculat an optmal lvl of at whch th human captal n th country, summarzd by ths gnral masur of schoolng (GS), s maxmzd. W carry out ths xrcs n th followng scton. 5. Optmal 8

19 Gvn that th rlatonshp btwn human captal and s dscrbd by th followng quadratc quaton: HC ˆ ˆ ˆ X t s possbl to fnd th optmal, that s, th lvl of at whch th human captal (.., schoolng) s maxmzd. Th maxmum HC s attand at * satsfs: ˆ ˆ whch Usng our gnral masur of schoolng, and substtutng our sgnfcant stmats of ˆ and ˆ from Tabl 5 n th abov quaton, w fnd optmal * lvls undr ach scnaro. Strkngly, dspt th dffrnt mthods mployd, our analyss sm to pont to an optmal lvl around 4 (thousand USD pr capta). In partcular, usng OLS stmaton, th optmal s found to b 4.; usng proxyvarabls stmaton, th optmal s 3.86; and usng nstrumntal varabls stmaton, th optmal s Our data rval a strkng fact. It s that many countrs clustr at much lowr lvls of pr capta than th optmal calculatd lvls. Morovr, ths lowr lvls ar assocatd wth lowr ducaton lvls. Spcfcally, calculatng th smpl avrag human-captal varabls, for countrs wth pr capta abov and blow any arbtrary lvl, shows that hgh- countrs attan much hghr schoolng lvls than low- countrs. For xampl, w choos a cutoff pont of =, and rport our fndngs n Tabl 6 blow. Tabl 6: Avrag Human Captal, by Lvls In partcular, w know th crtcal pont found s a maxmum and not a mnmum gvn that th coffcnt of s postv and th coffcnt of s ngatv, rndrng a concav functon of schoolng wth rspct to. 3 On can do ths xrcs for th othr masurs of human captal, say trtary ducaton, to fnd that optmal lvls ar smlar to th abov rportd stmats, and gnrally hovr around

20 Low Hgh Man Std. Dvaton Man Std. Dvaton Scondary Enrollmnt (%) Trtary Enrollmnt (%) Avrag Schoolng Yars Gnral Masur, GS NOTE: Low- dfns countrs (50-5) for whom th pr capta s blow (.., 000 USD), and Hgh- dfns (-3) countrs abov that lvl. Th gnral masur s a wghtd avrag of schoolng basd on hgh-school and collg nrollmnt rats; s txt for dtals. Tabl 6 draws a clar fact: countrs wth hgh (abov $,000 pr capta) attan hghr lvls of schoolng undr any and vry masur of human captal usd. On th on hand, ths provs th xstnc of th optmal pont, at last n rgards to human captal n th host country. On th othr hand, howvr, ths may pont to th possblty that many countrs ar caught wth a low-human-captal-trap, whr th lvl s not suffcntly larg to moblz thm to th maxmum potntal human captal. 6. CONCLUDING REMARKS 0

21 As a concluson, w should mphasz th concav, nvrtd-u shap of th rlaton btwn pr capta and human-captal formaton. Ths rlatonshp s clarr n th cas of trtary ducaton, whch may rval that tnds to b skll-basd and ras nqualty n most LDCs. Thr s also a clustrng of many countrs around a lowrthan-optmal lvl of. W conjctur that som of ths countrs may b affctd by a low-human-captal trap, as suggstd by som of our smulatons. Provng th ffctv xstnc (or nxstnc) of thos traps s an ntrstng avnu for futur rsarch. 7. APPENDIX Countrs ncludd n our sampls ar: Afghanstan, Albana, Algra, Angola, Antgua and Barbuda, Argntna, Armna, Aruba, Australa, Austra, Azrbajan, Th Bahamas, Bahran, Bangladsh, Barbados, Blarus, Blgum, Blz, Bnn, Bhutan, Bolva, Bosna and Hrzgovna, Botswana, Brazl, Brun Darussalam, Bulgara, Burkna Faso, Burund, Camboda, Canada, Cap Vrd, Cntral Afrcan Rpublc, Chad, Chl, Chna, Colomba, Comoros, Dm. Rp. of Congo, Congo Rp., Costa Rca, Cot d'ivor, Croata, Cyprus, Czch Rpublc, Dnmark, Djbout, Domnca, Domncan Rpublc, Ecuador, Egypt, El Salvador, Estona, Ethopa, Fj, Franc, Gabon, Th Gamba, Gorga, Grmany, Ghana, Grc, Grnada, Guatmala, Guna, Guna-Bssau, Guyana, Hat, Honduras, Hong Kong (SAR Chna), Hungary, Icland, Inda, Indonsa, Islamc Rp. of Iran, Iraq, Isral, Italy, Jamaca, Japan, Jordan, Kazakhstan, Knya, Krbat, Rp. of Kora, Kyrgyz Rpublc, Lao P.D.R., Latva, Lbanon, Lsotho, Lbra, Lbya, Lthuana, Macao SAR, Macdona FYR, Madagascar, Malaw, Malaysa, Maldvs, Mal, Malta, Maurtana, Maurtus, Mxco, Moldova, Mongola, Morocco, Mozambqu, Myanmar, Namba, Npal, Nthrlands Antlls, Th Nthrlands, Nw Zaland, Ncaragua, Ngr, Ngra, Norway, Oman, Pakstan, Panama, Paraguay, Pru, Phlppns, Poland, Portugal, Romana, Russan Fdraton, Rwanda, Samoa, Sao, Tom and Prncp, Saud Araba, Sngal, Srba, Sychlls, Srra Lon, Slovak Rpublc, Slovna, Solomon Islands, Span, Sr Lanka, St. Ktts and Nvs, St. Luca, St. Vncnt and th Grnadns, Sudan, Swazland, Swdn, Swtzrland, Syran Arab Rpublc, Tajkstan, Tanzana, Thaland, Togo, Tonga, Trndad and Tobago, Tunsa, Turky, Turkmnstan, Uganda, Ukran, Untd Kngdom, Untd Stats, Uruguay, Uzbkstan, Vanuatu, R.B. d Vnzula, Wst Bank and Gaza, Rp. of Ymn, Zamba, Zmbabw. 8. REFERENCES

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