Journl of Publc Economcs 74 (1999) 351 393 www.elsever.nl/ locte/ econbse More equl but less moble? Educton fnncng nd ntergenertonl moblty n Itly nd n the US *, Aldo Rustchn b, c Dnele Checch, Andre Ichno Stte Unversty, Mln, Itly b Europen Unversty Insttute, IGIER nd CEPR, V de Roccettn 9, 50016 Sn Domenco d Fesole (FI), Itly c Tlburg Unversty, CentER, Tlburg, Netherlnds Receved 1 My 1998; receved n revsed form 1 Februry 1999; ccepted 1 Mrch 1999 Abstrct A centrlsed nd egltrn school system reduces the cost of educton for poor fmles, nd so t should reduce ncome nequlty nd mke ntergenertonl moblty eser. In ths pper we provde evdence tht Itly, compred to the USA, dsplys less ncome nequlty, s expected gven the type of school system, but lso less ntergenertonl upwrd moblty between occuptons nd between educton levels. We explore some of the resons whch cn expln ths puzzlng result nd conclude tht n world n whch fmly bckground s mportnt for lbor mrket success, centrlsed nd egltrn tertry educton does not necessrly help poor chldren nd my tke wy from them fundmentl tool to prove ther tlent nd to compete wth rch chldren. 1999 Elsever Scence S.A. All rghts reserved. Keywords: Educton fnncng; Intergenertonl moblty JEL clssfcton: I22; J62 1. Introducton The Itln school system cn be chrctersed s prevlently centrlsed nd *Correspondng uthor. Tel.: 139-055-468-5222; fx: 139-055-468-5202. E-ml ddress: chno@ue.t (A. Ichno) 0047-2727/ 99/ $ see front mtter 1999 Elsever Scence S.A. All rghts reserved. PII: S0047-2727(99)00040-7
352 D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 publc system fnnced by the government through txton, whch provdes the sme qulty of educton to everybody. The US system, nsted, cn be chrctersed s prevlently decentrlsed nd prvte system n the sense tht publc educton s mnly fnnced t the locl level nd the shre of students gong to prvte school s substntlly hgher. Gven ths chrcterston, n Itln fmly t low level of ncome (whch cn reflect low level of cqured humn cptl) should hve the sme level of educton vlble s hgher ncome fmly. A US low ncome (nd low humn cptl) fmly, should nsted hve the ddtonl dsdvntge of low expendture n educton decded by prents (s result of lower drect nvestment or becuse of loctonl choces n communtes n whch preferences 1 re for lower tx rtes nd worse schoolng nsttutons). Wthn ths frmework t would seem resonble to predct for Itly more compressed dstrbuton of humn cptl nvestments (nd therefore of ncomes) mtched by hgher lkelhood of upwrd moblty for poor fmles. The exstng comprtve emprcl evdence on Itly nd the US suggests tht the frst prt of ths predcton s supported by the evdence: Itly s ndeed chrctersed by less ncome nequlty thn the US. In our study, we extend the comprson by lookng jontly t the ssues of ncome dstrbuton nd ntergenertonl moblty, nd we fnd tht the second prt of the predcton s nsted flsfed. Stndrd mesures of ntergenertonl moblty between occuptons nd between educton levels ndcte tht n Itly poor nd non-educted fmles re less lkely to nvest n the educton of ther chldren nd to move up long the occuptonl ldder. In other words, the Itln system cn be chrctersed s n offer of equl opportuntes tht hs surprsngly not been ccepted by the Itln poor fmles. Ths s the puzzle tht we would lke to ddress n our pper. We would lke to understnd why the Itln school system, whch s strongly egltrn n the qulty nd cost of the educton provded to rch nd poor fmles, fls to generte t lest the sme degree of ntergenertonl moblty whch prevls n the US, where the school system s nsted hghly decentrlsed nd nonegltrn. We beleve tht ths comprson between Itly nd the US my suggest helpful mprovements n the desgn of publc educton systems. Our theoretcl model dentfes some fctors tht cn reduce the cpcty of these systems to generte suffcent mount of ntergenertonl moblty. We show tht these fctors re prtculrly strong when the ndvdul effort s reltvely more mportnt thn the qulty of educton for successful ccumulton of humn cptl. In ths cse, 1 In the bsence of perfect fnncl mrkets, low ncome fmles re prevented from rechng the optml level of nvestment n educton (see Glor nd Zer, 1993; Bnerjee nd Newmn, 1993). In ddton, when educton fnncng s provded loclly, loctonl choces n communtes, where preferences re for lower tx rtes, provde worse schoolng (see Benbou, 1996,b).
D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 353 even f the cost of schoolng s low, the return to schoolng s lso low nd the offer of better qulty of educton to poor fmles hs lttle vlue to them. Ths s nsted the cse n whch decentrlsed nd prvte system does better job n rsng the return to schoolng, thereby mkng the nvestment n humn cptl more ttrctve for poor fmles even f t s more costly. We rgue tht ths could be the cse of the Itln publc unversty system, whose egltrn nd stndrdzed qulty does not ttrct the expected eductonl nvestment of poor fmles. Indeed, the Itln system does not offer rel opportunty for chldren of lower ncome fmles to emerge nd to keep the returns of ther eductonl nvestment. The pper s orgnsed s follows. The evdence on occuptonl nd eductonl moblty s presented nd dscussed n Secton 2. Secton 3 shows why ths evdence represents puzzle, nd descrbes nformlly how we thnk t cn be explned. Ths explnton s then presented formlly n Sectons 4 6. Concludng remrks on the mplctons for the desgn of publc educton systems follow. 2. Evdence on the puzzle 2.1. Occuptonl moblty Socl moblty s defned nd mesured n mny dfferent wys n the lterture. Among economsts, some uthors focus on trnstons between ncome clsses or between percentles of the ncome dstrbuton (Atknson, 1980 81) whle others look t the speed of men regresson of ncomes cross genertons (Becker nd Tomes, 1986; Solon, 1992; Zmmermn, 1992); mong socologsts, nsted, the ttenton s concentrted on trnstons between occuptons rnked ccordng to socl prestge (Tremn nd Gnzeboom, 1990) or on the trnstons between socl clsses (Erckson nd Goldthorpe, 1992). In generl whle economsts tend to study moblty n terms of ncomes, socologsts re more lkely to focus on occuptons. Our pproch cn be chrctersed s sort of ntermedte thrd wy tht we 2 dopt prtly becuse of dt lmttons but lso becuse t offers some dvntges from the pont of vew of chevng menngful nterntonl comprson nd complements n hopefully nterestng wy the exstng lterture. Socologsts hve been rgung for long tme tht becuse of temporry ncome fluctutons nd mesurement errors, yerly ncome chnges re msledng upwrdly bsed ndctor of moblty f the gol s to mesure trnstons between long term economc sttus. Cstng ths rgument n n econometrc frmework, Solon (1992) nd Zmmermn (1992) propose verges of ndvdul ncomes on subsequent yers s mesure of long term sttus, but we cnnot follow ther 2 See Appendx A.
354 D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 suggeston becuse we do not hve the necessry nformton for Itly. We tke nsted rod more fmlr to socologsts nd focus on occuptons s ndctors of economc sttus; but we lso deprt from the socologcl lterture becuse we do not rnk occuptons ccordng to socl prestge nor do we ggregte them ccordng to subjectvely defned socl clsses. Gven the nformton contned n our dtsets, the concept of socl moblty tht we cn mesure s represented by moblty between occuptons rnked ccordng to the medn ncome pd by ech occupton n the generton of 3 chldren n ech country. The reder should therefore keep n mnd tht n ths study, dynsty s clssfed s moble only f the occupton of the son s dfferent from the occupton of the fther. Tke the cse of fther nd son n the sme occupton whch s hghly pd n reltve terms when the fther s observed, but whch s pd less thn verge when the son s observed. Accordng to our defnton ths dynsty s clssfed s mmoble even f, n terms of ndvdul ncomes, t experences downwrd moblty. Income chnges tht tke plce wthn the sme occupton but cross genertons cnnot be mesured n our dtsets nd do not mply moblty ccordng to our defnton. Vce vers, the cse of fther nd son possbly ernng the sme ncomes but workng n two dfferent occuptons s consdered here s cse of ntergenertonl moblty. Therefore, ntergenertonl moblty n ths study hs to be nterpreted s moblty between occuptons even f occuptons re rnked on the bss of ncomes. Wth ths cvet n mnd we begn our nlyss wth the evdence on nequlty. The exstence of greter lbor ncome nequlty n the US n comprson to Itly 4 hs lredy been documented n the lterture nd s confrmed n the dtsets used n ths study: s shown n Tble 1, wthn ech generton ll the most common ndctors of ncome nequlty proposed n the lterture re clerly 5 lrger n the US smple. The comprtve evdence on ntergenertonl socl moblty for Itly nd the US s, nsted, less documented. Tbles 2 nd 3 present the mtrces of trnston between occuptonl ncome clsses defned s proportons of equl sze of the (log) dfference between the hghest nd the lowest occuptonl ncomes n the 3 Cowell nd Schluster (1998) suggest tht the use of ctegorcl dt should ncrese the robustness of moblty mesures. We lso performed our nlyss usng socologcl ndexes of prestge to rnk occuptons, but our results concernng the reltve performnce of the two countres n terms of occuptonl moblty do not chnge. We present the evdence bsed on ncome rnkng becuse t s less conventonl from methodologcl pont of vew nd becuse t llows for n nlyss of the relton between eductonl moblty nd occuptonl moblty. Such nlyss s mpossble f occuptons re rnked ccordng to ndctors of prestge constructed on the bss of eductonl chevements. 4 See, for exmple: Gottshlk nd Smeedng (1997), Erckson nd Ichno (1994) nd Brndoln (1998). 5 For descrpton of these ndctors see the ppendx of the CEPR WP verson of ths pper (n. 1466, October 1996). Gven tht n ech country occuptonl ncomes for both genertons re computed on the dstrbuton of chldren, nequlty dffers cross genertons only becuse of chnges n the dstrbuton of ech generton cross occuptons.
D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 355 Tble 1 Inequlty mesures for Itly nd the US Mesure Itly US Itly US Fther Fther Son Son 90 10 percentle dfferentl 140.6 164.3 131.5 150.3 Reltve men devton 12.2 14.6 13.2 14.3 Coeffcent of vrton 33.8 37.5 34.8 36.0 Stndrd devton of logs 30.0 35.6 31.3 34.9 Gn coeffcent 16.8 20.2 17.9 19.6 Atknson (e 5 2) 8.7 11.8 9.3 11.4 Thel entropy 5.0 6.6 5.5 6.1 All mesures re expressed n % terms. Hgher vlues mply greter nequlty. Tble 2 Itly: nterclss trnston probbltes Son C1 Son C2 Son C3 Son C4 Abs. freq. Fther C1 21.8 50.4 22.3 5.4 367 Fther C2 12.0 55.9 25.8 6.3 884 Fther C3 5.9 27.0 51.6 15.5 341 Fther C4 4.0 16.2 32.4 47.3 74 Abs. freq. 209 783 510 164 1666 Ech cell contns the row-to-column trnston probblty. C1 C4 re ncome clsses defned s ntervls of equl sze of the (log) dfference between the hghest nd the lowest occuptonl ncomes. Tble 3 US: nterclss trnston probbltes Son C1 Son C2 Son C3 Son C4 Abs. freq. Fther C1 25.9 36.4 31.4 6.3 239 Fther C2 22.5 37.7 29.7 10.1 337 Fther C3 9.3 31.0 41.7 18.0 355 Fther C4 4.2 15.1 42.0 38.7 119 Abs. freq. 176 342 373 159 1050 Ech cell contns the row-to-column trnston probblty. C1 C4 re ncome clsses defned s ntervls of equl sze of the (log) dfference between the hghest nd the lowest occuptonl ncomes. two countres (see Tble 4). Accordng to ths ggregton strtegy, n ech country these clsses spn over the sme percentge ncrese n occuptonl 6 ncomes. 6 We obtn smlr results wth dfferent ggregton strteges, lke for exmple the ggregton bsed on qurtles of the occuptonl ncome dstrbuton (see the CEPR WP verson of ths pper, n. 1466, October 1996). We prefer the ggregton bsed on the ncome clsses descrbed n the text becuse, gven the skewness of the ncome dstrbuton, qurtles (n prtculr the fourth) my group together very dshomogeneous occuptonl ncomes. Therefore smlr trnstons n terms of qurtles my men very dfferent trnstons n terms of occuptonl ncomes. Furthermore, the focus on bsolute nsted of reltve trnstons s consstent wth the theoretcl nlyss presented n Secton 4.
356 D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 Tble 4 Income clsses for the Unted Sttes nd for Itly Clss 1 Mnmum 100 100 Medn 130 135 Mxmum 139 144 Clss 2 Mnmum 148 150 Medn 174 164 Mxmum 215 216 Clss 3 Mnmum 215 219 Medn 261 234 Mxmum 314 318 Clss 4 Mnmum 322 331 Medn 337 369 Mxmum 463 474 Sttstcs bsed on the dstrbuton of sons ncomes; results re smlr for the dstrbuton of fthers. Mnmum occuptonl ncome normlzed to 100. Income clsses re defned s ntervls of equl sze of the (log) dfference between the hghest nd the lowest occuptonl ncomes. US Itly Dfferences between the two countres re pprent from the smple nspecton of these trnston mtrces: n prtculr, the probbltes of persstence long the mn dgonl re lrger n Itly for the three upper clsses. The fct tht persstence n the frst clss s nsted hgher n the US my be nterpreted s evdence on the role of ghettos n ths ltter country. But the probblty to rech the two hghest clsses from the bottom s hgher n the US (37.7%) thn n Itly (27.7%) whle the probblty of persstence n the top clss s hgher n ths ltter country (47.3% gnst 38.7%). If one computes on the bss of these mtrces the most stndrd sclr ndctors of moblty tht hve been proposed n the 7 lterture, the US pper unmbguously chrctersed by greter ntergenertonl 8 moblty (see Tble 5). In order to nvestgte the sttstcl sgnfcnce of the dfferences n ntergenertonl moblty n Itly nd n the US, we ggregte the four ncome clsses defned bove n two groups nd we estmte probt model of the probblty tht the son s n the hghest of these two groups. We defne the hghest group s the unon of the clsses 3 nd 4 tht were descrbed n Tble 4. Hence, the dependent vrble of our probt models tkes vlue 1 f the son s n ncome clss 3 or 4,.e. f hs occuptonl ncome s greter thn the ncome correspondng to hlf of the percentge dfference between the mxmum nd the mnmum of the dstrbuton of occuptonl ncomes. We estmte ths probblty s functon of dummy 7 See: Boudon (1974), Bbby (1975), Atknson (1980 81), Atknson et l. (1981), Atknson (1983), Brtholomew (1982), Sommers nd Conlsk (1979), Shorrocks (1978), Geweke et l. (1986), Conlsk (1989), Conlsk (1990) nd Drdnon (1992). 8 For descrpton of these ndctors, see the ppendx of the CEPR WP verson of ths pper (n. 1466, October 1996).
D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 357 Tble 5 Sclr ndctors of moblty for nterclss trnston mtrces Itly US Eq. opp. ML 5 1 2 ul2u 0.55 0.65 1 k 2 tr(p) MT 5]] k 2 1 0.74 0.85 1 (1/(k21)) MD 5 1 2 udet(p)u 0.79 0.90 1 MB 5 o oj fju 2 ju 0.62 0.80 MA5 o oj fjuw 2 Wju 22.44 27.55 ul2u s the modulus of the second greter egenvlue; tr(p) nd det(p) re, respectvely, the trce nd the determnton of the nterclss trnston mtrx P; k s the number of clsses; fj s the jont frequency n cell (, j); the dstnce u 2 ju s the number of clss borders crossed n the trnston from to j. uw2 Wju s the percentge dfference between medn ncomes of clss nd j. ndctor for the ncome group of fthers (tht tkes vlue 1 f the fther s n ncome clss 3 or 4) nd of two dummy ndctors for the educton levels of fthers nd sons. In both genertons nd n both countres the educton ndctors tke vlue 1 f the ndvdul hs college degree. Age controls re lso ncluded n the regressons. The results of ths exercse re presented n Tble 6 whch reports, for ech regresson, the chnge n the probblty tht the son s n the hghest group due to 9 chnge from 0 to 1 of ech ndependent dummy vrble. These effects re evluted t smple verges. In model 1 only the fmly bckground vrbles re ncluded s regressors: whle the effect of the fther s educton s equl n the two 10 countres, the effects of the fther s ncome clss s sgnfcntly lrger n Itly. In model 2 the educton dummy for the son s ntroduced, nd the effect of the fther s educton dsppers n both countres: ths s well known result n the 11 lterture nd suggests tht most of the effect of prentl educton on sons occuptonl chevements works ndrectly through the effects on sons educton. The effect of the occuptonl ncome clss of fthers, however, remns sgnfcntly dfferent from zero n both countres, nd sgnfcntly lrger n Itly thn n the US. Whle n the US the effect of sons educton s lrger thn the effect of prentl ncome, n Itly the opposte s true. To put t more drectly, n Itly t s better to... choose the rght fmly thn to obtn college degree. Comng to the comprson between models 2 nd 3, n both countres lkelhood rto test rejects the hypothess tht fmly bckground s rrelevnt: ddng prentl chrcterstcs to sons chrcterstcs (.e. gong from model 3 to 2 model 2) ncreses the predctve cpcty (pseudo R ) of the model by 150% n Itly; n the US the ncrese s much lower, beng equl to just 19%. 9 For the ge controls the reported effect s tht of n nfntesml ge ncrese. 10 Here nd for the rest of ths tble, dfferences between coeffcents hve been tested usng pproprtely constructed t-tests; the null hypothess of equl coeffcents hs been rejected wth P-vlues smller thn 0.001. 11 See for exmple Tremn nd Yp (1989).
Tble 6 Determnnts of the probblty tht son s n ncome clss 3 or 4 Itly Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 Fther n ncome clss 3 or 4 0.37 0.35 0.22 0.19 (0.03) (0.03) (0.03) (0.03) Fther wth college degree 0.18 0.02 0.19 0.05 (0.09) (0.09) (0.04) (0.05) Son wth college degree 0.31 0.39 0.47 0.50 (0.05) (0.05) (0.03) (0.03) Fther s ge 20.001 20.001 0.009 0.004 (0.002) (0.002) (0.002) (0.003) Son s ge 20.003 20.03 0.005 0.007 (0.001) (0.001) (0.004) (0.003) Observed prob. 0.427 0.427 0.427 0.508 0.508 0.508 Predcted prob. 0.427 0.428 0.428 0.511 0.532 0.530 2 Pseudo R 0.08 0.10 0.04 0.07 0.19 0.16 Log-lkelhood 2939 2918 2984 2665 2578 2597 Smple sze 1505 1505 1505 1037 1037 1037 Mxmum lkelhood estmtes of probt model n whch the dependent vrble tkes vlue 1 when the son s n ncome clss 3 or 4. The tble reports the probblty effects, evluted t the smple verges, due to dscrete chnge of ech dummy ndependent vrble. For the ge controls the reported effects re those of n nfntesml ge chnge. US 358 D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393
D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 359 The probt estmtes presented n Tble 6 suggest tht n both countres the occuptonl clss of fthers s n mportnt determnnt of the occuptonl chevement of sons, but n Itly the effect s much stronger thn n the US n bsolute terms nd reltvely to the effect of sons educton levels. We turn now to the evdence on ntergenertonl moblty between educton levels n whch the reltve lck of upwrd moblty n Itly ppers even more strkng. 2.2. Eductonl moblty The comprson cross countres of eductonl moblty ptterns s certnly not 12 n esy tsk gven the enormous dfferences between ntonl educton systems. One strtegy tht seems resonble to us conssts of comprng the probbltes of rechng the hghest eductonl degree offered by the schoolng system of ech country. Dsregrdng post grdute studes, whch both n Itly nd n the US concern very smll frcton of the populton, we consder the college degree 13 (lure n Itly) s the relevnt hghest eductonl degree. We therefore begn our nlyss of eductonl moblty by consderng the probbltes of dynstc trnstons between the followng two eductonl ctegores: ll the ndvduls wthout college degree re clssfed s hvng low educton, whle those holdng college degree re n the hgh educton group. Tble 7 presents the dstrbuton cross these eductonl ctegores n ech generton nd n ech country. Itly s chrctersed n both genertons by 14 lower frcton of college grdutes, but experences the lrgest percentge shft towrds hgher educton from one generton to the other: whle n the US the frcton of grdutes ncreses by 69%, n Itly the sme frcton ncreses by 200%. Yet not ll Itln dynstes shred n the sme wy ths greter opportunty to rech college degree. Tbles 8 nd 9 present, for Itly nd the US respectvely, the ntergenertonl trnston probbltes between the eductonl ctegores tht we hve just 12 See Shvt nd Blossfeld (1993). 13 We hve clssfed n the hgh educton group ll those ndvduls holdng college degree or Ph.D. degree n the US smple, or hvng obtned lure or dottorto d rcerc n the Itln smple. Ths clssfcton corresponds to the UNESCO clssfcton ISCED 6 nd ISCED 7, nd requres 18 nd 16 yers of school ttendnce, respectvely, n the two countres. People who ttended some yers of college wthout obtnng ny degree were not consdered s college degree holders. In the cse of Itly we hve lso used n lterntve clssfcton scheme: n ths cse we hve ncluded n the hgh educton group ll those ndvduls holdng t lest dplom d mturt` degree.e. secondry school degree correspondng to ISCED 5 clssfcton scheme; n such cse the mnmum number of yers of school ttendnce s 15. 14 Note tht, ccordng to OECD (1996), Itly hs the lowest frcton of college grdutes mong ll the OECD countres nd n ll the relevnt ge clsses.
360 D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 Tble 7 Actul mrgnl nd lmtng dstrbutons for educton n Itly nd the US Itly Itly Itly Itly US US E15no coll. E25coll. E15no HS E25HS1 E15no coll. E25coll. Fther 0.97 0.03 0.92 0.08 0.84 0.16 Son 0.91 0.09 0.71 0.29 0.73 0.27 Lmt 0.83 0.17 0.30 0.70 0.65 0.35 Mrgnl nd lmtng dstrbutons refer to the mtrces of eductonl trnston probbltes. Ech lmtng dstrbuton s obtned under the ssumpton tht the correspondent mtrx descrbes Mrkov process. For Itly: hgh educton5college degree n column 1 nd hgh school degree or more n column 2; for the US: hgh educton5college degree. Tble 8 Itly: trnston probbltes from no college to college Son E1 Son E2 Abs. freq. Fther E1 92.9 7.1 1462 Fther E2 34.9 65.1 43 Abs. freq. 1374 131 1505 Ech cell contns the row-to-column trnston probblty. E1, no college degree; E2, completed college degree. Tble 9 US: trnston probbltes from no college to college Son E1 Son E2 Abs. freq. Fther E1 79.2 20.8 870 Fther E2 38.9 61.1 167 Abs. freq. 754 283 1037 Ech cell contns the row-to-column trnston probblty. E1, no college degree; E2, completed college degree. 15 descrbed. In Itly, the probblty tht the son of grdute s grdute s hgher thn n the US (65.1% vs. 61.0%); vce vers the probblty tht the son of non-grdute reches college degree s substntlly lower n Itly thn n the US (7.1% vs. 20.8%). The nspecton of these trnston probbltes clerly suggests tht the opportuntes of obtnng college degree re more uneqully dstrbuted n Itly thn n the US, even f Itly experences more substntl ncrese of the proporton of college grdutes from one generton to the other. 15 Becuse of some mssng nformton on school ttendnce mong fthers, the number of son fther prs reduces to 1505 observtons for Itly nd to 1037 for the US whenever the educton of fthers s consdered n the nlyss.
D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 361 Tble 10 Sclr ndctors of moblty for eductonl trnston mtrces Itly US Itly Eq. opp. E25coll. E25coll. E25HS or 1 p 12 /p11 OR 5]] 24.6 6.0 27.3 1 p 22 /p21 k 2 tr(p) MT 5]] 0.42 0.60 0.34 1 k 2 1 MB 5 o oj fju 2 ju 0.12 0.27 0.14 OR s the odds rto; n 232 mtrx the ndexes MT, MD nd ML defned n Tble 5 re ll equl; tr(p) s the trce of the nterclss trnston mtrx P; k s the number of clsses; fj s the jont frequency n cell (, j); the dstnce u 2 ju s the number of borders crossed n the trnston from to j. The odds rtos for the two trnston mtrces, reported n Tble 10, show tht the odds of obtnng college degree n Itly re lmost 25 tmes hgher f the fther hs college degree, whle n the US hvng grdute fther ncreses the odds only by 6 tmes. Hence, both countres do not ensure stuton of equl opportuntes n the trnstons between educton levels, but Itly ppers to be more dstnt thn the US from such stuton. Ths s confrmed lso by the other 16 sclr ndctors contned n Tble 10. One mght rgue tht college degree mens more n Itly thn n the US n terms of humn cptl cquston. Indeed t lest one ddtonl yer of schoolng s requred n Itly to obtn lure nd n some dscplnes, lke engneerng or medcne, the lure nvolves eductonl currcul tht n the US re requred for postgrdute studes only. Therefore, s fr s Itly s concerned, we provde evdence lso for dfferent clssfcton of eductonl ctegores ccordng to whch the hgh educton group ncludes ll the ndvduls who hve obtned hgh school degree or more. Tble 7 shows tht wth ths lterntve clssfcton Itly s chrctersed by n even lrger ncrese of the frcton of hghly educted dynstes (262%); furthermore, mong sons, the proporton of hghly educted ndvduls n Itly (hgh school or more) becomes smlr to the proporton of hghly educted ndvduls n the US (college or more). Yet even wth such fvourble clssfcton, the opportuntes of rechng the hgher eductonl ctegory re more uneqully dstrbuted n Itly thn n the US (see Tbles 10 nd 11). The odds of rechng hgh school degree or more re now even lrger f the fther s n the sme eductonl ctegory (the odds rto s 27.3) nd the dstnce 16 When we estmte probt model for hgher educton (not reported here see the CEPR WP verson of ths pper, n. 1466, October 1996), we fnd tht the coeffcent on fther s ncome nd educton re hgher n Itly thn n the US.
362 D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 Tble 11 Itly: trnston probbltes from less thn hgh school to hgh school or 1 Son E1 Son E2 Abs. freq. Fther E1 75.9 24.1 1389 Fther E2 10.3 89.7 116 Abs. freq. 1066 439 1505 Ech cell contns the row-to-column trnston probblty. E1, less thn hgh school; E2, completed hgh school or more. from stuton of equl opportuntes ncreses wth respect to the prevous 17 clssfcton (see the ndctor MT n Tble 10). 2.3. How robust s ths evdence? Whle there re severl nterntonl comprsons of ncome nequlty whch 18 confrm our rnkng of Itly nd the US, comprtve studes of ntergenertonl moblty whch nclude Itly re very rre. It s nevertheless ressurng tht, to our knowledge, the exstng studes confrm the essence of our fndngs. For exmple, usng mtrces of trnstons between socl clsses defned ccordng to the prestge of occuptons, Erckson nd Goldthorpe (1992) fnd tht Itly dsplys less moblty. Smlr results re obtned by Schzzerotto nd Bson (1996) pplyng the methodology of Erckson nd Goldthorpe to the sme dtset tht we nlyse n ths pper. In study of eductonl ttnment cross cohorts, Shvt nd Blossfeld (1993) fnd declne of the mpct of fthers occuptonl sttus on sons eductonl chevements n the US, wheres the opposte trend s observed n Itly. It my be rgued tht ll these studes, s well s ours, fce the problem tht Itly nd the US re compred t qute dfferent stges of development. In our cse, whle the ndvduls n the generton of sons grew up pproxmtely n the 19 sme yers n the two countres, lrge frcton of the Itln fthers were lredy lve n the 19th century whle none of the US fthers ws born before the 20 yer 1900. Even ssumng tht the two countres were t the sme stge of development n the generton of sons t would be hrd to mke the sme clm for the generton of fthers. Most of the Itln fthers went to school n prevlng 17 Only the Brtholomew ndex of movement MB ndctes more moblty for Itly wth ths lterntve eductonl clssfcton, but ths should not be surprsng gven tht MB s n ndctor of movement not n ndctor of equlty of opportuntes (see the ppendx of the CEPR WP verson of ths pper, n. 1466, October 1996); ts vlue s drven by the structurl shft towrds hgher educton tht chrctersed Itly n the post-wr perod, but t hdes the exstence of unequl opportuntes. 18 For exmple the ones quoted n footnote 4. 19 Between 1920 nd 1960 n Itly nd between 1931 nd 1961 n the US. 20 The rnge of vrtons of brth yers of fthers s comprsed between 1863 nd 1939 for Itly nd between 1900 nd 1947 for the US.
D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 363 grculturl socety where only 5 yers of educton were compulsory. On the contrry, Amercn fthers were brought up n consderbly more ndustrlzed socety, where t lest 10 yers of educton were compulsory lmost everywhere. The trnsformtons experenced by the Itln socety between the two genertons hve certnly been more profound thn the trnsformtons experenced by the Amercn socety. Although ths feture of our dt my pper s problem we beleve tht t ctully enhnces the robustness of our results. Indeed, despte the deeper structurl chnges experenced by Itly durng the perod of observton (consder for exmple the much lrger frcton of sons who bndoned the grculturl occuptons of ther fthers, or the postwr extenson of compulsory educton), we fnd less occuptonl nd eductonl moblty n Itly thn n the US. Furthermore, snce our gol s to mesure the degree of occuptonl moblty s perceved by the sons, t should not be perceved s problem the fct tht n both countres we rnk lso fthers occuptons ccordng to the dstrbuton of ncomes n the generton of sons (see Appendx A). Ths dstrbuton smply provdes unt of mesurement whch reflects the crter most lkely to be used by sons to evlute the drecton nd dstnce of the occuptonl chnge wth respect to ther fthers. Another potentl source of bs n our dt could orgnte from the fct tht Amercn sons re on verge 11 yers younger thn the Itln ones (see Tble 12). However, we thnk tht lso ths feture of the dt should renforce our results. Snce Itln chldren re on verge older, they must hve hd more tme to get rd of the effects of n unfvorble fmly bckground. Vce-vers, fmly bckground should be more mportnt n the US where chldren re observed erler n ther creers. Ths s becuse we expect fmly networkng to be more mportnt t the begnnng of creer thn t the end. Nevertheless, despte the fct tht the younger ge of sons should mke fmly bckground more mportnt n the US, we fnd tht t mtters more n Itly. More problemtc re the potentl bses generted by the dfferent smplng nd dt collecton procedures for the two countres. The Itln survey (see Tble 12 Age dstrbuton for both genertons n Itly nd n the US Country Fther/ son Av. ge S.D. Mn. ge Mx. ge Itly Fther 47 7 31 83 N51666 Son 44 11 25 65 Unted Sttes Fther 47 7 27 74 N51050 Son 33 5 25 59 Itln dt refer to 1666 fther son prs; sons were ntervewed n 1985, nd nformton regrdng ther fthers refers to the yer n whch sons were 14 yers old. Source: Indgne nzonle sull moblt` socle. US dt refer to 1050 fther son prs; nformton on sons refers to 1990, whle nformton on fthers refers to 1974. Source: Pnel Study of Income Dynmcs.
364 D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 Appendx A) s desgned to provde ntonwde representtve smple of the populton of sons nd precludes the possblty of ttrton between genertons becuse the nformton on fthers s obtned from sons recollectons. In the PSID, nsted, both genertons re drectly observed, but poor households re over-represented nd ttrton mples tht for some dynstes the nformton on sons s not vlble. The over-representton of poor households should bs downwrd the mesurement of moblty for the US, snce ntergenertonl persstence s hgher n low 21 ncome fmles. However, f ttrton s more lkely mong poor households, moblty my nsted be overestmted n the sme country. The fct tht for Itly nformton on fthers s obtned from sons recollectons whle for the US t s drectly observed, should nsted renforce unmbguously our conclusons, n s much s sons recollectons re more subject to mesurement error. Our dtsets certnly do not offer the best possble expermentl stuton one would lke to hve n order to compre ntergenertonl moblty cross countres. Nevertheless we beleve tht most of the sources of bs whch we cn dentfy tend to renforce our concluson. To the best of our knowledge, ths concluson s lso not contrdcted by the exstng lterture. It seems fr to conclude tht fmly bckground s more mportnt determnnt of ndvdul socl fortunes n Itly thn n the US. 3. Is ths puzzle? There re nturl objectons to our posng the emprcl evdence descrbed bove s puzzle. These potentl objectons fll nto two dfferent groups. The frst group denes some of the bsc premses of our resonng: n prtculr tht the Itln schoolng system should be expected to nduce more moblty thn the US one. The second group provdes nsted lterntve smple explntons of the lower moblty n Itly, whch do not tke nto consderton the schoolng system. In prtculr, t hs been suggested tht brrers to entry nto/ext from certn 22 occuptons could expln the lck of occuptonl moblty n Itly. Whle we re not wre of hrd evdence suggestng tht nsttutonl brrers to 23 entry nd ext from occuptons should be hgher n Itly thn n the US, n ths secton we show tht the dfferences n the two educton systems re nsted substntl. Furthermore, ll the elements of ths comprson suggest tht the decentrlzed nd non-egltrn US school system should not hve generted more equlty of eductonl nd occuptonl opportuntes thn the centrlzed 21 See Mullgn (1997) nd Lllrd (1998). 22 See, for exmple, Coblt nd Schzzerotto (1994) nd Schzzerotto nd Bson (1996). 23 Just to gve n exmple, both countres regulte n very smlr wys the ccess to lberl professons lke those of medcl doctors, lwyers or rchtects.
D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 365 nd egltrn Itln system. Even f ccess to the hgher-sttus occuptons were substntlly more restrcted n Itly thn n the US, the chrcterstcs of the two educton systems should hve t lest prtlly compensted for the dfferent ncentves to upwrd moblty nduced by the lbor mrket n the two countres. On the contrry, we observe tht eductonl moblty (n prtculr upwrd moblty) s bnormlly lower n Itly thn n the US. For these resons, we beleve tht the objectons descrbed bove re not entrely convncng. Further reserch on the comprson of moblty n dfferent countres, nd on the resons for the dfferences, s certnly necessry, but t the present stte of knowledge our evdence seems ndeed to represent puzzle. The rest of the pper wll be devoted to descrbng our proposed explnton of the puzzle, whch we wll frst sketch nformlly t the end of ths secton. We should lso sy from the outset tht we do not vew our proposed explnton s n lterntve to others. Whle we do not deny the possblty of other explntons of the lck of moblty n Itly (lke, for exmple, the non-compettveness of lbor mrkets), we do thnk tht these other explntons cnnot ccount lone for the entre evdence nd tht our explnton s t lest necessry complement. 3.1. Educton n the two countres: centrlzton vs. decentrlzton A frst fundmentl dfference s tht whle both countres spend smlr 24 frcton of GNP on publc educton, the sources of publc fundng re very dfferent. In Itly, 83.1% of publc expendtures for prmry nd secondry educton comes from the centrl government s opposed to locl uthortes, wheres n the US only 7.9% of ths expendture s centrlly fnnced t the federl 25 level nd s much s 44.3% s fnnced nsted t the locl level (cty or county). Ths s crucl dfference from the pont of vew of ths pper: n the US, ndependently of how much fundng comes from prvte sources, publc educton should lso ncrese the role of fmly bckground s determnnt of eductonl decsons becuse of the effect of prentl loctonl choces n communtes chrctersed by dfferent combntons of locl tx rtes, housng prces nd qulty of schoolng nsttutons. As we hve shown bove, however, the role of fmly bckground s nsted surprsngly more mportnt n Itly where educton s not only fnnced mnly out of publc sources but these sources re lso strctly controlled by the centrl government. 24 In 1993, the ncdence of publc expendture for educton on GNP ws 5.0% n Itly nd 5.1% n the US. (Dt from OECD, 1996.) In ths secton we re only ble to present fgures for recent yers, but s fr s we cn tell from the vlble scrce sttstcs for prevous yers, these fgures re qulttvely representtve of the school systems tht the generton of sons were fcng n the two countres. Note lso tht despte never endng post-wr prlmentry debte, the bsc structure of the Itln educton system s stll the one of the reform desgned n 1924 by Govnn Gentle, the Mnster of Educton of the fscst regme. 25 Dt from OECD (1996).
366 D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 In ddton to ths fundmentl dfference, severl other nsttutonl fetures of the two systems emphsze centrlston n Itly nd decentrlston n the US. For exmple, the ge of compulsory educton whch s determned by lw t the prlmentry level n Itly, whle n the US s dctted t the stte level, rngng between 8 nd 13 yers, wth n verge of 10.05 yers nd stndrd devton 26 of 1.19 yers. Furthermore, n Itly the types of eductonl currcul vlble n both prvte nd publc schools re estblshed by prlmentry lw t the centrl level. For ech type nd level of schoolng prlment estblshes lso the subjects tht hve to be tught, the outlnes of techng progrms for ech subject, the textbook prces (for compulsory educton), the evluton nd grdng methods nd even the dly tme of entrnce nd ext from school nd vcton perods. Therefore, for exmple, prlmentry vote s n prncple needed to uthorse school not to tech gven subject or to tech dfferent new one. At dfferent but stll centrlsed level, the Mnster of Educton ssues 600 documents (crcolr mnsterl) ech yer n whch ddtonl nstructons re gven to techers nd hedmsters wth the precse gol of mkng the educton system s unform s possble over the entre country. As result, for ech level nd type of school, fnl exms re unformly defned, nd n prtculr for the hghschool degree the wrtten exm questons re dentcl for ll students nd dmnstered n the sme dy over the entre country. Note tht prvte schools lso hve to obey these lws nd regultons f they wnt to obtn legl vlue for 27 the degrees tht they offer. The recrutment of techers s lso completely centrlsed n Itly, wth unform requrements for ech type nd level of educton: sprnt techers hve to compete n ntonl compettons nd to pss smlr fnl exms n order to be uthorsed to tech (ths hppens lso for unversty professors). The techers slres re centrlly determned on the bss of senorty nd of level of schoolng, wth bsclly no room for ndvdully bsed dfferentton. At the other extreme, the US publc educton system s fr from feturng smlr effort med t centrlsng nd mkng s unform s possble ny spect of the eductonl process. Where the US system comes closer to centrlston s n the requrements of stndrd unform exms for dmsson to hgher levels of schoolng. However, these exms re not mposed by ny lw nd, prdoxclly, they re probbly the most explct ndcton of the degree of decentrlston nd dversty of the eductonl currcul offered by US schools. 26 Two yers of compulsory educton were ntlly ntroduced n Itly n 1859, subsequently rsed to three n 1877 nd to 6 n 1904. The ctul oblgton of 8 yers ws ntroduced n 1962 (Lw n.1859, 31/12/1962). In the cse of the US, Bowles nd Gnts (1976) report tht wde movement n fvor of rsng compulsory educton to the secondry level occurred n the US durng the 1920s nd the 1930s; however regonl dfferences perssted much longer. Fgures on ctul compulsory ges n the US re tken from the US Educton Deprtment (1995). 27 See, for exmple, the Itln Lw DL 297 16/4/94, Testo unco delle dsposzon legsltve vgent n mter d struzone, reltve lle scuole d ogn ordne e grdo.
D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 367 The decentrlston of publc educton fnncng n the US mkes the quntty nd moreover the qulty of publc educton vlble to chld hevly dependent on the loctonl choces nd on the ncome of the fmly of orgn. However, n ddton to the possblty of choosng the qulty of publc educton wth ther feet, US fmles hve lso the opton of well-estblshed prvte educton system prtculrly t the unversty level. The proportons of students enrolled n prvte schools n Itly re 8.1%, 7.8% nd 3.5%, respectvely, for prmry, secondry nd tertry educton; n the US the nlogous proportons re hgher, beng equl, respectvely to 12.0%, 9.1% nd 21.8%. The dfference s 28 prtculrly strkng for tertry educton. Furthermore, n the US the proporton of publc sources n the expendtures for tertry educton s only 51.7% (n 1993) whle n Itly t reches 89.8%. Therefore n ddton to the crucl effect of the decentrlston of publc educton fundng nd regultons, the dfferentton of eductonl currcul n the US s strengthened by the greter dffuson of prvte schools. It s of course dffcult to mesure how much the decentrlston of fundng for publc educton nd the greter dffuson of prvte schools result n n effectvely more dshomogeneous qulty of educton provded by the US system. It my be ndctve, however, to observe tht whle the coeffcent of vrton cross the 20 Itln regons of the pupl-to-techers verge rtos s 6.5% (for prmry nd secondry educton) the correspondent coeffcent of vrton cross US sttes s 30 13.2%. The stndrd errors of (comprble cross countres) textscores for redng nd nrrtve cpbltes re, respectvely, 3.4 nd 3.6 n Itly nd 4.8 31 nd 4.9 n the US. Ths evdence, lbet certnly not conclusve, s consstent wth the vew tht the centrlly funded nd centrlly dmnstered Itln publc educton system provdes qulty of educton tht s more unform nd less expensve thn the qulty provded by the decentrlsed nd more lrgely prvte US system. Yet, s we hve seen, whle the Itln system succeeds n genertng lower ncome nequlty, t fls to generte more ntergenertonl moblty nd more equlty of opportuntes. In Secton 4 we present model whch bulds on the exstng lterture on prvte nd publc educton systems n order to shed some lght on ths emprcl puzzle nd, more generlly, on the reltonshp between ncome 29 28 Dt for the US refer to yer 93/94 nd for Itly to yer 94/95. See US Educton Deprtment (1995) nd ISTAT (1995). 29 Note tht whle the ncdence of publc educton expendture on GNP s smlr n the two countres (see footnote 24), the ncdence of totl expendture dffers, beng equl to 5.1% n Itly nd 6.8% n the US. The dscrepncy s due to the dmenson of prvte expendture n the US. (Dt from OECD, 1996). 30 Our computtons re bsed on US Educton Deprtment (1995) nd on ISTAT (1995). 31 US Educton Deprtment (1995). Unfortuntely smlrly comprble fgures for mthemtcl textscores, whch would suffer less from the bses due to dfferent lngustc bckgrounds n the US nd dfferent dlects n Itly, re not vlble.
368 D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 nequlty nd ntergenertonl moblty. Frst, however, we wnt to sketch nformlly the story tht our model proposes. 32 3.2. A possble explnton: the role of ncentves We buld n prtculr on Glomm nd Rvkumr (1992) but we dd n mportnt element: people hve tlent, whch s n essentl requrement n the 33 cquston of humn cptl. The consderton of tlent s wht mkes the problem of moblty nterestng from n economc pont of vew: wthout moblty socety my ssgn hgh tlented people to low educton groups, nd people wth low tlent to hgh educton groups; beyond resons of frness, ths s n 34 undesrble feture of n mmoble socety. Tlent s trnsmtted from fther to son wth some persstence nd cnnot be drectly observed. Tlent should be nterpreted s the combnton of the genetc nd envronmentl trnsfers from prents to chldren; so the ssumpton of 35 persstence s plusble ndependently of ny belef on genetc trnsmsson. Tlent relztons re restrcted for smplcty to two, hgh nd low. The only test for tlent s performnce t school. If someone ttempts to cqure educton, nd succeeds, he hs hgh tlent; whle, f he fls, he hs low tlent. Therefore, school s sortng mechnsm only works for those who choose to nvest n humn cptl. Snce tlent s mperfectly observble, ech person cn only try to mke some nference bout t from fmly hstory. So the most mportnt decsons, n prtculr those determnng the nvestment n humn cptl, re tken on the bss of the belef tht ech person hs on hs own tlent. The hgher ths belef, the more lkely person s to nvest n educton: n fct we shll see tht the rtonl decson s to nvest n educton f nd only f the subjectve belef of hvng the necessry tlent s hgher thn crtcl threshold. We refer to ths s the self-confdence fctor, lthough we hve 32 Ths relton hs been surprsngly somewht neglected n the lterture. An mportnt excepton s represented by the work of Atknson (n prtculr Atknson, 1980 81, 1983) who tkes up the chllenge posed n Pen (1971) to buld brdge between the fgures on vertcl moblty nd ncome dstrbuton. More recently, lso the model proposed by Glor nd Tsddon (1996) n whch, nequlty nd ntergenertonl moblty re postvely correlted nd drven by the pce of technologcl nnovtons. 33 Note tht, by focusng on the role of tlent nd self-confdence s determnnts of humn cptl nvestment decsons, our model dds to Glomm nd Rvkumr (1992) the consderton of moblty whch they do not ddress. In ther model the predcted moblty s necessrly zero, snce dynsty whch hs n ncome hgher thn nother n the ntl perod hs hgher ncome forever. The reson for the dfference s cler: n the model of Glomm nd Rvkumr there s no tlent, persstent or..d. 34 We re spekng loosely here on purpose: the full nlyss of the mplctons of our model for welfre nd effcency s beyond the gols of the present pper. 35 As we wll see, wthout persstence the problem of moblty becomes trvl nd our model fetures perfect moblty ndependently of the schoolng system.
D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 369 to remember tht t s perfectly rtonl consderton, snce ths belef 36 summrzes ll the nformton person hs bout hs own tlent. Ths belef becomes n mportnt wy n whch fmly bckground ffects the decson of chld. A fmly my be stuck t low levels of educton for sequence of perods becuse the prevous fmly experences hve gven ts members low confdence. Therefore, frcton of the populton hs hgh tlent, but does not use t, becuse of the dverse belef. We sy tht socety s more moble f lrger frcton of the people n the low ncome group mkes n effort to ncrese personl ncome through n eductonl nvestment. The key ssue tht we nlyze n ths stylzed frmework s whch nsttutonl set-up for schoolng (centrlzed nd funded through txton vs. decentrlzed nd funded prvtely) mkes socety more moble n the bove sense, nd why. Gven ths chrcterzton of moblty, t s desrble to ncrese t f one wnts to reduce the probblty tht tlented ndvduls remn stuck wth low humn cptl. In publc school system n whch unform educton qulty s offered to everyone, the combnton of txes nd eductonl expendtures trnsfers revenues from hgh ncome fmles to low ncome fmles, nd mkes more educton vlble to the ltter, t no ddtonl cost. In prvte school system hgher ncome mkes the choce of schoolng eser; so ncome nequlty tends to be more persstent n ths context. The trnsfer of resources nduced by the publc system nd commonly quoted n ts support, cretes ndeed n mportnt ncentve for low ncome fmles to ncrese ther humn cptl nd tends to rse the degree of moblty nduced by publc educton. There re however other fctors, whch go n the opposte drecton. Frst, n prvte system, hgher prentl ncome drectly ncreses the mount of resources vlble for the educton of the son, whle t does not n publc system. If people re ltrusts, ths dds to the ttrctveness of hgher educton becuse one knows tht f the nvestment n humn cptl s successful one wll be ble to trnsfer more resources to the next generton; n publc system, the eductonl trnsfer to the next generton s centrlly determned ndependently of prentl ncome. Second, sngle tx rte my force some prents to rte of expendture n educton lower thn they would desre, thereby mkng less lkely n otherwse ttrctve nvestment n educton for ther sons. Fnlly, the fct tht the tx rte s unque mkes useless ny nformton tht person my cqure on hs nd hs son s personl bltes, becuse he cnnot djust the expense n educton for the son ccordng to ths nformton. Even f they do not prevl, these three fctors certnly reduce the cpcty of 36 Emprcl evdence on the role of self-confdence s lmted. In n NLS smple Lllrd (1998) fnds sgnfcnt effect of... fmly dummy vrbles mesurng whether or not the son expects much help from hs prents to pursue hgher educton nd how much hs prents encourged hm to pursue hgher educton (p. 17). These dummes re sgnfcnt n predctng both school performnce nd ernngs.
370 D. Checch et l. / Journl of Publc Economcs 74 (1999) 351 393 publc, centrlzed nd egltrn system to ncrese ntergenertonl moblty. Wth our model we wnt to ttrct ttenton to the condtons whch my renforce these fctors, n order to vod them nd to mprove the desgn of publc educton systems. We wll explore these condtons wth the help of numercl computtons fter the forml presentton of the model. 4. The model 4.1. Humn cptl nd wges The economy hs sequence of dfferent genertons. Populton s contnuum, ech person lves for two perods nd s productve only n the second. Hs producton depends on hs humn cptl, whch s descrbed by rel number h. He erns wge equl to h. There re nfntely mny perods; n ech perod t the dstrbuton of humn cptl s denoted by G ; the totl humn cptl s therefore: t Ht5EhdG t(h) (4.1) 4.2. The technology for humn cptl Ech person hs bsc workng blty, of qulty normlsed to 1, nd nturl tlent, whch hs no drect productve use, but s crtcl n cqurng ddtonl humn cptl. Tlent s denoted by [ hl, Hj; t s trnsmtted from fther to son wth some persstence. More precsely, tlent follows frst order Mrkov process: P( 5 Hu 5 H) 5 P( 5 Lu 5 L) 5 1 2 t11 t t11 t wth [ (0, 1/2). Tlent s not lwys known exctly: we denote by n the belef t tht the tlent of the member born t t of the dynsty s H. It wll be cler n the sequel who holds ths belef. A hgher humn cptl cn be produced by the combnton of lernng effort, the help of n eductonl system, nd the drect or ndrect contrbuton of the humn cptl of the fther. We ssume tht ths s possble only f the tlent of the person s of the hgh type. The technology hs (s n Glomm nd Rvkumr, 1992) Cobb Dougls functonl form. More precsely, ht11 5H g 1 f 5 L; t11 b d t d t t t11 us1 2 n e h f 5 H; where n s the lesure enjoyed, e s the qulty of educton, nd h s the humn t t t cptl of the fther. Tlent cnnot be drectly observed; the only wy to determne t s to put t to